Subgroups — C₂×#72237549 #72337522

Order 2048.

At least 14647 conjugacy classes of subgroups; only the 4864 normal subgroups are shown.

The subgroup lattice has 1129 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499153	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#501201	C₂	1	4	yes	maximal, complemented
3	C₂×#501192	C₂	1	4	yes	maximal, complemented
4	C₂×#501197	C₂	1	4	yes	maximal, complemented
5	C₂×#6437988	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#494761	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#499126	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#498916	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#494752	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#501188	C₂	1	4	yes	maximal, complemented
11	C₂×#494361	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#7622450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10577322	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#498943	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#494587	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#6438015	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#33553	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#12755	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6437575	C₂	1	1	yes	maximal, characteristic, complemented
20	#72237549	C₂	1	32	yes	maximal, direct product factor
21	C₂×#63090	C₂²	1	1	yes	characteristic, complemented
22	C₂²×#3537	C₂²	1	1	yes	characteristic
23	C₂×#62811	C₂²	1	1	yes	characteristic
24	#10577322	C₂²	1	16	yes	complemented
25	C₂×#61651	C₂²	1	2	yes	complemented
26	C₂×#61648	C₂²	1	2	yes	complemented
27	C₂×#61633	C₂²	1	2	yes	complemented
28	C₂×#61630	C₂²	1	2	yes	complemented
29	C₂×#60753	C₂²	1	1	yes	characteristic
30	C₂×#60753	C₂²	1	1	yes	characteristic
31	C₂²×#3027	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#3025	C₂²	1	1	yes	characteristic
33	C₂×#60369	C₂²	1	1	yes	characteristic
34	C₂×#60369	C₂²	1	1	yes	characteristic
35	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#3021	C₂²	1	1	yes	characteristic, complemented
37	C₂×#60231	C₂²	1	1	yes	characteristic
38	C₂×#60070	C₂²	1	1	yes	characteristic, complemented
39	C₂×#60076	C₂²	1	1	yes	characteristic, complemented
40	C₂×#33553	C₂²	1	4	yes	complemented
41	C₂×#33553	C₂²	1	4	yes	complemented
42	C₂×#33553	C₂²	1	16	yes	complemented
43	C₂²×#2134	C₂²	1	1	yes	characteristic, complemented
44	C₂²×#2128	C₂²	1	1	yes	characteristic, complemented
45	#7622450	C₂²	1	16	yes	complemented
46	C₂×#33351	C₂²	1	2	yes	complemented
47	C₂×#33349	C₂²	1	2	yes	complemented
48	C₂×#33350	C₂²	1	2	yes	complemented
49	C₂×#33348	C₂²	1	2	yes	complemented
50	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
51	C₂×#33347	C₂²	1	1	yes	characteristic, complemented
52	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
53	C₂²×#2122	C₂²	1	1	yes	characteristic, complemented
54	C₂²×#2120	C₂²	1	1	yes	characteristic
55	C₂²×#2120	C₂²	1	1	yes	characteristic
56	#6438015	C₂²	1	16	yes	complemented
57	C₂×#24410	C₂²	1	4	yes	complemented
58	C₂×#24408	C₂²	1	4	yes	complemented
59	#6437988	C₂²	1	16	yes	complemented
60	C₂×#24422	C₂²	1	4	yes	complemented
61	C₂×#24420	C₂²	1	4	yes	complemented
62	#6437575	C₂²	1	16	yes	complemented
63	C₂×#23885	C₂²	1	2	yes	complemented
64	C₂×#23884	C₂²	1	2	yes	complemented
65	C₂×#23883	C₂²	1	2	yes	complemented
66	C₂×#23882	C₂²	1	2	yes	complemented
67	C₂²×#1914	C₂²	1	1	yes	characteristic, complemented
68	C₂×#21009	C₂²	1	1	yes	characteristic, complemented
69	C₂²×#1910	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#1891	C₂²	1	1	yes	characteristic
71	C₂×#20892	C₂²	1	1	yes	characteristic, complemented
72	C₂×#20860	C₂²	1	1	yes	characteristic, complemented
73	C₂×#20623	C₂²	1	1	yes	characteristic, complemented
74	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
75	C₂×#20612	C₂²	1	1	yes	characteristic, complemented
76	#501201	C₂²	1	64	yes	complemented
77	#501197	C₂²	1	64	yes	complemented
78	#501192	C₂²	1	64	yes	complemented
79	#501188	C₂²	1	64	yes	complemented
80	#499153	C₂²	1	16	yes	complemented
81	C₂×#13434	C₂²	1	4	yes	complemented
82	C₂×#13432	C₂²	1	4	yes	complemented
83	#499126	C₂²	1	16	yes	complemented
84	C₂×#13437	C₂²	1	4	yes	complemented
85	C₂×#13436	C₂²	1	4	yes	complemented
86	#498943	C₂²	1	16	yes	complemented
87	C₂×#13355	C₂²	1	4	yes	complemented
88	C₂×#13353	C₂²	1	4	yes	complemented
89	#498916	C₂²	1	16	yes	complemented
90	C₂×#13361	C₂²	1	4	yes	complemented
91	C₂×#13360	C₂²	1	4	yes	complemented
92	#494761	C₂²	1	16	yes	complemented
93	C₂×#13103	C₂²	1	4	yes	complemented
94	C₂×#13102	C₂²	1	4	yes	complemented
95	#494752	C₂²	1	16	yes	complemented
96	C₂×#13099	C₂²	1	4	yes	complemented
97	C₂×#13098	C₂²	1	4	yes	complemented
98	#494587	C₂²	1	16	yes	complemented
99	C₂×#13046	C₂²	1	4	yes	complemented
100	C₂×#13045	C₂²	1	4	yes	complemented
101	#494361	C₂²	1	16	yes	complemented
102	C₂×#12963	C₂²	1	4	yes	complemented
103	C₂×#12962	C₂²	1	4	yes	complemented
104	C₂×#12755	C₂²	1	4	yes	complemented
105	C₂×#12755	C₂²	1	4	yes	complemented
106	C₂×#12755	C₂²	1	16	yes	complemented
107	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
108	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
109	C₂×#12579	C₂²	1	1	yes	characteristic, complemented
110	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
111	C₂²×#585	C₂³	1	1	yes	characteristic
112	C₂²×#585	C₂³	1	1	yes	characteristic
113	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
114	#63090	C₂³	1	8	yes	complemented
115	C₂×#3586	C₂³	1	2	yes	complemented
116	C₂×#3585	C₂³	1	2	yes	complemented
117	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
118	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
119	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
120	C₂³×AGL(1,ℤ/8)	D₄	1	1	yes	characteristic, complemented
121	C₂²×#568	C₂³	1	1	yes	characteristic
122	#62811	D₄	1	8	yes	complemented
123	#62811	C₂³	1	8	yes	—
124	C₂×#3487	D₄	1	1	yes	characteristic, complemented
125	C₂×#3487	C₂³	1	1	yes	characteristic
126	C₂×#3486	D₄	1	1	yes	characteristic, complemented
127	C₂×#3486	C₂³	1	1	yes	characteristic
128	C₂×#3485	D₄	1	1	yes	characteristic, complemented
129	C₂×#3485	C₂³	1	1	yes	characteristic
130	C₂×#3484	D₄	1	1	yes	characteristic, complemented
131	C₂×#3484	C₂³	1	1	yes	characteristic
132	C₂×#3537	C₂³	1	2	yes	—
133	C₂×#3537	C₂³	1	2	yes	—
134	C₂×#3537	C₂³	1	8	yes	—
135	C₂×#3449	D₄	1	1	yes	characteristic, complemented
136	C₂×#3449	C₂³	1	1	yes	characteristic
137	C₂²×#535	C₂³	1	1	yes	characteristic
138	C₂²×#535	C₂³	1	1	yes	characteristic
139	C₂²×#525	D₄	1	1	yes	characteristic, complemented
