Subgroups — #72312631

Order 2048.

At least 11647 conjugacy classes of subgroups; only the 5812 normal subgroups are shown.

The subgroup lattice has 1144 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72312612	C₂	1	1	yes	maximal, characteristic, complemented
2	#72312596	C₂	1	16	yes	maximal, complemented
3	#72312590	C₂	1	8	yes	maximal, complemented
4	#72312585	C₂	1	8	yes	maximal, complemented
5	#72312580	C₂	1	2	yes	maximal, complemented
6	#72312574	C₂	1	2	yes	maximal, complemented
7	#72312566	C₂	1	2	yes	maximal, complemented
8	#72312562	C₂	1	2	yes	maximal, complemented
9	#72312550	C₂	1	2	yes	maximal, complemented
10	#72312539	C₂	1	2	yes	maximal, complemented
11	#72312528	C₂	1	2	yes	maximal, complemented
12	#72312522	C₂	1	2	yes	maximal, complemented
13	#72312515	C₂	1	1	yes	maximal, characteristic, complemented
14	#72312508	C₂	1	1	yes	maximal, characteristic, complemented
15	#72312497	C₂	1	1	yes	maximal, characteristic, complemented
16	#72312492	C₂	1	2	yes	maximal, complemented
17	#72268516	C₂	1	2	yes	maximal, complemented
18	#72249727	C₂	1	2	yes	maximal, complemented
19	C₂³×#2010	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#6437463	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#394195	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#393988	C₂	1	2	yes	maximal, complemented
23	C₂³×#575	C₂²	1	1	yes	characteristic, complemented
24	C₂×#62811	C₂²	1	2	yes	complemented
25	C₂×#62811	C₂²	1	2	yes	complemented
26	C₂³×#525	C₂²	1	1	yes	characteristic
27	C₂³×#525	C₂²	1	2	yes	complemented
28	C₂×#60444	C₂²	1	1	yes	characteristic, complemented
29	C₂×#60387	C₂²	1	2	yes	complemented
30	C₂×#60387	C₂²	1	2	yes	complemented
31	C₂×#60387	C₂²	1	2	yes	complemented
32	C₂×#60359	C₂²	1	2	yes	complemented
33	C₂³×#407	C₂²	1	1	yes	characteristic, complemented
34	C₂³×#421	C₂²	1	2	yes	complemented
35	#7672320	C₂²	1	8	yes	complemented
36	#7672135	C₂²	1	8	yes	complemented
37	#7671870	C₂²	1	8	yes	complemented
38	#7671478	C₂²	1	8	yes	complemented
39	C₂×#36614	C₂²	1	2	yes	complemented
40	#7629144	C₂²	1	2	yes	complemented
41	#7629122	C₂²	1	2	yes	complemented
42	#7629122	C₂²	1	2	yes	complemented
43	#7629120	C₂²	1	2	yes	complemented
44	#7628650	C₂²	1	2	yes	—
45	#7628650	C₂²	1	2	yes	complemented
46	#7628649	C₂²	1	2	yes	—
47	#7628649	C₂²	1	2	yes	complemented
48	#7625530	C₂²	1	2	yes	complemented
49	#7625530	C₂²	1	2	yes	complemented
50	#6437932	C₂²	1	16	yes	complemented
51	#6437931	C₂²	1	16	yes	complemented
52	#6437474	C₂²	1	16	yes	complemented
53	#6437473	C₂²	1	16	yes	complemented
54	C₂×#23899	C₂²	1	4	yes	complemented
55	C₂×#23898	C₂²	1	8	yes	complemented
56	C₂×#23897	C₂²	1	4	yes	complemented
57	#6431889	C₂²	1	2	yes	complemented
58	#6431881	C₂²	1	2	yes	complemented
59	C₂²×#2010	C₂²	1	1	yes	characteristic
60	C₂²×#2010	C₂²	1	2	yes	complemented
61	C₂²×#2010	C₂²	1	8	yes	complemented
62	C₂²×#2010	C₂²	1	8	yes	complemented
63	C₂²×#2010	C₂²	1	2	yes	complemented
64	C₂²×#2010	C₂²	1	1	yes	characteristic, complemented
65	C₂²×#2010	C₂²	1	1	yes	characteristic, complemented
66	C₂²×#2010	C₂²	1	1	yes	characteristic, complemented
67	C₂²×#2010	C₂²	1	1	yes	characteristic, complemented
68	C₂²×#2010	C₂²	1	2	yes	complemented
69	C₂²×#2010	C₂²	1	1	yes	characteristic, complemented
70	C₂²×#2010	C₂²	1	2	yes	complemented
71	C₂²×#2010	C₂²	1	2	yes	complemented
72	C₂²×#2010	C₂²	1	2	yes	complemented
73	#6431733	C₂²	1	2	yes	complemented
74	#6431733	C₂²	1	2	yes	complemented
75	#6431733	C₂²	1	2	yes	complemented
76	#6431722	C₂²	1	2	yes	complemented
77	#6431722	C₂²	1	2	yes	complemented
78	#6431722	C₂²	1	2	yes	complemented
79	C₂×#21012	C₂²	1	2	yes	complemented
80	C₂×#21012	C₂²	1	2	yes	complemented
81	C₂×#21012	C₂²	1	2	yes	complemented
82	C₂×#20989	C₂²	1	2	yes	complemented
83	C₂×#20989	C₂²	1	2	yes	complemented
84	C₂×#20979	C₂²	1	2	yes	complemented
85	#6371439	C₂²	1	2	yes	complemented
86	#6371439	C₂²	1	2	yes	complemented
87	#6371439	C₂²	1	2	yes	complemented
88	C₂×#20902	C₂²	1	2	yes	complemented
89	#6371298	C₂²	1	2	yes	complemented
90	#6370746	C₂²	1	2	yes	complemented
91	C₂×#20605	C₂²	1	2	yes	complemented
92	C₂×#20591	C₂²	1	1	yes	characteristic, complemented
93	C₂×#20591	C₂²	1	1	yes	characteristic, complemented
94	C₂×#20579	C₂²	1	1	yes	characteristic, complemented
95	C₂³×H(3,ℤ/4)	C₂²	1	1	yes	characteristic, complemented
96	#454357	C₂²	1	8	yes	complemented
97	#454356	C₂²	1	8	yes	complemented
98	#453976	C₂²	1	4	yes	complemented
99	#453975	C₂²	1	8	yes	complemented
100	#453974	C₂²	1	4	yes	complemented
101	#422791	C₂²	1	16	yes	complemented
102	#422790	C₂²	1	16	yes	complemented
103	#418427	C₂²	1	16	yes	complemented
104	#418426	C₂²	1	16	yes	complemented
105	#417820	C₂²	1	16	yes	complemented
106	#417819	C₂²	1	16	yes	complemented
107	#417559	C₂²	1	16	yes	complemented
108	#417558	C₂²	1	16	yes	complemented
109	#395124	C₂²	1	16	yes	complemented
110	#395123	C₂²	1	16	yes	complemented
111	#394195	C₂²	1	8	yes	complemented
112	#394195	C₂²	1	8	yes	complemented
113	#393988	C₂²	1	16	yes	complemented
114	#393988	C₂²	1	16	yes	complemented
115	#393978	C₂²	1	8	yes	complemented
116	#393977	C₂²	1	8	yes	complemented
117	#393976	C₂²	1	8	yes	complemented
118	#393975	C₂²	1	8	yes	complemented
119	#375779	C₂²	1	8	yes	complemented
120	#375778	C₂²	1	8	yes	complemented
121	#368730	C₂²	1	16	yes	complemented
122	#368729	C₂²	1	16	yes	complemented
123	#364423	C₂²	1	16	yes	complemented
124	#364422	C₂²	1	16	yes	complemented
125	#359438	C₂²	1	8	yes	complemented
126	#359437	C₂²	1	4	yes	complemented
127	#359436	C₂²	1	4	yes	complemented
128	#358017	C₂²	1	2	yes	complemented
129	#357879	C₂²	1	2	yes	complemented
130	C₂×#11100	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11100	C₂²	1	1	yes	characteristic, complemented
132	#357648	C₂²	1	2	yes	complemented
133	#357648	C₂²	1	2	yes	complemented
134	#357648	C₂²	1	2	yes	complemented
135	C₂×#10994	C₂²	1	2	yes	complemented
136	C₂×#10994	C₂²	1	2	yes	complemented
137	C₂×#10994	C₂²	1	2	yes	complemented
138	C₂×#10994	C₂²	1	2	yes	complemented
139	C₂×#10994	C₂²	1	2	yes	complemented
140	C₂×#10994	C₂²	1	2	yes	complemented
141	#357478	C₂²	1	2	yes	complemented
142	#357478	C₂²	1	2	yes	complemented
143	#357478	C₂²	1	2	yes	complemented
144	#357426	C₂²	1	2	yes	complemented
145	#357426	C₂²	1	2	yes	complemented
146	#354040	C₂²	1	2	yes	complemented
147	#354040	C₂²	1	2	yes	complemented
148	#354040	C₂²	1	2	yes	complemented
149	#353902	C₂²	1	2	yes	complemented
150	#353420	C₂²	1	2	yes	complemented
