Subgroups — C₂×#72236900 #72337501

Order 2048.

At least 7989 conjugacy classes of subgroups; only the 4864 normal subgroups are shown.

The subgroup lattice has 782 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×#493737	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#6372723	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#500807	C₂	1	4	yes	maximal, complemented
4	C₂²×#12778	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#500813	C₂	1	8	yes	maximal, complemented
6	C₂×#493620	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10577667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#495198	C₂	1	2	yes	maximal, complemented
9	C₂×#499126	C₂	1	2	yes	maximal, complemented
10	C₂×#7622874	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#500810	C₂	1	4	yes	maximal, complemented
12	C₂×#498898	C₂	1	2	yes	maximal, complemented
13	C₂×#6629045	C₂	1	2	yes	maximal, complemented
14	C₂²×#33559	C₂	1	1	yes	maximal, characteristic, complemented
15	#72236900	C₂	1	32	yes	maximal, direct product factor
16	C₂×#63076	C₂²	1	1	yes	characteristic, complemented
17	C₂×#62759	C₂²	1	1	yes	characteristic
18	C₂²×#3549	C₂²	1	1	yes	characteristic
19	#10577667	C₂²	1	16	yes	complemented
20	C₂×#62336	C₂²	1	4	yes	complemented
21	C₂×#62328	C₂²	1	2	yes	complemented
22	C₂×#62326	C₂²	1	2	yes	complemented
23	C₂×#60753	C₂²	1	2	yes	—
24	C₂×#60454	C₂²	1	2	yes	—
25	C₂×#60398	C₂²	1	2	yes	complemented
26	C₂²×#3027	C₂²	1	2	yes	complemented
27	C₂²×#3018	C₂²	1	1	yes	characteristic
28	C₂×#60144	C₂²	1	1	yes	characteristic
29	#7622874	C₂²	1	16	yes	complemented
30	C₂×#33561	C₂²	1	2	yes	complemented
31	C₂×#33560	C₂²	1	4	yes	complemented
32	C₂×#33559	C₂²	1	4	yes	—
33	C₂×#33559	C₂²	1	16	yes	complemented
34	C₂×#33559	C₂²	1	4	yes	complemented
35	C₂×#33559	C₂²	1	2	yes	complemented
36	C₂×#33358	C₂²	1	2	yes	complemented
37	C₂²×#2128	C₂²	1	2	yes	complemented
38	C₂²×#2126	C₂²	1	1	yes	characteristic
39	C₂²×#2126	C₂²	1	1	yes	characteristic
40	C₂×#33347	C₂²	1	2	yes	complemented
41	C₂²×#2122	C₂²	1	2	yes	complemented
42	#6629045	C₂²	1	32	yes	complemented
43	C₂×#32948	C₂²	1	8	yes	complemented
44	C₂×#32947	C₂²	1	8	yes	complemented
45	#6372723	C₂²	1	16	yes	complemented
46	C₂×#21478	C₂²	1	4	yes	complemented
47	C₂×#21477	C₂²	1	4	yes	complemented
48	C₂×#21009	C₂²	1	2	yes	complemented
49	C₂²×#1910	C₂²	1	2	yes	complemented
50	C₂²×#1884	C₂²	1	1	yes	characteristic
51	C₂×#20860	C₂²	1	1	yes	characteristic, complemented
52	C₂×#20671	C₂²	1	2	yes	complemented
53	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
54	C₂×#20401	C₂²	1	1	yes	characteristic, complemented
55	#500813	C₂²	1	128	yes	complemented
56	#500810	C₂²	1	64	yes	complemented
57	#500807	C₂²	1	64	yes	complemented
58	#499126	C₂²	1	32	yes	complemented
59	C₂×#13437	C₂²	1	8	yes	complemented
60	C₂×#13436	C₂²	1	8	yes	complemented
61	#498898	C₂²	1	32	yes	complemented
62	C₂×#13351	C₂²	1	8	yes	complemented
63	C₂×#13350	C₂²	1	8	yes	complemented
64	#495198	C₂²	1	32	yes	complemented
65	C₂×#13231	C₂²	1	8	yes	complemented
66	C₂×#13229	C₂²	1	8	yes	complemented
67	#493737	C₂²	1	16	yes	complemented
68	C₂×#12808	C₂²	1	4	yes	complemented
69	C₂×#12807	C₂²	1	4	yes	complemented
70	#493620	C₂²	1	16	yes	complemented
71	C₂×#12780	C₂²	1	4	yes	complemented
72	C₂×#12779	C₂²	1	2	yes	complemented
73	C₂×#12778	C₂²	1	4	yes	complemented
74	C₂×#12778	C₂²	1	4	yes	complemented
75	C₂×#12778	C₂²	1	2	yes	complemented
76	C₂×#12778	C₂²	1	16	yes	complemented
77	C₂×#12577	C₂²	1	2	yes	complemented
78	C₂²×#585	C₂³	1	1	yes	characteristic
79	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
80	#63076	C₂³	1	8	yes	complemented
81	C₂×#3573	C₂³	1	4	yes	complemented
82	C₂²×#568	D₄	1	1	yes	characteristic, complemented
83	C₂²×#568	C₂³	1	1	yes	characteristic
84	C₂²×#568	C₂³	1	1	yes	characteristic
85	#62759	C₂³	1	8	yes	—
86	C₂×#3550	C₂³	1	1	yes	characteristic
87	C₂×#3549	C₂³	1	8	yes	—
88	C₂×#3549	C₂³	1	2	yes	—
89	C₂×#3549	C₂³	1	2	yes	—
90	C₂×#3549	C₂³	1	1	yes	characteristic
91	C₂×#3551	C₂³	1	2	yes	—
92	C₂×#3449	C₂³	1	2	yes	—
93	C₂²×#535	C₂³	1	2	yes	—
94	C₂²×#532	C₂³	1	1	yes	characteristic
95	#62336	C₂³	1	32	yes	complemented
96	#62328	C₂³	1	16	yes	complemented
97	#62326	C₂³	1	16	yes	complemented