140	C₂²×#525	C₂³	1	1	yes	characteristic
141	C₂×#3428	D₄	1	1	yes	characteristic, complemented
142	#61651	C₂³	1	16	yes	complemented
143	#61648	C₂³	1	16	yes	complemented
144	#61633	C₂³	1	16	yes	complemented
145	#61630	C₂³	1	16	yes	complemented
146	#60753	C₂³	1	8	yes	—
147	#60753	C₂³	1	8	yes	—
148	C₂×#3200	C₂³	1	2	yes	—
149	C₂×#3200	C₂³	1	2	yes	—
150	C₂×#3199	C₂³	1	2	yes	—
151	C₂×#3199	C₂³	1	2	yes	—
152	C₂×#3027	C₂³	1	4	yes	—
153	C₂×#3027	C₂³	1	8	yes	complemented
154	C₂×#3025	C₂³	1	2	yes	—
155	C₂×#3025	C₂³	1	2	yes	—
156	C₂×#3025	C₂³	1	8	yes	—
157	#60387	C₂³	1	8	yes	complemented
158	C₂×#3022	C₂³	1	2	yes	complemented
159	C₂×#3021	C₂³	1	4	yes	—
160	C₂×#3021	C₂³	1	8	yes	complemented
161	C₂×#3021	C₂³	1	2	yes	complemented
162	#60369	D₄	1	8	yes	complemented
163	#60369	D₄	1	8	yes	complemented
164	#60369	C₂³	1	8	yes	—
165	#60369	C₂³	1	8	yes	—
166	C₂×#3010	D₄	1	2	yes	complemented
167	C₂×#3010	D₄	1	2	yes	complemented
168	C₂×#3010	C₂³	1	2	yes	—
169	C₂×#3010	C₂³	1	2	yes	—
170	C₂×#3008	D₄	1	2	yes	complemented
171	C₂×#3008	D₄	1	2	yes	complemented
172	C₂×#3008	C₂³	1	2	yes	—
173	C₂×#3008	C₂³	1	2	yes	—
174	#60231	C₂³	1	8	yes	—
175	C₂×#2978	C₂³	1	2	yes	—
176	C₂×#2977	C₂³	1	2	yes	—
177	C₂×#2896	D₄	1	1	yes	characteristic, complemented
178	C₂×#2896	D₄	1	1	yes	characteristic, complemented
179	C₂×#2896	D₄	1	1	yes	characteristic, complemented
180	C₂×#2896	D₄	1	1	yes	characteristic, complemented
181	#60076	C₂³	1	8	yes	complemented
182	C₂×#2889	C₂³	1	2	yes	complemented
183	C₂×#2888	C₂³	1	2	yes	complemented
184	C₂²×#413	C₂³	1	1	yes	characteristic
185	C₂²×#413	C₂³	1	1	yes	characteristic
186	C₂²×#413	C₂³	1	1	yes	characteristic
187	#60070	C₂³	1	8	yes	complemented
188	C₂×#2884	C₂³	1	2	yes	complemented
189	C₂×#2883	C₂³	1	2	yes	complemented
190	C₂²×#410	C₂³	1	1	yes	characteristic
191	C₂²×#410	C₂³	1	1	yes	characteristic
192	C₂²×#410	C₂³	1	1	yes	characteristic
193	C₂×#2879	C₂³	1	1	yes	characteristic
194	C₂×#2879	C₂³	1	1	yes	characteristic
195	#33553	C₂³	1	32	yes	complemented
196	#33553	C₂³	1	32	yes	complemented
197	C₂×#2134	C₂³	1	4	yes	—
198	C₂×#2134	C₂³	1	8	yes	complemented
199	C₂×#2128	C₂³	1	4	yes	—
200	C₂×#2128	C₂³	1	8	yes	complemented
201	#33351	C₂³	1	16	yes	complemented
202	#33350	C₂³	1	16	yes	complemented
203	#33349	C₂³	1	16	yes	complemented
204	#33348	C₂³	1	16	yes	complemented
205	#33347	C₂³	1	8	yes	complemented
206	#33347	C₂³	1	8	yes	complemented
207	C₂×#2123	C₂³	1	2	yes	complemented
208	C₂×#2123	C₂³	1	2	yes	complemented
209	C₂×#2122	C₂³	1	4	yes	—
210	C₂×#2122	C₂³	1	4	yes	—
211	C₂×#2122	C₂³	1	8	yes	complemented
212	C₂×#2122	C₂³	1	2	yes	complemented
213	C₂×#2122	C₂³	1	2	yes	complemented
214	C₂×#2122	C₂³	1	8	yes	complemented
215	C₂×#2120	D₄	1	2	yes	—
216	C₂×#2120	D₄	1	2	yes	—
217	C₂×#2120	D₄	1	8	yes	—
218	C₂×#2120	C₂³	1	2	yes	—
219	C₂×#2120	C₂³	1	2	yes	—
220	C₂×#2120	C₂³	1	8	yes	—
221	C₂×#2120	C₂³	1	2	yes	—
222	C₂×#2120	C₂³	1	2	yes	—
223	C₂×#2120	C₂³	1	8	yes	—
224	C₂²×#352	D₄	1	2	yes	—
225	C₂²×AΣL(1,𝔽₁₆)	D₄	1	2	yes	—
226	#24422	C₂³	1	32	yes	complemented
227	#24420	C₂³	1	32	yes	complemented
228	#24410	C₂³	1	32	yes	complemented
229	#24408	C₂³	1	32	yes	complemented
230	#23885	C₂³	1	16	yes	complemented
231	#23884	C₂³	1	16	yes	complemented
232	#23883	C₂³	1	16	yes	complemented
233	#23882	C₂³	1	16	yes	complemented
234	C₂×#1914	C₂³	1	4	yes	—
235	C₂×#1914	C₂³	1	8	yes	complemented
236	#21009	C₂³	1	8	yes	complemented
237	C₂×#1910	C₂³	1	4	yes	—
238	C₂×#1910	C₂³	1	8	yes	complemented
239	C₂×#1910	C₂³	1	2	yes	complemented
240	C₂×#1909	C₂³	1	2	yes	complemented
241	C₂×#1891	C₂³	1	2	yes	—
242	C₂×#1891	C₂³	1	2	yes	—
243	C₂×#1891	C₂³	1	8	yes	—
244	#20892	C₂³	1	8	yes	complemented
245	C₂×#1868	C₂³	1	4	yes	complemented
246	#20860	C₂³	1	8	yes	complemented
247	C₂×#1858	C₂³	1	4	yes	complemented
248	#20623	C₂³	1	8	yes	complemented
249	C₂×#1796	C₂³	1	2	yes	complemented
250	C₂×#1795	C₂³	1	2	yes	complemented
251	#20620	C₂³	1	8	yes	complemented
252	C₂×#1794	C₂³	1	4	yes	complemented
253	#20612	C₂³	1	8	yes	complemented
254	C₂×#1791	C₂³	1	4	yes	complemented
255	#13437	C₂³	1	32	yes	complemented
256	#13436	C₂³	1	32	yes	complemented
257	#13434	C₂³	1	32	yes	complemented
258	#13432	C₂³	1	32	yes	complemented
259	#13361	C₂³	1	32	yes	complemented
260	#13360	C₂³	1	32	yes	complemented
261	#13355	C₂³	1	32	yes	complemented
262	#13353	C₂³	1	32	yes	complemented
263	#13103	C₂³	1	32	yes	complemented
264	#13102	C₂³	1	32	yes	complemented
265	#13099	C₂³	1	32	yes	complemented
266	#13098	C₂³	1	32	yes	complemented
267	#13046	C₂³	1	32	yes	complemented
268	#13045	C₂³	1	32	yes	complemented
269	#12963	C₂³	1	32	yes	complemented
270	#12962	C₂³	1	32	yes	complemented
271	#12755	C₂³	1	32	yes	complemented
272	#12755	C₂³	1	32	yes	complemented
273	#12589	C₂³	1	8	yes	complemented
274	#12589	C₂³	1	8	yes	complemented
275	C₂×#1395	C₂³	1	4	yes	complemented
276	C₂×#1395	C₂³	1	4	yes	complemented
277	#12579	C₂³	1	8	yes	complemented
278	C₂×#1392	C₂³	1	4	yes	complemented
279	#12577	C₂³	1	8	yes	complemented
280	C₂×#1391	C₂³	1	4	yes	complemented
281	C₂×#585	C₂×D₄	1	4	yes	—
282	C₂×#585	C₂×D₄	1	4	yes	—
283	C₂×#585	C₂×D₄	1	4	yes	—
284	C₂×#585	C₂⁴	1	4	yes	—
285	C₂×#585	C₂⁴	1	2	yes	—
286	C₂×#585	C₂⁴	1	4	yes	—
287	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
288	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
289	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
290	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
291	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
292	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
293	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
294	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
295	C₂³×#41	C₂×D₄	1	1	yes	characteristic
296	C₂³×#41	C₂×D₄	1	1	yes	characteristic
297	C₂³×#41	C₂×D₄	1	1	yes	characteristic
298	C₂³×#41	C₂×D₄	1	1	yes	characteristic
299	C₂³×#41	C₂×D₄	1	1	yes	characteristic
300	C₂³×#41	C₂×D₄	1	1	yes	characteristic
301	C₂³×#41	C₂×D₄	1	1	yes	characteristic
302	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
304	C₂³×#41	C₂×D₄	1	8	yes	complemented
305	C₂³×#41	C₂⁴	1	1	yes	characteristic
306	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
308	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
309	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
310	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
311	#3586	C₂⁴	1	8	yes	complemented
312	#3585	C₂⁴	1	8	yes	complemented
313	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
314	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
315	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
316	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
