Subgroups — C₂×#72237529 #72337518

Order 2048.

Only the 5160 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 760 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×#499828	C₂	1	4	yes	maximal, complemented
2	C₂×#499820	C₂	1	4	yes	maximal, complemented
3	C₂×#499827	C₂	1	4	yes	maximal, complemented
4	C₂×#494761	C₂	1	2	yes	maximal, complemented
5	C₂×#498941	C₂	1	2	yes	maximal, complemented
6	C₂×#10577322	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#493410	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#499819	C₂	1	4	yes	maximal, complemented
9	C₂×#498898	C₂	1	2	yes	maximal, complemented
10	C₂×#494587	C₂	1	2	yes	maximal, complemented
11	C₂×#6628885	C₂	1	2	yes	maximal, complemented
12	C₂×#10574874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#33553	C₂	1	2	yes	maximal, complemented
14	#72237529	C₂	1	32	yes	maximal, direct product factor
15	C₂×#63103	C₂²	1	1	yes	characteristic, complemented
16	C₂²×#3537	C₂²	1	1	yes	characteristic, complemented
17	C₂×#62811	C₂²	1	1	yes	characteristic
18	#10577322	C₂²	1	16	yes	complemented
19	C₂×#61651	C₂²	1	2	yes	complemented
20	C₂×#61648	C₂²	1	2	yes	complemented
21	C₂×#61633	C₂²	1	2	yes	complemented
22	C₂×#61630	C₂²	1	2	yes	complemented
23	C₂×#60753	C₂²	1	2	yes	complemented
24	C₂×#60402	C₂²	1	2	yes	complemented
25	C₂×#60400	C₂²	1	2	yes	complemented
26	C₂×#60398	C₂²	1	2	yes	complemented
27	C₂²×#3027	C₂²	1	2	yes	complemented
28	C₂²×#3025	C₂²	1	2	yes	—
29	#10574874	C₂²	1	16	yes	complemented
30	C₂×#60401	C₂²	1	2	yes	complemented
31	C₂×#60399	C₂²	1	2	yes	complemented
32	C₂×#60369	C₂²	1	2	yes	—
33	C₂²×#3021	C₂²	1	2	yes	complemented
34	C₂×#60231	C₂²	1	1	yes	characteristic, complemented
35	C₂×#60070	C₂²	1	1	yes	characteristic, complemented
36	C₂×#33553	C₂²	1	8	yes	complemented
37	C₂×#33553	C₂²	1	8	yes	complemented
38	C₂×#33553	C₂²	1	32	yes	complemented
39	C₂×#33369	C₂²	1	1	yes	characteristic, complemented
40	C₂×#33358	C₂²	1	1	yes	characteristic, complemented
41	C₂²×#2128	C₂²	1	2	yes	complemented
42	C₂²×#2122	C₂²	1	2	yes	complemented
43	C₂²×#2120	C₂²	1	2	yes	complemented
44	#6628885	C₂²	1	32	yes	complemented
45	C₂×#32895	C₂²	1	8	yes	complemented
46	C₂×#32894	C₂²	1	8	yes	complemented
47	C₂×#20623	C₂²	1	2	yes	complemented
48	C₂×#20620	C₂²	1	2	yes	complemented
49	C₂×#20612	C₂²	1	2	yes	complemented
50	#499828	C₂²	1	64	yes	complemented
51	#499827	C₂²	1	64	yes	complemented
52	#499820	C₂²	1	64	yes	complemented
53	#499819	C₂²	1	64	yes	complemented
54	#498941	C₂²	1	32	yes	complemented
55	C₂×#13354	C₂²	1	8	yes	complemented
56	C₂×#13353	C₂²	1	8	yes	complemented
57	#498898	C₂²	1	32	yes	complemented
58	C₂×#13351	C₂²	1	8	yes	complemented
59	C₂×#13350	C₂²	1	8	yes	complemented
60	#494761	C₂²	1	32	yes	complemented
61	C₂×#13103	C₂²	1	8	yes	complemented
62	C₂×#13102	C₂²	1	8	yes	complemented
63	#494587	C₂²	1	32	yes	complemented
64	C₂×#13046	C₂²	1	8	yes	complemented
65	C₂×#13045	C₂²	1	8	yes	complemented
66	#493410	C₂²	1	16	yes	complemented
67	C₂×#12714	C₂²	1	2	yes	complemented
68	C₂×#12712	C₂²	1	2	yes	complemented
69	C₂×#12713	C₂²	1	2	yes	complemented
70	C₂×#12711	C₂²	1	2	yes	complemented
71	C₂×#12589	C₂²	1	2	yes	complemented
72	C₂×#12577	C₂²	1	2	yes	complemented
73	#63103	C₂³	1	8	yes	complemented
74	C₂×2₋¹⁺⁶	C₂³	1	2	yes	complemented
75	C₂×H(7,𝔽₂)	C₂³	1	2	yes	complemented
76	C₂²×#585	C₂³	1	2	yes	—
77	C₂²×#585	C₂³	1	1	yes	characteristic
78	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
79	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
80	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
81	#62811	D₄	1	8	yes	complemented
82	#62811	C₂³	1	8	yes	—
83	C₂×#3487	D₄	1	1	yes	characteristic, complemented
84	C₂×#3487	C₂³	1	1	yes	characteristic
85	C₂×#3486	D₄	1	1	yes	characteristic, complemented
86	C₂×#3486	C₂³	1	1	yes	characteristic
87	C₂×#3485	D₄	1	1	yes	characteristic, complemented
88	C₂×#3485	C₂³	1	1	yes	characteristic
89	C₂×#3484	D₄	1	1	yes	characteristic, complemented
90	C₂×#3484	C₂³	1	1	yes	characteristic
91	C₂×#3537	C₂³	1	2	yes	complemented
92	C₂×#3537	C₂³	1	2	yes	complemented
93	C₂×#3537	C₂³	1	8	yes	complemented
94	C₂×#3449	D₄	1	1	yes	characteristic, complemented
95	C₂×#3449	C₂³	1	1	yes	characteristic
96	C₂²×#535	C₂³	1	2	yes	—
97	C₂²×#525	D₄	1	1	yes	characteristic, complemented
98	C₂²×#525	C₂³	1	1	yes	characteristic
99	C₂×#3428	D₄	1	1	yes	characteristic, complemented
100	#61651	C₂³	1	16	yes	complemented
101	#61648	C₂³	1	16	yes	complemented
102	#61633	C₂³	1	16	yes	complemented
103	#61630	C₂³	1	16	yes	complemented