151	#353319	C₂²	1	1	yes	characteristic, complemented
152	#353319	C₂²	1	1	yes	characteristic, complemented
153	C₂×#10717	C₂²	1	1	yes	characteristic, complemented
154	C₂×#10716	C₂²	1	2	yes	complemented
155	C₂²×#585	C₂³	1	2	yes	—
156	C₂⁴×#41	C₂³	1	2	yes	—
157	C₂⁴×#41	C₂³	1	1	yes	characteristic
158	C₂⁶×C₄	C₂³	1	1	yes	characteristic
159	C₂²×#575	C₂³	1	2	yes	—
160	C₂²×#575	C₂³	1	2	yes	—
161	C₂²×#575	C₂³	1	1	yes	characteristic
162	C₂²×#575	C₂³	1	1	yes	characteristic
163	C₂²×#575	C₂³	1	8	yes	—
164	C₂²×#575	C₂³	1	1	yes	characteristic
165	C₂²×#575	C₂³	1	2	yes	—
166	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
167	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
168	C₂×#3489	C₂³	1	8	yes	—
169	C₂×#3488	C₂³	1	8	yes	—
170	C₂×#3487	C₂³	1	4	yes	complemented
171	C₂×#3486	C₂³	1	4	yes	complemented
172	C₂×#3485	C₂³	1	4	yes	complemented
173	C₂×#3484	C₂³	1	4	yes	complemented
174	C₂×#3449	C₂³	1	2	yes	—
175	C₂×#3449	C₂³	1	2	yes	—
176	C₂×#3449	C₂³	1	2	yes	—
177	C₂×#3449	C₂³	1	2	yes	—
178	C₂×#3449	C₂³	1	2	yes	—
179	C₂²×#525	D₄	1	2	yes	—
180	C₂²×#525	D₄	1	4	yes	—
181	C₂²×#525	D₄	1	2	yes	—
182	C₂²×#525	C₂³	1	2	yes	—
183	C₂²×#525	C₂³	1	2	yes	—
184	C₂²×#525	C₂³	1	2	yes	—
185	C₂²×#525	C₂³	1	2	yes	—
186	C₂²×#525	C₂³	1	2	yes	—
187	C₂²×#525	C₂³	1	8	yes	—
188	C₂²×#525	C₂³	1	8	yes	—
189	C₂²×#525	C₂³	1	2	yes	—
190	C₂²×#525	C₂³	1	4	yes	—
191	C₂²×#525	C₂³	1	2	yes	—
192	C₂²×#525	C₂³	1	2	yes	—
193	C₂²×#525	C₂³	1	2	yes	—
194	C₂³×#123	D₄	1	2	yes	—
195	C₂³×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₂³×#121	C₂³	1	2	yes	—
197	C₂³×#120	D₄	1	2	yes	—
198	C₂×#3428	C₂³	1	2	yes	—
199	C₂×#3428	C₂³	1	2	yes	—
200	C₂³×C₄×D₄	D₄	1	4	yes	—
201	C₂³×#117	C₂³	1	1	yes	characteristic
202	C₂³×#117	C₂³	1	2	yes	—
203	#60444	C₂³	1	8	yes	—
204	C₂×#3020	C₂³	1	8	yes	complemented
205	C₂×#3020	C₂³	1	8	yes	complemented
206	C₂×#3020	C₂³	1	8	yes	complemented
207	C₂×#3019	C₂³	1	8	yes	complemented
208	C₂×#3019	C₂³	1	8	yes	complemented
209	C₂×#3019	C₂³	1	8	yes	complemented
210	#60359	C₂³	1	16	yes	—
211	C₂×#2911	C₂³	1	1	yes	characteristic
212	C₂²×#421	C₂³	1	2	yes	—
213	C₂²×#421	C₂³	1	2	yes	—
214	C₂²×#421	C₂³	1	2	yes	—
215	C₂²×#421	C₂³	1	2	yes	—
216	C₂²×#421	C₂³	1	2	yes	—
217	C₂²×#421	C₂³	1	2	yes	—
218	C₂²×#421	C₂³	1	2	yes	—
219	C₂²×#421	C₂³	1	16	yes	—
220	C₂²×#421	C₂³	1	2	yes	—
221	C₂²×#421	C₂³	1	2	yes	—
222	C₂²×#421	C₂³	1	2	yes	—
223	C₂²×#421	C₂³	1	2	yes	—
224	C₂²×#421	C₂³	1	2	yes	—
225	C₂×#2896	C₂³	1	2	yes	—
226	C₂×#2896	C₂³	1	2	yes	—
227	C₂×#2896	C₂³	1	2	yes	—
228	C₂²×#413	C₂³	1	2	yes	—
229	C₂²×#413	C₂³	1	2	yes	—
230	C₂²×#413	C₂³	1	2	yes	—
231	C₂²×#413	C₂³	1	2	yes	—
232	C₂²×#407	C₂³	1	1	yes	characteristic
233	C₂²×#407	C₂³	1	1	yes	characteristic
234	C₂²×#407	C₂³	1	4	yes	—
235	C₂²×#407	C₂³	1	4	yes	—
236	C₂²×#407	C₂³	1	1	yes	characteristic
237	C₂²×#407	C₂³	1	1	yes	characteristic
238	C₂²×#407	C₂³	1	1	yes	characteristic
239	C₂²×#407	C₂³	1	2	yes	—
240	C₂²×#407	C₂³	1	1	yes	characteristic
241	C₂²×#407	C₂³	1	2	yes	—
242	#36624	D₄	1	8	yes	complemented
243	#36614	C₂³	1	8	yes	—
244	#36614	C₂³	1	8	yes	—
245	#35661	C₂³	1	8	yes	complemented
246	#35659	C₂³	1	8	yes	complemented
247	#35634	C₂³	1	8	yes	complemented
248	#35633	C₂³	1	8	yes	complemented
249	#35565	C₂³	1	8	yes	complemented
250	#35563	C₂³	1	8	yes	complemented
251	#35514	C₂³	1	8	yes	complemented
252	#35512	C₂³	1	8	yes	complemented
253	#35306	D₄	1	8	yes	complemented
254	#35306	C₂³	1	8	yes	—
255	#35305	C₂³	1	8	yes	—
256	#35252	D₄	1	8	yes	complemented
257	#35252	C₂³	1	8	yes	—
258	#35250	C₂³	1	8	yes	—
259	#35242	D₄	1	4	yes	complemented
260	#35242	C₂³	1	4	yes	complemented
261	#35223	C₂³	1	8	yes	complemented
262	#35222	D₄	1	4	yes	complemented
263	#35222	C₂³	1	4	yes	complemented
264	#35150	C₂³	1	8	yes	complemented
265	#35149	D₄	1	4	yes	complemented
266	#35149	D₄	1	4	yes	complemented
267	#35149	C₂³	1	4	yes	complemented
268	#35149	C₂³	1	4	yes	complemented
269	#34738	D₄	1	16	yes	complemented
270	#34633	D₄	1	8	yes	complemented
271	#34204	C₂³	1	8	yes	—
272	#34203	C₂³	1	8	yes	—
273	#34201	C₂³	1	8	yes	complemented
274	#34200	C₂³	1	8	yes	complemented
275	#34052	C₂³	1	2	yes	—
276	#34052	C₂³	1	2	yes	—
277	#34044	C₂³	1	2	yes	—
278	#34044	C₂³	1	2	yes	—
279	#34044	C₂³	1	2	yes	—
280	#34044	C₂³	1	2	yes	—
281	#34044	C₂³	1	2	yes	—
282	C₂×#2280	C₂³	1	2	yes	—
283	C₂×#2280	C₂³	1	2	yes	—
284	C₂×#2280	C₂³	1	2	yes	—
285	#33996	C₂³	1	2	yes	—
286	#23499	C₂³	1	16	yes	complemented
287	#23494	C₂³	1	8	yes	complemented
288	#23493	C₂³	1	8	yes	complemented
289	C₂×#2010	D₄	1	16	yes	complemented
290	C₂×#2010	C₂³	1	8	yes	—
291	C₂×#2010	C₂³	1	16	yes	—
292	C₂×#2010	C₂³	1	4	yes	—
293	C₂×#2010	C₂³	1	4	yes	—
294	C₂×#2010	C₂³	1	8	yes	—
295	C₂×#2010	C₂³	1	8	yes	—
296	C₂×#2010	C₂³	1	8	yes	—
297	C₂×#2010	C₂³	1	4	yes	—
298	C₂×#2010	C₂³	1	4	yes	—
299	C₂×#2010	C₂³	1	8	yes	complemented
300	C₂×#2010	C₂³	1	8	yes	complemented
301	C₂×#2010	C₂³	1	4	yes	complemented
302	C₂×#2010	C₂³	1	4	yes	complemented
303	C₂×#2010	C₂³	1	16	yes	complemented
304	C₂×#2010	C₂³	1	16	yes	complemented
305	C₂×#2010	C₂³	1	8	yes	complemented
306	C₂×#2010	C₂³	1	8	yes	complemented
307	C₂×#2010	C₂³	1	8	yes	complemented
308	#23409	C₂³	1	16	yes	complemented
309	#23409	C₂³	1	16	yes	complemented
310	#23409	C₂³	1	16	yes	complemented
311	#23403	C₂³	1	8	yes	complemented
312	#23403	C₂³	1	8	yes	complemented
313	#23403	C₂³	1	8	yes	complemented
314	#23402	C₂³	1	8	yes	complemented
315	#23402	C₂³	1	8	yes	complemented
316	#23402	C₂³	1	8	yes	complemented
317	C₂×#1912	C₂³	1	8	yes	complemented
318	C₂×#1912	C₂³	1	8	yes	complemented
319	C₂×#1912	C₂³	1	8	yes	complemented
320	C₂×#1911	C₂³	1	8	yes	complemented
321	C₂×#1911	C₂³	1	8	yes	complemented
322	C₂×#1911	C₂³	1	8	yes	complemented
323	C₂×#1901	C₂³	1	8	yes	—
324	C₂×#1901	C₂³	1	8	yes	—
325	C₂×#1900	C₂³	1	8	yes	—
326	C₂×#1900	C₂³	1	8	yes	—
327	#20979	C₂³	1	16	yes	—
328	#20943	C₂³	1	16	yes	complemented
329	#20943	C₂³	1	16	yes	complemented
330	#20943	C₂³	1	16	yes	complemented
331	#20902	C₂³	1	16	yes	—
332	#20864	C₂³	1	16	yes	complemented
333	#20617	C₂³	1	8	yes	complemented
334	#20616	C₂³	1	8	yes	complemented
335	#20605	C₂³	1	16	yes	—
336	C₂×#1785	C₂³	1	4	yes	complemented
337	C₂×#1785	C₂³	1	4	yes	complemented
338	C₂×#1784	C₂³	1	2	yes	complemented
339	C₂×#1784	C₂³	1	2	yes	complemented
340	C₂×#1783	C₂³	1	2	yes	complemented
341	C₂×#1783	C₂³	1	2	yes	complemented
342	#20579	C₂³	1	4	yes	—
343	#20579	C₂³	1	4	yes	—
344	C₂×#1742	C₂³	1	2	yes	—
345	C₂×#1742	C₂³	1	2	yes	—
346	C₂×#1742	C₂³	1	2	yes	—
347	C₂×#1742	C₂³	1	2	yes	—
348	C₂×#1733	C₂³	1	2	yes	—