317	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	2	yes	complemented
318	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
319	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
320	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
321	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
322	C₂³×SD₁₆	C₂×D₄	1	2	yes	complemented
323	C₂³×D₈	C₂×D₄	1	2	yes	complemented
324	C₂³×D₈	C₂×D₄	1	2	yes	complemented
325	C₂×#568	C₂⁴	1	2	yes	—
326	C₂×#568	C₂⁴	1	4	yes	—
327	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
328	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
329	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
330	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
331	#3537	C₂⁴	1	8	yes	—
332	#3537	C₂⁴	1	8	yes	—
333	#3487	C₂×D₄	1	8	yes	complemented
334	#3487	C₂×D₄	1	4	yes	complemented
335	#3487	C₂⁴	1	4	yes	—
336	#3486	C₂×D₄	1	8	yes	complemented
337	#3486	C₂×D₄	1	4	yes	complemented
338	#3486	C₂⁴	1	4	yes	—
339	#3485	C₂×D₄	1	8	yes	complemented
340	#3485	C₂×D₄	1	4	yes	complemented
341	#3485	C₂⁴	1	4	yes	—
342	#3484	C₂×D₄	1	8	yes	complemented
343	#3484	C₂×D₄	1	4	yes	complemented
344	#3484	C₂⁴	1	4	yes	—
345	#3449	C₂×D₄	1	4	yes	—
346	#3449	C₂×D₄	1	8	yes	complemented
347	#3449	C₂⁴	1	4	yes	—
348	C₂×#536	C₂×D₄	1	1	yes	characteristic
349	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
350	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
351	C₂×#536	C₂⁴	1	1	yes	characteristic
352	C₂×#535	C₂×D₄	1	2	yes	—
353	C₂×#535	C₂×D₄	1	4	yes	—
354	C₂×#535	C₂×D₄	1	2	yes	—
355	C₂×#535	C₂×D₄	1	4	yes	—
356	C₂×#535	C₂×D₄	1	1	yes	characteristic
357	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
358	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
359	C₂×#535	C₂⁴	1	2	yes	—
360	C₂×#535	C₂⁴	1	4	yes	—
361	C₂×#535	C₂⁴	1	2	yes	—
362	C₂×#535	C₂⁴	1	4	yes	—
363	C₂×#535	C₂⁴	1	1	yes	characteristic
364	C₂×#525	C₂×D₄	1	4	yes	—
365	C₂×#525	C₂×D₄	1	1	yes	characteristic
366	C₂×#525	C₂×D₄	1	1	yes	characteristic
367	C₂×#525	C₂×D₄	1	1	yes	characteristic
368	C₂×#525	C₂×D₄	1	1	yes	characteristic
369	C₂×#525	C₂×D₄	1	4	yes	—
370	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
371	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
372	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
373	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
374	C₂×#525	C₂×D₄	1	8	yes	complemented
375	C₂×#525	#41	1	4	yes	—
376	C₂×#525	#41	1	1	yes	characteristic
377	C₂×#525	#41	1	1	yes	characteristic
378	C₂×#525	C₂⁴	1	1	yes	characteristic
379	C₂×#525	C₂⁴	1	1	yes	characteristic
380	C₂×#525	C₂⁴	1	4	yes	—
381	C₂²×#123	C₂×D₄	1	1	yes	characteristic
382	C₂²×#123	#41	1	1	yes	characteristic
383	C₂²×#120	C₂×D₄	1	1	yes	characteristic
384	C₂²×#120	#41	1	1	yes	characteristic
385	#3428	C₂×D₄	1	8	yes	complemented
386	C₂×#519	C₂×D₄	1	1	yes	characteristic, complemented
387	C₂×#519	C₂×D₄	1	1	yes	characteristic, complemented
388	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
389	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
390	C₂²×#117	C₂×D₄	1	1	yes	characteristic
391	C₂²×#117	C₂×D₄	1	1	yes	characteristic
392	C₂²×#117	C₂×D₄	1	1	yes	characteristic
393	C₂²×#117	C₂×D₄	1	1	yes	characteristic
394	#3200	C₂⁴	1	8	yes	—
395	#3200	C₂⁴	1	8	yes	—
396	#3199	C₂⁴	1	8	yes	—
397	#3199	C₂⁴	1	8	yes	—
398	#3027	C₂⁴	1	16	yes	—
399	#3025	C₂⁴	1	8	yes	—
400	#3025	C₂⁴	1	8	yes	—
401	#3022	C₂⁴	1	8	yes	complemented
402	#3021	C₂⁴	1	16	yes	—
403	#3021	C₂⁴	1	8	yes	complemented
404	#3010	C₂×D₄	1	16	yes	complemented
405	#3010	C₂×D₄	1	8	yes	complemented
406	#3010	C₂×D₄	1	16	yes	complemented
407	#3010	C₂×D₄	1	8	yes	complemented
408	#3010	C₂⁴	1	8	yes	—
409	#3010	C₂⁴	1	8	yes	—
410	#3008	C₂×D₄	1	16	yes	complemented
411	#3008	C₂×D₄	1	8	yes	complemented
412	#3008	C₂×D₄	1	16	yes	complemented
413	#3008	C₂×D₄	1	8	yes	complemented
414	#3008	C₂⁴	1	8	yes	—
415	#3008	C₂⁴	1	8	yes	—
416	#2978	C₂⁴	1	8	yes	—
417	#2977	C₂⁴	1	8	yes	—
418	#2896	C₂×D₄	1	8	yes	complemented
419	#2896	C₂×D₄	1	8	yes	complemented
420	#2896	C₂×D₄	1	8	yes	complemented
421	#2896	C₂×D₄	1	8	yes	complemented
422	C₂×#419	C₂×D₄	1	2	yes	complemented
423	C₂×#419	C₂×D₄	1	2	yes	complemented
424	C₂×#418	C₂×D₄	1	2	yes	complemented
425	C₂×#418	C₂×D₄	1	2	yes	complemented
426	C₂×#416	C₂×D₄	1	2	yes	complemented
427	C₂×#416	C₂×D₄	1	2	yes	complemented
428	C₂×#416	C₂×D₄	1	2	yes	complemented
429	C₂×#416	C₂×D₄	1	2	yes	complemented
430	#2889	C₂⁴	1	8	yes	complemented
431	#2888	C₂⁴	1	8	yes	complemented
432	C₂×#413	C₂×D₄	1	2	yes	—
433	C₂×#413	C₂×D₄	1	4	yes	—
434	C₂×#413	C₂⁴	1	2	yes	—
435	C₂×#413	C₂⁴	1	4	yes	—
436	C₂×#413	C₂⁴	1	2	yes	—
437	C₂×#413	C₂⁴	1	4	yes	—
438	C₂×#413	C₂⁴	1	2	yes	—
439	C₂×#413	C₂⁴	1	4	yes	—
440	C₂²×#100	C₂×D₄	1	2	yes	—
441	#2884	C₂⁴	1	8	yes	complemented
442	#2883	C₂⁴	1	8	yes	complemented
443	C₂×#410	C₂×D₄	1	2	yes	—
444	C₂×#410	C₂×D₄	1	4	yes	—
445	C₂×#410	C₂⁴	1	2	yes	—
446	C₂×#410	C₂⁴	1	2	yes	—
447	C₂×#410	C₂⁴	1	4	yes	—
448	C₂×#410	C₂⁴	1	4	yes	—
449	C₂×#410	C₂⁴	1	2	yes	—
450	C₂×#410	C₂⁴	1	4	yes	—
451	C₂²×#99	C₂×D₄	1	2	yes	—
452	#2879	C₂×D₄	1	4	yes	—
453	#2879	C₂×D₄	1	4	yes	—
454	#2879	C₂⁴	1	4	yes	—
455	#2879	C₂⁴	1	4	yes	—
456	C₂×#408	C₂×D₄	1	2	yes	—
457	C₂×#408	C₂×D₄	1	2	yes	—
458	C₂×#408	C₂⁴	1	2	yes	—
459	C₂×#408	C₂⁴	1	2	yes	—
460	#2134	C₂⁴	1	16	yes	—
461	#2128	C₂⁴	1	16	yes	—
462	#2123	C₂⁴	1	8	yes	complemented
463	#2123	C₂⁴	1	8	yes	complemented
464	#2122	C₂⁴	1	16	yes	—
465	#2122	C₂⁴	1	16	yes	—
466	#2122	C₂⁴	1	8	yes	complemented
467	#2122	C₂⁴	1	8	yes	complemented
468	#2120	C₂×D₄	1	16	yes	—
469	#2120	C₂×D₄	1	16	yes	—
470	#2120	C₂×D₄	1	8	yes	—
471	#2120	C₂×D₄	1	8	yes	—
472	#2120	C₂⁴	1	8	yes	—
473	#2120	C₂⁴	1	8	yes	—
474	#2120	C₂⁴	1	8	yes	—
475	#2120	C₂⁴	1	8	yes	—
476	C₂×#352	C₂×D₄	1	4	yes	—
477	C₂×#352	C₂×D₄	1	4	yes	—
478	C₂×#352	C₂×D₄	1	16	yes	—
479	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	4	yes	—
480	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	4	yes	—
481	C₂×AΣL(1,𝔽₁₆)	C₂×D₄	1	16	yes	—
482	#1914	C₂⁴	1	16	yes	—
483	#1910	C₂⁴	1	16	yes	—
484	#1910	C₂⁴	1	8	yes	complemented
485	#1909	C₂⁴	1	8	yes	complemented
486	#1891	C₂⁴	1	8	yes	—
487	#1891	C₂⁴	1	8	yes	—
488	#1868	C₂⁴	1	16	yes	complemented
489	#1858	C₂⁴	1	16	yes	complemented
490	#1796	C₂⁴	1	8	yes	complemented
491	#1795	C₂⁴	1	8	yes	complemented
492	#1794	C₂⁴	1	16	yes	complemented
493	#1791	C₂⁴	1	16	yes	complemented
494	#1395	C₂⁴	1	16	yes	complemented
495	#1395	C₂⁴	1	16	yes	complemented
496	#1392	C₂⁴	1	16	yes	complemented
497	#1391	C₂⁴	1	16	yes	complemented
498	C₂⁶	#121	1	1	yes	characteristic
499	#585	C₂⁵	1	4	yes	—
500	C₂×2₋¹⁺⁴	#120	1	4	yes	—
501	C₂×2₋¹⁺⁴	#120	1	4	yes	—
502	C₂×2₋¹⁺⁴	#120	1	4	yes	—
