Subgroups — #72311718

Order 2048.

At least 7896 conjugacy classes of subgroups; only the 5264 normal subgroups are shown.

The subgroup lattice has 967 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311704	C₂	1	1	yes	maximal, characteristic, complemented
2	#72311701	C₂	1	1	yes	maximal, characteristic, complemented
3	#72311691	C₂	1	1	yes	maximal, characteristic, complemented
4	#72311678	C₂	1	4	yes	maximal, complemented
5	#72311661	C₂	1	8	yes	maximal, complemented
6	#72311653	C₂	1	8	yes	maximal, complemented
7	#72311641	C₂	1	8	yes	maximal, complemented
8	#72311631	C₂	1	16	yes	maximal, complemented
9	#72308125	C₂	1	4	yes	maximal, complemented
10	C₂³×#3109	C₂	1	1	yes	maximal, characteristic, complemented
11	#72264565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#6346637	C₂	1	2	yes	maximal, complemented
13	#72250438	C₂	1	2	yes	maximal, complemented
14	#72249998	C₂	1	2	yes	maximal, complemented
15	#72249980	C₂	1	2	yes	maximal, complemented
16	C₂×#6629283	C₂	1	1	yes	maximal, characteristic, complemented
17	#72237121	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#62812	C₂²	1	1	yes	characteristic, complemented
19	C₂³×#532	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×#3109	C₂²	1	2	yes	—
22	C₂²×#3109	C₂²	1	8	yes	complemented
23	C₂²×#3109	C₂²	1	8	yes	complemented
24	C₂²×#3109	C₂²	1	4	yes	complemented
25	C₂²×#3109	C₂²	1	2	yes	complemented
26	C₂²×#3109	C₂²	1	2	yes	complemented
27	C₂³×#481	C₂²	1	2	yes	complemented
28	C₂³×#447	C₂²	1	2	yes	complemented
29	C₂³×#432	C₂²	1	1	yes	characteristic, complemented
30	#7672136	C₂²	1	4	yes	complemented
31	#7671479	C₂²	1	4	yes	complemented
32	#7670725	C₂²	1	4	yes	complemented
33	#7670204	C₂²	1	4	yes	—
34	#7635132	C₂²	1	8	yes	complemented
35	C₂×#36624	C₂²	1	1	yes	characteristic
36	#7628666	C₂²	1	1	yes	characteristic, complemented
37	#7628665	C₂²	1	1	yes	characteristic, complemented
38	C₂×#34963	C₂²	1	2	yes	complemented
39	#7625531	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×#525	C₂²	1	1	yes	characteristic
41	#6629283	C₂²	1	8	yes	complemented
42	#6629283	C₂²	1	8	yes	complemented
43	C₂×#33004	C₂²	1	4	yes	complemented
44	C₂×#32979	C₂²	1	2	yes	complemented
45	C₂×#32878	C₂²	1	2	yes	complemented
46	C₂×#20738	C₂²	1	2	yes	complemented
47	C₂×#20715	C₂²	1	1	yes	characteristic, complemented
48	C₂×#18203	C₂²	1	8	yes	complemented
49	C₂×#18194	C₂²	1	8	yes	complemented
50	C₂×#18186	C₂²	1	8	yes	complemented
51	C₂×#18178	C₂²	1	8	yes	complemented
52	C₂×#18152	C₂²	1	16	yes	complemented
53	C₂×#17595	C₂²	1	2	yes	complemented
54	C₂×#17595	C₂²	1	2	yes	complemented
55	C₂×#17595	C₂²	1	2	yes	complemented
56	C₂×#17363	C₂²	1	2	yes	complemented
57	#613868	C₂²	1	8	yes	complemented
58	#613437	C₂²	1	4	yes	complemented
59	#613009	C₂²	1	2	yes	complemented
60	#612792	C₂²	1	2	yes	complemented
61	#607843	C₂²	1	4	yes	complemented
62	#607767	C₂²	1	4	yes	complemented