98	#60753	C₂³	1	16	yes	—
99	C₂×#3200	C₂³	1	4	yes	—
100	C₂×#3199	C₂³	1	4	yes	—
101	#60454	D₄	1	16	yes	complemented
102	#60454	C₂³	1	16	yes	—
103	C₂×#3058	D₄	1	4	yes	complemented
104	C₂×#3058	C₂³	1	4	yes	—
105	C₂×#3057	D₄	1	4	yes	complemented
106	C₂×#3057	C₂³	1	4	yes	—
107	#60398	C₂³	1	16	yes	complemented
108	C₂×#3028	C₂³	1	4	yes	complemented
109	C₂×#3027	C₂³	1	8	yes	—
110	C₂×#3027	C₂³	1	16	yes	complemented
111	C₂×#3027	C₂³	1	4	yes	complemented
112	C₂×#3018	D₄	1	2	yes	—
113	C₂×#3018	D₄	1	2	yes	—
114	C₂×#3018	D₄	1	8	yes	—
115	C₂×#3018	C₂³	1	2	yes	—
116	C₂×#3018	C₂³	1	2	yes	—
117	C₂×#3018	C₂³	1	8	yes	—
118	C₂²×#455	D₄	1	2	yes	—
119	C₂²×#453	D₄	1	2	yes	—
120	#60144	D₄	1	8	yes	complemented
121	#60144	C₂³	1	8	yes	—
122	C₂×#2932	D₄	1	2	yes	complemented
123	C₂×#2932	C₂³	1	2	yes	—
124	C₂×#2931	D₄	1	2	yes	complemented
125	C₂×#2931	C₂³	1	2	yes	—
126	C₂×#2911	D₄	1	2	yes	complemented
127	C₂²×#423	D₄	1	1	yes	characteristic, complemented
128	C₂×#2896	D₄	1	2	yes	complemented
129	C₂²×#418	D₄	1	2	yes	complemented
130	C₂²×#413	C₂³	1	1	yes	characteristic
131	C₂²×#410	C₂³	1	2	yes	—
132	C₂²×#410	C₂³	1	2	yes	—
133	C₂²×#410	C₂³	1	1	yes	characteristic
134	C₂×#2879	D₄	1	1	yes	characteristic, complemented
135	C₂×#2879	C₂³	1	1	yes	characteristic
136	C₂²×C₄×M₁₆	D₄	1	1	yes	characteristic, complemented
137	#33561	C₂³	1	16	yes	complemented
138	#33560	C₂³	1	32	yes	complemented
139	#33559	C₂³	1	32	yes	—
140	#33559	C₂³	1	32	yes	complemented
141	#33559	C₂³	1	16	yes	complemented
142	#33358	C₂³	1	16	yes	complemented
143	C₂×#2129	C₂³	1	4	yes	complemented
144	C₂×#2128	C₂³	1	8	yes	—
145	C₂×#2128	C₂³	1	16	yes	complemented
146	C₂×#2128	C₂³	1	4	yes	complemented
147	C₂×#2126	C₂³	1	2	yes	—
148	C₂×#2126	C₂³	1	2	yes	—
149	C₂×#2126	C₂³	1	8	yes	—
150	C₂×#2126	C₂³	1	2	yes	—
151	C₂×#2126	C₂³	1	2	yes	—
152	C₂×#2126	C₂³	1	8	yes	—
153	#33347	C₂³	1	16	yes	complemented
154	C₂×#2123	C₂³	1	4	yes	complemented
155	C₂×#2122	C₂³	1	8	yes	—
156	C₂×#2122	C₂³	1	16	yes	complemented
157	C₂×#2122	C₂³	1	4	yes	complemented
158	#32948	C₂³	1	64	yes	complemented
159	#32947	C₂³	1	64	yes	complemented
160	#21478	C₂³	1	32	yes	complemented
161	#21477	C₂³	1	32	yes	complemented
162	#21009	C₂³	1	16	yes	complemented
163	C₂×#1910	C₂³	1	8	yes	—
164	C₂×#1910	C₂³	1	16	yes	complemented
165	C₂×#1910	C₂³	1	4	yes	complemented
166	C₂×#1909	C₂³	1	4	yes	complemented
167	C₂×#1884	C₂³	1	2	yes	—
168	C₂×#1884	C₂³	1	2	yes	—
169	C₂×#1884	C₂³	1	8	yes	—
170	#20860	C₂³	1	8	yes	complemented
171	C₂×#1858	C₂³	1	4	yes	complemented
172	#20671	C₂³	1	16	yes	complemented
173	C₂×#1812	C₂³	1	8	yes	complemented
174	#20620	C₂³	1	8	yes	complemented
175	C₂×#1794	C₂³	1	4	yes	complemented
176	#20401	C₂³	1	8	yes	complemented
177	C₂×#1757	C₂³	1	4	yes	complemented
178	#13437	C₂³	1	64	yes	complemented
179	#13436	C₂³	1	64	yes	complemented
180	#13351	C₂³	1	64	yes	complemented
181	#13350	C₂³	1	64	yes	complemented
182	#13231	C₂³	1	64	yes	complemented
183	#13229	C₂³	1	64	yes	complemented
184	#12808	C₂³	1	32	yes	complemented
185	#12807	C₂³	1	32	yes	complemented
186	#12780	C₂³	1	32	yes	complemented
187	#12779	C₂³	1	16	yes	complemented
188	#12778	C₂³	1	32	yes	complemented
189	#12778	C₂³	1	32	yes	complemented
190	#12778	C₂³	1	16	yes	complemented
191	#12577	C₂³	1	16	yes	complemented
192	C₂×#1391	C₂³	1	8	yes	complemented
193	C₂×#585	C₂×D₄	1	2	yes	—
194	C₂×#585	C₂×D₄	1	4	yes	—
195	C₂×#585	C₂⁴	1	2	yes	—
196	C₂×#585	C₂⁴	1	4	yes	—
197	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
198	C₂³×#41	C₂×D₄	1	1	yes	characteristic
199	C₂³×#41	C₂×D₄	1	2	yes	—
200	C₂³×#41	C₂⁴	1	1	yes	characteristic
201	C₂⁴×D₄	C₂×D₄	1	2	yes	—
202	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	complemented
203	C₂³×SD₁₆	C₂×D₄	1	4	yes	complemented
204	C₂³×D₈	C₂×D₄	1	4	yes	complemented
205	#3573	C₂⁴	1	16	yes	complemented
206	C₂×#568	C₂×D₄	1	4	yes	—
207	C₂×#568	C₂×D₄	1	8	yes	—
208	C₂×#568	C₂×D₄	1	8	yes	complemented
209	C₂×#568	C₂⁴	1	2	yes	—
210	C₂×#568	C₂⁴	1	4	yes	—
211	C₂×#568	C₂⁴	1	4	yes	—
212	C₂²×#131	C₂×D₄	1	4	yes	—
213	C₂²×#131	C₂×D₄	1	2	yes	—
214	C₂²×#131	C₂×D₄	1	2	yes	complemented
215	C₂²×#131	C₂×D₄	1	2	yes	complemented
216	C₂²×#131	C₂⁴	1	2	yes	—
217	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