503	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
504	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
505	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
506	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
507	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
508	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
509	C₂×2₋¹⁺⁴	C₂⁵	1	2	yes	—
510	C₂×H(5,𝔽₂)	#120	1	4	yes	—
511	C₂×H(5,𝔽₂)	#120	1	4	yes	—
512	C₂×H(5,𝔽₂)	#120	1	4	yes	—
513	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
514	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
515	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
516	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
517	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
518	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
519	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
520	C₂²×#41	#120	1	1	yes	characteristic
521	C₂²×#41	#120	1	1	yes	characteristic
522	C₂²×#41	#120	1	4	yes	—
523	C₂²×#41	#120	1	1	yes	characteristic
524	C₂²×#41	#120	1	1	yes	characteristic
525	C₂²×#41	#120	1	4	yes	—
526	C₂²×#41	#120	1	4	yes	—
527	C₂²×#41	#120	1	1	yes	characteristic
528	C₂²×#41	#120	1	1	yes	characteristic
529	C₂²×#41	#120	1	4	yes	—
530	C₂²×#41	#120	1	4	yes	—
531	C₂²×#41	#120	1	4	yes	—
532	C₂²×#41	#120	1	1	yes	characteristic
533	C₂²×#41	#120	1	1	yes	characteristic
534	C₂²×#41	#120	1	1	yes	characteristic
535	C₂²×#41	#120	1	1	yes	characteristic
536	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
537	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
538	C₂²×#41	C₂²×D₄	1	4	yes	—
539	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
540	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
541	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
542	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
543	C₂²×#41	C₂²×D₄	1	4	yes	—
544	C₂²×#41	C₂²×D₄	1	4	yes	—
545	C₂²×#41	C₂²×D₄	1	4	yes	—
546	C₂²×#41	C₂²×D₄	1	4	yes	—
547	C₂²×#41	C₂²×D₄	1	4	yes	—
548	C₂²×#41	C₂²×D₄	1	4	yes	—
549	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
550	C₂²×#41	C₂²×D₄	1	2	yes	—
551	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
552	C₂²×#41	C₂²×D₄	1	2	yes	—
553	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
554	C₂²×#41	C₂²×D₄	1	2	yes	—
555	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
556	C₂²×#41	C₂²×D₄	1	2	yes	—
557	C₂²×#41	C₂²×D₄	1	4	yes	complemented
558	C₂²×#41	C₂²×D₄	1	4	yes	complemented
559	C₂²×#41	C₂×#41	1	1	yes	characteristic
560	C₂²×#41	C₂×#41	1	2	yes	—
561	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
562	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
563	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
564	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
565	C₂²×#41	C₂⁵	1	1	yes	characteristic
566	C₂²×#41	C₂⁵	1	2	yes	—
567	C₂³×Q₈	#120	1	1	yes	characteristic
568	C₂³×Q₈	#120	1	1	yes	characteristic
569	C₂³×Q₈	#120	1	1	yes	characteristic
570	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
571	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
572	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
573	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
574	C₂³×Q₈	C₂²×D₄	1	4	yes	complemented
575	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
576	C₂³×D₄	#120	1	1	yes	characteristic
577	C₂³×D₄	#120	1	1	yes	characteristic
578	C₂³×D₄	#120	1	1	yes	characteristic
579	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
580	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
581	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
582	C₂³×D₄	C₂²×D₄	1	2	yes	—
583	C₂³×D₄	C₂²×D₄	1	4	yes	—
584	C₂³×D₄	C₂²×D₄	1	2	yes	—
585	C₂³×D₄	C₂²×D₄	1	4	yes	—
586	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
587	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
588	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
589	C₂³×D₄	C₂×#41	1	1	yes	characteristic
590	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
591	C₂⁴×C₄	#121	1	1	yes	characteristic
592	C₂⁴×C₄	#121	1	1	yes	characteristic
593	C₂⁴×C₄	#121	1	1	yes	characteristic
594	C₂⁴×C₄	#121	1	4	yes	—
595	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
596	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
597	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
598	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
599	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
600	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
601	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	8	yes	complemented
602	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	8	yes	complemented
603	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	8	yes	complemented
604	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	8	yes	complemented
605	C₂²×SD₁₆	C₂²×D₄	1	8	yes	complemented
606	C₂²×SD₁₆	C₂²×D₄	1	8	yes	complemented
607	C₂²×D₈	C₂²×D₄	1	8	yes	complemented
608	C₂²×D₈	C₂²×D₄	1	8	yes	complemented
609	#568	C₂⁵	1	4	yes	—
610	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
611	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
612	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
613	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
614	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
615	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
616	C₂³×C₈	C₂²×D₄	1	2	yes	—
617	C₂³×C₈	C₂²×D₄	1	2	yes	—
618	#536	C₂²×D₄	1	4	yes	—
619	#536	C₂²×D₄	1	2	yes	—
620	#536	C₂²×D₄	1	4	yes	complemented
621	#536	C₂²×D₄	1	4	yes	complemented
622	#536	C₂⁵	1	2	yes	—
623	#535	C₂²×D₄	1	8	yes	—
624	#535	C₂²×D₄	1	4	yes	—
625	#535	C₂²×D₄	1	4	yes	—
626	#535	C₂²×D₄	1	2	yes	—
627	#535	C₂²×D₄	1	8	yes	—
628	#535	C₂²×D₄	1	4	yes	—
629	#535	C₂²×D₄	1	4	yes	complemented
630	#535	C₂²×D₄	1	4	yes	complemented
631	#535	C₂⁵	1	4	yes	—
632	#535	C₂⁵	1	4	yes	—
633	#535	C₂⁵	1	2	yes	—
634	#525	#121	1	4	yes	—
635	#525	#121	1	4	yes	—
636	#525	#121	1	4	yes	—
637	#525	#121	1	4	yes	—
638	#525	#121	1	4	yes	—
639	#525	#121	1	4	yes	—
640	#525	C₂²×D₄	1	4	yes	—
641	#525	C₂²×D₄	1	4	yes	—
642	#525	C₂²×D₄	1	2	yes	—
643	#525	C₂²×D₄	1	2	yes	—
644	#525	C₂²×D₄	1	4	yes	—
645	#525	C₂²×D₄	1	2	yes	—
646	#525	C₂²×D₄	1	4	yes	—
647	#525	C₂²×D₄	1	2	yes	—
648	#525	C₂²×D₄	1	4	yes	complemented
649	#525	C₂²×D₄	1	4	yes	complemented
650	#525	C₂²×D₄	1	4	yes	complemented
651	#525	C₂²×D₄	1	4	yes	complemented
652	#525	C₂×#41	1	4	yes	—
653	#525	C₂×#41	1	4	yes	—
654	#525	C₂×#41	1	2	yes	—
655	#525	C₂×#41	1	2	yes	—
656	#525	C₂⁵	1	2	yes	—
657	#525	C₂⁵	1	2	yes	—
658	C₂×#123	#121	1	1	yes	characteristic
659	C₂×#123	#121	1	1	yes	characteristic
660	C₂×#123	#121	1	1	yes	characteristic
661	C₂×#123	#121	1	4	yes	—