104	#60753	C₂³	1	16	yes	complemented
105	C₂×#3200	C₂³	1	4	yes	complemented
106	C₂×#3199	C₂³	1	4	yes	complemented
107	#60402	C₂³	1	16	yes	complemented
108	#60401	C₂³	1	16	yes	complemented
109	#60400	C₂³	1	16	yes	complemented
110	#60399	C₂³	1	16	yes	complemented
111	#60398	C₂³	1	16	yes	complemented
112	C₂×#3028	C₂³	1	4	yes	complemented
113	C₂×#3027	C₂³	1	8	yes	—
114	C₂×#3027	C₂³	1	16	yes	complemented
115	C₂×#3027	C₂³	1	4	yes	complemented
116	C₂×#3025	D₄	1	4	yes	complemented
117	C₂×#3025	D₄	1	4	yes	complemented
118	C₂×#3025	D₄	1	16	yes	complemented
119	C₂×#3025	C₂³	1	4	yes	—
120	C₂×#3025	C₂³	1	4	yes	—
121	C₂×#3025	C₂³	1	16	yes	—
122	C₂²×#458	D₄	1	4	yes	complemented
123	C₂²×B(4,𝔽₂)	D₄	1	4	yes	complemented
124	C₂×#3021	C₂³	1	8	yes	—
125	C₂×#3021	C₂³	1	16	yes	complemented
126	#60369	D₄	1	16	yes	complemented
127	#60369	C₂³	1	16	yes	—
128	C₂×#3010	D₄	1	4	yes	complemented
129	C₂×#3010	C₂³	1	4	yes	—
130	C₂×#3008	D₄	1	4	yes	complemented
131	C₂×#3008	C₂³	1	4	yes	—
132	#60231	C₂³	1	8	yes	complemented
133	C₂×#2978	C₂³	1	2	yes	complemented
134	C₂×#2977	C₂³	1	2	yes	complemented
135	C₂×#2896	D₄	1	2	yes	complemented
136	C₂×#2896	D₄	1	2	yes	complemented
137	C₂²×#413	C₂³	1	2	yes	—
138	#60070	C₂³	1	8	yes	complemented
139	C₂×#2884	C₂³	1	2	yes	complemented
140	C₂×#2883	C₂³	1	2	yes	complemented
141	C₂²×#410	C₂³	1	2	yes	—
142	C₂²×#410	C₂³	1	2	yes	—
143	C₂×#2879	C₂³	1	2	yes	—
144	#33553	C₂³	1	64	yes	complemented
145	#33553	C₂³	1	64	yes	complemented
146	#33369	C₂³	1	8	yes	complemented
147	C₂×#2135	C₂³	1	2	yes	complemented
148	C₂×#2134	C₂³	1	2	yes	complemented
149	#33358	C₂³	1	8	yes	complemented
150	C₂×#2129	C₂³	1	2	yes	complemented
151	C₂×#2128	C₂³	1	8	yes	complemented
152	C₂×#2128	C₂³	1	16	yes	complemented
153	C₂×#2128	C₂³	1	2	yes	complemented
154	C₂×#2122	C₂³	1	8	yes	complemented
155	C₂×#2122	C₂³	1	16	yes	complemented
156	C₂×#2120	C₂³	1	4	yes	complemented
157	C₂×#2120	C₂³	1	4	yes	complemented
158	C₂×#2120	C₂³	1	16	yes	complemented
159	#32895	C₂³	1	64	yes	complemented
160	#32894	C₂³	1	64	yes	complemented
161	#20623	C₂³	1	16	yes	complemented
162	C₂×#1796	C₂³	1	4	yes	complemented
163	C₂×#1795	C₂³	1	4	yes	complemented
164	#20620	C₂³	1	16	yes	complemented
165	C₂×#1794	C₂³	1	8	yes	complemented
166	#20612	C₂³	1	16	yes	complemented
167	C₂×#1791	C₂³	1	8	yes	complemented
168	#13354	C₂³	1	64	yes	complemented
169	#13353	C₂³	1	64	yes	complemented
170	#13351	C₂³	1	64	yes	complemented
171	#13350	C₂³	1	64	yes	complemented
172	#13103	C₂³	1	64	yes	complemented
173	#13102	C₂³	1	64	yes	complemented
174	#13046	C₂³	1	64	yes	complemented
175	#13045	C₂³	1	64	yes	complemented
176	#12714	C₂³	1	16	yes	complemented
177	#12713	C₂³	1	16	yes	complemented
178	#12712	C₂³	1	16	yes	complemented
179	#12711	C₂³	1	16	yes	complemented
180	#12589	C₂³	1	16	yes	complemented
181	C₂×#1395	C₂³	1	8	yes	complemented
182	#12577	C₂³	1	16	yes	complemented
183	C₂×#1391	C₂³	1	8	yes	complemented
184	2₋¹⁺⁶	C₂⁴	1	8	yes	complemented
185	H(7,𝔽₂)	C₂⁴	1	8	yes	complemented
186	C₂×#585	C₂×D₄	1	4	yes	—
187	C₂×#585	C₂×D₄	1	8	yes	—
188	C₂×#585	C₂×D₄	1	4	yes	—
189	C₂×#585	C₂×D₄	1	8	yes	—
190	C₂×#585	C₂⁴	1	4	yes	—
191	C₂×#585	C₂⁴	1	4	yes	—
192	C₂×#585	C₂⁴	1	8	yes	—
193	C₂²×2₋¹⁺⁴	C₂×D₄	1	1	yes	characteristic
194	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
195	C₂²×2₋¹⁺⁴	C₂⁴	1	1	yes	characteristic
196	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
197	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
198	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
199	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
200	C₂³×#41	C₂×D₄	1	2	yes	—
201	C₂³×#41	C₂×D₄	1	1	yes	characteristic
202	C₂³×#41	C₂×D₄	1	2	yes	—
203	C₂³×#41	C₂×D₄	1	1	yes	characteristic
204	C₂³×#41	C₂×D₄	1	1	yes	characteristic
205	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂³×#41	C₂×D₄	1	8	yes	complemented
208	C₂³×#41	C₂⁴	1	1	yes	characteristic
209	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
212	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
213	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	complemented
214	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	complemented
215	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	complemented
216	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	complemented
217	C₂³×SD₁₆	C₂×D₄	1	4	yes	complemented
218	C₂³×D₈	C₂×D₄	1	4	yes	complemented
219	C₂³×M₁₆	C₂×D₄	1	2	yes	complemented
220	C₂³×M₁₆	C₂×D₄	1	2	yes	complemented
221	#3537	C₂⁴	1	8	yes	complemented
222	#3537	C₂⁴	1	8	yes	complemented
223	#3487	C₂×D₄	1	8	yes	complemented