218	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
219	C₂³×M₁₆	C₂×D₄	1	2	yes	—
220	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
221	C₂³×M₁₆	C₂×D₄	1	2	yes	—
222	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
223	#3551	C₂⁴	1	8	yes	—
224	#3550	C₂⁴	1	4	yes	—
225	#3549	C₂⁴	1	8	yes	—
226	#3549	C₂⁴	1	8	yes	—
227	#3549	C₂⁴	1	4	yes	—
228	#3449	C₂×D₄	1	8	yes	—
229	#3449	C₂⁴	1	8	yes	—
230	C₂×#536	C₂×D₄	1	2	yes	—
231	C₂×#536	C₂⁴	1	2	yes	—
232	C₂×#535	C₂×D₄	1	2	yes	—
233	C₂×#535	C₂×D₄	1	4	yes	—
234	C₂×#535	C₂×D₄	1	8	yes	—
235	C₂×#535	C₂⁴	1	4	yes	—
236	C₂×#535	C₂⁴	1	2	yes	—
237	C₂×#535	C₂⁴	1	8	yes	—
238	C₂×#532	C₂×D₄	1	1	yes	characteristic
239	C₂×#532	C₂×D₄	1	1	yes	characteristic
240	C₂×#532	C₂×D₄	1	4	yes	—
241	C₂×#532	C₂×D₄	1	4	yes	—
242	C₂×#532	C₂×D₄	1	1	yes	characteristic
243	C₂×#532	C₂×D₄	1	1	yes	characteristic
244	C₂×#532	#41	1	4	yes	—
245	C₂×#532	#41	1	1	yes	characteristic
246	C₂×#532	#41	1	1	yes	characteristic
247	C₂×#532	C₂⁴	1	1	yes	characteristic
248	C₂×#532	C₂⁴	1	1	yes	characteristic
249	C₂×#532	C₂⁴	1	4	yes	—
250	C₂²×C₄⋊Q₈	#41	1	1	yes	characteristic
251	C₂²×#127	C₂×D₄	1	1	yes	characteristic
252	C₂²×#124	C₂×D₄	1	1	yes	characteristic
253	C₂²×#124	#41	1	1	yes	characteristic
254	C₂²×#117	C₂×D₄	1	2	yes	—
255	C₂²×#117	C₂×D₄	1	2	yes	—
256	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
257	#3200	C₂⁴	1	16	yes	—
258	#3199	C₂⁴	1	16	yes	—
259	#3058	C₂×D₄	1	32	yes	complemented
260	#3058	C₂×D₄	1	16	yes	complemented
261	#3058	C₂⁴	1	16	yes	—
262	#3057	C₂×D₄	1	32	yes	complemented
263	#3057	C₂×D₄	1	16	yes	complemented
264	#3057	C₂⁴	1	16	yes	—
265	#3028	C₂⁴	1	16	yes	complemented
266	#3027	C₂⁴	1	32	yes	—
267	#3027	C₂⁴	1	16	yes	complemented
268	#3018	C₂×D₄	1	16	yes	—
269	#3018	C₂×D₄	1	16	yes	—
270	#3018	C₂×D₄	1	8	yes	—
271	#3018	C₂×D₄	1	8	yes	—
272	#3018	C₂⁴	1	8	yes	—
273	#3018	C₂⁴	1	8	yes	—
274	C₂×#455	C₂×D₄	1	4	yes	—
275	C₂×#455	C₂×D₄	1	4	yes	—
276	C₂×#455	C₂×D₄	1	16	yes	—
277	C₂×#453	C₂×D₄	1	4	yes	—
278	C₂×#453	C₂×D₄	1	4	yes	—
279	C₂×#453	C₂×D₄	1	16	yes	—
280	#2932	C₂×D₄	1	16	yes	complemented
281	#2932	C₂×D₄	1	8	yes	complemented
282	#2932	C₂⁴	1	8	yes	—
283	#2931	C₂×D₄	1	8	yes	complemented
284	#2931	C₂×D₄	1	16	yes	complemented
285	#2931	C₂⁴	1	8	yes	—
286	#2911	C₂×D₄	1	16	yes	complemented
287	C₂×#427	C₂×D₄	1	4	yes	complemented
288	C₂×#427	C₂×D₄	1	4	yes	complemented
289	C₂×#423	C₂×D₄	1	2	yes	complemented
290	C₂×#423	C₂×D₄	1	2	yes	complemented
291	C₂×#423	C₂×D₄	1	8	yes	complemented
292	#2896	C₂×D₄	1	16	yes	complemented
293	C₂×#419	C₂×D₄	1	4	yes	complemented
294	C₂×#418	C₂×D₄	1	4	yes	complemented
295	C₂×#418	C₂×D₄	1	4	yes	complemented
296	C₂×#418	C₂×D₄	1	4	yes	complemented
297	C₂×#418	C₂×D₄	1	16	yes	complemented
298	C₂×#413	C₂×D₄	1	2	yes	—
299	C₂×#413	C₂×D₄	1	4	yes	—
300	C₂×#413	C₂⁴	1	2	yes	—
301	C₂×#413	C₂⁴	1	4	yes	—
302	C₂²×#100	C₂×D₄	1	2	yes	—
303	C₂×#410	C₂⁴	1	4	yes	—
304	C₂×#410	C₂⁴	1	4	yes	—
305	C₂×#410	C₂⁴	1	8	yes	—
306	C₂×#410	C₂⁴	1	8	yes	—
307	C₂×#410	C₂⁴	1	2	yes	—
308	C₂×#410	C₂⁴	1	4	yes	—
309	#2879	C₂×D₄	1	4	yes	—
310	#2879	C₂×D₄	1	8	yes	complemented
311	#2879	C₂⁴	1	4	yes	—
312	C₂×#408	C₂×D₄	1	2	yes	—
313	C₂×#408	C₂×D₄	1	2	yes	complemented
314	C₂×#408	C₂×D₄	1	2	yes	complemented
315	C₂×#408	C₂⁴	1	2	yes	—
316	C₂×C₄×M₁₆	C₂×D₄	1	8	yes	complemented
317	C₂²×#97	C₂×D₄	1	2	yes	complemented
318	C₂²×C₄×C₈	C₂×D₄	1	2	yes	complemented
319	#2129	C₂⁴	1	16	yes	complemented
320	#2128	C₂⁴	1	32	yes	—
321	#2128	C₂⁴	1	16	yes	complemented
322	#2126	C₂⁴	1	8	yes	—
323	#2126	C₂⁴	1	8	yes	—
324	#2126	C₂⁴	1	8	yes	—
325	#2126	C₂⁴	1	8	yes	—
326	#2123	C₂⁴	1	16	yes	complemented
327	#2122	C₂⁴	1	32	yes	—
328	#2122	C₂⁴	1	16	yes	complemented
329	#1910	C₂⁴	1	32	yes	—
330	#1910	C₂⁴	1	16	yes	complemented
331	#1909	C₂⁴	1	16	yes	complemented
332	#1884	C₂⁴	1	8	yes	—
333	#1884	C₂⁴	1	8	yes	—
334	#1858	C₂⁴	1	16	yes	complemented
335	#1812	C₂⁴	1	32	yes	complemented
336	#1794	C₂⁴	1	16	yes	complemented
337	#1757	C₂⁴	1	16	yes	complemented
338	#1391	C₂⁴	1	32	yes	complemented
339	#585	C₂²×D₄	1	8	yes	—
340	#585	C₂²×D₄	1	4	yes	—
341	#585	C₂⁵	1	4	yes	—
342	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
343	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