662	C₂×#123	#121	1	1	yes	characteristic
663	C₂×#123	#121	1	4	yes	—
664	C₂×#123	C₂²×D₄	1	1	yes	characteristic
665	C₂×#123	C₂²×D₄	1	1	yes	characteristic
666	C₂×#123	C₂²×D₄	1	4	yes	—
667	C₂×#123	C₂×#41	1	1	yes	characteristic
668	C₂×#123	C₂×#41	1	1	yes	characteristic
669	C₂×#123	C₂×#41	1	4	yes	—
670	C₂×#120	#121	1	1	yes	characteristic
671	C₂×#120	#121	1	1	yes	characteristic
672	C₂×#120	#121	1	1	yes	characteristic
673	C₂×#120	#121	1	4	yes	—
674	C₂×#120	#121	1	1	yes	characteristic
675	C₂×#120	#121	1	4	yes	—
676	C₂×#120	C₂²×D₄	1	1	yes	characteristic
677	C₂×#120	C₂²×D₄	1	1	yes	characteristic
678	C₂×#120	C₂²×D₄	1	4	yes	—
679	C₂×#120	C₂×#41	1	1	yes	characteristic
680	C₂×#120	C₂×#41	1	1	yes	characteristic
681	C₂×#120	C₂×#41	1	4	yes	—
682	#519	C₂²×D₄	1	4	yes	complemented
683	#519	C₂²×D₄	1	4	yes	complemented
684	#518	C₂²×D₄	1	4	yes	complemented
685	#518	C₂²×D₄	1	4	yes	complemented
686	C₂×#117	#121	1	1	yes	characteristic
687	C₂×#117	#121	1	1	yes	characteristic
688	C₂×#117	#121	1	4	yes	—
689	C₂×#117	C₂²×D₄	1	1	yes	characteristic
690	C₂×#117	C₂²×D₄	1	1	yes	characteristic
691	C₂×#117	C₂²×D₄	1	2	yes	—
692	C₂×#117	C₂²×D₄	1	2	yes	—
693	C₂×#117	C₂²×D₄	1	4	yes	—
694	C₂×#117	C₂²×D₄	1	4	yes	—
695	C₂×#117	C₂²×D₄	1	4	yes	—
696	C₂×#117	C₂²×D₄	1	1	yes	characteristic
697	C₂×#117	C₂²×D₄	1	1	yes	characteristic
698	C₂×#117	C₂²×D₄	1	4	yes	—
699	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
700	C₂²×C₂²⋊C₄	#121	1	1	yes	characteristic
701	#419	C₂²×D₄	1	8	yes	complemented
702	#419	C₂²×D₄	1	8	yes	complemented
703	#418	C₂²×D₄	1	8	yes	complemented
704	#418	C₂²×D₄	1	8	yes	complemented
705	#416	C₂²×D₄	1	8	yes	complemented
706	#416	C₂²×D₄	1	8	yes	complemented
707	#416	C₂²×D₄	1	8	yes	complemented
708	#416	C₂²×D₄	1	8	yes	complemented
709	#413	C₂²×D₄	1	8	yes	—
710	#413	C₂²×D₄	1	4	yes	—
711	#413	C₂⁵	1	4	yes	—
712	#413	C₂⁵	1	4	yes	—
713	#413	C₂⁵	1	4	yes	—
714	C₂×#100	C₂²×D₄	1	4	yes	—
715	C₂×#100	C₂²×D₄	1	8	yes	—
716	#410	C₂²×D₄	1	8	yes	—
717	#410	C₂²×D₄	1	4	yes	—
718	#410	C₂⁵	1	4	yes	—
719	#410	C₂⁵	1	4	yes	—
720	#410	C₂⁵	1	4	yes	—
721	C₂×#99	C₂²×D₄	1	4	yes	—
722	C₂×#99	C₂²×D₄	1	8	yes	—
723	#408	C₂²×D₄	1	8	yes	—
724	#408	C₂²×D₄	1	4	yes	—
725	#408	C₂²×D₄	1	8	yes	—
726	#408	C₂²×D₄	1	4	yes	—
727	#408	C₂⁵	1	4	yes	—
728	#408	C₂⁵	1	4	yes	—
729	#352	C₂²×D₄	1	16	yes	—
730	#352	C₂²×D₄	1	16	yes	—
731	AΣL(1,𝔽₁₆)	C₂²×D₄	1	16	yes	—
732	AΣL(1,𝔽₁₆)	C₂²×D₄	1	16	yes	—
733	C₂⁵	C₂×#121	1	1	yes	characteristic
734	C₂⁵	C₂×#121	1	1	yes	characteristic
735	C₂⁵	C₂×#121	1	1	yes	characteristic
736	C₂⁵	C₂×#121	1	4	yes	—
737	C₂⁵	D₄²	1	1	yes	characteristic
738	C₂⁵	#546	1	1	yes	characteristic
739	C₂×#41	B(4,𝔽₂)	1	2	yes	—
740	C₂×#41	B(4,𝔽₂)	1	2	yes	—
741	C₂×#41	B(4,𝔽₂)	1	4	yes	—
742	C₂×#41	C₂×#120	1	4	yes	—
743	C₂×#41	C₂×#120	1	4	yes	—
744	C₂×#41	C₂×#120	1	4	yes	—
745	C₂×#41	C₂×#120	1	4	yes	—
746	C₂×#41	C₂×#120	1	4	yes	—
747	C₂×#41	C₂×#120	1	4	yes	—
748	C₂×#41	C₂×#120	1	2	yes	—
749	C₂×#41	C₂×#120	1	2	yes	—
750	C₂×#41	C₂×#120	1	4	yes	—
751	C₂×#41	C₂×#120	1	4	yes	—
752	C₂×#41	C₂×#120	1	2	yes	—
753	C₂×#41	C₂×#120	1	2	yes	—
754	C₂×#41	C₂×#120	1	4	yes	—
755	C₂×#41	C₂×#120	1	2	yes	—
756	C₂×#41	C₂×#120	1	2	yes	—
757	C₂×#41	C₂×#120	1	4	yes	—
758	C₂×#41	C₂×#120	1	2	yes	—
759	C₂×#41	C₂×#120	1	2	yes	—
760	C₂×#41	C₂×#120	1	2	yes	—
761	C₂×#41	C₂×#121	1	2	yes	—
762	C₂×#41	C₂×#121	1	2	yes	—
763	C₂×#41	C₂×#121	1	2	yes	—
764	C₂×#41	#534	1	2	yes	—
765	C₂×#41	#534	1	2	yes	—
766	C₂×#41	#534	1	2	yes	—
767	C₂×#41	D₄²	1	2	yes	—
768	C₂×#41	D₄²	1	2	yes	—
769	C₂×#41	D₄²	1	2	yes	—
770	C₂×#41	D₄²	1	2	yes	—
771	C₂×#41	D₄²	1	2	yes	—
772	C₂×#41	D₄²	1	2	yes	—
773	C₂×#41	#546	1	2	yes	—
774	C₂×#41	#546	1	2	yes	—
775	C₂×#41	#546	1	2	yes	—
776	C₂×#41	#546	1	2	yes	—
777	C₂×#41	#546	1	2	yes	—
778	C₂×#41	#546	1	2	yes	—
779	C₂×#41	C₂³×D₄	1	2	yes	—
780	C₂×#41	C₂³×D₄	1	2	yes	—
781	C₂×#41	C₂³×D₄	1	2	yes	—
782	C₂×#41	C₂³×D₄	1	2	yes	—
783	C₂×#41	C₂³×D₄	1	2	yes	—
784	C₂×#41	C₂³×D₄	1	2	yes	—
785	C₂×#41	C₂³×D₄	1	2	yes	—
786	C₂×#41	C₂³×D₄	1	1	yes	characteristic
787	C₂×#41	C₂³×D₄	1	1	yes	characteristic
788	C₂×#41	C₂³×D₄	1	2	yes	—
789	C₂×#41	C₂³×D₄	1	1	yes	characteristic
790	C₂×#41	C₂³×D₄	1	2	yes	—
791	C₂×#41	C₂³×D₄	1	2	yes	—
792	C₂×#41	C₂³×D₄	1	1	yes	characteristic
793	C₂×#41	C₂²×#41	1	2	yes	—
794	C₂×#41	C₂²×#41	1	1	yes	characteristic
795	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
796	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
797	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
798	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂×#41	C₂⁶	1	1	yes	characteristic
800	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
801	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
802	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
803	C₂²×Q₈	C₂×#120	1	2	yes	—
804	C₂²×Q₈	C₂×#120	1	4	yes	—
805	C₂²×Q₈	C₂×#120	1	2	yes	—
806	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
807	C₂²×Q₈	C₂×#120	1	4	yes	—
808	C₂²×Q₈	C₂×#120	1	4	yes	—
809	C₂²×Q₈	C₂×#120	1	2	yes	—
810	C₂²×Q₈	#534	1	1	yes	characteristic
811	C₂²×Q₈	#534	1	2	yes	—
812	C₂²×Q₈	D₄²	1	1	yes	characteristic
813	C₂²×Q₈	D₄²	1	2	yes	—
814	C₂²×Q₈	#546	1	1	yes	characteristic
815	C₂²×Q₈	#546	1	2	yes	—
816	C₂²×Q₈	C₂³×D₄	1	2	yes	—
817	C₂²×Q₈	C₂³×D₄	1	2	yes	—
818	C₂²×Q₈	C₂³×D₄	1	2	yes	—
819	C₂²×Q₈	C₂³×D₄	1	2	yes	—
820	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂²×Q₈	C₂×H(5,𝔽₂)	1	2	yes	—
822	C₂²×D₄	C₂×#120	1	1	yes	characteristic
823	C₂²×D₄	C₂×#120	1	1	yes	characteristic
824	C₂²×D₄	C₂×#120	1	1	yes	characteristic
825	C₂²×D₄	C₂×#120	1	2	yes	—
826	C₂²×D₄	C₂×#120	1	4	yes	—
827	C₂²×D₄	C₂×#120	1	2	yes	—
828	C₂²×D₄	C₂×#120	1	1	yes	characteristic
829	C₂²×D₄	C₂×#120	1	4	yes	—
830	C₂²×D₄	C₂×#120	1	4	yes	—
831	C₂²×D₄	C₂×#120	1	2	yes	—
832	C₂²×D₄	C₂×#121	1	1	yes	characteristic
833	C₂²×D₄	C₂×#121	1	1	yes	characteristic
834	C₂²×D₄	C₂×#121	1	2	yes	—
835	C₂²×D₄	C₂×#121	1	2	yes	—
836	C₂²×D₄	#534	1	1	yes	characteristic
837	C₂²×D₄	#534	1	2	yes	—
838	C₂²×D₄	D₄²	1	1	yes	characteristic
839	C₂²×D₄	D₄²	1	2	yes	—
840	C₂²×D₄	D₄²	1	1	yes	characteristic
841	C₂²×D₄	D₄²	1	2	yes	—
842	C₂²×D₄	D₄²	1	1	yes	characteristic
843	C₂²×D₄	D₄²	1	2	yes	—
844	C₂²×D₄	#546	1	1	yes	characteristic
845	C₂²×D₄	#546	1	2	yes	—
846	C₂²×D₄	#546	1	1	yes	characteristic
847	C₂²×D₄	#546	1	2	yes	—
848	C₂²×D₄	#546	1	1	yes	characteristic
849	C₂²×D₄	#546	1	2	yes	—
850	C₂²×D₄	C₂³×D₄	1	2	yes	—
851	C₂²×D₄	C₂³×D₄	1	2	yes	—
852	C₂²×D₄	C₂³×D₄	1	4	yes	—
853	C₂²×D₄	C₂³×D₄	1	2	yes	—
854	C₂²×D₄	C₂³×D₄	1	4	yes	—
855	C₂²×D₄	C₂³×D₄	1	2	yes	—
856	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
857	C₂²×D₄	C₂³×D₄	1	2	yes	—
858	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