224	#3487	C₂×D₄	1	4	yes	complemented
225	#3487	C₂⁴	1	4	yes	—
226	#3486	C₂×D₄	1	8	yes	complemented
227	#3486	C₂×D₄	1	4	yes	complemented
228	#3486	C₂⁴	1	4	yes	—
229	#3485	C₂×D₄	1	8	yes	complemented
230	#3485	C₂×D₄	1	4	yes	complemented
231	#3485	C₂⁴	1	4	yes	—
232	#3484	C₂×D₄	1	8	yes	complemented
233	#3484	C₂×D₄	1	4	yes	complemented
234	#3484	C₂⁴	1	4	yes	—
235	#3449	C₂×D₄	1	4	yes	—
236	#3449	C₂×D₄	1	8	yes	complemented
237	#3449	C₂⁴	1	4	yes	—
238	C₂×#536	C₂×D₄	1	1	yes	characteristic
239	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#536	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂×#536	C₂⁴	1	1	yes	characteristic
242	C₂×#535	C₂×D₄	1	1	yes	characteristic
243	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
244	C₂×#535	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂×#535	C₂×D₄	1	4	yes	complemented
246	C₂×#535	C₂×D₄	1	8	yes	complemented
247	C₂×#535	C₂⁴	1	4	yes	—
248	C₂×#535	C₂⁴	1	1	yes	characteristic
249	C₂×#535	C₂⁴	1	8	yes	—
250	C₂×#525	C₂×D₄	1	2	yes	—
251	C₂×#525	C₂×D₄	1	2	yes	—
252	C₂×#525	C₂×D₄	1	8	yes	—
253	C₂×#525	C₂×D₄	1	1	yes	characteristic
254	C₂×#525	C₂×D₄	1	1	yes	characteristic
255	C₂×#525	C₂×D₄	1	4	yes	—
256	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
257	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
259	C₂×#525	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂×#525	C₂×D₄	1	8	yes	complemented
261	C₂×#525	C₂⁴	1	1	yes	characteristic
262	C₂×#525	C₂⁴	1	1	yes	characteristic
263	C₂×#525	C₂⁴	1	4	yes	—
264	C₂²×#123	C₂×D₄	1	2	yes	—
265	C₂²×#120	C₂×D₄	1	2	yes	—
266	#3428	C₂×D₄	1	8	yes	complemented
267	C₂×#519	C₂×D₄	1	1	yes	characteristic, complemented
268	C₂×#519	C₂×D₄	1	1	yes	characteristic, complemented
269	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
270	C₂×#518	C₂×D₄	1	1	yes	characteristic, complemented
271	C₂²×#117	C₂×D₄	1	1	yes	characteristic
272	C₂²×#117	C₂×D₄	1	1	yes	characteristic
273	C₂²×#117	C₂×D₄	1	2	yes	complemented
274	#3200	C₂⁴	1	16	yes	complemented
275	#3199	C₂⁴	1	16	yes	complemented
276	#3028	C₂⁴	1	16	yes	complemented
277	#3027	C₂⁴	1	32	yes	—
278	#3027	C₂⁴	1	16	yes	complemented
279	#3025	C₂×D₄	1	16	yes	complemented
280	#3025	C₂×D₄	1	16	yes	complemented
281	#3025	C₂×D₄	1	32	yes	complemented
282	#3025	C₂×D₄	1	32	yes	complemented
283	#3025	C₂⁴	1	16	yes	—
284	#3025	C₂⁴	1	16	yes	—
285	C₂×#458	C₂×D₄	1	8	yes	complemented
286	C₂×#458	C₂×D₄	1	8	yes	complemented
287	C₂×#458	C₂×D₄	1	32	yes	complemented
288	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
289	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	complemented
290	C₂×B(4,𝔽₂)	C₂×D₄	1	32	yes	complemented
291	#3021	C₂⁴	1	32	yes	—
292	#3010	C₂×D₄	1	16	yes	complemented
293	#3010	C₂×D₄	1	32	yes	complemented
294	#3010	C₂⁴	1	16	yes	—
295	#3008	C₂×D₄	1	16	yes	complemented
296	#3008	C₂×D₄	1	32	yes	complemented
297	#3008	C₂⁴	1	16	yes	—
298	#2978	C₂⁴	1	8	yes	complemented
299	#2977	C₂⁴	1	8	yes	complemented
300	#2896	C₂×D₄	1	16	yes	complemented
301	#2896	C₂×D₄	1	16	yes	complemented
302	C₂×#419	C₂×D₄	1	4	yes	complemented
303	C₂×#418	C₂×D₄	1	4	yes	complemented
304	C₂×#416	C₂×D₄	1	4	yes	complemented
305	C₂×#416	C₂×D₄	1	4	yes	complemented
306	C₂×#413	C₂⁴	1	4	yes	—
307	C₂×#413	C₂⁴	1	8	yes	—
308	#2884	C₂⁴	1	8	yes	complemented
309	#2883	C₂⁴	1	8	yes	complemented
310	C₂×#410	C₂×D₄	1	4	yes	—
311	C₂×#410	C₂×D₄	1	8	yes	—
312	C₂×#410	C₂⁴	1	4	yes	—
313	C₂×#410	C₂⁴	1	8	yes	—
314	C₂×#410	C₂⁴	1	4	yes	—
315	C₂×#410	C₂⁴	1	8	yes	—
316	C₂²×#99	C₂×D₄	1	4	yes	—
317	#2879	C₂×D₄	1	8	yes	complemented
318	#2879	C₂⁴	1	8	yes	—
319	C₂×#408	C₂×D₄	1	4	yes	complemented
320	C₂×#408	C₂⁴	1	4	yes	—
321	#2135	C₂⁴	1	8	yes	complemented
322	#2134	C₂⁴	1	8	yes	complemented
323	#2129	C₂⁴	1	8	yes	complemented
324	#2128	C₂⁴	1	32	yes	complemented
325	#2128	C₂⁴	1	8	yes	complemented
326	#2122	C₂⁴	1	32	yes	complemented
327	#2120	C₂⁴	1	16	yes	complemented
328	#2120	C₂⁴	1	16	yes	complemented
329	#1796	C₂⁴	1	16	yes	complemented
330	#1795	C₂⁴	1	16	yes	complemented
331	#1794	C₂⁴	1	32	yes	complemented
332	#1791	C₂⁴	1	32	yes	complemented
333	#1395	C₂⁴	1	32	yes	complemented
334	#1391	C₂⁴	1	32	yes	complemented
335	C₂⁶	#120	1	1	yes	characteristic
336	#585	C₂²×D₄	1	8	yes	—
337	#585	C₂²×D₄	1	16	yes	—
338	#585	C₂⁵	1	8	yes	—
339	C₂×2₋¹⁺⁴	#120	1	4	yes	—
340	C₂×2₋¹⁺⁴	#120	1	8	yes	—
341	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
342	C₂×2₋¹⁺⁴	C₂²×D₄	1	8	yes	—
343	C₂×2₋¹⁺⁴	C₂²×D₄	1	2	yes	—
344	C₂×2₋¹⁺⁴	C₂²×D₄	1	4	yes	—
345	C₂×2₋¹⁺⁴	C₂⁵	1	2	yes	—
346	C₂×H(5,𝔽₂)	#120	1	4	yes	—
347	C₂×H(5,𝔽₂)	#120	1	8	yes	—