349	C₂×#1733	C₂³	1	2	yes	—
350	C₂×#1733	C₂³	1	2	yes	—
351	C₂×#1733	C₂³	1	2	yes	—
352	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
353	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
354	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
355	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
356	C₂²×H(3,ℤ/4)	C₂³	1	8	yes	—
357	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
358	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
359	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
360	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	—
361	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
362	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
363	#11224	C₂³	1	16	yes	complemented
364	#11156	C₂³	1	8	yes	complemented
365	#11155	C₂³	1	8	yes	complemented
366	#11100	C₂³	1	4	yes	complemented
367	#11100	C₂³	1	4	yes	complemented
368	#11100	C₂³	1	8	yes	complemented
369	#11072	C₂³	1	16	yes	complemented
370	#11072	C₂³	1	16	yes	complemented
371	#11072	C₂³	1	16	yes	complemented
372	#10994	C₂³	1	16	yes	complemented
373	#10994	C₂³	1	8	yes	complemented
374	#10994	C₂³	1	8	yes	complemented
375	#10994	C₂³	1	16	yes	complemented
376	#10994	C₂³	1	8	yes	complemented
377	#10994	C₂³	1	8	yes	complemented
378	#10994	C₂³	1	16	yes	complemented
379	#10994	C₂³	1	8	yes	complemented
380	#10994	C₂³	1	8	yes	complemented
381	#10990	C₂³	1	8	yes	complemented
382	#10990	C₂³	1	8	yes	complemented
383	#10990	C₂³	1	8	yes	complemented
384	#10989	C₂³	1	8	yes	complemented
385	#10989	C₂³	1	8	yes	complemented
386	#10989	C₂³	1	8	yes	complemented
387	#10968	C₂³	1	8	yes	complemented
388	#10968	C₂³	1	8	yes	complemented
389	#10967	C₂³	1	8	yes	complemented
390	#10967	C₂³	1	8	yes	complemented
391	#10949	C₂³	1	16	yes	complemented
392	#10949	C₂³	1	16	yes	complemented
393	#10949	C₂³	1	16	yes	complemented
394	#10888	C₂³	1	16	yes	complemented
395	#10741	C₂³	1	8	yes	complemented
396	#10740	C₂³	1	8	yes	complemented
397	#10728	C₂³	1	4	yes	complemented
398	#10728	C₂³	1	4	yes	complemented
399	#10727	C₂³	1	4	yes	complemented
400	#10727	C₂³	1	4	yes	complemented
401	#10717	C₂³	1	8	yes	—
402	#10716	C₂³	1	16	yes	—
403	C₂⁷	C₂×D₄	1	1	yes	characteristic
404	C₂²×2₋¹⁺⁴	C₂⁴	1	4	yes	—
405	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
406	C₂³×#41	C₂×D₄	1	2	yes	—
407	C₂³×#41	C₂×D₄	1	2	yes	—
408	C₂³×#41	C₂×D₄	1	2	yes	complemented
409	C₂³×#41	C₂×D₄	1	2	yes	complemented
410	C₂³×#41	C₂×D₄	1	8	yes	complemented
411	C₂³×#41	C₂⁴	1	2	yes	—
412	C₂³×#41	C₂⁴	1	2	yes	—
413	C₂³×#41	C₂⁴	1	2	yes	—
414	C₂³×#41	C₂⁴	1	8	yes	—
415	C₂³×#41	C₂⁴	1	2	yes	—
416	C₂³×#41	C₂⁴	1	2	yes	—
417	C₂⁴×Q₈	C₂×D₄	1	2	yes	complemented
418	C₂⁴×Q₈	C₂⁴	1	1	yes	characteristic
419	C₂⁴×D₄	C₂×D₄	1	2	yes	—
420	C₂⁴×D₄	C₂×D₄	1	4	yes	—
421	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
422	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
423	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
424	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
425	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
426	C₂⁵×C₄	C₂×D₄	1	2	yes	—
427	C₂⁵×C₄	C₂×D₄	1	2	yes	—
428	C₂⁵×C₄	C₂×D₄	1	2	yes	—
429	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
430	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
431	C₂⁵×C₄	C₂⁴	1	2	yes	—
432	C₂⁵×C₄	C₂⁴	1	2	yes	—
433	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
434	C₂×#575	C₂×D₄	1	8	yes	complemented
435	C₂×#575	C₂⁴	1	8	yes	—
436	C₂×#575	C₂⁴	1	8	yes	—
437	C₂×#575	C₂⁴	1	4	yes	—
438	C₂×#575	C₂⁴	1	4	yes	—
439	C₂×#575	C₂⁴	1	4	yes	—
440	C₂×#575	C₂⁴	1	8	yes	—
441	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
442	C₂³×M₁₆	C₂⁴	1	2	yes	—
443	C₂³×M₁₆	C₂⁴	1	2	yes	—
444	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
445	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
446	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
447	C₂³×M₁₆	C₂⁴	1	4	yes	—
448	C₂³×M₁₆	C₂⁴	1	4	yes	—
449	C₂×#537	C₂⁴	1	8	yes	—
450	C₂×#536	C₂×D₄	1	4	yes	complemented
451	C₂×#536	C₂×D₄	1	4	yes	complemented
452	C₂×#536	C₂×D₄	1	4	yes	complemented
453	C₂×#536	C₂⁴	1	4	yes	—
454	C₂×#536	C₂⁴	1	4	yes	—
455	C₂×#536	C₂⁴	1	4	yes	—
456	C₂×#536	C₂⁴	1	4	yes	—
457	C₂×#535	C₂×D₄	1	4	yes	complemented
458	C₂×#535	C₂×D₄	1	4	yes	complemented
459	C₂×#535	C₂×D₄	1	4	yes	complemented
460	C₂×#535	C₂⁴	1	4	yes	—
461	C₂×#535	C₂⁴	1	4	yes	—
462	C₂×#535	C₂⁴	1	4	yes	—
463	C₂×#535	C₂⁴	1	4	yes	—
464	C₂×#532	C₂×D₄	1	8	yes	complemented
465	C₂×#532	C₂×D₄	1	8	yes	complemented
466	C₂×#532	C₂×D₄	1	8	yes	complemented
467	C₂×#525	C₂×D₄	1	4	yes	—
468	C₂×#525	C₂×D₄	1	4	yes	—
469	C₂×#525	C₂×D₄	1	4	yes	—
470	C₂×#525	C₂×D₄	1	4	yes	—
471	C₂×#525	C₂×D₄	1	8	yes	—
472	C₂×#525	C₂×D₄	1	8	yes	—
473	C₂×#525	C₂×D₄	1	16	yes	complemented
474	C₂×#525	C₂×D₄	1	4	yes	complemented
475	C₂×#525	C₂×D₄	1	4	yes	complemented
476	C₂×#525	C₂⁴	1	4	yes	—
477	C₂×#525	C₂⁴	1	4	yes	—
478	C₂×#525	C₂⁴	1	4	yes	—
479	C₂×#525	C₂⁴	1	4	yes	—
480	C₂×#525	C₂⁴	1	8	yes	—
481	C₂×#525	C₂⁴	1	8	yes	—
482	C₂×#525	C₂⁴	1	4	yes	—
483	C₂×#525	C₂⁴	1	4	yes	—
484	C₂×#525	C₂⁴	1	8	yes	—
485	C₂×#525	C₂⁴	1	8	yes	—
486	C₂²×#123	C₂×D₄	1	8	yes	—
487	C₂²×#123	C₂×D₄	1	4	yes	—
488	C₂²×#123	C₂×D₄	1	4	yes	—
489	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	—
490	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	—
491	C₂²×C₂²⋊Q₈	C₂×D₄	1	4	yes	complemented
492	C₂²×C₂²⋊Q₈	C₂⁴	1	4	yes	—
493	C₂²×C₂²⋊Q₈	C₂⁴	1	4	yes	—
494	C₂²×#121	C₂×D₄	1	4	yes	—
495	C₂²×#121	C₂×D₄	1	4	yes	—
496	C₂²×#121	C₂×D₄	1	4	yes	complemented
497	C₂²×#121	C₂⁴	1	4	yes	—
498	C₂²×#121	C₂⁴	1	4	yes	—
499	C₂²×#120	C₂×D₄	1	8	yes	—
500	C₂²×#120	C₂×D₄	1	4	yes	—
501	C₂²×#120	C₂×D₄	1	4	yes	—
502	C₂×#520	C₂⁴	1	8	yes	—
503	C₂×#519	C₂⁴	1	4	yes	—
504	C₂×#518	C₂⁴	1	4	yes	—
505	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
506	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
507	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
508	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
509	C₂²×#117	C₂×D₄	1	2	yes	—
510	C₂²×#117	C₂×D₄	1	2	yes	—
511	C₂²×#117	C₂×D₄	1	4	yes	complemented
512	C₂²×#117	C₂×D₄	1	8	yes	complemented
513	C₂²×#117	C₂⁴	1	2	yes	—
514	C₂²×#117	C₂⁴	1	2	yes	—
515	C₂²×#117	C₂⁴	1	2	yes	—
516	C₂²×#117	C₂⁴	1	8	yes	—
517	C₂²×#117	C₂⁴	1	2	yes	—
518	C₂²×#117	C₂⁴	1	2	yes	—
519	C₂²×#117	C₂⁴	1	2	yes	—
520	C₂²×#117	C₂⁴	1	2	yes	—
521	C₂³×C₄⋊C₄	C₂×D₄	1	4	yes	—
522	C₂³×C₄⋊C₄	C₂⁴	1	2	yes	—
523	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
524	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