63	#607563	C₂²	1	1	yes	characteristic, complemented
64	#514210	C₂²	1	2	yes	complemented
65	#246143	C₂²	1	64	yes	complemented
66	#246103	C₂²	1	64	yes	complemented
67	#246052	C₂²	1	32	yes	complemented
68	#246039	C₂²	1	32	yes	complemented
69	#246012	C₂²	1	32	yes	complemented
70	#245999	C₂²	1	32	yes	complemented
71	#234605	C₂²	1	8	yes	complemented
72	#234601	C₂²	1	8	yes	complemented
73	#234559	C₂²	1	16	yes	complemented
74	#234507	C₂²	1	8	yes	complemented
75	#234499	C₂²	1	8	yes	complemented
76	#232299	C₂²	1	8	yes	complemented
77	#232292	C₂²	1	8	yes	complemented
78	#232283	C₂²	1	16	yes	complemented
79	#232247	C₂²	1	16	yes	complemented
80	#196416	C₂²	1	8	yes	complemented
81	#196407	C₂²	1	4	yes	complemented
82	#196396	C₂²	1	4	yes	complemented
83	#196377	C₂²	1	8	yes	complemented
84	#196023	C₂²	1	4	yes	complemented
85	#196022	C₂²	1	4	yes	complemented
86	#196018	C₂²	1	8	yes	complemented
87	#195942	C₂²	1	4	yes	complemented
88	#195923	C₂²	1	4	yes	complemented
89	#195225	C₂²	1	16	yes	complemented
90	#195207	C₂²	1	8	yes	complemented
91	#195202	C₂²	1	8	yes	complemented
92	#195137	C₂²	1	16	yes	complemented
93	#185051	C₂²	1	4	yes	complemented
94	#185046	C₂²	1	4	yes	complemented
95	#185043	C₂²	1	8	yes	complemented
96	#185024	C₂²	1	8	yes	complemented
97	#181754	C₂²	1	2	yes	complemented
98	#181008	C₂²	1	2	yes	complemented
99	C₂⁵×D₄	C₂³	1	1	yes	characteristic
100	C₂×#3497	C₂³	1	2	yes	complemented
101	C₂×#3496	C₂³	1	4	yes	—
102	C₂×#3496	C₂³	1	2	yes	complemented
103	C₂×#3449	C₂³	1	4	yes	complemented
104	C₂²×#532	D₄	1	2	yes	complemented
105	C₂²×#532	D₄	1	1	yes	characteristic, complemented
106	C₂²×#532	D₄	1	4	yes	complemented
107	C₂²×#532	D₄	1	1	yes	characteristic, complemented
108	C₂²×#532	D₄	1	4	yes	complemented
109	C₂²×#532	C₂³	1	1	yes	characteristic
110	C₂²×#532	C₂³	1	1	yes	characteristic
111	C₂²×#532	C₂³	1	4	yes	—
112	C₂²×#532	C₂³	1	4	yes	—
113	C₂²×#532	C₂³	1	2	yes	—
114	C₂²×#532	C₂³	1	1	yes	characteristic
115	C₂³×C₄⋊Q₈	D₄	1	1	yes	characteristic, complemented
116	C₂³×#127	D₄	1	1	yes	characteristic, complemented
117	C₂²×#525	D₄	1	1	yes	characteristic
118	C₂³×#121	C₂³	1	2	yes	—
119	C₂²×C₄×#41	C₂³	1	1	yes	characteristic
120	C₂³×C₄×D₄	D₄	1	2	yes	complemented
121	C₂³×C₄×D₄	C₂³	1	2	yes	—
122	C₂³×C₄×D₄	C₂³	1	4	yes	—
123	C₂³×C₄×D₄	C₂³	1	2	yes	—
124	C₂³×C₄×D₄	C₂³	1	4	yes	—
125	C₂⁴×C₄⋊C₄	C₂³	1	1	yes	characteristic
126	C₂⁴×C₄²	C₂³	1	1	yes	characteristic
127	C₂×#3109	D₄	1	32	yes	complemented
128	C₂×#3109	C₂³	1	8	yes	—
129	C₂×#3109	C₂³	1	32	yes	—
130	C₂×#3109	C₂³	1	8	yes	—
131	C₂×#3109	C₂³	1	8	yes	—
132	C₂×#3109	C₂³	1	8	yes	—
133	C₂×#3109	C₂³	1	8	yes	complemented
134	C₂×#3109	C₂³	1	8	yes	complemented
135	C₂²×#481	C₂³	1	4	yes	—
136	C₂²×#481	C₂³	1	16	yes	—
137	C₂²×#481	C₂³	1	4	yes	—
138	C₂²×#481	C₂³	1	4	yes	—
139	C₂²×#447	C₂³	1	4	yes	—
140	C₂²×#447	C₂³	1	16	yes	—
141	C₂²×#447	C₂³	1	4	yes	—