348	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
349	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
350	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
351	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
352	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
353	C₂×H(5,𝔽₂)	C₂²×D₄	1	16	yes	—
354	C₂×H(5,𝔽₂)	C₂⁵	1	2	yes	—
355	C₂²×#41	#120	1	2	yes	—
356	C₂²×#41	#120	1	2	yes	—
357	C₂²×#41	#120	1	2	yes	—
358	C₂²×#41	#120	1	4	yes	—
359	C₂²×#41	#120	1	8	yes	—
360	C₂²×#41	#120	1	8	yes	—
361	C₂²×#41	#120	1	4	yes	—
362	C₂²×#41	#120	1	1	yes	characteristic
363	C₂²×#41	#120	1	1	yes	characteristic
364	C₂²×#41	#120	1	2	yes	—
365	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
366	C₂²×#41	C₂²×D₄	1	2	yes	—
367	C₂²×#41	C₂²×D₄	1	2	yes	—
368	C₂²×#41	C₂²×D₄	1	4	yes	—
369	C₂²×#41	C₂²×D₄	1	2	yes	—
370	C₂²×#41	C₂²×D₄	1	4	yes	—
371	C₂²×#41	C₂²×D₄	1	2	yes	—
372	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
373	C₂²×#41	C₂²×D₄	1	2	yes	—
374	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
375	C₂²×#41	C₂²×D₄	1	8	yes	—
376	C₂²×#41	C₂²×D₄	1	4	yes	—
377	C₂²×#41	C₂²×D₄	1	4	yes	—
378	C₂²×#41	C₂²×D₄	1	4	yes	—
379	C₂²×#41	C₂²×D₄	1	8	yes	—
380	C₂²×#41	C₂²×D₄	1	4	yes	complemented
381	C₂²×#41	C₂²×D₄	1	4	yes	complemented
382	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
384	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
385	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
386	C₂²×#41	C₂⁵	1	1	yes	characteristic
387	C₂²×#41	C₂⁵	1	2	yes	—
388	C₂³×Q₈	#120	1	1	yes	characteristic
389	C₂³×Q₈	#120	1	2	yes	—
390	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
391	C₂³×Q₈	C₂²×D₄	1	2	yes	—
392	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
393	C₂³×Q₈	C₂²×D₄	1	4	yes	complemented
394	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂³×D₄	#120	1	1	yes	characteristic
396	C₂³×D₄	#120	1	2	yes	—
397	C₂³×D₄	C₂²×D₄	1	2	yes	—
398	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
399	C₂³×D₄	C₂²×D₄	1	2	yes	—
400	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
401	C₂³×D₄	C₂²×D₄	1	4	yes	—
402	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
403	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
404	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂⁴×C₄	#120	1	1	yes	characteristic
406	C₂⁴×C₄	#120	1	1	yes	characteristic
407	C₂⁴×C₄	#120	1	4	yes	—
408	C₂⁴×C₄	#120	1	1	yes	characteristic
409	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
410	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
411	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
412	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
413	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
414	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	16	yes	complemented
415	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	16	yes	complemented
416	C₂²×SD₁₆	C₂²×D₄	1	16	yes	complemented
417	C₂²×D₈	C₂²×D₄	1	16	yes	complemented
418	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
419	C₂²×M₁₆	C₂²×D₄	1	8	yes	complemented
420	C₂²×M₁₆	C₂²×D₄	1	8	yes	complemented
421	C₂³×C₈	C₂²×D₄	1	4	yes	—
422	#536	C₂²×D₄	1	4	yes	—
423	#536	C₂²×D₄	1	2	yes	—
424	#536	C₂²×D₄	1	4	yes	complemented
425	#536	C₂²×D₄	1	4	yes	complemented
426	#536	C₂⁵	1	2	yes	—
427	#535	C₂²×D₄	1	4	yes	—
428	#535	C₂²×D₄	1	8	yes	—
429	#535	C₂²×D₄	1	2	yes	—
430	#535	C₂²×D₄	1	16	yes	complemented
431	#535	C₂²×D₄	1	4	yes	complemented
432	#535	C₂²×D₄	1	4	yes	complemented
433	#535	C₂⁵	1	8	yes	—
434	#535	C₂⁵	1	2	yes	—
435	#525	#120	1	4	yes	—
436	#525	#120	1	4	yes	—
437	#525	#120	1	8	yes	—
438	#525	#120	1	8	yes	—
439	#525	C₂²×D₄	1	4	yes	—
440	#525	C₂²×D₄	1	4	yes	—
441	#525	C₂²×D₄	1	8	yes	—
442	#525	C₂²×D₄	1	8	yes	—
443	#525	C₂²×D₄	1	4	yes	—
444	#525	C₂²×D₄	1	2	yes	—
445	#525	C₂²×D₄	1	4	yes	—
446	#525	C₂²×D₄	1	2	yes	—
447	#525	C₂²×D₄	1	4	yes	complemented
448	#525	C₂²×D₄	1	4	yes	complemented
449	#525	C₂²×D₄	1	4	yes	complemented
450	#525	C₂²×D₄	1	4	yes	complemented
451	#525	C₂⁵	1	2	yes	—
452	#525	C₂⁵	1	2	yes	—
453	C₂×#123	#120	1	2	yes	—
454	C₂×#123	#120	1	2	yes	—
455	C₂×#123	#120	1	8	yes	—
456	C₂×#123	C₂²×D₄	1	2	yes	—
457	C₂×#123	C₂²×D₄	1	2	yes	—
458	C₂×#123	C₂²×D₄	1	8	yes	—
459	C₂×#120	#120	1	2	yes	—
460	C₂×#120	#120	1	2	yes	—
461	C₂×#120	#120	1	8	yes	—
462	C₂×#120	C₂²×D₄	1	2	yes	—
463	C₂×#120	C₂²×D₄	1	2	yes	—
464	C₂×#120	C₂²×D₄	1	8	yes	—
465	#519	C₂²×D₄	1	4	yes	complemented
466	#519	C₂²×D₄	1	4	yes	complemented
467	#518	C₂²×D₄	1	4	yes	complemented
468	#518	C₂²×D₄	1	4	yes	complemented
469	C₂×#117	#120	1	2	yes	—