525	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
526	C₂³×C₄²	C₂×D₄	1	2	yes	—
527	C₂³×C₄²	C₂×D₄	1	4	yes	complemented
528	#2911	C₂⁴	1	4	yes	—
529	C₂×#421	C₂×D₄	1	16	yes	complemented
530	C₂×#421	C₂⁴	1	8	yes	—
531	C₂×#421	C₂⁴	1	8	yes	—
532	C₂×#421	C₂⁴	1	8	yes	—
533	C₂×#421	C₂⁴	1	8	yes	—
534	C₂×#421	C₂⁴	1	8	yes	—
535	C₂×#421	C₂⁴	1	8	yes	—
536	C₂×#421	C₂⁴	1	8	yes	—
537	C₂×#421	C₂⁴	1	8	yes	—
538	C₂×#421	C₂⁴	1	8	yes	—
539	C₂×#421	C₂⁴	1	8	yes	—
540	C₂×#421	C₂⁴	1	8	yes	—
541	C₂×#421	C₂⁴	1	8	yes	—
542	#2896	C₂⁴	1	8	yes	—
543	#2896	C₂⁴	1	8	yes	—
544	#2896	C₂⁴	1	8	yes	—
545	C₂²×#101	C₂⁴	1	4	yes	—
546	C₂²×#101	C₂⁴	1	4	yes	—
547	C₂²×#101	C₂⁴	1	4	yes	—
548	C₂²×#101	C₂⁴	1	4	yes	—
549	C₂²×#100	C₂⁴	1	4	yes	—
550	C₂²×#100	C₂⁴	1	4	yes	—
551	C₂²×#100	C₂⁴	1	4	yes	—
552	C₂²×#100	C₂⁴	1	4	yes	—
553	C₂×#407	C₂×D₄	1	8	yes	complemented
554	C₂×#407	C₂⁴	1	8	yes	—
555	C₂×#407	C₂⁴	1	4	yes	—
556	C₂×#407	C₂⁴	1	2	yes	—
557	C₂×#407	C₂⁴	1	2	yes	—
558	C₂×#407	C₂⁴	1	2	yes	—
559	C₂×#407	C₂⁴	1	2	yes	—
560	C₂×#407	C₂⁴	1	2	yes	—
561	C₂×#407	C₂⁴	1	2	yes	—
562	C₂×#407	C₂⁴	1	4	yes	—
563	C₂×#407	C₂⁴	1	8	yes	—
564	C₂×#407	C₂⁴	1	2	yes	—
565	C₂×#407	C₂⁴	1	2	yes	—
566	#2857	C₂×D₄	1	16	yes	complemented
567	#2856	C₂×D₄	1	16	yes	complemented
568	#2850	C₂×D₄	1	16	yes	complemented
569	#2850	C₂×D₄	1	16	yes	complemented
570	#2621	C₂×D₄	1	16	yes	complemented
571	#2620	C₂×D₄	1	16	yes	complemented
572	#2620	C₂×D₄	1	16	yes	complemented
573	#2619	C₂×D₄	1	16	yes	complemented
574	#2436	C₂×D₄	1	16	yes	complemented
575	#2435	C₂×D₄	1	16	yes	complemented
576	#2434	C₂×D₄	1	16	yes	complemented
577	#2433	C₂×D₄	1	16	yes	complemented
578	#2432	C₂×D₄	1	16	yes	complemented
579	#2432	C₂×D₄	1	16	yes	complemented
580	#2431	C₂×D₄	1	16	yes	complemented
581	#2431	C₂×D₄	1	16	yes	complemented
582	#2317	C₂×D₄	1	8	yes	complemented
583	#2317	C₂⁴	1	8	yes	—
584	#2316	C₂⁴	1	8	yes	—
585	#2311	C₂×D₄	1	8	yes	complemented
586	#2311	C₂⁴	1	8	yes	—
587	#2311	C₂⁴	1	8	yes	—
588	#2311	C₂⁴	1	8	yes	—
589	#2310	C₂×D₄	1	4	yes	complemented
590	#2310	C₂×D₄	1	4	yes	complemented
591	#2310	C₂×D₄	1	4	yes	complemented
592	#2310	C₂⁴	1	4	yes	—
593	#2310	C₂⁴	1	4	yes	—
594	#2309	C₂×D₄	1	4	yes	complemented
595	#2309	C₂×D₄	1	4	yes	complemented
596	#2309	C₂×D₄	1	4	yes	complemented
597	#2309	C₂⁴	1	4	yes	—
598	#2309	C₂⁴	1	4	yes	—
599	#2297	C₂×D₄	1	8	yes	complemented
600	#2297	C₂×D₄	1	8	yes	complemented
601	#2297	C₂×D₄	1	8	yes	complemented
602	#2297	C₂×D₄	1	8	yes	complemented
603	#2285	C₂×D₄	1	8	yes	complemented
604	#2280	C₂×D₄	1	4	yes	complemented
605	#2280	C₂×D₄	1	4	yes	complemented
606	#2280	C₂⁴	1	8	yes	—
607	#2280	C₂⁴	1	4	yes	—
608	#2280	C₂⁴	1	4	yes	—
609	#2280	C₂⁴	1	8	yes	—
610	#2274	C₂⁴	1	8	yes	—
611	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
612	#2010	C₂×D₄	1	32	yes	complemented
613	#2010	C₂×D₄	1	32	yes	complemented
614	C₂×#343	C₂⁴	1	8	yes	—
615	C₂×#343	C₂⁴	1	8	yes	—
616	C₂×#343	C₂⁴	1	8	yes	—
617	C₂×#343	C₂⁴	1	8	yes	—
618	#1733	C₂⁴	1	8	yes	—
619	#1733	C₂⁴	1	8	yes	—
620	#1733	C₂⁴	1	8	yes	—
621	#1733	C₂⁴	1	8	yes	—
622	C₂×H(3,ℤ/4)	C₂×D₄	1	8	yes	complemented
623	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
624	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
625	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
626	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
627	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
628	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
629	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
630	C₂×H(3,ℤ/4)	C₂⁴	1	8	yes	—
631	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
632	C₂×H(3,ℤ/4)	C₂⁴	1	4	yes	—
633	C₂⁶	C₂²×D₄	1	1	yes	characteristic
634	C₂⁶	C₂²×D₄	1	1	yes	characteristic
635	C₂⁶	C₂²×D₄	1	2	yes	—
636	C₂⁶	C₂²×D₄	1	2	yes	—
637	C₂⁶	C₂²×D₄	1	1	yes	characteristic
638	C₂⁶	C₂²×D₄	1	2	yes	—
639	C₂²×#41	C₂²×D₄	1	8	yes	—
640	C₂²×#41	C₂²×D₄	1	4	yes	—
641	C₂²×#41	C₂²×D₄	1	4	yes	—
642	C₂²×#41	C₂²×D₄	1	4	yes	—
643	C₂²×#41	C₂²×D₄	1	8	yes	—
644	C₂²×#41	C₂²×D₄	1	8	yes	—
645	C₂²×#41	C₂²×D₄	1	4	yes	—
646	C₂²×#41	C₂²×D₄	1	4	yes	—
647	C₂²×#41	C₂²×D₄	1	4	yes	—
648	C₂²×#41	C₂²×D₄	1	4	yes	—
649	C₂²×#41	H(5,𝔽₂)	1	8	yes	—
650	C₂²×#41	C₂⁵	1	4	yes	—
651	C₂²×#41	C₂⁵	1	4	yes	—
652	C₂²×#41	C₂⁵	1	4	yes	—
653	C₂³×Q₈	C₂²×D₄	1	2	yes	—
654	C₂³×Q₈	C₂²×D₄	1	2	yes	—
655	C₂³×Q₈	C₂²×D₄	1	2	yes	—
656	C₂³×Q₈	C₂²×D₄	1	8	yes	—
657	C₂³×Q₈	C₂²×D₄	1	2	yes	—
658	C₂³×Q₈	C₂⁵	1	2	yes	—
659	C₂³×D₄	C₂²×D₄	1	2	yes	—
660	C₂³×D₄	C₂²×D₄	1	2	yes	—
661	C₂³×D₄	C₂²×D₄	1	4	yes	—
662	C₂³×D₄	C₂²×D₄	1	2	yes	—
663	C₂³×D₄	C₂²×D₄	1	8	yes	—
664	C₂³×D₄	C₂²×D₄	1	4	yes	—
665	C₂³×D₄	C₂²×D₄	1	2	yes	—
666	C₂³×D₄	C₂²×D₄	1	8	yes	—
667	C₂³×D₄	C₂²×D₄	1	8	yes	—
668	C₂³×D₄	C₂⁵	1	2	yes	—
669	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
670	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
671	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
672	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
673	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
674	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
675	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
676	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
677	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
678	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
679	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
680	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
681	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
682	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
683	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
684	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
685	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
686	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
687	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
688	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
689	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
690	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
691	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
692	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
693	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	—
694	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
695	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
696	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
697	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
698	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
699	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