344	C₂²×#41	#121	1	1	yes	characteristic
345	C₂²×#41	#121	1	1	yes	characteristic
346	C₂²×#41	#121	1	4	yes	—
347	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
348	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
349	C₂²×#41	C₂²×D₄	1	4	yes	—
350	C₂²×#41	C₂²×D₄	1	8	yes	—
351	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
352	C₂²×#41	C₂²×D₄	1	2	yes	—
353	C₂²×#41	C₂²×D₄	1	2	yes	—
354	C₂²×#41	C₂²×D₄	1	4	yes	—
355	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
356	C₂²×#41	C₂²×D₄	1	2	yes	—
357	C₂²×#41	C₂×#41	1	1	yes	characteristic
358	C₂²×#41	C₂×#41	1	2	yes	—
359	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
360	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
361	C₂²×#41	C₂⁵	1	1	yes	characteristic
362	C₂²×#41	C₂⁵	1	2	yes	—
363	C₂³×Q₈	#121	1	1	yes	characteristic
364	C₂³×Q₈	C₂²×D₄	1	2	yes	—
365	C₂³×Q₈	C₂×#41	1	1	yes	characteristic
366	C₂³×D₄	#121	1	1	yes	characteristic
367	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
368	C₂³×D₄	C₂²×D₄	1	4	yes	—
369	C₂³×D₄	C₂²×D₄	1	8	yes	—
370	C₂³×D₄	C₂²×D₄	1	2	yes	—
371	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
372	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
373	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
374	C₂²×SD₁₆	C₂²×D₄	1	16	yes	complemented
375	C₂²×D₈	C₂²×D₄	1	16	yes	complemented
376	#568	C₂⁵	1	4	yes	—
377	C₂×#131	#120	1	8	yes	—
378	C₂×#131	#120	1	16	yes	—
379	C₂×#131	C₂²×D₄	1	8	yes	—
380	C₂×#131	C₂²×D₄	1	16	yes	—
381	C₂×#131	C₂²×D₄	1	4	yes	—
382	C₂×#131	C₂²×D₄	1	8	yes	—
383	C₂×#131	C₂²×D₄	1	8	yes	complemented
384	C₂×#131	C₂²×D₄	1	8	yes	complemented
385	C₂×#131	C₂⁵	1	4	yes	—
386	C₂²×M₁₆	#120	1	2	yes	—
387	C₂²×M₁₆	#120	1	4	yes	—
388	C₂²×M₁₆	#120	1	4	yes	—
389	C₂²×M₁₆	#120	1	8	yes	—
390	C₂²×M₁₆	#120	1	1	yes	characteristic
391	C₂²×M₁₆	#120	1	2	yes	—
392	C₂²×M₁₆	#120	1	4	yes	—
393	C₂²×M₁₆	#120	1	8	yes	—
394	C₂²×M₁₆	#120	1	1	yes	characteristic
395	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
396	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
397	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
398	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
399	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
400	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
401	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
402	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
403	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
404	C₂³×C₈	#120	1	2	yes	—
405	C₂³×C₈	#120	1	4	yes	—
406	C₂³×C₈	C₂²×D₄	1	2	yes	—
407	C₂³×C₈	C₂²×D₄	1	4	yes	—
408	C₂³×C₈	C₂²×D₄	1	2	yes	—
409	#536	C₂²×D₄	1	8	yes	—
410	#536	C₂²×D₄	1	4	yes	—
411	#536	C₂⁵	1	4	yes	—
412	#535	C₂²×D₄	1	16	yes	—
413	#535	C₂²×D₄	1	8	yes	—
414	#535	C₂²×D₄	1	8	yes	—
415	#535	C₂²×D₄	1	4	yes	—
416	#535	C₂⁵	1	8	yes	—
417	#535	C₂⁵	1	4	yes	—
418	#532	#121	1	4	yes	—
419	#532	#121	1	4	yes	—
420	#532	#121	1	4	yes	—
421	#532	#121	1	4	yes	—
422	#532	#121	1	4	yes	—
423	#532	#121	1	4	yes	—
424	#532	C₂²×D₄	1	4	yes	—
425	#532	C₂²×D₄	1	4	yes	—
426	#532	C₂²×D₄	1	2	yes	—
427	#532	C₂²×D₄	1	2	yes	—
428	#532	C₂²×D₄	1	4	yes	—
429	#532	C₂²×D₄	1	2	yes	—
430	#532	C₂²×D₄	1	2	yes	—
431	#532	C₂²×D₄	1	4	yes	—
432	#532	C₂×#41	1	4	yes	—
433	#532	C₂×#41	1	4	yes	—
434	#532	C₂×#41	1	2	yes	—
435	#532	C₂×#41	1	2	yes	—
436	#532	C₂⁵	1	2	yes	—
437	#532	C₂⁵	1	2	yes	—
438	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
439	C₂×C₄⋊Q₈	#121	1	1	yes	characteristic
440	C₂×C₄⋊Q₈	#121	1	4	yes	—
441	C₂×C₄⋊Q₈	C₂×#41	1	1	yes	characteristic
442	C₂×C₄⋊Q₈	C₂×#41	1	1	yes	characteristic
443	C₂×C₄⋊Q₈	C₂×#41	1	4	yes	—
444	C₂×#127	#121	1	1	yes	characteristic
445	C₂×#127	#121	1	1	yes	characteristic
446	C₂×#127	#121	1	4	yes	—
447	C₂×#127	C₂²×D₄	1	1	yes	characteristic
448	C₂×#127	C₂²×D₄	1	1	yes	characteristic
449	C₂×#127	C₂²×D₄	1	4	yes	—
450	C₂×#124	#121	1	1	yes	characteristic
451	C₂×#124	#121	1	1	yes	characteristic
452	C₂×#124	#121	1	4	yes	—
453	C₂×#124	#121	1	1	yes	characteristic
454	C₂×#124	#121	1	1	yes	characteristic
455	C₂×#124	#121	1	4	yes	—
456	C₂×#124	C₂²×D₄	1	1	yes	characteristic
457	C₂×#124	C₂²×D₄	1	1	yes	characteristic
458	C₂×#124	C₂²×D₄	1	4	yes	—
459	C₂×#124	C₂×#41	1	1	yes	characteristic
460	C₂×#124	C₂×#41	1	1	yes	characteristic