470	C₂×#117	#120	1	4	yes	—
471	C₂×#117	C₂²×D₄	1	1	yes	characteristic
472	C₂×#117	C₂²×D₄	1	1	yes	characteristic
473	C₂×#117	C₂²×D₄	1	4	yes	—
474	C₂×#117	C₂²×D₄	1	4	yes	—
475	C₂×#117	C₂²×D₄	1	1	yes	characteristic
476	C₂×#117	C₂²×D₄	1	1	yes	characteristic
477	C₂×#117	C₂²×D₄	1	4	yes	—
478	C₂×#117	C₂²×D₄	1	8	yes	complemented
479	C₂²×C₂²⋊C₄	#120	1	2	yes	—
480	#458	C₂²×D₄	1	32	yes	complemented
481	#458	C₂²×D₄	1	32	yes	complemented
482	B(4,𝔽₂)	C₂²×D₄	1	32	yes	complemented
483	B(4,𝔽₂)	C₂²×D₄	1	32	yes	complemented
484	#419	C₂²×D₄	1	16	yes	complemented
485	#418	C₂²×D₄	1	16	yes	complemented
486	#416	C₂²×D₄	1	16	yes	complemented
487	#416	C₂²×D₄	1	16	yes	complemented
488	#413	C₂⁵	1	8	yes	—
489	#410	C₂²×D₄	1	8	yes	—
490	#410	C₂²×D₄	1	16	yes	—
491	#410	C₂⁵	1	8	yes	—
492	#410	C₂⁵	1	8	yes	—
493	C₂×#99	C₂²×D₄	1	8	yes	—
494	C₂×#99	C₂²×D₄	1	16	yes	—
495	#408	C₂²×D₄	1	8	yes	—
496	#408	C₂²×D₄	1	16	yes	complemented
497	#408	C₂⁵	1	8	yes	—
498	C₂⁵	C₂×#120	1	1	yes	characteristic
499	C₂⁵	C₂×#120	1	1	yes	characteristic
500	C₂⁵	C₂×#120	1	4	yes	—
501	C₂⁵	C₂×#120	1	1	yes	characteristic
502	C₂⁵	D₄²	1	2	yes	—
503	H(5,𝔽₂)	C₂³×D₄	1	16	yes	—
504	C₂×#41	B(4,𝔽₂)	1	8	yes	—
505	C₂×#41	B(4,𝔽₂)	1	8	yes	—
506	C₂×#41	C₂×#120	1	2	yes	—
507	C₂×#41	C₂×#120	1	4	yes	—
508	C₂×#41	C₂×#120	1	2	yes	—
509	C₂×#41	C₂×#120	1	4	yes	—
510	C₂×#41	C₂×#120	1	4	yes	—
511	C₂×#41	C₂×#120	1	4	yes	—
512	C₂×#41	C₂×#120	1	2	yes	—
513	C₂×#41	C₂×#120	1	4	yes	—
514	C₂×#41	C₂×#120	1	8	yes	—
515	C₂×#41	C₂×#120	1	8	yes	—
516	C₂×#41	C₂×#120	1	8	yes	—
517	C₂×#41	C₂×#120	1	2	yes	—
518	C₂×#41	C₂×#120	1	4	yes	—
519	C₂×#41	C₂×#120	1	8	yes	—
520	C₂×#41	#534	1	2	yes	—
521	C₂×#41	#534	1	2	yes	—
522	C₂×#41	#534	1	2	yes	—
523	C₂×#41	D₄²	1	4	yes	—
524	C₂×#41	D₄²	1	4	yes	—
525	C₂×#41	D₄²	1	4	yes	—
526	C₂×#41	D₄²	1	4	yes	—
527	C₂×#41	D₄²	1	4	yes	—
528	C₂×#41	D₄²	1	4	yes	—
529	C₂×#41	C₂³×D₄	1	2	yes	—
530	C₂×#41	C₂³×D₄	1	1	yes	characteristic
531	C₂×#41	C₂³×D₄	1	2	yes	—
532	C₂×#41	C₂³×D₄	1	4	yes	—
533	C₂×#41	C₂³×D₄	1	2	yes	—
534	C₂×#41	C₂³×D₄	1	2	yes	—
535	C₂×#41	C₂³×D₄	1	4	yes	—
536	C₂×#41	C₂³×D₄	1	4	yes	—
537	C₂×#41	C₂³×D₄	1	2	yes	—
538	C₂×#41	C₂³×D₄	1	4	yes	—
539	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
541	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
542	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
543	C₂×#41	C₂⁶	1	1	yes	characteristic
544	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
545	C₂²×Q₈	C₂×#120	1	1	yes	characteristic
546	C₂²×Q₈	C₂×#120	1	4	yes	—
547	C₂²×Q₈	C₂×#120	1	8	yes	—
548	C₂²×Q₈	C₂×#120	1	4	yes	—
549	C₂²×Q₈	C₂×#120	1	2	yes	—
550	C₂²×Q₈	C₂×#120	1	2	yes	—
551	C₂²×Q₈	#534	1	1	yes	characteristic
552	C₂²×Q₈	#534	1	2	yes	—
553	C₂²×Q₈	D₄²	1	2	yes	—
554	C₂²×Q₈	D₄²	1	4	yes	—
555	C₂²×Q₈	C₂³×D₄	1	2	yes	—
556	C₂²×Q₈	C₂³×D₄	1	2	yes	—
557	C₂²×Q₈	C₂³×D₄	1	4	yes	—
558	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂²×Q₈	C₂×H(5,𝔽₂)	1	2	yes	—
560	C₂²×D₄	C₂×#120	1	2	yes	—
561	C₂²×D₄	C₂×#120	1	4	yes	—
562	C₂²×D₄	C₂×#120	1	1	yes	characteristic
563	C₂²×D₄	C₂×#120	1	1	yes	characteristic
564	C₂²×D₄	C₂×#120	1	4	yes	—
565	C₂²×D₄	C₂×#120	1	8	yes	—
566	C₂²×D₄	C₂×#120	1	4	yes	—
567	C₂²×D₄	C₂×#120	1	2	yes	—
568	C₂²×D₄	C₂×#120	1	2	yes	—
569	C₂²×D₄	#534	1	1	yes	characteristic
570	C₂²×D₄	#534	1	2	yes	—
571	C₂²×D₄	D₄²	1	2	yes	—
572	C₂²×D₄	D₄²	1	4	yes	—
573	C₂²×D₄	D₄²	1	2	yes	—
574	C₂²×D₄	D₄²	1	4	yes	—
575	C₂²×D₄	D₄²	1	2	yes	—
576	C₂²×D₄	D₄²	1	4	yes	—
577	C₂²×D₄	C₂³×D₄	1	2	yes	—
578	C₂²×D₄	C₂³×D₄	1	8	yes	—
579	C₂²×D₄	C₂³×D₄	1	2	yes	—
580	C₂²×D₄	C₂³×D₄	1	4	yes	—
581	C₂²×D₄	C₂³×D₄	1	2	yes	—
582	C₂²×D₄	C₂³×D₄	1	4	yes	—
583	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
584	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
585	C₂³×C₄	C₂×#120	1	2	yes	—
586	C₂³×C₄	C₂×#120	1	1	yes	characteristic
587	C₂³×C₄	C₂×#120	1	1	yes	characteristic
588	C₂³×C₄	C₂×#120	1	2	yes	—
589	C₂³×C₄	C₂×#120	1	2	yes	—
590	C₂³×C₄	C₂×#120	1	4	yes	—
591	C₂³×C₄	C₂×#120	1	1	yes	characteristic
592	C₂³×C₄	C₂×#120	1	4	yes	—
593	C₂³×C₄	C₂×#120	1	1	yes	characteristic
594	C₂³×C₄	C₂×#120	1	2	yes	—
595	C₂³×C₄	C₂×#120	1	2	yes	—
596	C₂³×C₄	C₂×#120	1	4	yes	—
597	C₂³×C₄	C₂×#120	1	4	yes	—
598	C₂³×C₄	C₂×#120	1	1	yes	characteristic
599	C₂³×C₄	#534	1	1	yes	characteristic
600	C₂³×C₄	#534	1	2	yes	—
601	C₂³×C₄	#534	1	1	yes	characteristic
602	C₂³×C₄	D₄²	1	4	yes	—
603	C₂³×C₄	D₄²	1	2	yes	—
604	C₂³×C₄	D₄²	1	2	yes	—
605	C₂³×C₄	D₄²	1	4	yes	—
606	C₂³×C₄	D₄²	1	2	yes	—
607	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
608	C₂³×C₄	C₂³×D₄	1	2	yes	—
609	C₂³×C₄	C₂³×D₄	1	2	yes	—