859	C₂²×D₄	C₂²×#41	1	2	yes	—
860	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
861	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
862	C₂³×C₄	C₂×#120	1	1	yes	characteristic
863	C₂³×C₄	C₂×#120	1	2	yes	—
864	C₂³×C₄	C₂×#120	1	1	yes	characteristic
865	C₂³×C₄	C₂×#120	1	1	yes	characteristic
866	C₂³×C₄	C₂×#120	1	2	yes	—
867	C₂³×C₄	C₂×#120	1	2	yes	—
868	C₂³×C₄	C₂×#120	1	1	yes	characteristic
869	C₂³×C₄	C₂×#121	1	1	yes	characteristic
870	C₂³×C₄	C₂×#121	1	2	yes	—
871	C₂³×C₄	C₂×#121	1	1	yes	characteristic
872	C₂³×C₄	C₂×#121	1	1	yes	characteristic
873	C₂³×C₄	C₂×#121	1	4	yes	—
874	C₂³×C₄	C₂×#121	1	4	yes	—
875	C₂³×C₄	C₂×#121	1	2	yes	—
876	C₂³×C₄	C₂×#121	1	4	yes	—
877	C₂³×C₄	C₂×#121	1	2	yes	—
878	C₂³×C₄	#534	1	1	yes	characteristic
879	C₂³×C₄	#534	1	2	yes	—
880	C₂³×C₄	#534	1	1	yes	characteristic
881	C₂³×C₄	D₄²	1	1	yes	characteristic
882	C₂³×C₄	D₄²	1	2	yes	—
883	C₂³×C₄	D₄²	1	1	yes	characteristic
884	C₂³×C₄	D₄²	1	1	yes	characteristic
885	C₂³×C₄	D₄²	1	2	yes	—
886	C₂³×C₄	#546	1	1	yes	characteristic
887	C₂³×C₄	#546	1	2	yes	—
888	C₂³×C₄	#546	1	1	yes	characteristic
889	C₂³×C₄	#546	1	1	yes	characteristic
890	C₂³×C₄	#546	1	2	yes	—
891	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
892	C₂³×C₄	C₂³×D₄	1	2	yes	—
893	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
894	C₂³×C₄	C₂³×D₄	1	2	yes	—
895	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
896	C₂³×C₄	C₂³×D₄	1	2	yes	—
897	C₂³×C₄	C₂³×D₄	1	2	yes	—
898	C₂³×C₄	C₂³×D₄	1	2	yes	—
899	C₂×M₁₆	C₂³×D₄	1	4	yes	—
900	C₂×M₁₆	C₂³×D₄	1	4	yes	—
901	C₂²×C₈	C₂³×D₄	1	4	yes	—
902	C₂²×C₈	C₂³×D₄	1	4	yes	—
903	#123	C₂×#121	1	4	yes	—
904	#123	C₂×#121	1	2	yes	—
905	#123	C₂×#121	1	4	yes	—
906	#123	C₂×#121	1	2	yes	—
907	#123	C₂×#121	1	4	yes	—
908	#123	C₂×#121	1	2	yes	—
909	#123	C₂×#121	1	4	yes	—
910	#123	C₂×#121	1	2	yes	—
911	#123	C₂³×D₄	1	2	yes	—
912	#123	C₂³×D₄	1	2	yes	—
913	#123	C₂²×#41	1	2	yes	—
914	#123	C₂²×#41	1	2	yes	—
915	#120	C₂×#121	1	4	yes	—
916	#120	C₂×#121	1	2	yes	—
917	#120	C₂×#121	1	4	yes	—
918	#120	C₂×#121	1	2	yes	—
919	#120	C₂×#121	1	4	yes	—
920	#120	C₂×#121	1	2	yes	—
921	#120	C₂×#121	1	4	yes	—
922	#120	C₂×#121	1	2	yes	—
923	#120	C₂³×D₄	1	2	yes	—
924	#120	C₂³×D₄	1	2	yes	—
925	#120	C₂²×#41	1	2	yes	—
926	#120	C₂²×#41	1	2	yes	—
927	#117	C₂×#121	1	4	yes	—
928	#117	C₂×#121	1	4	yes	—
929	#117	C₂×#121	1	2	yes	—
930	#117	C₂×#121	1	2	yes	—
931	#117	C₂³×D₄	1	2	yes	—
932	#117	C₂³×D₄	1	2	yes	—
933	#117	C₂³×D₄	1	4	yes	—
934	#117	C₂³×D₄	1	4	yes	—
935	#117	C₂³×D₄	1	2	yes	—
936	#117	C₂³×D₄	1	2	yes	—
937	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
938	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
939	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
940	C₂×C₂²⋊C₄	C₂×#121	1	1	yes	characteristic
941	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
942	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
943	#100	C₂³×D₄	1	8	yes	—
944	#99	C₂³×D₄	1	8	yes	—
945	C₂⁴	#2410	1	1	yes	characteristic
946	C₂⁴	#2410	1	1	yes	characteristic
947	C₂⁴	#2410	1	1	yes	characteristic
948	C₂⁴	#2410	1	2	yes	—
949	C₂⁴	#2410	1	2	yes	—
950	C₂⁴	#2410	1	2	yes	—
951	C₂⁴	#2410	1	1	yes	characteristic
952	C₂⁴	C₂²×#121	1	1	yes	characteristic
953	C₂⁴	C₂²×#121	1	2	yes	—
954	C₂⁴	C₂²×#121	1	2	yes	—
955	C₂⁴	C₂²×#121	1	2	yes	—
956	C₂⁴	C₂×D₄²	1	1	yes	characteristic
957	C₂⁴	C₂×D₄²	1	2	yes	—
958	C₂⁴	C₂×#546	1	1	yes	characteristic
959	C₂⁴	C₂×#546	1	2	yes	—
960	#41	C₂×B(4,𝔽₂)	1	8	yes	—
961	#41	C₂×B(4,𝔽₂)	1	8	yes	—
962	C₂×Q₈	#2410	1	2	yes	—
963	C₂×Q₈	#2410	1	2	yes	—
964	C₂×Q₈	#2410	1	2	yes	—
965	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
966	C₂×Q₈	C₂×B(4,𝔽₂)	1	2	yes	—
967	C₂×Q₈	C₂²×#120	1	2	yes	—
968	C₂×Q₈	C₂²×#120	1	2	yes	—
969	C₂×Q₈	C₂²×#120	1	2	yes	—
970	C₂×Q₈	C₂²×#120	1	2	yes	—
971	C₂×Q₈	C₂×#534	1	2	yes	—
972	C₂×Q₈	C₂×#534	1	1	yes	characteristic
973	C₂×Q₈	C₂×D₄²	1	2	yes	—
974	C₂×Q₈	C₂×D₄²	1	1	yes	characteristic
975	C₂×Q₈	C₂×#546	1	2	yes	—
976	C₂×Q₈	C₂×#546	1	1	yes	characteristic
977	C₂×Q₈	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
978	C₂×D₄	#2410	1	2	yes	—
979	C₂×D₄	#2410	1	2	yes	—
980	C₂×D₄	#2410	1	2	yes	—
981	C₂×D₄	#2410	1	2	yes	—
982	C₂×D₄	#2410	1	2	yes	—
983	C₂×D₄	#2410	1	2	yes	—
984	C₂×D₄	#2410	1	2	yes	—
985	C₂×D₄	#2410	1	2	yes	—
986	C₂×D₄	#2410	1	2	yes	—
987	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
988	C₂×D₄	C₂×B(4,𝔽₂)	1	2	yes	—
989	C₂×D₄	C₂²×#120	1	2	yes	—
990	C₂×D₄	C₂²×#120	1	2	yes	—
991	C₂×D₄	C₂²×#120	1	2	yes	—
992	C₂×D₄	C₂²×#120	1	2	yes	—
993	C₂×D₄	C₂²×#121	1	2	yes	—
994	C₂×D₄	C₂²×#121	1	1	yes	characteristic
995	C₂×D₄	C₂²×#121	1	2	yes	—
996	C₂×D₄	C₂²×#121	1	1	yes	characteristic
997	C₂×D₄	C₂×#534	1	2	yes	—
998	C₂×D₄	C₂×#534	1	1	yes	characteristic
999	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1000	C₂×D₄	C₂×D₄²	1	2	yes	—
1001	C₂×D₄	C₂×D₄²	1	2	yes	—
1002	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1003	C₂×D₄	C₂×D₄²	1	1	yes	characteristic
1004	C₂×D₄	C₂×D₄²	1	2	yes	—
1005	C₂×D₄	C₂×#546	1	1	yes	characteristic
1006	C₂×D₄	C₂×#546	1	2	yes	—
1007	C₂×D₄	C₂×#546	1	2	yes	—
1008	C₂×D₄	C₂×#546	1	1	yes	characteristic
1009	C₂×D₄	C₂×#546	1	1	yes	characteristic
1010	C₂×D₄	C₂×#546	1	2	yes	—
1011	C₂×D₄	C₂⁴×D₄	1	1	yes	characteristic
1012	C₂×D₄	C₂³×#41	1	1	yes	characteristic
1013	C₂×D₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1014	C₂²×C₄	#2410	1	1	yes	characteristic
1015	C₂²×C₄	#2410	1	1	yes	characteristic
1016	C₂²×C₄	#2410	1	2	yes	—
1017	C₂²×C₄	#2410	1	2	yes	—
1018	C₂²×C₄	#2410	1	2	yes	—
1019	C₂²×C₄	#2410	1	1	yes	characteristic
1020	C₂²×C₄	#2410	1	2	yes	—
1021	C₂²×C₄	#2410	1	2	yes	—
1022	C₂²×C₄	#2410	1	2	yes	—
1023	C₂²×C₄	#2410	1	2	yes	—
1024	C₂²×C₄	#2410	1	2	yes	—
1025	C₂²×C₄	#2410	1	2	yes	—
1026	C₂²×C₄	#2410	1	2	yes	—
1027	C₂²×C₄	#2410	1	2	yes	—
1028	C₂²×C₄	#2410	1	2	yes	—
1029	C₂²×C₄	#2410	1	1	yes	characteristic
1030	C₂²×C₄	#2410	1	2	yes	—
1031	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1032	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1033	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
1034	C₂²×C₄	#3026	1	1	yes	characteristic
1035	C₂²×C₄	#3026	1	2	yes	—
1036	C₂²×C₄	#3026	1	1	yes	characteristic
1037	C₂²×C₄	C₂²×#120	1	2	yes	—
1038	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1039	C₂²×C₄	C₂²×#120	1	2	yes	—
1040	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1041	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×#120	1	2	yes	—
1043	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×#120	1	2	yes	—
1045	C₂²×C₄	C₂²×#121	1	2	yes	—
1046	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×#121	1	2	yes	—
1048	C₂²×C₄	C₂²×#121	1	2	yes	—
1049	C₂²×C₄	C₂×#534	1	1	yes	characteristic
1050	C₂²×C₄	C₂×#534	1	2	yes	—