461	C₂×#124	C₂×#41	1	4	yes	—
462	C₂×#117	C₂²×D₄	1	2	yes	—
463	C₂×#117	C₂²×D₄	1	2	yes	—
464	C₂×#117	C₂²×D₄	1	4	yes	—
465	C₂×#117	C₂²×D₄	1	8	yes	—
466	C₂×#117	C₂²×D₄	1	8	yes	—
467	C₂²×C₄²	#121	1	1	yes	characteristic
468	C₂²×C₄²	#121	1	1	yes	characteristic
469	C₂²×C₄²	#121	1	1	yes	characteristic
470	C₂²×C₄²	#121	1	1	yes	characteristic
471	C₂²×C₄²	#121	1	4	yes	—
472	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
473	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
474	C₂²×C₄²	C₂²×D₄	1	4	yes	—
475	#455	C₂²×D₄	1	16	yes	—
476	#455	C₂²×D₄	1	16	yes	—
477	#453	C₂²×D₄	1	16	yes	—
478	#453	C₂²×D₄	1	16	yes	—
479	#427	C₂²×D₄	1	16	yes	complemented
480	#427	C₂²×D₄	1	16	yes	complemented
481	#423	C₂²×D₄	1	8	yes	complemented
482	#423	C₂²×D₄	1	8	yes	complemented
483	#419	C₂²×D₄	1	16	yes	complemented
484	#418	C₂²×D₄	1	16	yes	complemented
485	#418	C₂²×D₄	1	16	yes	complemented
486	#418	C₂²×D₄	1	16	yes	complemented
487	#413	C₂²×D₄	1	8	yes	—
488	#413	C₂²×D₄	1	4	yes	—
489	#413	C₂⁵	1	4	yes	—
490	C₂×#100	C₂²×D₄	1	4	yes	—
491	C₂×#100	C₂²×D₄	1	8	yes	—
492	#410	C₂⁵	1	4	yes	—
493	#410	C₂⁵	1	8	yes	—
494	#410	C₂⁵	1	8	yes	—
495	#408	C₂²×D₄	1	8	yes	—
496	#408	C₂²×D₄	1	4	yes	—
497	#408	C₂²×D₄	1	8	yes	complemented
498	#408	C₂²×D₄	1	8	yes	complemented
499	#408	C₂⁵	1	4	yes	—
500	C₂×#97	C₂²×D₄	1	8	yes	complemented
501	C₂×C₄×C₈	C₂²×D₄	1	8	yes	complemented
502	C₂⁵	#535	1	1	yes	characteristic
503	C₂⁵	D₄²	1	2	yes	—
504	H(5,𝔽₂)	C₂³×D₄	1	8	yes	—
505	C₂×#41	C₂×#120	1	4	yes	—
506	C₂×#41	C₂×#120	1	2	yes	—
507	C₂×#41	C₂×#121	1	4	yes	—
508	C₂×#41	C₂×#121	1	4	yes	—
509	C₂×#41	C₂×#121	1	2	yes	—
510	C₂×#41	C₂×#121	1	2	yes	—
511	C₂×#41	C₂×#121	1	2	yes	—
512	C₂×#41	C₂×#121	1	2	yes	—
513	C₂×#41	C₂×#121	1	2	yes	—
514	C₂×#41	#535	1	4	yes	—
515	C₂×#41	#535	1	2	yes	—
516	C₂×#41	D₄²	1	4	yes	—
517	C₂×#41	D₄²	1	4	yes	—
518	C₂×#41	D₄²	1	4	yes	—
519	C₂×#41	#546	1	4	yes	—
520	C₂×#41	#546	1	4	yes	—
521	C₂×#41	#546	1	4	yes	—
522	C₂×#41	C₂³×D₄	1	2	yes	—
523	C₂×#41	C₂³×D₄	1	2	yes	—
524	C₂×#41	C₂³×D₄	1	1	yes	characteristic
525	C₂×#41	C₂³×D₄	1	2	yes	—
526	C₂×#41	C₂³×D₄	1	2	yes	—
527	C₂×#41	C₂³×D₄	1	4	yes	—
528	C₂×#41	C₂³×D₄	1	2	yes	—
529	C₂×#41	C₂³×D₄	1	1	yes	characteristic
530	C₂×#41	C₂²×#41	1	2	yes	—
531	C₂×#41	C₂²×#41	1	1	yes	characteristic
532	C₂×#41	C₂×H(5,𝔽₂)	1	4	yes	—
533	C₂×#41	C₂×H(5,𝔽₂)	1	2	yes	—
534	C₂×#41	C₂⁶	1	1	yes	characteristic
535	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
536	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
537	C₂²×Q₈	C₂×#121	1	4	yes	—
538	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
539	C₂²×Q₈	C₂×#121	1	2	yes	—
540	C₂²×Q₈	#546	1	2	yes	—
541	C₂²×Q₈	#546	1	4	yes	—
542	C₂²×Q₈	C₂³×D₄	1	4	yes	—
543	C₂²×Q₈	C₂²×#41	1	1	yes	characteristic
544	C₂²×Q₈	C₂²×#41	1	2	yes	—
545	C₂²×D₄	C₂×#121	1	1	yes	characteristic
546	C₂²×D₄	C₂×#121	1	1	yes	characteristic
547	C₂²×D₄	C₂×#121	1	4	yes	—
548	C₂²×D₄	C₂×#121	1	1	yes	characteristic
549	C₂²×D₄	C₂×#121	1	2	yes	—
550	C₂²×D₄	#535	1	2	yes	—
551	C₂²×D₄	#535	1	4	yes	—
552	C₂²×D₄	D₄²	1	2	yes	—
553	C₂²×D₄	D₄²	1	2	yes	—
554	C₂²×D₄	D₄²	1	4	yes	—
555	C₂²×D₄	D₄²	1	4	yes	—
556	C₂²×D₄	#546	1	2	yes	—
557	C₂²×D₄	#546	1	4	yes	—
558	C₂²×D₄	C₂³×D₄	1	8	yes	—
559	C₂²×D₄	C₂³×D₄	1	4	yes	—
560	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
561	C₂²×D₄	C₂³×D₄	1	2	yes	—
562	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
563	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
564	C₂³×C₄	C₂×#120	1	2	yes	—
565	C₂³×C₄	C₂×#120	1	4	yes	—
566	C₂³×C₄	C₂×#120	1	1	yes	characteristic
567	C₂³×C₄	C₂×#120	1	2	yes	—
568	C₂³×C₄	C₂×#120	1	1	yes	characteristic
569	C₂³×C₄	C₂×#121	1	1	yes	characteristic
570	C₂³×C₄	C₂×#121	1	1	yes	characteristic
571	C₂³×C₄	C₂×#121	1	2	yes	—
572	C₂³×C₄	#535	1	1	yes	characteristic
573	C₂³×C₄	#535	1	2	yes	—
574	C₂³×C₄	D₄²	1	2	yes	—
575	C₂³×C₄	D₄²	1	4	yes	—
576	C₂³×C₄	#546	1	2	yes	—
577	C₂³×C₄	#546	1	4	yes	—
578	C₂³×C₄	#546	1	2	yes	—
579	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
580	C₂³×C₄	C₂³×D₄	1	2	yes	—
581	C₂³×C₄	C₂³×D₄	1	2	yes	—
582	C₂³×C₄	C₂³×D₄	1	4	yes	—
583	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
584	C₂×M₁₆	B(4,𝔽₂)	1	2	yes	—
585	C₂×M₁₆	B(4,𝔽₂)	1	4	yes	—