610	C₂³×C₄	C₂³×D₄	1	4	yes	—
611	C₂³×C₄	C₂³×D₄	1	2	yes	—
612	C₂³×C₄	C₂³×D₄	1	2	yes	—
613	C₂×M₁₆	C₂³×D₄	1	8	yes	—
614	C₂²×C₈	C₂³×D₄	1	8	yes	—
615	#123	C₂×#120	1	8	yes	—
616	#123	C₂×#120	1	4	yes	—
617	#123	C₂×#120	1	8	yes	—
618	#123	C₂×#120	1	4	yes	—
619	#123	C₂³×D₄	1	4	yes	—
620	#123	C₂³×D₄	1	4	yes	—
621	#120	C₂×#120	1	8	yes	—
622	#120	C₂×#120	1	4	yes	—
623	#120	C₂×#120	1	8	yes	—
624	#120	C₂×#120	1	4	yes	—
625	#120	C₂³×D₄	1	4	yes	—
626	#120	C₂³×D₄	1	4	yes	—
627	#117	C₂×#120	1	2	yes	—
628	#117	C₂×#120	1	2	yes	—
629	#117	C₂×#120	1	8	yes	—
630	#117	C₂³×D₄	1	2	yes	—
631	#117	C₂³×D₄	1	2	yes	—
632	#117	C₂³×D₄	1	2	yes	—
633	#117	C₂³×D₄	1	2	yes	—
634	#117	C₂³×D₄	1	8	yes	—
635	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
638	#99	C₂³×D₄	1	16	yes	—
639	C₂⁴	#2403	1	2	yes	—
640	C₂⁴	#2403	1	1	yes	characteristic
641	C₂⁴	#2403	1	4	yes	—
642	C₂⁴	#2403	1	2	yes	—
643	C₂⁴	#2403	1	1	yes	characteristic
644	C₂⁴	C₂²×#120	1	2	yes	—
645	C₂⁴	C₂²×#120	1	1	yes	characteristic
646	C₂⁴	C₂²×#120	1	2	yes	—
647	C₂⁴	C₂²×#120	1	2	yes	—
648	C₂⁴	C₂×D₄²	1	4	yes	—
649	C₂⁴	C₂×D₄²	1	2	yes	—
650	#41	C₂×B(4,𝔽₂)	1	32	yes	—
651	C₂×Q₈	#2403	1	2	yes	—
652	C₂×Q₈	#2403	1	4	yes	—
653	C₂×Q₈	C₂×B(4,𝔽₂)	1	4	yes	—
654	C₂×Q₈	C₂×B(4,𝔽₂)	1	4	yes	—
655	C₂×Q₈	C₂²×#120	1	2	yes	—
656	C₂×Q₈	C₂²×#120	1	2	yes	—
657	C₂×Q₈	C₂²×#120	1	4	yes	—
658	C₂×Q₈	C₂×#534	1	2	yes	—
659	C₂×Q₈	C₂×#534	1	1	yes	characteristic
660	C₂×Q₈	C₂×D₄²	1	2	yes	—
661	C₂×Q₈	C₂×D₄²	1	4	yes	—
662	C₂×Q₈	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
663	C₂×D₄	#2403	1	4	yes	—
664	C₂×D₄	#2403	1	4	yes	—
665	C₂×D₄	#2403	1	4	yes	—
666	C₂×D₄	#2403	1	2	yes	—
667	C₂×D₄	#2403	1	4	yes	—
668	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
669	C₂×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
670	C₂×D₄	C₂²×#120	1	4	yes	—
671	C₂×D₄	C₂²×#120	1	2	yes	—
672	C₂×D₄	C₂²×#120	1	2	yes	—
673	C₂×D₄	C₂²×#120	1	2	yes	—
674	C₂×D₄	C₂²×#120	1	4	yes	—
675	C₂×D₄	C₂×#534	1	2	yes	—
676	C₂×D₄	C₂×#534	1	1	yes	characteristic
677	C₂×D₄	C₂×D₄²	1	2	yes	—
678	C₂×D₄	C₂×D₄²	1	4	yes	—
679	C₂×D₄	C₂×D₄²	1	2	yes	—
680	C₂×D₄	C₂×D₄²	1	4	yes	—
681	C₂×D₄	C₂×D₄²	1	2	yes	—
682	C₂×D₄	C₂×D₄²	1	4	yes	—
683	C₂×D₄	C₂⁴×D₄	1	2	yes	—
684	C₂×D₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
685	C₂²×C₄	#2403	1	2	yes	—
686	C₂²×C₄	#2403	1	1	yes	characteristic
687	C₂²×C₄	#2403	1	2	yes	—
688	C₂²×C₄	#2403	1	1	yes	characteristic
689	C₂²×C₄	#2403	1	2	yes	—
690	C₂²×C₄	#2403	1	2	yes	—
691	C₂²×C₄	#2403	1	2	yes	—
692	C₂²×C₄	#2403	1	4	yes	—
693	C₂²×C₄	#2403	1	2	yes	—
694	C₂²×C₄	#2403	1	4	yes	—
695	C₂²×C₄	#2403	1	4	yes	—
696	C₂²×C₄	#2403	1	4	yes	—
697	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
698	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
699	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
700	C₂²×C₄	C₂²×#120	1	2	yes	—
701	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
702	C₂²×C₄	C₂²×#120	1	2	yes	—
703	C₂²×C₄	C₂²×#120	1	2	yes	—
704	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
705	C₂²×C₄	C₂²×#120	1	4	yes	—
706	C₂²×C₄	C₂²×#120	1	2	yes	—
707	C₂²×C₄	C₂²×#120	1	2	yes	—
708	C₂²×C₄	C₂²×#120	1	2	yes	—
709	C₂²×C₄	C₂×#534	1	2	yes	—
710	C₂²×C₄	C₂×#534	1	1	yes	characteristic
711	C₂²×C₄	C₂×#534	1	1	yes	characteristic
712	C₂²×C₄	C₂×#534	1	2	yes	—
713	C₂²×C₄	C₂×D₄²	1	2	yes	—
714	C₂²×C₄	C₂×D₄²	1	4	yes	—
715	C₂²×C₄	C₂×D₄²	1	4	yes	—
716	C₂²×C₄	C₂×D₄²	1	2	yes	—
717	C₂²×C₄	C₂×D₄²	1	2	yes	—
718	C₂²×C₄	C₂×D₄²	1	4	yes	—
719	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
721	C₂²⋊C₄	C₂²×#120	1	4	yes	—
722	C₂²⋊C₄	C₂²×#120	1	4	yes	—
723	C₂³	#23900	1	2	yes	—
724	C₂³	#23900	1	2	yes	—
725	C₂³	C₂×#2403	1	2	yes	—
726	C₂³	C₂×#2403	1	1	yes	characteristic
727	C₂³	C₂×#2403	1	4	yes	—
728	C₂³	C₂×#2403	1	2	yes	—
729	C₂³	C₂×#2403	1	2	yes	—
730	C₂³	C₂×#2403	1	1	yes	characteristic
731	C₂³	C₂³×#120	1	1	yes	characteristic
732	C₂³	C₂²×D₄²	1	2	yes	—
733	Q₈	C₂²×B(4,𝔽₂)	1	8	yes	—
734	D₄	C₂²×B(4,𝔽₂)	1	8	yes	—
735	C₂×C₄	#23900	1	8	yes	—
736	C₂×C₄	#23900	1	2	yes	—
737	C₂×C₄	#23900	1	2	yes	—
738	C₂×C₄	C₂×#2403	1	1	yes	characteristic
739	C₂×C₄	C₂×#2403	1	2	yes	—
740	C₂×C₄	C₂×#2403	1	1	yes	characteristic
741	C₂×C₄	C₂×#2403	1	2	yes	—
742	C₂×C₄	C₂×#2403	1	2	yes	—
743	C₂×C₄	C₂×#2403	1	4	yes	—
744	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
745	C₂×C₄	C₂²×B(4,𝔽₂)	1	8	yes	—
746	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
747	C₂×C₄	C₂³×#120	1	1	yes	characteristic
748	C₂×C₄	C₂²×#534	1	1	yes	characteristic
749	C₂×C₄	C₂²×D₄²	1	2	yes	—
750	C₂²	C₂×#23900	1	1	yes	characteristic