700	C₂⁴×C₄	C₂⁵	1	2	yes	—
701	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
702	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
703	C₂⁴×C₄	C₂⁵	1	2	yes	—
704	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
705	#575	C₂²×D₄	1	16	yes	—
706	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
707	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
708	C₂²×M₁₆	H(5,𝔽₂)	1	4	yes	—
709	C₂²×M₁₆	C₂⁵	1	4	yes	—
710	C₂²×M₁₆	C₂⁵	1	4	yes	—
711	C₂²×M₁₆	C₂⁵	1	2	yes	—
712	C₂²×M₁₆	C₂⁵	1	2	yes	—
713	C₂²×M₁₆	C₂⁵	1	2	yes	—
714	C₂²×M₁₆	C₂⁵	1	2	yes	—
715	C₂×C₄⋊Q₈	C₂²×D₄	1	8	yes	complemented
716	C₂×C₄⋊Q₈	C₂²×D₄	1	8	yes	complemented
717	C₂×C₄⋊Q₈	C₂²×D₄	1	8	yes	complemented
718	C₂×#127	C₂²×D₄	1	8	yes	complemented
719	C₂×#127	C₂²×D₄	1	8	yes	complemented
720	C₂×#127	C₂²×D₄	1	8	yes	complemented
721	C₂×#124	C₂²×D₄	1	8	yes	complemented
722	C₂×#124	C₂²×D₄	1	8	yes	complemented
723	C₂×#124	C₂²×D₄	1	8	yes	complemented
724	C₂×#124	C₂²×D₄	1	8	yes	complemented
725	C₂×#124	C₂²×D₄	1	8	yes	complemented
726	C₂×#124	C₂²×D₄	1	8	yes	complemented
727	#525	C₂²×D₄	1	16	yes	—
728	#525	C₂²×D₄	1	16	yes	—
729	C₂×#123	#120	1	8	yes	—
730	C₂×#123	#120	1	8	yes	—
731	C₂×#123	#120	1	16	yes	—
732	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
733	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
734	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
735	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
736	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
737	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
738	C₂×#121	C₂²×D₄	1	8	yes	—
739	C₂×#121	C₂²×D₄	1	8	yes	—
740	C₂×#121	C₂²×D₄	1	8	yes	—
741	C₂×#121	C₂²×D₄	1	8	yes	—
742	C₂×#121	C₂²×D₄	1	8	yes	—
743	C₂×#121	C₂²×D₄	1	8	yes	—
744	C₂×#120	#120	1	8	yes	—
745	C₂×#120	#120	1	8	yes	—
746	C₂×#120	#120	1	16	yes	—
747	C₂×C₄×D₄	#120	1	16	yes	—
748	C₂×C₄×D₄	#120	1	16	yes	—
749	C₂×C₄×D₄	#120	1	16	yes	—
750	C₂×C₄×D₄	#120	1	16	yes	—
751	C₂×#117	C₂²×D₄	1	4	yes	—
752	C₂×#117	C₂²×D₄	1	4	yes	—
753	C₂×#117	C₂²×D₄	1	4	yes	—
754	C₂×#117	C₂²×D₄	1	4	yes	—
755	C₂×#117	C₂²×D₄	1	4	yes	—
756	C₂×#117	C₂²×D₄	1	8	yes	—
757	C₂×#117	C₂²×D₄	1	4	yes	—
758	C₂×#117	C₂²×D₄	1	4	yes	—
759	C₂×#117	C₂²×D₄	1	4	yes	—
760	C₂×#117	C₂²×D₄	1	16	yes	—
761	C₂×#117	C₂²×D₄	1	4	yes	—
762	C₂×#117	H(5,𝔽₂)	1	8	yes	—
763	C₂×#117	C₂⁵	1	4	yes	—
764	C₂×#117	C₂⁵	1	4	yes	—
765	C₂×#117	C₂⁵	1	4	yes	—
766	C₂×#117	C₂⁵	1	4	yes	—
767	C₂×#117	C₂⁵	1	4	yes	—
768	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
769	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
770	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	—
771	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	—
772	C₂²×C₄⋊C₄	C₂⁵	1	4	yes	—
773	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
774	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
775	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
776	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
777	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
778	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
779	C₂²×C₄²	C₂²×D₄	1	4	yes	—
780	C₂²×C₄²	C₂²×D₄	1	4	yes	—
781	C₂²×C₄²	C₂²×D₄	1	4	yes	—
782	C₂²×C₄²	C₂²×D₄	1	4	yes	—
783	C₂²×C₄²	C₂²×D₄	1	4	yes	—
784	C₂²×C₄²	C₂²×D₄	1	16	yes	—
785	C₂²×C₄²	C₂²×D₄	1	4	yes	—
786	#421	C₂²×D₄	1	32	yes	—
787	#407	C₂²×D₄	1	8	yes	—
788	#407	C₂²×D₄	1	8	yes	—
789	#391	C₂²×D₄	1	16	yes	complemented
790	#391	C₂²×D₄	1	16	yes	complemented
791	#391	C₂²×D₄	1	16	yes	complemented
792	#391	C₂²×D₄	1	16	yes	complemented
793	#390	C₂²×D₄	1	16	yes	complemented
794	#390	C₂²×D₄	1	16	yes	complemented
795	#390	C₂²×D₄	1	16	yes	complemented
796	#390	C₂²×D₄	1	16	yes	complemented
797	#384	C₂²×D₄	1	16	yes	complemented
798	#382	C₂²×D₄	1	16	yes	complemented
799	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
800	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
801	H(3,ℤ/4)	C₂²×D₄	1	16	yes	—
802	C₂⁵	C₂×#120	1	2	yes	—
803	C₂⁵	C₂×#120	1	4	yes	—
804	C₂⁵	C₂×#120	1	2	yes	—
805	C₂⁵	#534	1	1	yes	characteristic
806	C₂⁵	#534	1	2	yes	—
807	C₂⁵	#534	1	1	yes	characteristic
808	C₂⁵	D₄²	1	4	yes	—
809	C₂⁵	C₂³×D₄	1	2	yes	—
810	C₂⁵	C₂³×D₄	1	1	yes	characteristic
811	C₂⁵	C₂³×D₄	1	4	yes	—
812	C₂⁵	C₂³×D₄	1	1	yes	characteristic
813	C₂⁵	C₂³×D₄	1	2	yes	—
814	C₂⁵	C₂³×D₄	1	1	yes	characteristic
815	C₂×#41	D₄²	1	16	yes	complemented
816	C₂×#41	C₂³×D₄	1	8	yes	—
817	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
818	C₂²×Q₈	D₄²	1	8	yes	complemented
819	C₂²×Q₈	C₂³×D₄	1	4	yes	—
820	C₂²×Q₈	C₂³×D₄	1	4	yes	—
821	C₂²×Q₈	C₂³×D₄	1	4	yes	—
822	C₂²×Q₈	C₂³×D₄	1	4	yes	—
823	C₂²×Q₈	C₂³×D₄	1	4	yes	—
824	C₂²×D₄	C₂×#120	1	8	yes	—
825	C₂²×D₄	C₂×#120	1	8	yes	—
826	C₂²×D₄	C₂×#120	1	16	yes	—
827	C₂²×D₄	C₂×#120	1	16	yes	—
828	C₂²×D₄	D₄²	1	8	yes	complemented
829	C₂²×D₄	C₂³×D₄	1	4	yes	—
830	C₂²×D₄	C₂³×D₄	1	4	yes	—
831	C₂²×D₄	C₂³×D₄	1	4	yes	—
832	C₂²×D₄	C₂³×D₄	1	4	yes	—
833	C₂²×D₄	C₂³×D₄	1	4	yes	—
834	C₂³×C₄	C₂×#120	1	8	yes	—
835	C₂³×C₄	C₂×#120	1	8	yes	—
836	C₂³×C₄	C₂×#120	1	4	yes	—
837	C₂³×C₄	C₂×#120	1	4	yes	—
838	C₂³×C₄	C₂×#120	1	2	yes	—
839	C₂³×C₄	C₂×#120	1	4	yes	—
840	C₂³×C₄	C₂×#120	1	4	yes	—
841	C₂³×C₄	C₂×#120	1	4	yes	—
842	C₂³×C₄	C₂×#120	1	2	yes	—
843	C₂³×C₄	#534	1	2	yes	—
844	C₂³×C₄	#534	1	2	yes	—
845	C₂³×C₄	#534	1	2	yes	—
846	C₂³×C₄	#534	1	2	yes	—
847	C₂³×C₄	#534	1	1	yes	characteristic
848	C₂³×C₄	#534	1	1	yes	characteristic
849	C₂³×C₄	#534	1	2	yes	—
850	C₂³×C₄	D₄²	1	4	yes	—
851	C₂³×C₄	D₄²	1	4	yes	—
852	C₂³×C₄	D₄²	1	4	yes	—
853	C₂³×C₄	D₄²	1	2	yes	—
854	C₂³×C₄	D₄²	1	2	yes	—
855	C₂³×C₄	D₄²	1	4	yes	—
856	C₂³×C₄	D₄²	1	4	yes	—
857	C₂³×C₄	D₄²	1	4	yes	—
858	C₂³×C₄	D₄²	1	4	yes	—
859	C₂³×C₄	D₄²	1	4	yes	—
860	C₂³×C₄	D₄²	1	4	yes	—
861	C₂³×C₄	D₄²	1	2	yes	—
862	C₂³×C₄	D₄²	1	2	yes	—
863	C₂³×C₄	D₄²	1	4	yes	—
864	C₂³×C₄	D₄²	1	4	yes	—
865	C₂³×C₄	D₄²	1	4	yes	—
866	C₂³×C₄	D₄²	1	4	yes	—
867	C₂³×C₄	D₄²	1	1	yes	characteristic
868	C₂³×C₄	D₄²	1	1	yes	characteristic
869	C₂³×C₄	D₄²	1	2	yes	—
870	C₂³×C₄	D₄²	1	2	yes	—
871	C₂³×C₄	D₄²	1	2	yes	—
872	C₂³×C₄	D₄²	1	2	yes	—
873	C₂³×C₄	D₄²	1	2	yes	—
874	C₂³×C₄	D₄²	1	1	yes	characteristic
875	C₂³×C₄	D₄²	1	1	yes	characteristic
876	C₂³×C₄	D₄²	1	2	yes	—
877	C₂³×C₄	C₂³×D₄	1	2	yes	—
878	C₂³×C₄	C₂³×D₄	1	2	yes	—
879	C₂³×C₄	C₂³×D₄	1	2	yes	—
880	C₂³×C₄	C₂³×D₄	1	4	yes	—
881	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
882	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
883	C₂³×C₄	C₂³×D₄	1	4	yes	—
884	C₂³×C₄	C₂³×D₄	1	4	yes	—
885	C₂³×C₄	C₂³×D₄	1	4	yes	—
886	C₂³×C₄	C₂³×D₄	1	4	yes	—
887	C₂³×C₄	C₂³×D₄	1	2	yes	—