586	C₂×M₁₆	C₂×#120	1	4	yes	—
587	C₂×M₁₆	C₂×#120	1	8	yes	—
588	C₂×M₁₆	C₂×#120	1	8	yes	—
589	C₂×M₁₆	C₂×#120	1	16	yes	—
590	C₂×M₁₆	C₂×#120	1	4	yes	—
591	C₂×M₁₆	C₂×#120	1	8	yes	—
592	C₂×M₁₆	C₂×#120	1	4	yes	—
593	C₂×M₁₆	C₂³×D₄	1	4	yes	—
594	C₂×M₁₆	C₂³×D₄	1	8	yes	—
595	C₂×M₁₆	C₂³×D₄	1	4	yes	—
596	C₂²×C₈	C₂×#120	1	2	yes	—
597	C₂²×C₈	C₂×#120	1	4	yes	—
598	C₂²×C₈	C₂×#120	1	4	yes	—
599	C₂²×C₈	C₂×#120	1	8	yes	—
600	C₂²×C₈	C₂×#120	1	8	yes	—
601	C₂²×C₈	C₂×#120	1	16	yes	—
602	C₂²×C₈	C₂×#120	1	2	yes	—
603	C₂²×C₈	C₂³×D₄	1	4	yes	—
604	C₂²×C₈	C₂³×D₄	1	8	yes	—
605	C₂²×C₈	C₂³×D₄	1	4	yes	—
606	C₄⋊Q₈	C₂×#121	1	4	yes	—
607	C₄⋊Q₈	C₂×#121	1	2	yes	—
608	C₄⋊Q₈	C₂×#121	1	2	yes	—
609	C₄⋊Q₈	C₂×#121	1	4	yes	—
610	C₄⋊Q₈	C₂²×#41	1	2	yes	—
611	C₄⋊Q₈	C₂²×#41	1	2	yes	—
612	#127	C₂×#121	1	2	yes	—
613	#127	C₂×#121	1	4	yes	—
614	#127	C₂×#121	1	4	yes	—
615	#127	C₂×#121	1	2	yes	—
616	#127	C₂³×D₄	1	2	yes	—
617	#127	C₂³×D₄	1	2	yes	—
618	#124	C₂×#121	1	2	yes	—
619	#124	C₂×#121	1	4	yes	—
620	#124	C₂×#121	1	2	yes	—
621	#124	C₂×#121	1	4	yes	—
622	#124	C₂×#121	1	4	yes	—
623	#124	C₂×#121	1	2	yes	—
624	#124	C₂×#121	1	2	yes	—
625	#124	C₂×#121	1	4	yes	—
626	#124	C₂³×D₄	1	2	yes	—
627	#124	C₂³×D₄	1	2	yes	—
628	#124	C₂²×#41	1	2	yes	—
629	#124	C₂²×#41	1	2	yes	—
630	#117	C₂³×D₄	1	8	yes	—
631	#117	C₂³×D₄	1	4	yes	—
632	#117	C₂³×D₄	1	4	yes	—
633	C₂×C₄²	C₂×#121	1	1	yes	characteristic
634	C₂×C₄²	C₂×#121	1	1	yes	characteristic
635	C₂×C₄²	C₂×#121	1	1	yes	characteristic
636	C₂×C₄²	C₂×#121	1	4	yes	—
637	C₂×C₄²	C₂×#121	1	4	yes	—
638	C₂×C₄²	C₂×#121	1	1	yes	characteristic
639	C₂×C₄²	C₂×#121	1	4	yes	—
640	C₂×C₄²	C₂×#121	1	4	yes	—
641	C₂×C₄²	C₂×#121	1	2	yes	—
642	C₂×C₄²	C₂×#121	1	2	yes	—
643	C₂×C₄²	C₂³×D₄	1	2	yes	—
644	C₂×C₄²	C₂³×D₄	1	2	yes	—
645	#100	C₂³×D₄	1	8	yes	—
646	C₂⁴	#2408	1	2	yes	—
647	C₂⁴	#2408	1	1	yes	characteristic
648	C₂⁴	#2408	1	4	yes	—
649	C₂⁴	#2408	1	2	yes	—
650	C₂⁴	#2408	1	1	yes	characteristic
651	C₂⁴	C₂×#535	1	1	yes	characteristic
652	C₂⁴	C₂×#535	1	2	yes	—
653	C₂⁴	C₂×D₄²	1	2	yes	—
654	C₂⁴	C₂×D₄²	1	4	yes	—
655	C₂×Q₈	#2408	1	2	yes	—
656	C₂×Q₈	#2408	1	4	yes	—
657	C₂×Q₈	C₂²×#121	1	2	yes	—
658	C₂×Q₈	C₂²×#121	1	2	yes	—
659	C₂×Q₈	C₂²×#121	1	2	yes	—
660	C₂×Q₈	C₂²×#121	1	1	yes	characteristic
661	C₂×Q₈	C₂×#546	1	4	yes	—
662	C₂×Q₈	C₂×#546	1	2	yes	—
663	C₂×Q₈	C₂³×#41	1	1	yes	characteristic
664	C₂×D₄	#2408	1	4	yes	—
665	C₂×D₄	#2408	1	2	yes	—
666	C₂×D₄	#2408	1	4	yes	—
667	C₂×D₄	#2408	1	4	yes	—
668	C₂×D₄	#2408	1	4	yes	—
669	C₂×D₄	C₂²×#121	1	2	yes	—
670	C₂×D₄	C₂²×#121	1	2	yes	—
671	C₂×D₄	C₂²×#121	1	1	yes	characteristic
672	C₂×D₄	C₂²×#121	1	2	yes	—
673	C₂×D₄	C₂×#535	1	2	yes	—
674	C₂×D₄	C₂×#535	1	4	yes	—
675	C₂×D₄	C₂×D₄²	1	2	yes	—
676	C₂×D₄	C₂×D₄²	1	4	yes	—
677	C₂×D₄	C₂×D₄²	1	4	yes	—
678	C₂×D₄	C₂×D₄²	1	2	yes	—
679	C₂×D₄	C₂×#546	1	2	yes	—
680	C₂×D₄	C₂×#546	1	4	yes	—
681	C₂×D₄	C₂⁴×D₄	1	1	yes	characteristic
682	C₂×D₄	C₂²×H(5,𝔽₂)	1	2	yes	—
683	C₂²×C₄	#2408	1	1	yes	characteristic
684	C₂²×C₄	#2408	1	2	yes	—
685	C₂²×C₄	#2408	1	2	yes	—
686	C₂²×C₄	#2408	1	2	yes	—
687	C₂²×C₄	#2408	1	2	yes	—
688	C₂²×C₄	#2408	1	2	yes	—
689	C₂²×C₄	#2408	1	4	yes	—
690	C₂²×C₄	#2408	1	4	yes	—
691	C₂²×C₄	#2408	1	4	yes	—
692	C₂²×C₄	#2408	1	4	yes	—
693	C₂²×C₄	#2408	1	1	yes	characteristic
694	C₂²×C₄	#2408	1	2	yes	—
695	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
696	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
697	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
698	C₂²×C₄	#3025	1	1	yes	characteristic
699	C₂²×C₄	#3025	1	2	yes	—
700	C₂²×C₄	#3025	1	1	yes	characteristic
701	C₂²×C₄	C₂²×#120	1	4	yes	—
702	C₂²×C₄	C₂²×#120	1	2	yes	—
703	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
704	C₂²×C₄	C₂²×#120	1	2	yes	—
705	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
706	C₂²×C₄	C₂²×#120	1	2	yes	—
707	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
708	C₂²×C₄	C₂²×#121	1	2	yes	—
709	C₂²×C₄	C₂²×#121	1	2	yes	—
710	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
711	C₂²×C₄	C₂×#535	1	2	yes	—
712	C₂²×C₄	C₂×#535	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄²	1	4	yes	—
714	C₂²×C₄	C₂×D₄²	1	2	yes	—
715	C₂²×C₄	C₂×#546	1	2	yes	—
716	C₂²×C₄	C₂×#546	1	4	yes	—
717	C₂²×C₄	C₂×#546	1	4	yes	—
718	C₂²×C₄	C₂×#546	1	2	yes	—