1051	C₂²×C₄	C₂×#534	1	2	yes	—
1052	C₂²×C₄	C₂×#534	1	1	yes	characteristic
1053	C₂²×C₄	C₂×D₄²	1	2	yes	—
1054	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1055	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1056	C₂²×C₄	C₂×D₄²	1	2	yes	—
1057	C₂²×C₄	C₂×D₄²	1	2	yes	—
1058	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1059	C₂²×C₄	C₂×#546	1	2	yes	—
1060	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1061	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1062	C₂²×C₄	C₂×#546	1	2	yes	—
1063	C₂²×C₄	C₂×#546	1	2	yes	—
1064	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
1068	C₂²⋊C₄	C₂²×#121	1	2	yes	—
1069	C₂²⋊C₄	C₂²×#121	1	2	yes	—
1070	C₂²⋊C₄	C₂²×#121	1	2	yes	—
1071	C₂²⋊C₄	C₂²×#121	1	2	yes	—
1072	C₂³	#24404	1	1	yes	characteristic
1073	C₂³	#24404	1	1	yes	characteristic
1074	C₂³	#24404	1	2	yes	—
1075	C₂³	C₂×#2410	1	1	yes	characteristic
1076	C₂³	C₂×#2410	1	2	yes	—
1077	C₂³	C₂×#2410	1	1	yes	characteristic
1078	C₂³	C₂×#2410	1	1	yes	characteristic
1079	C₂³	C₂×#2410	1	2	yes	—
1080	C₂³	C₂×#2410	1	1	yes	characteristic
1081	C₂³	C₂×#2410	1	2	yes	—
1082	C₂³	C₂×#2410	1	2	yes	—
1083	C₂³	C₂³×#121	1	1	yes	characteristic
1084	C₂³	C₂²×D₄²	1	1	yes	characteristic
1085	C₂³	C₂²×#546	1	1	yes	characteristic
1086	Q₈	C₂²×B(4,𝔽₂)	1	4	yes	—
1087	D₄	C₂²×B(4,𝔽₂)	1	4	yes	—
1088	C₂×C₄	#24404	1	2	yes	—
1089	C₂×C₄	#24404	1	2	yes	—
1090	C₂×C₄	#24404	1	2	yes	—
1091	C₂×C₄	#24404	1	2	yes	—
1092	C₂×C₄	#24404	1	2	yes	—
1093	C₂×C₄	#24404	1	1	yes	characteristic
1094	C₂×C₄	#24404	1	1	yes	characteristic
1095	C₂×C₄	C₂×#2410	1	1	yes	characteristic
1096	C₂×C₄	C₂×#2410	1	2	yes	—
1097	C₂×C₄	C₂×#2410	1	2	yes	—
1098	C₂×C₄	C₂×#2410	1	1	yes	characteristic
1099	C₂×C₄	C₂×#2410	1	1	yes	characteristic
1100	C₂×C₄	C₂×#2410	1	2	yes	—
1101	C₂×C₄	C₂×#2410	1	2	yes	—
1102	C₂×C₄	C₂×#2410	1	1	yes	characteristic
1103	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1104	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
1105	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
1106	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1107	C₂×C₄	C₂×#3026	1	1	yes	characteristic
1108	C₂×C₄	C₂×#3026	1	2	yes	—
1109	C₂×C₄	C₂×#3026	1	2	yes	—
1110	C₂×C₄	C₂×#3026	1	1	yes	characteristic
1111	C₂×C₄	C₂³×#120	1	1	yes	characteristic
1112	C₂×C₄	C₂²×#534	1	1	yes	characteristic
1113	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
1114	C₂×C₄	C₂²×#546	1	1	yes	characteristic
1115	C₂²	C₂×#24404	1	1	yes	characteristic
1116	C₂²	C₂×#24404	1	2	yes	—
1117	C₂²	C₂×#24404	1	2	yes	—
1118	C₂²	C₂×#24404	1	1	yes	characteristic
1119	C₂²	C₂²×#2410	1	1	yes	characteristic
1120	C₄	C₂×#24404	1	2	yes	—
1121	C₄	C₂×#24404	1	2	yes	—
1122	C₄	C₂×#24404	1	1	yes	characteristic
1123	C₄	C₂×#24404	1	1	yes	characteristic
1124	C₄	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
1125	C₄	C₂²×#3026	1	1	yes	characteristic
1126	C₂	#72237549	1	2	yes	direct product factor
1127	C₂	C₂²×#24404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#24404
commutator, Frattini, cosocle	C₂×#41	C₂⁶
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#585 ◁ G
LECS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#499153	C₂	semidirect
2. C₂×#501201	C₂	semidirect
3. C₂×#501192	C₂	semidirect
4. C₂×#501197	C₂	semidirect
5. C₂×#6437988	C₂	semidirect
6. C₂×#494761	C₂	semidirect
7. C₂×#499126	C₂	semidirect
8. C₂×#498916	C₂	semidirect
9. C₂×#494752	C₂	semidirect
10. C₂×#501188	C₂	semidirect
11. C₂×#494361	C₂	semidirect
12. C₂×#7622450	C₂	semidirect
13. C₂×#10577322	C₂	semidirect
14. C₂×#498943	C₂	semidirect
15. C₂×#494587	C₂	semidirect
16. C₂×#6438015	C₂	semidirect
17. C₂²×#33553	C₂	semidirect
18. C₂²×#12755	C₂	semidirect
19. C₂×#6437575	C₂	semidirect
20. #72237549	C₂	direct (N × H)
21. C₂×#63090	C₂²	semidirect
24. #10577322	C₂²	semidirect
25. C₂×#61651	C₂²	semidirect
26. C₂×#61648	C₂²	semidirect
27. C₂×#61633	C₂²	semidirect
28. C₂×#61630	C₂²	semidirect
31. C₂²×#3027	C₂²	semidirect
35. C₂×#60387	C₂²	semidirect
36. C₂²×#3021	C₂²	semidirect
38. C₂×#60070	C₂²	semidirect
39. C₂×#60076	C₂²	semidirect
40. C₂×#33553	C₂²	semidirect
41. C₂×#33553	C₂²	semidirect
42. C₂×#33553	C₂²	semidirect
43. C₂²×#2134	C₂²	semidirect
44. C₂²×#2128	C₂²	semidirect
45. #7622450	C₂²	semidirect
46. C₂×#33351	C₂²	semidirect
47. C₂×#33349	C₂²	semidirect
48. C₂×#33350	C₂²	semidirect
49. C₂×#33348	C₂²	semidirect
50. C₂×#33347	C₂²	semidirect
51. C₂×#33347	C₂²	semidirect
52. C₂²×#2122	C₂²	semidirect
53. C₂²×#2122	C₂²	semidirect
56. #6438015	C₂²	semidirect
57. C₂×#24410	C₂²	semidirect
58. C₂×#24408	C₂²	semidirect
59. #6437988	C₂²	semidirect
60. C₂×#24422	C₂²	semidirect
61. C₂×#24420	C₂²	semidirect
62. #6437575	C₂²	semidirect
63. C₂×#23885	C₂²	semidirect
64. C₂×#23884	C₂²	semidirect
65. C₂×#23883	C₂²	semidirect
66. C₂×#23882	C₂²	semidirect
67. C₂²×#1914	C₂²	semidirect
68. C₂×#21009	C₂²	semidirect
69. C₂²×#1910	C₂²	semidirect
71. C₂×#20892	C₂²	semidirect
72. C₂×#20860	C₂²	semidirect
73. C₂×#20623	C₂²	semidirect
74. C₂×#20620	C₂²	semidirect
75. C₂×#20612	C₂²	semidirect
76. #501201	C₂²	semidirect
77. #501197	C₂²	semidirect
78. #501192	C₂²	semidirect
79. #501188	C₂²	semidirect
80. #499153	C₂²	semidirect
81. C₂×#13434	C₂²	semidirect
82. C₂×#13432	C₂²	semidirect
83. #499126	C₂²	semidirect
84. C₂×#13437	C₂²	semidirect
85. C₂×#13436	C₂²	semidirect
86. #498943	C₂²	semidirect
87. C₂×#13355	C₂²	semidirect
88. C₂×#13353	C₂²	semidirect
89. #498916	C₂²	semidirect
90. C₂×#13361	C₂²	semidirect
91. C₂×#13360	C₂²	semidirect
92. #494761	C₂²	semidirect
93. C₂×#13103	C₂²	semidirect
94. C₂×#13102	C₂²	semidirect
95. #494752	C₂²	semidirect
96. C₂×#13099	C₂²	semidirect
97. C₂×#13098	C₂²	semidirect
98. #494587	C₂²	semidirect
99. C₂×#13046	C₂²	semidirect
100. C₂×#13045	C₂²	semidirect
101. #494361	C₂²	semidirect
102. C₂×#12963	C₂²	semidirect
103. C₂×#12962	C₂²	semidirect
104. C₂×#12755	C₂²	semidirect
105. C₂×#12755	C₂²	semidirect
106. C₂×#12755	C₂²	semidirect
107. C₂×#12589	C₂²	semidirect
108. C₂×#12589	C₂²	semidirect
109. C₂×#12579	C₂²	semidirect
110. C₂×#12577	C₂²	semidirect
113. C₂⁴×#41	D₄	semidirect
114. #63090	C₂³	semidirect
115. C₂×#3586	C₂³	semidirect
116. C₂×#3585	C₂³	semidirect
117. C₂³×AGL(1,ℤ/8)	D₄	semidirect
118. C₂³×AGL(1,ℤ/8)	D₄	semidirect
119. C₂³×AGL(1,ℤ/8)	D₄	semidirect
120. C₂³×AGL(1,ℤ/8)	D₄	semidirect
122. #62811	D₄	semidirect
124. C₂×#3487	D₄	semidirect
126. C₂×#3486	D₄	semidirect
128. C₂×#3485	D₄	semidirect
130. C₂×#3484	D₄	semidirect
135. C₂×#3449	D₄	semidirect
139. C₂²×#525	D₄	semidirect
141. C₂×#3428	D₄	semidirect
142. #61651	C₂³	semidirect
143. #61648	C₂³	semidirect
144. #61633	C₂³	semidirect
145. #61630	C₂³	semidirect