888	C₂³×C₄	C₂³×D₄	1	8	yes	—
889	C₂³×C₄	C₂³×D₄	1	2	yes	—
890	C₂³×C₄	C₂³×D₄	1	2	yes	—
891	C₂³×C₄	C₂³×D₄	1	2	yes	—
892	C₂³×C₄	C₂³×D₄	1	2	yes	—
893	C₂³×C₄	C₂³×D₄	1	2	yes	—
894	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
895	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
896	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
897	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
898	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
899	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
900	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
901	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
902	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
903	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
904	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
905	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
906	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
907	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
908	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
909	C₂³×C₄	#585	1	2	yes	—
910	C₂³×C₄	C₂⁶	1	1	yes	characteristic
911	C₂×M₁₆	C₂³×D₄	1	4	yes	—
912	C₂×M₁₆	C₂³×D₄	1	4	yes	—
913	C₂×M₁₆	C₂×H(5,𝔽₂)	1	4	yes	—
914	#117	D₄²	1	16	yes	complemented
915	#117	C₂³×D₄	1	8	yes	—
916	#117	C₂×H(5,𝔽₂)	1	8	yes	—
917	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
918	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
919	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
920	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
921	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
922	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
923	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
924	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
925	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
926	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
927	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
928	C₂×C₄²	C₂×#120	1	8	yes	—
929	C₂×C₄²	C₂×#120	1	8	yes	—
930	C₂×C₄²	D₄²	1	16	yes	complemented
931	C₂×C₄²	C₂³×D₄	1	8	yes	—
932	C₂×C₄²	C₂³×D₄	1	8	yes	—
933	C₂×C₄²	C₂³×D₄	1	8	yes	—
934	C₂×C₄²	C₂³×D₄	1	8	yes	—
935	C₂⁴	#2403	1	1	yes	characteristic
936	C₂⁴	#2403	1	2	yes	—
937	C₂⁴	#2403	1	4	yes	—
938	C₂⁴	#2403	1	2	yes	—
939	C₂⁴	#2403	1	4	yes	—
940	C₂⁴	#2403	1	2	yes	—
941	C₂⁴	#2403	1	1	yes	characteristic
942	C₂⁴	C₂²×#120	1	4	yes	—
943	C₂⁴	C₂²×#120	1	8	yes	—
944	C₂⁴	C₂²×#120	1	4	yes	—
945	C₂⁴	C₂²×#120	1	2	yes	—
946	C₂⁴	C₂²×#120	1	2	yes	—
947	C₂⁴	C₂×#534	1	2	yes	—
948	C₂⁴	C₂×#534	1	2	yes	—
949	C₂⁴	C₂×#534	1	1	yes	characteristic
950	C₂⁴	C₂×#534	1	1	yes	characteristic
951	C₂⁴	C₂×D₄²	1	2	yes	—
952	C₂⁴	C₂×D₄²	1	2	yes	—
953	C₂⁴	C₂×D₄²	1	2	yes	—
954	C₂⁴	#3484	1	4	yes	—
955	C₂⁴	#3496	1	2	yes	—
956	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
957	C₂×Q₈	C₂×D₄²	1	8	yes	—
958	C₂×D₄	C₂×D₄²	1	8	yes	—
959	C₂²×C₄	#2403	1	2	yes	—
960	C₂²×C₄	#2403	1	2	yes	—
961	C₂²×C₄	#2403	1	4	yes	—
962	C₂²×C₄	#2403	1	4	yes	—
963	C₂²×C₄	#2403	1	4	yes	—
964	C₂²×C₄	#2403	1	4	yes	—
965	C₂²×C₄	#2403	1	4	yes	—
966	C₂²×C₄	#2403	1	4	yes	—
967	C₂²×C₄	#2403	1	2	yes	—
968	C₂²×C₄	#2403	1	4	yes	—
969	C₂²×C₄	#2403	1	2	yes	—
970	C₂²×C₄	#2403	1	1	yes	characteristic
971	C₂²×C₄	#2403	1	2	yes	—
972	C₂²×C₄	#2403	1	1	yes	characteristic
973	C₂²×C₄	#2403	1	2	yes	—
974	C₂²×C₄	#2403	1	4	yes	—
975	C₂²×C₄	#2403	1	2	yes	—
976	C₂²×C₄	C₂²×#120	1	8	yes	—
977	C₂²×C₄	C₂²×#120	1	4	yes	—
978	C₂²×C₄	C₂²×#120	1	4	yes	—
979	C₂²×C₄	C₂²×#120	1	16	yes	—
980	C₂²×C₄	C₂²×#120	1	2	yes	—
981	C₂²×C₄	C₂²×#120	1	2	yes	—
982	C₂²×C₄	C₂×#534	1	2	yes	—
983	C₂²×C₄	C₂×#534	1	2	yes	—
984	C₂²×C₄	C₂×#534	1	1	yes	characteristic
985	C₂²×C₄	C₂×#534	1	1	yes	characteristic
986	C₂²×C₄	C₂×D₄²	1	2	yes	—
987	C₂²×C₄	C₂×D₄²	1	2	yes	—
988	C₂²×C₄	C₂×D₄²	1	4	yes	—
989	C₂²×C₄	C₂×D₄²	1	4	yes	—
990	C₂²×C₄	C₂×D₄²	1	4	yes	—
991	C₂²×C₄	C₂×D₄²	1	4	yes	—
992	C₂²×C₄	C₂×D₄²	1	2	yes	—
993	C₂²×C₄	C₂×D₄²	1	2	yes	—
994	C₂²×C₄	C₂×D₄²	1	4	yes	—
995	C₂²×C₄	C₂×D₄²	1	2	yes	—
996	C₂²×C₄	C₂×D₄²	1	2	yes	—
997	C₂²×C₄	C₂×D₄²	1	4	yes	—
998	C₂²×C₄	C₂×D₄²	1	2	yes	—
999	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1000	C₂²×C₄	C₂×D₄²	1	2	yes	—
1001	C₂²×C₄	C₂×D₄²	1	2	yes	—
1002	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1003	C₂²×C₄	C₂×D₄²	1	2	yes	—
1004	C₂²×C₄	C₂×D₄²	1	2	yes	—
1005	C₂²×C₄	C₂×D₄²	1	2	yes	—
1006	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1007	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1008	C₂²×C₄	C₂×D₄²	1	2	yes	—
1009	C₂²×C₄	C₂×D₄²	1	4	yes	—
1010	C₂²×C₄	C₂×D₄²	1	4	yes	—
1011	C₂²×C₄	C₂×D₄²	1	4	yes	—
1012	C₂²×C₄	C₂×D₄²	1	4	yes	—
1013	C₂²×C₄	#3484	1	2	yes	—
1014	C₂²×C₄	#3484	1	2	yes	—
1015	C₂²×C₄	#3484	1	4	yes	—
1016	C₂²×C₄	#3484	1	4	yes	—
1017	C₂²×C₄	#3484	1	4	yes	—
1018	C₂²×C₄	#3484	1	4	yes	—
1019	C₂²×C₄	#3484	1	4	yes	—
1020	C₂²×C₄	#3484	1	4	yes	—
1021	C₂²×C₄	#3484	1	4	yes	—
1022	C₂²×C₄	#3488	1	2	yes	—
1023	C₂²×C₄	#3488	1	2	yes	—
1024	C₂²×C₄	#3488	1	4	yes	—
1025	C₂²×C₄	#3488	1	4	yes	—
1026	C₂²×C₄	#3496	1	2	yes	—
1027	C₂²×C₄	#3496	1	4	yes	—
1028	C₂²×C₄	#3496	1	4	yes	—
1029	C₂²×C₄	#3498	1	4	yes	—
1030	C₂²×C₄	#3498	1	4	yes	—
1031	C₂²×C₄	#3532	1	2	yes	—
1032	C₂²×C₄	#3532	1	2	yes	—
1033	C₂²×C₄	#3534	1	2	yes	—
1034	C₂²×C₄	#3534	1	2	yes	—
1035	C₂²×C₄	#3537	1	2	yes	—
1036	C₂²×C₄	#3537	1	2	yes	—
1037	C₂²×C₄	#3537	1	4	yes	—
1038	C₂²×C₄	#3537	1	4	yes	—
1039	C₂²×C₄	#3543	1	2	yes	—
1040	C₂²×C₄	#3543	1	2	yes	—
1041	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
1042	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
1043	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
1048	C₂²×C₄	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
1050	C₂²×C₄	C₂×#585	1	1	yes	characteristic
1051	C₄²	C₂×D₄²	1	16	yes	—
1052	C₂³	C₂×#2403	1	4	yes	—
1053	C₂³	C₂×#2403	1	2	yes	—
1054	C₂³	C₂×#2403	1	2	yes	—
1055	C₂³	C₂×#2403	1	1	yes	characteristic
1056	C₂³	C₂×#2403	1	2	yes	—
1057	C₂³	C₂×#2403	1	1	yes	characteristic
1058	C₂³	#35680	1	4	yes	—
1059	C₂³	#35680	1	4	yes	—
1060	C₂³	D₄×#120	1	4	yes	—
1061	C₂³	D₄×#120	1	4	yes	—
1062	C₂³	#37672	1	2	yes	—
1063	C₂³	#37672	1	2	yes	—
1064	C₂³	#40584	1	2	yes	—
1065	C₂³	#40584	1	2	yes	—
1066	C₂³	C₂³×#120	1	2	yes	—
1067	C₂³	C₂²×#534	1	1	yes	characteristic
1068	C₂³	C₂²×D₄²	1	1	yes	characteristic
1069	C₂³	C₂×#3484	1	2	yes	—
1070	C₂³	C₂×#3496	1	1	yes	characteristic
1071	C₂×C₄	C₂×#2403	1	2	yes	—
1072	C₂×C₄	C₂×#2403	1	4	yes	—
1073	C₂×C₄	C₂×#2403	1	2	yes	—
1074	C₂×C₄	C₂×#2403	1	2	yes	—
1075	C₂×C₄	C₂×#2403	1	1	yes	characteristic