719	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
721	M₁₆	C₂×B(4,𝔽₂)	1	8	yes	—
722	M₁₆	C₂×B(4,𝔽₂)	1	8	yes	—
723	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
724	C₂×C₈	C₂×B(4,𝔽₂)	1	4	yes	—
725	C₂×C₈	C₂²×#120	1	4	yes	—
726	C₂×C₈	C₂²×#120	1	8	yes	—
727	C₂×C₈	C₂²×#120	1	4	yes	—
728	C₄²	C₂²×#121	1	2	yes	—
729	C₄²	C₂²×#121	1	2	yes	—
730	C₄²	C₂²×#121	1	2	yes	—
731	C₄²	C₂²×#121	1	2	yes	—
732	C₂³	#24260	1	1	yes	characteristic
733	C₂³	#24260	1	1	yes	characteristic
734	C₂³	#24260	1	2	yes	—
735	C₂³	C₂×#2408	1	1	yes	characteristic
736	C₂³	C₂×#2408	1	2	yes	—
737	C₂³	C₂×#2408	1	4	yes	—
738	C₂³	C₂×#2408	1	2	yes	—
739	C₂³	C₂×#2408	1	1	yes	characteristic
740	C₂³	C₂×#2408	1	2	yes	—
741	C₂³	C₂²×#535	1	1	yes	characteristic
742	C₂³	C₂²×D₄²	1	2	yes	—
743	C₂×C₄	#24260	1	2	yes	—
744	C₂×C₄	#24260	1	2	yes	—
745	C₂×C₄	#24260	1	2	yes	—
746	C₂×C₄	#24260	1	2	yes	—
747	C₂×C₄	#24260	1	2	yes	—
748	C₂×C₄	#24260	1	1	yes	characteristic
749	C₂×C₄	#24260	1	1	yes	characteristic
750	C₂×C₄	C₂×#2408	1	1	yes	characteristic
751	C₂×C₄	C₂×#2408	1	2	yes	—
752	C₂×C₄	C₂×#2408	1	2	yes	—
753	C₂×C₄	C₂×#2408	1	4	yes	—
754	C₂×C₄	C₂×#2408	1	2	yes	—
755	C₂×C₄	C₂×#2408	1	1	yes	characteristic
756	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
757	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
758	C₂×C₄	C₂²×B(4,𝔽₂)	1	2	yes	—
759	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
760	C₂×C₄	C₂×#3025	1	1	yes	characteristic
761	C₂×C₄	C₂×#3025	1	2	yes	—
762	C₂×C₄	C₂×#3025	1	2	yes	—
763	C₂×C₄	C₂×#3025	1	1	yes	characteristic
764	C₂×C₄	C₂³×#120	1	1	yes	characteristic
765	C₂×C₄	C₂³×#121	1	1	yes	characteristic
766	C₂×C₄	C₂²×#546	1	2	yes	—
767	C₈	C₂²×B(4,𝔽₂)	1	8	yes	—
768	C₂²	C₂×#24260	1	2	yes	—
769	C₂²	C₂×#24260	1	1	yes	characteristic
770	C₂²	C₂×#24260	1	2	yes	—
771	C₂²	C₂×#24260	1	1	yes	characteristic
772	C₂²	C₂²×#2408	1	1	yes	characteristic
773	C₄	C₂×#24260	1	2	yes	—
774	C₄	C₂×#24260	1	1	yes	characteristic
775	C₄	C₂×#24260	1	2	yes	—
776	C₄	C₂×#24260	1	1	yes	characteristic
777	C₄	C₂³×B(4,𝔽₂)	1	1	yes	characteristic
778	C₄	C₂²×#3025	1	1	yes	characteristic
779	C₂	#72236900	1	2	yes	direct product factor
780	C₂	C₂²×#24260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#24260
commutator, Frattini, cosocle	C₂×#41	C₂⁶
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#568 ◁ 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×#493737	C₂	semidirect
2. C₂×#6372723	C₂	semidirect
3. C₂×#500807	C₂	semidirect
4. C₂²×#12778	C₂	semidirect
5. C₂×#500813	C₂	semidirect
6. C₂×#493620	C₂	semidirect
7. C₂×#10577667	C₂	semidirect
8. C₂×#495198	C₂	semidirect
9. C₂×#499126	C₂	semidirect
10. C₂×#7622874	C₂	semidirect
11. C₂×#500810	C₂	semidirect
12. C₂×#498898	C₂	semidirect
13. C₂×#6629045	C₂	semidirect
14. C₂²×#33559	C₂	semidirect
15. #72236900	C₂	direct (N × H)
16. C₂×#63076	C₂²	semidirect
19. #10577667	C₂²	semidirect
20. C₂×#62336	C₂²	semidirect
21. C₂×#62328	C₂²	semidirect
22. C₂×#62326	C₂²	semidirect
25. C₂×#60398	C₂²	semidirect
26. C₂²×#3027	C₂²	semidirect
29. #7622874	C₂²	semidirect
30. C₂×#33561	C₂²	semidirect
31. C₂×#33560	C₂²	semidirect
33. C₂×#33559	C₂²	semidirect
34. C₂×#33559	C₂²	semidirect
35. C₂×#33559	C₂²	semidirect
36. C₂×#33358	C₂²	semidirect
37. C₂²×#2128	C₂²	semidirect
40. C₂×#33347	C₂²	semidirect
41. C₂²×#2122	C₂²	semidirect
42. #6629045	C₂²	semidirect
43. C₂×#32948	C₂²	semidirect
44. C₂×#32947	C₂²	semidirect
45. #6372723	C₂²	semidirect
46. C₂×#21478	C₂²	semidirect
47. C₂×#21477	C₂²	semidirect
48. C₂×#21009	C₂²	semidirect
49. C₂²×#1910	C₂²	semidirect
51. C₂×#20860	C₂²	semidirect
52. C₂×#20671	C₂²	semidirect
53. C₂×#20620	C₂²	semidirect
54. C₂×#20401	C₂²	semidirect
55. #500813	C₂²	semidirect
56. #500810	C₂²	semidirect
57. #500807	C₂²	semidirect
58. #499126	C₂²	semidirect
59. C₂×#13437	C₂²	semidirect
60. C₂×#13436	C₂²	semidirect
61. #498898	C₂²	semidirect
62. C₂×#13351	C₂²	semidirect
63. C₂×#13350	C₂²	semidirect
64. #495198	C₂²	semidirect
65. C₂×#13231	C₂²	semidirect
66. C₂×#13229	C₂²	semidirect
67. #493737	C₂²	semidirect
68. C₂×#12808	C₂²	semidirect
69. C₂×#12807	C₂²	semidirect
70. #493620	C₂²	semidirect
71. C₂×#12780	C₂²	semidirect
72. C₂×#12779	C₂²	semidirect
73. C₂×#12778	C₂²	semidirect