153. C₂×#3027	C₂³	semidirect
157. #60387	C₂³	semidirect
158. C₂×#3022	C₂³	semidirect
160. C₂×#3021	C₂³	semidirect
161. C₂×#3021	C₂³	semidirect
162. #60369	D₄	semidirect
163. #60369	D₄	semidirect
166. C₂×#3010	D₄	semidirect
167. C₂×#3010	D₄	semidirect
170. C₂×#3008	D₄	semidirect
171. C₂×#3008	D₄	semidirect
177. C₂×#2896	D₄	semidirect
178. C₂×#2896	D₄	semidirect
179. C₂×#2896	D₄	semidirect
180. C₂×#2896	D₄	semidirect
181. #60076	C₂³	semidirect
182. C₂×#2889	C₂³	semidirect
183. C₂×#2888	C₂³	semidirect
187. #60070	C₂³	semidirect
188. C₂×#2884	C₂³	semidirect
189. C₂×#2883	C₂³	semidirect
195. #33553	C₂³	semidirect
196. #33553	C₂³	semidirect
198. C₂×#2134	C₂³	semidirect
200. C₂×#2128	C₂³	semidirect
201. #33351	C₂³	semidirect
202. #33350	C₂³	semidirect
203. #33349	C₂³	semidirect
204. #33348	C₂³	semidirect
205. #33347	C₂³	semidirect
206. #33347	C₂³	semidirect
207. C₂×#2123	C₂³	semidirect
208. C₂×#2123	C₂³	semidirect
211. C₂×#2122	C₂³	semidirect
212. C₂×#2122	C₂³	semidirect
213. C₂×#2122	C₂³	semidirect
214. C₂×#2122	C₂³	semidirect
226. #24422	C₂³	semidirect
227. #24420	C₂³	semidirect
228. #24410	C₂³	semidirect
229. #24408	C₂³	semidirect
230. #23885	C₂³	semidirect
231. #23884	C₂³	semidirect
232. #23883	C₂³	semidirect
233. #23882	C₂³	semidirect
235. C₂×#1914	C₂³	semidirect
236. #21009	C₂³	semidirect
238. C₂×#1910	C₂³	semidirect
239. C₂×#1910	C₂³	semidirect
240. C₂×#1909	C₂³	semidirect
244. #20892	C₂³	semidirect
245. C₂×#1868	C₂³	semidirect
246. #20860	C₂³	semidirect
247. C₂×#1858	C₂³	semidirect
248. #20623	C₂³	semidirect
249. C₂×#1796	C₂³	semidirect
250. C₂×#1795	C₂³	semidirect
251. #20620	C₂³	semidirect
252. C₂×#1794	C₂³	semidirect
253. #20612	C₂³	semidirect
254. C₂×#1791	C₂³	semidirect
255. #13437	C₂³	semidirect
256. #13436	C₂³	semidirect
257. #13434	C₂³	semidirect
258. #13432	C₂³	semidirect
259. #13361	C₂³	semidirect
260. #13360	C₂³	semidirect
261. #13355	C₂³	semidirect
262. #13353	C₂³	semidirect
263. #13103	C₂³	semidirect
264. #13102	C₂³	semidirect
265. #13099	C₂³	semidirect
266. #13098	C₂³	semidirect
267. #13046	C₂³	semidirect
268. #13045	C₂³	semidirect
269. #12963	C₂³	semidirect
270. #12962	C₂³	semidirect
271. #12755	C₂³	semidirect
272. #12755	C₂³	semidirect
273. #12589	C₂³	semidirect
274. #12589	C₂³	semidirect
275. C₂×#1395	C₂³	semidirect
276. C₂×#1395	C₂³	semidirect
277. #12579	C₂³	semidirect
278. C₂×#1392	C₂³	semidirect
279. #12577	C₂³	semidirect
280. C₂×#1391	C₂³	semidirect
302. C₂³×#41	C₂×D₄	semidirect
303. C₂³×#41	C₂×D₄	semidirect
304. C₂³×#41	C₂×D₄	semidirect
306. C₂⁴×Q₈	C₂×D₄	semidirect
309. C₂⁴×D₄	C₂×D₄	semidirect
311. #3586	C₂⁴	semidirect
312. #3585	C₂⁴	semidirect
313. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
314. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
315. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
316. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
317. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
318. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
319. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
320. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
321. C₂³×SD₁₆	C₂×D₄	semidirect
322. C₂³×SD₁₆	C₂×D₄	semidirect
323. C₂³×D₈	C₂×D₄	semidirect
324. C₂³×D₈	C₂×D₄	semidirect
333. #3487	C₂×D₄	semidirect
334. #3487	C₂×D₄	semidirect
336. #3486	C₂×D₄	semidirect
337. #3486	C₂×D₄	semidirect
339. #3485	C₂×D₄	semidirect
340. #3485	C₂×D₄	semidirect
342. #3484	C₂×D₄	semidirect
343. #3484	C₂×D₄	semidirect
346. #3449	C₂×D₄	semidirect
349. C₂×#536	C₂×D₄	semidirect
350. C₂×#536	C₂×D₄	semidirect
357. C₂×#535	C₂×D₄	semidirect
358. C₂×#535	C₂×D₄	semidirect
370. C₂×#525	C₂×D₄	semidirect
371. C₂×#525	C₂×D₄	semidirect
372. C₂×#525	C₂×D₄	semidirect
373. C₂×#525	C₂×D₄	semidirect
374. C₂×#525	C₂×D₄	semidirect
385. #3428	C₂×D₄	semidirect
386. C₂×#519	C₂×D₄	semidirect
387. C₂×#519	C₂×D₄	semidirect
388. C₂×#518	C₂×D₄	semidirect
389. C₂×#518	C₂×D₄	semidirect
401. #3022	C₂⁴	semidirect
403. #3021	C₂⁴	semidirect
404. #3010	C₂×D₄	semidirect
405. #3010	C₂×D₄	semidirect
406. #3010	C₂×D₄	semidirect
407. #3010	C₂×D₄	semidirect
410. #3008	C₂×D₄	semidirect
411. #3008	C₂×D₄	semidirect
412. #3008	C₂×D₄	semidirect
413. #3008	C₂×D₄	semidirect
418. #2896	C₂×D₄	semidirect
419. #2896	C₂×D₄	semidirect
420. #2896	C₂×D₄	semidirect
421. #2896	C₂×D₄	semidirect
422. C₂×#419	C₂×D₄	semidirect
423. C₂×#419	C₂×D₄	semidirect
424. C₂×#418	C₂×D₄	semidirect
425. C₂×#418	C₂×D₄	semidirect
426. C₂×#416	C₂×D₄	semidirect
427. C₂×#416	C₂×D₄	semidirect
428. C₂×#416	C₂×D₄	semidirect
429. C₂×#416	C₂×D₄	semidirect
430. #2889	C₂⁴	semidirect
431. #2888	C₂⁴	semidirect
441. #2884	C₂⁴	semidirect
442. #2883	C₂⁴	semidirect
462. #2123	C₂⁴	semidirect
463. #2123	C₂⁴	semidirect
466. #2122	C₂⁴	semidirect
467. #2122	C₂⁴	semidirect
484. #1910	C₂⁴	semidirect
485. #1909	C₂⁴	semidirect
488. #1868	C₂⁴	semidirect
489. #1858	C₂⁴	semidirect
490. #1796	C₂⁴	semidirect
491. #1795	C₂⁴	semidirect
492. #1794	C₂⁴	semidirect
493. #1791	C₂⁴	semidirect
494. #1395	C₂⁴	semidirect
495. #1395	C₂⁴	semidirect
496. #1392	C₂⁴	semidirect
497. #1391	C₂⁴	semidirect
557. C₂²×#41	C₂²×D₄	semidirect
558. C₂²×#41	C₂²×D₄	semidirect
574. C₂³×Q₈	C₂²×D₄	semidirect
588. C₂³×D₄	C₂²×D₄	semidirect
601. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
602. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
603. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
604. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
605. C₂²×SD₁₆	C₂²×D₄	semidirect
606. C₂²×SD₁₆	C₂²×D₄	semidirect
607. C₂²×D₈	C₂²×D₄	semidirect
608. C₂²×D₈	C₂²×D₄	semidirect
620. #536	C₂²×D₄	semidirect
621. #536	C₂²×D₄	semidirect
629. #535	C₂²×D₄	semidirect
630. #535	C₂²×D₄	semidirect
648. #525	C₂²×D₄	semidirect
649. #525	C₂²×D₄	semidirect
650. #525	C₂²×D₄	semidirect
651. #525	C₂²×D₄	semidirect
682. #519	C₂²×D₄	semidirect
683. #519	C₂²×D₄	semidirect
684. #518	C₂²×D₄	semidirect
685. #518	C₂²×D₄	semidirect
701. #419	C₂²×D₄	semidirect
702. #419	C₂²×D₄	semidirect
703. #418	C₂²×D₄	semidirect
704. #418	C₂²×D₄	semidirect
705. #416	C₂²×D₄	semidirect
706. #416	C₂²×D₄	semidirect
707. #416	C₂²×D₄	semidirect
708. #416	C₂²×D₄	semidirect
1126. C₂	#72237549	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#499153	2
C₂×#501201	2
C₂×#501192	2
C₂×#501197	2
C₂×#6437988	2
C₂×#494761	2
C₂×#499126	2
C₂×#498916	2
C₂×#494752	2
C₂×#501188	2
C₂×#494361	2
C₂×#7622450	2
C₂×#10577322	2
C₂×#498943	2
C₂×#494587	2
C₂×#6438015	2
C₂²×#33553	2
C₂²×#12755	2
C₂×#6437575	2
#72237549	2

Subgroups — C2×#72237549 #72337522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72237549 #72337522