751	C₂²	C₂×#23900	1	4	yes	—
752	C₂²	C₂×#23900	1	1	yes	characteristic
753	C₂²	C₂²×#2403	1	1	yes	characteristic
754	C₄	C₂×#23900	1	2	yes	—
755	C₄	C₂×#23900	1	4	yes	—
756	C₄	C₂³×B(4,𝔽₂)	1	2	yes	—
757	C₂	C₂²×#23900	1	1	yes	characteristic
758	C₂	#72237529	1	2	yes	direct product factor

	subgroup	G/H
center, socle	C₂²	C₂×#23900
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×#499828	C₂	semidirect
2. C₂×#499820	C₂	semidirect
3. C₂×#499827	C₂	semidirect
4. C₂×#494761	C₂	semidirect
5. C₂×#498941	C₂	semidirect
6. C₂×#10577322	C₂	semidirect
7. C₂×#493410	C₂	semidirect
8. C₂×#499819	C₂	semidirect
9. C₂×#498898	C₂	semidirect
10. C₂×#494587	C₂	semidirect
11. C₂×#6628885	C₂	semidirect
12. C₂×#10574874	C₂	semidirect
13. C₂²×#33553	C₂	semidirect
14. #72237529	C₂	direct (N × H)
15. C₂×#63103	C₂²	semidirect
16. C₂²×#3537	C₂²	semidirect
18. #10577322	C₂²	semidirect
19. C₂×#61651	C₂²	semidirect
20. C₂×#61648	C₂²	semidirect
21. C₂×#61633	C₂²	semidirect
22. C₂×#61630	C₂²	semidirect
23. C₂×#60753	C₂²	semidirect
24. C₂×#60402	C₂²	semidirect
25. C₂×#60400	C₂²	semidirect
26. C₂×#60398	C₂²	semidirect
27. C₂²×#3027	C₂²	semidirect
29. #10574874	C₂²	semidirect
30. C₂×#60401	C₂²	semidirect
31. C₂×#60399	C₂²	semidirect
33. C₂²×#3021	C₂²	semidirect
34. C₂×#60231	C₂²	semidirect
35. C₂×#60070	C₂²	semidirect
36. C₂×#33553	C₂²	semidirect
37. C₂×#33553	C₂²	semidirect
38. C₂×#33553	C₂²	semidirect
39. C₂×#33369	C₂²	semidirect
40. C₂×#33358	C₂²	semidirect
41. C₂²×#2128	C₂²	semidirect
42. C₂²×#2122	C₂²	semidirect
43. C₂²×#2120	C₂²	semidirect
44. #6628885	C₂²	semidirect
45. C₂×#32895	C₂²	semidirect
46. C₂×#32894	C₂²	semidirect
47. C₂×#20623	C₂²	semidirect
48. C₂×#20620	C₂²	semidirect
49. C₂×#20612	C₂²	semidirect
50. #499828	C₂²	semidirect
51. #499827	C₂²	semidirect
52. #499820	C₂²	semidirect
53. #499819	C₂²	semidirect
54. #498941	C₂²	semidirect
55. C₂×#13354	C₂²	semidirect
56. C₂×#13353	C₂²	semidirect
57. #498898	C₂²	semidirect
58. C₂×#13351	C₂²	semidirect
59. C₂×#13350	C₂²	semidirect
60. #494761	C₂²	semidirect
61. C₂×#13103	C₂²	semidirect
62. C₂×#13102	C₂²	semidirect
63. #494587	C₂²	semidirect
64. C₂×#13046	C₂²	semidirect
65. C₂×#13045	C₂²	semidirect
66. #493410	C₂²	semidirect
67. C₂×#12714	C₂²	semidirect
68. C₂×#12712	C₂²	semidirect
69. C₂×#12713	C₂²	semidirect
70. C₂×#12711	C₂²	semidirect
71. C₂×#12589	C₂²	semidirect
72. C₂×#12577	C₂²	semidirect
73. #63103	C₂³	semidirect
74. C₂×2₋¹⁺⁶	C₂³	semidirect
75. C₂×H(7,𝔽₂)	C₂³	semidirect
78. C₂⁴×#41	D₄	semidirect
79. C₂³×AGL(1,ℤ/8)	D₄	semidirect
80. C₂³×AGL(1,ℤ/8)	D₄	semidirect
81. #62811	D₄	semidirect
83. C₂×#3487	D₄	semidirect
85. C₂×#3486	D₄	semidirect
87. C₂×#3485	D₄	semidirect
89. C₂×#3484	D₄	semidirect
91. C₂×#3537	C₂³	semidirect
92. C₂×#3537	C₂³	semidirect
93. C₂×#3537	C₂³	semidirect
94. C₂×#3449	D₄	semidirect
97. C₂²×#525	D₄	semidirect
99. C₂×#3428	D₄	semidirect
100. #61651	C₂³	semidirect
101. #61648	C₂³	semidirect
102. #61633	C₂³	semidirect
103. #61630	C₂³	semidirect
104. #60753	C₂³	semidirect
105. C₂×#3200	C₂³	semidirect
106. C₂×#3199	C₂³	semidirect
107. #60402	C₂³	semidirect
108. #60401	C₂³	semidirect
109. #60400	C₂³	semidirect
110. #60399	C₂³	semidirect
111. #60398	C₂³	semidirect
112. C₂×#3028	C₂³	semidirect
114. C₂×#3027	C₂³	semidirect
115. C₂×#3027	C₂³	semidirect
116. C₂×#3025	D₄	semidirect
117. C₂×#3025	D₄	semidirect
118. C₂×#3025	D₄	semidirect
122. C₂²×#458	D₄	semidirect
123. C₂²×B(4,𝔽₂)	D₄	semidirect
125. C₂×#3021	C₂³	semidirect
126. #60369	D₄	semidirect
128. C₂×#3010	D₄	semidirect
130. C₂×#3008	D₄	semidirect
132. #60231	C₂³	semidirect
133. C₂×#2978	C₂³	semidirect
134. C₂×#2977	C₂³	semidirect
135. C₂×#2896	D₄	semidirect
136. C₂×#2896	D₄	semidirect
138. #60070	C₂³	semidirect
139. C₂×#2884	C₂³	semidirect
140. C₂×#2883	C₂³	semidirect
144. #33553	C₂³	semidirect
145. #33553	C₂³	semidirect
146. #33369	C₂³	semidirect
147. C₂×#2135	C₂³	semidirect
148. C₂×#2134	C₂³	semidirect
149. #33358	C₂³	semidirect
150. C₂×#2129	C₂³	semidirect
151. C₂×#2128	C₂³	semidirect
152. C₂×#2128	C₂³	semidirect
153. C₂×#2128	C₂³	semidirect
154. C₂×#2122	C₂³	semidirect
155. C₂×#2122	C₂³	semidirect
156. C₂×#2120	C₂³	semidirect
157. C₂×#2120	C₂³	semidirect
158. C₂×#2120	C₂³	semidirect
159. #32895	C₂³	semidirect
160. #32894	C₂³	semidirect
161. #20623	C₂³	semidirect
162. C₂×#1796	C₂³	semidirect
163. C₂×#1795	C₂³	semidirect
164. #20620	C₂³	semidirect
165. C₂×#1794	C₂³	semidirect
166. #20612	C₂³	semidirect
167. C₂×#1791	C₂³	semidirect
168. #13354	C₂³	semidirect
169. #13353	C₂³	semidirect