142	C₂²×#447	C₂³	1	4	yes	—
143	C₂²×#432	C₂³	1	2	yes	—
144	C₂²×#432	C₂³	1	4	yes	—
145	C₂²×#432	C₂³	1	2	yes	—
146	C₂²×#432	C₂³	1	4	yes	—
147	C₂²×#432	C₂³	1	2	yes	—
148	C₂³×C₂²⋊C₈	C₂³	1	2	yes	—
149	#37679	C₂³	1	16	yes	complemented
150	#37678	C₂³	1	16	yes	complemented
151	#37673	C₂³	1	16	yes	—
152	#37672	C₂³	1	16	yes	—
153	#36624	D₄	1	2	yes	complemented
154	#36624	D₄	1	2	yes	complemented
155	#36624	D₄	1	2	yes	complemented
156	#36624	D₄	1	2	yes	complemented
157	#36624	C₂³	1	4	yes	—
158	#36624	C₂³	1	4	yes	—
159	C₂×#2857	D₄	1	2	yes	complemented
160	C₂×#2856	D₄	1	2	yes	complemented
161	C₂×#2854	C₂³	1	2	yes	—
162	C₂×#2847	C₂³	1	2	yes	—
163	#35178	C₂³	1	2	yes	complemented
164	#35166	C₂³	1	4	yes	complemented
165	#35165	C₂³	1	2	yes	complemented
166	#35001	C₂³	1	4	yes	—
167	#35000	C₂³	1	4	yes	—
168	C₂×#2598	C₂³	1	8	yes	complemented
169	C₂×#2487	C₂³	1	4	yes	—
170	C₂×#2408	C₂³	1	4	yes	—
171	#34641	C₂³	1	4	yes	complemented
172	#34633	C₂³	1	4	yes	complemented
173	C₂×#2398	C₂³	1	4	yes	complemented
174	C₂×#2397	C₂³	1	4	yes	complemented
175	#34206	C₂³	1	4	yes	complemented
176	#34205	C₂³	1	4	yes	—
177	#34070	C₂³	1	4	yes	complemented
178	C₂×C₄×C₂²⋊Q₈	D₄	1	2	yes	—
179	C₂×C₄×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₂×C₄×#123	D₄	1	2	yes	—
181	C₂×C₄×#123	C₂³	1	2	yes	—
182	C₂×C₄×#121	D₄	1	2	yes	—
183	C₂×C₄×#121	D₄	1	4	yes	complemented
184	C₂×C₄×#121	C₂³	1	2	yes	—
185	C₂×C₄×#120	D₄	1	2	yes	—
186	C₂×C₄×#120	C₂³	1	2	yes	—
187	C₂×#2297	D₄	1	1	yes	characteristic
188	C₂×#2296	D₄	1	1	yes	characteristic
189	C₂×#2290	C₂³	1	4	yes	—
190	C₂×#2285	C₂³	1	1	yes	characteristic
191	C₂×#2283	C₂³	1	2	yes	—
192	C₂×#2280	D₄	1	1	yes	characteristic
193	C₂×C₄²×D₄	D₄	1	4	yes	—
194	C₂×C₄×#117	C₂³	1	1	yes	characteristic
195	#33004	C₂³	1	32	yes	complemented
196	#32979	C₂³	1	16	yes	—
197	#32878	C₂³	1	16	yes	—
198	#20738	C₂³	1	8	yes	complemented
199	#20738	C₂³	1	8	yes	complemented
200	#20715	C₂³	1	4	yes	—
201	#20715	C₂³	1	4	yes	—
202	C₂×#1824	C₂³	1	4	yes	—
203	C₂×#1817	C₂³	1	2	yes	—
204	C₂×#1786	C₂³	1	4	yes	—
205	C₂×#1779	C₂³	1	2	yes	—
206	C₂×#1616	C₂³	1	32	yes	complemented
207	C₂×#1598	C₂³	1	32	yes	complemented
208	C₂×#1613	C₂³	1	32	yes	complemented
209	C₂×#1595	C₂³	1	32	yes	complemented
210	C₂×#1519	C₂³	1	8	yes	—
211	C₂×#1519	C₂³	1	8	yes	—
212	C₂×#1519	C₂³	1	8	yes	—
213	C₂×#1514	C₂³	1	8	yes	complemented
214	C₂×#1514	C₂³	1	8	yes	complemented
215	C₂×#1514	C₂³	1	8	yes	complemented
216	C₂×#1505	C₂³	1	8	yes	complemented
217	C₂×#1505	C₂³	1	8	yes	complemented
218	C₂×#1505	C₂³	1	8	yes	complemented
219	C₂×#1467	C₂³	1	4	yes	complemented
220	C₂×#1466	C₂³	1	4	yes	complemented
221	C₂×#1464	C₂³	1	8	yes	complemented
222	C₂×#1459	C₂³	1	8	yes	—
223	#14860	C₂³	1	16	yes	complemented
224	#14843	C₂³	1	8	yes	—
225	#14796	C₂³	1	16	yes	complemented
226	#14777	C₂³	1	8	yes	—
227	#14724	C₂³	1	8	yes	—
228	#14715	C₂³	1	8	yes	—
229	#14685	C₂³	1	2	yes	—