1076	C₂×C₄	C₂×#2403	1	1	yes	characteristic
1077	C₂×C₄	#35680	1	4	yes	—
1078	C₂×C₄	#35680	1	4	yes	—
1079	C₂×C₄	D₄×#120	1	4	yes	—
1080	C₂×C₄	D₄×#120	1	4	yes	—
1081	C₂×C₄	#37672	1	2	yes	—
1082	C₂×C₄	#37672	1	2	yes	—
1083	C₂×C₄	#40584	1	2	yes	—
1084	C₂×C₄	#40584	1	2	yes	—
1085	C₂×C₄	#42996	1	2	yes	—
1086	C₂×C₄	#42996	1	4	yes	—
1087	C₂×C₄	#42996	1	2	yes	—
1088	C₂×C₄	#43001	1	4	yes	—
1089	C₂×C₄	#43001	1	4	yes	—
1090	C₂×C₄	#43001	1	4	yes	—
1091	C₂×C₄	#43001	1	4	yes	—
1092	C₂×C₄	#43098	1	2	yes	—
1093	C₂×C₄	#43098	1	4	yes	—
1094	C₂×C₄	#43098	1	2	yes	—
1095	C₂×C₄	#58990	1	2	yes	—
1096	C₂×C₄	#58990	1	2	yes	—
1097	C₂×C₄	#58990	1	4	yes	—
1098	C₂×C₄	#58997	1	4	yes	—
1099	C₂×C₄	#58997	1	4	yes	—
1100	C₂×C₄	#58997	1	4	yes	—
1101	C₂×C₄	#58997	1	4	yes	—
1102	C₂×C₄	#59126	1	2	yes	—
1103	C₂×C₄	#59126	1	2	yes	—
1104	C₂×C₄	#59126	1	4	yes	—
1105	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄²	1	2	yes	—
1107	C₂×C₄	C₂²×D₄²	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄²	1	2	yes	—
1109	C₂×C₄	C₂²×D₄²	1	2	yes	—
1110	C₂×C₄	C₂×#3532	1	1	yes	characteristic
1111	C₂×C₄	C₂×#3534	1	1	yes	characteristic
1112	C₂×C₄	C₂×#3537	1	1	yes	characteristic
1113	C₂×C₄	C₂×#3537	1	2	yes	—
1114	C₂×C₄	C₂×#3543	1	1	yes	characteristic
1115	C₂×C₄	C₂×#3484	1	1	yes	characteristic
1116	C₂×C₄	C₂×#3484	1	2	yes	—
1117	C₂×C₄	C₂×#3484	1	2	yes	—
1118	C₂×C₄	C₂×#3484	1	2	yes	—
1119	C₂×C₄	C₂×#3496	1	2	yes	—
1120	C₂×C₄	C₂×#3488	1	2	yes	—
1121	C₂×C₄	C₂×#3488	1	1	yes	characteristic
1122	C₂×C₄	C₂×#3498	1	2	yes	—
1123	C₂²	#772778	1	2	yes	—
1124	C₂²	#772778	1	4	yes	—
1125	C₂²	#772778	1	2	yes	—
1126	C₂²	#6437463	1	4	yes	complemented
1127	C₂²	C₂²×#2403	1	1	yes	characteristic
1128	C₂²	C₂×#35680	1	2	yes	—
1129	C₂²	C₂×D₄×#120	1	2	yes	—
1130	C₂²	C₂×#37672	1	1	yes	characteristic
1131	C₂²	C₂×#40584	1	1	yes	characteristic
1132	C₄	#772778	1	2	yes	—
1133	C₄	#772778	1	4	yes	—
1134	C₄	#772778	1	2	yes	—
1135	C₄	C₂×#58990	1	1	yes	characteristic
1136	C₄	C₂×#58997	1	2	yes	—
1137	C₄	C₂×#59126	1	1	yes	characteristic
1138	C₄	C₂×#42996	1	1	yes	characteristic
1139	C₄	C₂×#43001	1	2	yes	—
1140	C₄	C₂×#43098	1	1	yes	characteristic
1141	C₂	C₂×#772778	1	1	yes	characteristic
1142	C₂	C₂×#6437463	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#2403
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
socle	C₂²	C₂²×#2403
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72312612	C₂	semidirect
2. #72312596	C₂	semidirect
3. #72312590	C₂	semidirect
4. #72312585	C₂	semidirect
5. #72312580	C₂	semidirect
6. #72312574	C₂	semidirect
7. #72312566	C₂	semidirect
8. #72312562	C₂	semidirect
9. #72312550	C₂	semidirect
10. #72312539	C₂	semidirect
11. #72312528	C₂	semidirect
12. #72312522	C₂	semidirect
13. #72312515	C₂	semidirect
14. #72312508	C₂	semidirect
15. #72312497	C₂	semidirect
16. #72312492	C₂	semidirect
17. #72268516	C₂	semidirect
18. #72249727	C₂	semidirect
19. C₂³×#2010	C₂	semidirect
20. C₂×#6437463	C₂	semidirect
21. C₂×#394195	C₂	semidirect
22. C₂×#393988	C₂	semidirect
23. C₂³×#575	C₂²	semidirect
24. C₂×#62811	C₂²	semidirect
25. C₂×#62811	C₂²	semidirect
27. C₂³×#525	C₂²	semidirect
28. C₂×#60444	C₂²	semidirect
29. C₂×#60387	C₂²	semidirect
30. C₂×#60387	C₂²	semidirect
31. C₂×#60387	C₂²	semidirect
32. C₂×#60359	C₂²	semidirect
33. C₂³×#407	C₂²	semidirect
34. C₂³×#421	C₂²	semidirect
35. #7672320	C₂²	semidirect
36. #7672135	C₂²	semidirect
37. #7671870	C₂²	semidirect
38. #7671478	C₂²	semidirect
39. C₂×#36614	C₂²	semidirect
40. #7629144	C₂²	semidirect
41. #7629122	C₂²	semidirect
42. #7629122	C₂²	semidirect
43. #7629120	C₂²	semidirect
45. #7628650	C₂²	semidirect
47. #7628649	C₂²	semidirect
48. #7625530	C₂²	semidirect
49. #7625530	C₂²	semidirect
50. #6437932	C₂²	semidirect
51. #6437931	C₂²	semidirect
52. #6437474	C₂²	semidirect
53. #6437473	C₂²	semidirect
54. C₂×#23899	C₂²	semidirect
55. C₂×#23898	C₂²	semidirect
56. C₂×#23897	C₂²	semidirect
57. #6431889	C₂²	semidirect
58. #6431881	C₂²	semidirect
60. C₂²×#2010	C₂²	semidirect
61. C₂²×#2010	C₂²	semidirect
62. C₂²×#2010	C₂²	semidirect
63. C₂²×#2010	C₂²	semidirect
64. C₂²×#2010	C₂²	semidirect
65. C₂²×#2010	C₂²	semidirect
66. C₂²×#2010	C₂²	semidirect
67. C₂²×#2010	C₂²	semidirect
68. C₂²×#2010	C₂²	semidirect
69. C₂²×#2010	C₂²	semidirect
70. C₂²×#2010	C₂²	semidirect
71. C₂²×#2010	C₂²	semidirect
72. C₂²×#2010	C₂²	semidirect
73. #6431733	C₂²	semidirect
74. #6431733	C₂²	semidirect
75. #6431733	C₂²	semidirect
76. #6431722	C₂²	semidirect
77. #6431722	C₂²	semidirect
78. #6431722	C₂²	semidirect
79. C₂×#21012	C₂²	semidirect
80. C₂×#21012	C₂²	semidirect
81. C₂×#21012	C₂²	semidirect
82. C₂×#20989	C₂²	semidirect
83. C₂×#20989	C₂²	semidirect
84. C₂×#20979	C₂²	semidirect
85. #6371439	C₂²	semidirect
86. #6371439	C₂²	semidirect
87. #6371439	C₂²	semidirect
88. C₂×#20902	C₂²	semidirect
89. #6371298	C₂²	semidirect
90. #6370746	C₂²	semidirect
91. C₂×#20605	C₂²	semidirect
92. C₂×#20591	C₂²	semidirect
93. C₂×#20591	C₂²	semidirect
94. C₂×#20579	C₂²	semidirect
95. C₂³×H(3,ℤ/4)	C₂²	semidirect
96. #454357	C₂²	semidirect
97. #454356	C₂²	semidirect
98. #453976	C₂²	semidirect
99. #453975	C₂²	semidirect
100. #453974	C₂²	semidirect
101. #422791	C₂²	semidirect
102. #422790	C₂²	semidirect
103. #418427	C₂²	semidirect
104. #418426	C₂²	semidirect
105. #417820	C₂²	semidirect
106. #417819	C₂²	semidirect
107. #417559	C₂²	semidirect
108. #417558	C₂²	semidirect
109. #395124	C₂²	semidirect
110. #395123	C₂²	semidirect
111. #394195	C₂²	semidirect
112. #394195	C₂²	semidirect
113. #393988	C₂²	semidirect
114. #393988	C₂²	semidirect
115. #393978	C₂²	semidirect
116. #393977	C₂²	semidirect
117. #393976	C₂²	semidirect
118. #393975	C₂²	semidirect
119. #375779	C₂²	semidirect
120. #375778	C₂²	semidirect
121. #368730	C₂²	semidirect
122. #368729	C₂²	semidirect
123. #364423	C₂²	semidirect
124. #364422	C₂²	semidirect
125. #359438	C₂²	semidirect
126. #359437	C₂²	semidirect
127. #359436	C₂²	semidirect
128. #358017	C₂²	semidirect
129. #357879	C₂²	semidirect
130. C₂×#11100	C₂²	semidirect
131. C₂×#11100	C₂²	semidirect
132. #357648	C₂²	semidirect
133. #357648	C₂²	semidirect
134. #357648	C₂²	semidirect
135. C₂×#10994	C₂²	semidirect
136. C₂×#10994	C₂²	semidirect
137. C₂×#10994	C₂²	semidirect
138. C₂×#10994	C₂²	semidirect
139. C₂×#10994	C₂²	semidirect
140. C₂×#10994	C₂²	semidirect
141. #357478	C₂²	semidirect
142. #357478	C₂²	semidirect
143. #357478	C₂²	semidirect
144. #357426	C₂²	semidirect
145. #357426	C₂²	semidirect
146. #354040	C₂²	semidirect
147. #354040	C₂²	semidirect