170. #13351	C₂³	semidirect
171. #13350	C₂³	semidirect
172. #13103	C₂³	semidirect
173. #13102	C₂³	semidirect
174. #13046	C₂³	semidirect
175. #13045	C₂³	semidirect
176. #12714	C₂³	semidirect
177. #12713	C₂³	semidirect
178. #12712	C₂³	semidirect
179. #12711	C₂³	semidirect
180. #12589	C₂³	semidirect
181. C₂×#1395	C₂³	semidirect
182. #12577	C₂³	semidirect
183. C₂×#1391	C₂³	semidirect
184. 2₋¹⁺⁶	C₂⁴	semidirect
185. H(7,𝔽₂)	C₂⁴	semidirect
205. C₂³×#41	C₂×D₄	semidirect
206. C₂³×#41	C₂×D₄	semidirect
207. C₂³×#41	C₂×D₄	semidirect
209. C₂⁴×Q₈	C₂×D₄	semidirect
210. C₂⁴×D₄	C₂×D₄	semidirect
211. C₂⁴×D₄	C₂×D₄	semidirect
213. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
214. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
215. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
216. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
217. C₂³×SD₁₆	C₂×D₄	semidirect
218. C₂³×D₈	C₂×D₄	semidirect
219. C₂³×M₁₆	C₂×D₄	semidirect
220. C₂³×M₁₆	C₂×D₄	semidirect
221. #3537	C₂⁴	semidirect
222. #3537	C₂⁴	semidirect
223. #3487	C₂×D₄	semidirect
224. #3487	C₂×D₄	semidirect
226. #3486	C₂×D₄	semidirect
227. #3486	C₂×D₄	semidirect
229. #3485	C₂×D₄	semidirect
230. #3485	C₂×D₄	semidirect
232. #3484	C₂×D₄	semidirect
233. #3484	C₂×D₄	semidirect
236. #3449	C₂×D₄	semidirect
239. C₂×#536	C₂×D₄	semidirect
240. C₂×#536	C₂×D₄	semidirect
243. C₂×#535	C₂×D₄	semidirect
244. C₂×#535	C₂×D₄	semidirect
245. C₂×#535	C₂×D₄	semidirect
246. C₂×#535	C₂×D₄	semidirect
256. C₂×#525	C₂×D₄	semidirect
257. C₂×#525	C₂×D₄	semidirect
258. C₂×#525	C₂×D₄	semidirect
259. C₂×#525	C₂×D₄	semidirect
260. C₂×#525	C₂×D₄	semidirect
266. #3428	C₂×D₄	semidirect
267. C₂×#519	C₂×D₄	semidirect
268. C₂×#519	C₂×D₄	semidirect
269. C₂×#518	C₂×D₄	semidirect
270. C₂×#518	C₂×D₄	semidirect
273. C₂²×#117	C₂×D₄	semidirect
274. #3200	C₂⁴	semidirect
275. #3199	C₂⁴	semidirect
276. #3028	C₂⁴	semidirect
278. #3027	C₂⁴	semidirect
279. #3025	C₂×D₄	semidirect
280. #3025	C₂×D₄	semidirect
281. #3025	C₂×D₄	semidirect
282. #3025	C₂×D₄	semidirect
285. C₂×#458	C₂×D₄	semidirect
286. C₂×#458	C₂×D₄	semidirect
287. C₂×#458	C₂×D₄	semidirect
288. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
289. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
290. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
292. #3010	C₂×D₄	semidirect
293. #3010	C₂×D₄	semidirect
295. #3008	C₂×D₄	semidirect
296. #3008	C₂×D₄	semidirect
298. #2978	C₂⁴	semidirect
299. #2977	C₂⁴	semidirect
300. #2896	C₂×D₄	semidirect
301. #2896	C₂×D₄	semidirect
302. C₂×#419	C₂×D₄	semidirect
303. C₂×#418	C₂×D₄	semidirect
304. C₂×#416	C₂×D₄	semidirect
305. C₂×#416	C₂×D₄	semidirect
308. #2884	C₂⁴	semidirect
309. #2883	C₂⁴	semidirect
317. #2879	C₂×D₄	semidirect
319. C₂×#408	C₂×D₄	semidirect
321. #2135	C₂⁴	semidirect
322. #2134	C₂⁴	semidirect
323. #2129	C₂⁴	semidirect
324. #2128	C₂⁴	semidirect
325. #2128	C₂⁴	semidirect
326. #2122	C₂⁴	semidirect
327. #2120	C₂⁴	semidirect
328. #2120	C₂⁴	semidirect
329. #1796	C₂⁴	semidirect
330. #1795	C₂⁴	semidirect
331. #1794	C₂⁴	semidirect
332. #1791	C₂⁴	semidirect
333. #1395	C₂⁴	semidirect
334. #1391	C₂⁴	semidirect
380. C₂²×#41	C₂²×D₄	semidirect
381. C₂²×#41	C₂²×D₄	semidirect
393. C₂³×Q₈	C₂²×D₄	semidirect
402. C₂³×D₄	C₂²×D₄	semidirect
403. C₂³×D₄	C₂²×D₄	semidirect
414. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
415. C₂×AGL(1,ℤ/8)	C₂²×D₄	semidirect
416. C₂²×SD₁₆	C₂²×D₄	semidirect
417. C₂²×D₈	C₂²×D₄	semidirect
419. C₂²×M₁₆	C₂²×D₄	semidirect
420. C₂²×M₁₆	C₂²×D₄	semidirect
424. #536	C₂²×D₄	semidirect
425. #536	C₂²×D₄	semidirect
430. #535	C₂²×D₄	semidirect
431. #535	C₂²×D₄	semidirect
432. #535	C₂²×D₄	semidirect
447. #525	C₂²×D₄	semidirect
448. #525	C₂²×D₄	semidirect
449. #525	C₂²×D₄	semidirect
450. #525	C₂²×D₄	semidirect
465. #519	C₂²×D₄	semidirect
466. #519	C₂²×D₄	semidirect
467. #518	C₂²×D₄	semidirect
468. #518	C₂²×D₄	semidirect
478. C₂×#117	C₂²×D₄	semidirect
480. #458	C₂²×D₄	semidirect
481. #458	C₂²×D₄	semidirect
482. B(4,𝔽₂)	C₂²×D₄	semidirect
483. B(4,𝔽₂)	C₂²×D₄	semidirect
484. #419	C₂²×D₄	semidirect
485. #418	C₂²×D₄	semidirect
486. #416	C₂²×D₄	semidirect
487. #416	C₂²×D₄	semidirect
496. #408	C₂²×D₄	semidirect
758. C₂	#72237529	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×#499828	2
C₂×#499820	2
C₂×#499827	2
C₂×#494761	2
C₂×#498941	2
C₂×#10577322	2
C₂×#493410	2
C₂×#499819	2
C₂×#498898	2
C₂×#494587	2
C₂×#6628885	2
C₂×#10574874	2
C₂²×#33553	2
#72237529	2

Subgroups — C2×#72237529 #72337518

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72237529 #72337518