230	#14683	C₂³	1	4	yes	—
231	#14680	C₂³	1	2	yes	—
232	#13959	C₂³	1	8	yes	complemented
233	#13924	C₂³	1	4	yes	—
234	#13902	C₂³	1	4	yes	—
235	#13847	C₂³	1	8	yes	complemented
236	#13753	C₂³	1	4	yes	—
237	#9968	C₂³	1	64	yes	complemented
238	#9962	C₂³	1	64	yes	complemented
239	#9921	C₂³	1	32	yes	complemented
240	#9920	C₂³	1	32	yes	complemented
241	#9915	C₂³	1	32	yes	complemented
242	#9914	C₂³	1	32	yes	complemented
243	#9118	C₂³	1	32	yes	complemented
244	#9113	C₂³	1	32	yes	—
245	#9086	C₂³	1	16	yes	complemented
246	#9084	C₂³	1	16	yes	complemented
247	#9081	C₂³	1	16	yes	—
248	#9079	C₂³	1	16	yes	—
249	#9045	C₂³	1	64	yes	complemented
250	#9041	C₂³	1	64	yes	complemented
251	#8332	C₂³	1	32	yes	complemented
252	#8328	C₂³	1	32	yes	—
253	#8023	C₂³	1	8	yes	—
254	#8022	C₂³	1	8	yes	complemented
255	#8018	C₂³	1	8	yes	complemented
256	#7912	C₂³	1	8	yes	complemented
257	#7910	C₂³	1	8	yes	complemented
258	#7907	C₂³	1	8	yes	—
259	C₂³×#41	C₂×D₄	1	1	yes	characteristic
260	C₂⁴×D₄	C₂×D₄	1	2	yes	—
261	C₂⁴×D₄	C₂⁴	1	2	yes	—
262	C₂⁴×D₄	C₂⁴	1	4	yes	—
263	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
264	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
265	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
266	C₂×#537	C₂⁴	1	8	yes	—
267	C₂×#534	C₂⁴	1	8	yes	—
268	C₂×#532	C₂×D₄	1	16	yes	—
269	C₂×#532	C₂×D₄	1	2	yes	—
270	C₂×#532	C₂×D₄	1	2	yes	—
271	C₂×#532	C₂×D₄	1	2	yes	—
272	C₂×#532	C₂×D₄	1	2	yes	—
273	C₂×#532	C₂×D₄	1	4	yes	—
274	C₂×#532	C₂×D₄	1	4	yes	—
275	C₂×#532	C₂×D₄	1	8	yes	—
276	C₂×#532	C₂×D₄	1	4	yes	—
277	C₂×#532	C₂×D₄	1	8	yes	—
278	C₂×#532	C₂×D₄	1	4	yes	—
279	C₂×#532	C₂×D₄	1	8	yes	—
280	C₂×#532	C₂×D₄	1	2	yes	—
281	C₂×#532	C₂×D₄	1	2	yes	—
282	C₂×#532	C₂⁴	1	2	yes	—
283	C₂×#532	C₂⁴	1	2	yes	—
284	C₂×#532	C₂⁴	1	2	yes	—
285	C₂×#532	C₂⁴	1	2	yes	—
286	C₂×#532	C₂⁴	1	8	yes	—
287	C₂×#532	C₂⁴	1	2	yes	—
288	C₂×#532	C₂⁴	1	2	yes	—
289	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄⋊Q₈	C₂×D₄	1	4	yes	—
292	C₂²×C₄⋊Q₈	C₂×D₄	1	2	yes	—
293	C₂²×C₄⋊Q₈	C₂×D₄	1	4	yes	—
294	C₂²×C₄⋊Q₈	C₂×D₄	1	1	yes	characteristic
295	C₂²×#127	C₂×D₄	1	1	yes	characteristic
296	C₂²×#127	C₂×D₄	1	1	yes	characteristic
297	C₂²×#127	C₂×D₄	1	4	yes	—
298	C₂²×#127	C₂×D₄	1	2	yes	—
299	C₂²×#127	C₂×D₄	1	4	yes	—
300	C₂²×#127	C₂×D₄	1	1	yes	characteristic
301	C₂²×#123	C₂×D₄	1	2	yes	—
302	C₂²×C₂²⋊Q₈	C₂×D₄	1	2	yes	—
303	C₂²×#121	C₂×D₄	1	2	yes	—
304	C₂²×#121	C₂×D₄	1	2	yes	—
305	C₂²×#121	C₂×D₄	1	8	yes	—
306	C₂²×#121	C₂×D₄	1	4	yes	—
307	C₂²×#121	C₂×D₄	1	2	yes	—
308	C₂²×#121	C₂⁴	1	2	yes	—
309	C₂²×#121	C₂⁴	1	2	yes	—
310	C₂²×#121	C₂⁴	1	8	yes	—
311	C₂²×#121	C₂⁴	1	2	yes	—
312	C₂²×#120	C₂×D₄	1	2	yes	—
313	C₂²×C₄×Q₈	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×Q₈	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
316	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
317	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