148. #354040	C₂²	semidirect
149. #353902	C₂²	semidirect
150. #353420	C₂²	semidirect
151. #353319	C₂²	semidirect
152. #353319	C₂²	semidirect
153. C₂×#10717	C₂²	semidirect
154. C₂×#10716	C₂²	semidirect
170. C₂×#3487	C₂³	semidirect
171. C₂×#3486	C₂³	semidirect
172. C₂×#3485	C₂³	semidirect
173. C₂×#3484	C₂³	semidirect
204. C₂×#3020	C₂³	semidirect
205. C₂×#3020	C₂³	semidirect
206. C₂×#3020	C₂³	semidirect
207. C₂×#3019	C₂³	semidirect
208. C₂×#3019	C₂³	semidirect
209. C₂×#3019	C₂³	semidirect
242. #36624	D₄	semidirect
245. #35661	C₂³	semidirect
246. #35659	C₂³	semidirect
247. #35634	C₂³	semidirect
248. #35633	C₂³	semidirect
249. #35565	C₂³	semidirect
250. #35563	C₂³	semidirect
251. #35514	C₂³	semidirect
252. #35512	C₂³	semidirect
253. #35306	D₄	semidirect
256. #35252	D₄	semidirect
259. #35242	D₄	semidirect
260. #35242	C₂³	semidirect
261. #35223	C₂³	semidirect
262. #35222	D₄	semidirect
263. #35222	C₂³	semidirect
264. #35150	C₂³	semidirect
265. #35149	D₄	semidirect
266. #35149	D₄	semidirect
267. #35149	C₂³	semidirect
268. #35149	C₂³	semidirect
269. #34738	D₄	semidirect
270. #34633	D₄	semidirect
273. #34201	C₂³	semidirect
274. #34200	C₂³	semidirect
286. #23499	C₂³	semidirect
287. #23494	C₂³	semidirect
288. #23493	C₂³	semidirect
289. C₂×#2010	D₄	semidirect
299. C₂×#2010	C₂³	semidirect
300. C₂×#2010	C₂³	semidirect
301. C₂×#2010	C₂³	semidirect
302. C₂×#2010	C₂³	semidirect
303. C₂×#2010	C₂³	semidirect
304. C₂×#2010	C₂³	semidirect
305. C₂×#2010	C₂³	semidirect
306. C₂×#2010	C₂³	semidirect
307. C₂×#2010	C₂³	semidirect
308. #23409	C₂³	semidirect
309. #23409	C₂³	semidirect
310. #23409	C₂³	semidirect
311. #23403	C₂³	semidirect
312. #23403	C₂³	semidirect
313. #23403	C₂³	semidirect
314. #23402	C₂³	semidirect
315. #23402	C₂³	semidirect
316. #23402	C₂³	semidirect
317. C₂×#1912	C₂³	semidirect
318. C₂×#1912	C₂³	semidirect
319. C₂×#1912	C₂³	semidirect
320. C₂×#1911	C₂³	semidirect
321. C₂×#1911	C₂³	semidirect
322. C₂×#1911	C₂³	semidirect
328. #20943	C₂³	semidirect
329. #20943	C₂³	semidirect
330. #20943	C₂³	semidirect
332. #20864	C₂³	semidirect
333. #20617	C₂³	semidirect
334. #20616	C₂³	semidirect
336. C₂×#1785	C₂³	semidirect
337. C₂×#1785	C₂³	semidirect
338. C₂×#1784	C₂³	semidirect
339. C₂×#1784	C₂³	semidirect
340. C₂×#1783	C₂³	semidirect
341. C₂×#1783	C₂³	semidirect
363. #11224	C₂³	semidirect
364. #11156	C₂³	semidirect
365. #11155	C₂³	semidirect
366. #11100	C₂³	semidirect
367. #11100	C₂³	semidirect
368. #11100	C₂³	semidirect
369. #11072	C₂³	semidirect
370. #11072	C₂³	semidirect
371. #11072	C₂³	semidirect
372. #10994	C₂³	semidirect
373. #10994	C₂³	semidirect
374. #10994	C₂³	semidirect
375. #10994	C₂³	semidirect
376. #10994	C₂³	semidirect
377. #10994	C₂³	semidirect
378. #10994	C₂³	semidirect
379. #10994	C₂³	semidirect
380. #10994	C₂³	semidirect
381. #10990	C₂³	semidirect
382. #10990	C₂³	semidirect
383. #10990	C₂³	semidirect
384. #10989	C₂³	semidirect
385. #10989	C₂³	semidirect
386. #10989	C₂³	semidirect
387. #10968	C₂³	semidirect
388. #10968	C₂³	semidirect
389. #10967	C₂³	semidirect
390. #10967	C₂³	semidirect
391. #10949	C₂³	semidirect
392. #10949	C₂³	semidirect
393. #10949	C₂³	semidirect
394. #10888	C₂³	semidirect
395. #10741	C₂³	semidirect
396. #10740	C₂³	semidirect
397. #10728	C₂³	semidirect
398. #10728	C₂³	semidirect
399. #10727	C₂³	semidirect
400. #10727	C₂³	semidirect
408. C₂³×#41	C₂×D₄	semidirect
409. C₂³×#41	C₂×D₄	semidirect
410. C₂³×#41	C₂×D₄	semidirect
417. C₂⁴×Q₈	C₂×D₄	semidirect
421. C₂⁴×D₄	C₂×D₄	semidirect
434. C₂×#575	C₂×D₄	semidirect
450. C₂×#536	C₂×D₄	semidirect
451. C₂×#536	C₂×D₄	semidirect
452. C₂×#536	C₂×D₄	semidirect
457. C₂×#535	C₂×D₄	semidirect
458. C₂×#535	C₂×D₄	semidirect
459. C₂×#535	C₂×D₄	semidirect
464. C₂×#532	C₂×D₄	semidirect
465. C₂×#532	C₂×D₄	semidirect
466. C₂×#532	C₂×D₄	semidirect
473. C₂×#525	C₂×D₄	semidirect
474. C₂×#525	C₂×D₄	semidirect
475. C₂×#525	C₂×D₄	semidirect
491. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
496. C₂²×#121	C₂×D₄	semidirect
511. C₂²×#117	C₂×D₄	semidirect
512. C₂²×#117	C₂×D₄	semidirect
527. C₂³×C₄²	C₂×D₄	semidirect
529. C₂×#421	C₂×D₄	semidirect
553. C₂×#407	C₂×D₄	semidirect
566. #2857	C₂×D₄	semidirect
567. #2856	C₂×D₄	semidirect
568. #2850	C₂×D₄	semidirect
569. #2850	C₂×D₄	semidirect
570. #2621	C₂×D₄	semidirect
571. #2620	C₂×D₄	semidirect
572. #2620	C₂×D₄	semidirect
573. #2619	C₂×D₄	semidirect
574. #2436	C₂×D₄	semidirect
575. #2435	C₂×D₄	semidirect
576. #2434	C₂×D₄	semidirect
577. #2433	C₂×D₄	semidirect
578. #2432	C₂×D₄	semidirect
579. #2432	C₂×D₄	semidirect
580. #2431	C₂×D₄	semidirect
581. #2431	C₂×D₄	semidirect
582. #2317	C₂×D₄	semidirect
585. #2311	C₂×D₄	semidirect
589. #2310	C₂×D₄	semidirect
590. #2310	C₂×D₄	semidirect
591. #2310	C₂×D₄	semidirect
594. #2309	C₂×D₄	semidirect
595. #2309	C₂×D₄	semidirect
596. #2309	C₂×D₄	semidirect
599. #2297	C₂×D₄	semidirect
600. #2297	C₂×D₄	semidirect
601. #2297	C₂×D₄	semidirect
602. #2297	C₂×D₄	semidirect
603. #2285	C₂×D₄	semidirect
604. #2280	C₂×D₄	semidirect
605. #2280	C₂×D₄	semidirect
611. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
612. #2010	C₂×D₄	semidirect
613. #2010	C₂×D₄	semidirect
622. C₂×H(3,ℤ/4)	C₂×D₄	semidirect
715. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
716. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
717. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
718. C₂×#127	C₂²×D₄	semidirect
719. C₂×#127	C₂²×D₄	semidirect
720. C₂×#127	C₂²×D₄	semidirect
721. C₂×#124	C₂²×D₄	semidirect
722. C₂×#124	C₂²×D₄	semidirect
723. C₂×#124	C₂²×D₄	semidirect
724. C₂×#124	C₂²×D₄	semidirect
725. C₂×#124	C₂²×D₄	semidirect
726. C₂×#124	C₂²×D₄	semidirect
789. #391	C₂²×D₄	semidirect
790. #391	C₂²×D₄	semidirect
791. #391	C₂²×D₄	semidirect
792. #391	C₂²×D₄	semidirect
793. #390	C₂²×D₄	semidirect
794. #390	C₂²×D₄	semidirect
795. #390	C₂²×D₄	semidirect
796. #390	C₂²×D₄	semidirect
797. #384	C₂²×D₄	semidirect
798. #382	C₂²×D₄	semidirect
815. C₂×#41	D₄²	semidirect
818. C₂²×Q₈	D₄²	semidirect
828. C₂²×D₄	D₄²	semidirect
914. #117	D₄²	semidirect
930. C₂×C₄²	D₄²	semidirect
1126. C₂²	#6437463	semidirect

Maximal subgroups

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

subgroup	index
#72312612	2
#72312596	2
#72312590	2
#72312585	2
#72312580	2
#72312574	2
#72312566	2
#72312562	2
#72312550	2
#72312539	2
#72312528	2
#72312522	2
#72312515	2
#72312508	2
#72312497	2
#72312492	2
#72268516	2
#72249727	2
C₂³×#2010	2
C₂×#6437463	2
C₂×#394195	2
C₂×#393988	2