74. C₂×#12778	C₂²	semidirect
75. C₂×#12778	C₂²	semidirect
76. C₂×#12778	C₂²	semidirect
77. C₂×#12577	C₂²	semidirect
79. C₂³×AGL(1,ℤ/8)	D₄	semidirect
80. #63076	C₂³	semidirect
81. C₂×#3573	C₂³	semidirect
82. C₂²×#568	D₄	semidirect
95. #62336	C₂³	semidirect
96. #62328	C₂³	semidirect
97. #62326	C₂³	semidirect
101. #60454	D₄	semidirect
103. C₂×#3058	D₄	semidirect
105. C₂×#3057	D₄	semidirect
107. #60398	C₂³	semidirect
108. C₂×#3028	C₂³	semidirect
110. C₂×#3027	C₂³	semidirect
111. C₂×#3027	C₂³	semidirect
120. #60144	D₄	semidirect
122. C₂×#2932	D₄	semidirect
124. C₂×#2931	D₄	semidirect
126. C₂×#2911	D₄	semidirect
127. C₂²×#423	D₄	semidirect
128. C₂×#2896	D₄	semidirect
129. C₂²×#418	D₄	semidirect
134. C₂×#2879	D₄	semidirect
136. C₂²×C₄×M₁₆	D₄	semidirect
137. #33561	C₂³	semidirect
138. #33560	C₂³	semidirect
140. #33559	C₂³	semidirect
141. #33559	C₂³	semidirect
142. #33358	C₂³	semidirect
143. C₂×#2129	C₂³	semidirect
145. C₂×#2128	C₂³	semidirect
146. C₂×#2128	C₂³	semidirect
153. #33347	C₂³	semidirect
154. C₂×#2123	C₂³	semidirect
156. C₂×#2122	C₂³	semidirect
157. C₂×#2122	C₂³	semidirect
158. #32948	C₂³	semidirect
159. #32947	C₂³	semidirect
160. #21478	C₂³	semidirect
161. #21477	C₂³	semidirect
162. #21009	C₂³	semidirect
164. C₂×#1910	C₂³	semidirect
165. C₂×#1910	C₂³	semidirect
166. C₂×#1909	C₂³	semidirect
170. #20860	C₂³	semidirect
171. C₂×#1858	C₂³	semidirect
172. #20671	C₂³	semidirect
173. C₂×#1812	C₂³	semidirect
174. #20620	C₂³	semidirect
175. C₂×#1794	C₂³	semidirect
176. #20401	C₂³	semidirect
177. C₂×#1757	C₂³	semidirect
178. #13437	C₂³	semidirect
179. #13436	C₂³	semidirect
180. #13351	C₂³	semidirect
181. #13350	C₂³	semidirect
182. #13231	C₂³	semidirect
183. #13229	C₂³	semidirect
184. #12808	C₂³	semidirect
185. #12807	C₂³	semidirect
186. #12780	C₂³	semidirect
187. #12779	C₂³	semidirect
188. #12778	C₂³	semidirect
189. #12778	C₂³	semidirect
190. #12778	C₂³	semidirect
191. #12577	C₂³	semidirect
192. C₂×#1391	C₂³	semidirect
202. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
203. C₂³×SD₁₆	C₂×D₄	semidirect
204. C₂³×D₈	C₂×D₄	semidirect
205. #3573	C₂⁴	semidirect
208. C₂×#568	C₂×D₄	semidirect
214. C₂²×#131	C₂×D₄	semidirect
215. C₂²×#131	C₂×D₄	semidirect
259. #3058	C₂×D₄	semidirect
260. #3058	C₂×D₄	semidirect
262. #3057	C₂×D₄	semidirect
263. #3057	C₂×D₄	semidirect
265. #3028	C₂⁴	semidirect
267. #3027	C₂⁴	semidirect
280. #2932	C₂×D₄	semidirect
281. #2932	C₂×D₄	semidirect
283. #2931	C₂×D₄	semidirect
284. #2931	C₂×D₄	semidirect
286. #2911	C₂×D₄	semidirect
287. C₂×#427	C₂×D₄	semidirect
288. C₂×#427	C₂×D₄	semidirect
289. C₂×#423	C₂×D₄	semidirect
290. C₂×#423	C₂×D₄	semidirect
291. C₂×#423	C₂×D₄	semidirect
292. #2896	C₂×D₄	semidirect
293. C₂×#419	C₂×D₄	semidirect
294. C₂×#418	C₂×D₄	semidirect
295. C₂×#418	C₂×D₄	semidirect
296. C₂×#418	C₂×D₄	semidirect
297. C₂×#418	C₂×D₄	semidirect
310. #2879	C₂×D₄	semidirect
313. C₂×#408	C₂×D₄	semidirect
314. C₂×#408	C₂×D₄	semidirect
316. C₂×C₄×M₁₆	C₂×D₄	semidirect
317. C₂²×#97	C₂×D₄	semidirect
318. C₂²×C₄×C₈	C₂×D₄	semidirect
319. #2129	C₂⁴	semidirect
321. #2128	C₂⁴	semidirect
326. #2123	C₂⁴	semidirect
328. #2122	C₂⁴	semidirect
330. #1910	C₂⁴	semidirect
331. #1909	C₂⁴	semidirect
334. #1858	C₂⁴	semidirect
335. #1812	C₂⁴	semidirect
336. #1794	C₂⁴	semidirect
337. #1757	C₂⁴	semidirect
338. #1391	C₂⁴	semidirect
374. C₂²×SD₁₆	C₂²×D₄	semidirect
375. C₂²×D₈	C₂²×D₄	semidirect
383. C₂×#131	C₂²×D₄	semidirect
384. C₂×#131	C₂²×D₄	semidirect
479. #427	C₂²×D₄	semidirect
480. #427	C₂²×D₄	semidirect
481. #423	C₂²×D₄	semidirect
482. #423	C₂²×D₄	semidirect
483. #419	C₂²×D₄	semidirect
484. #418	C₂²×D₄	semidirect
485. #418	C₂²×D₄	semidirect
486. #418	C₂²×D₄	semidirect
497. #408	C₂²×D₄	semidirect
498. #408	C₂²×D₄	semidirect
500. C₂×#97	C₂²×D₄	semidirect
501. C₂×C₄×C₈	C₂²×D₄	semidirect
779. C₂	#72236900	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×#493737	2
C₂×#6372723	2
C₂×#500807	2
C₂²×#12778	2
C₂×#500813	2
C₂×#493620	2
C₂×#10577667	2
C₂×#495198	2
C₂×#499126	2
C₂×#7622874	2
C₂×#500810	2
C₂×#498898	2
C₂×#6629045	2
C₂²×#33559	2
#72236900	2

Subgroups — C2×#72236900 #72337501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72236900 #72337501