318	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
319	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
320	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
321	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
322	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
323	C₂²×C₄×D₄	C₂×D₄	1	2	yes	—
324	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
325	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
326	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
327	C₂²×C₄×D₄	C₂×D₄	1	16	yes	complemented
328	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
329	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
330	C₂²×C₄×D₄	C₂⁴	1	8	yes	—
331	C₂²×C₄×D₄	C₂⁴	1	2	yes	—
332	C₂²×C₄×D₄	C₂⁴	1	1	yes	characteristic
333	C₂²×#117	C₂×D₄	1	1	yes	characteristic
334	C₂²×#117	C₂×D₄	1	1	yes	characteristic
335	C₂²×#117	C₂×D₄	1	1	yes	characteristic
336	C₂²×#117	C₂⁴	1	2	yes	—
337	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₂³×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₂³×C₄⋊C₄	C₂⁴	1	4	yes	—
340	C₂³×C₄²	C₂×D₄	1	2	yes	—
341	C₂³×C₄²	C₂×D₄	1	2	yes	—
342	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
343	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
344	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
345	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
346	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
347	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
348	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
349	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
350	C₂³×C₄²	C₂×D₄	1	2	yes	—
351	C₂³×C₄²	C₂×D₄	1	2	yes	—
352	C₂³×C₄²	C₂×D₄	1	2	yes	—
353	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
354	C₂³×C₄²	C₂×D₄	1	2	yes	—
355	C₂³×C₄²	C₂×D₄	1	2	yes	—
356	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
357	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
358	C₂³×C₄²	C₂⁴	1	2	yes	—
359	C₂³×C₄²	C₂⁴	1	2	yes	—
360	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
361	#3109	C₂×D₄	1	64	yes	complemented
362	#3109	C₂×D₄	1	64	yes	complemented
363	C₂×#481	C₂×D₄	1	32	yes	complemented
364	C₂×#481	C₂⁴	1	16	yes	—
365	C₂×#481	C₂⁴	1	16	yes	—
366	C₂×#481	C₂⁴	1	16	yes	—
367	C₂×#447	C₂×D₄	1	32	yes	complemented
368	C₂×#447	C₂⁴	1	16	yes	—
369	C₂×#447	C₂⁴	1	16	yes	—
370	C₂×#447	C₂⁴	1	16	yes	—
371	C₂×#432	C₂×D₄	1	16	yes	complemented
372	C₂×#432	C₂⁴	1	4	yes	—
373	C₂×#432	C₂⁴	1	4	yes	—
374	C₂×#432	C₂⁴	1	8	yes	—
375	C₂×#432	C₂⁴	1	4	yes	—
376	C₂×#432	C₂⁴	1	4	yes	—
377	C₂²×C₂²⋊C₈	C₂⁴	1	8	yes	—
378	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
379	C₂²×C₂²⋊C₈	C₂⁴	1	4	yes	—
380	#2857	C₂×D₄	1	4	yes	—
381	#2857	C₂×D₄	1	4	yes	—
382	#2857	C₂×D₄	1	4	yes	—
383	#2857	C₂×D₄	1	4	yes	—
384	#2856	C₂×D₄	1	4	yes	—
385	#2856	C₂×D₄	1	4	yes	—
386	#2856	C₂×D₄	1	4	yes	—
387	#2856	C₂×D₄	1	4	yes	—
388	#2854	C₂×D₄	1	4	yes	—
389	#2854	C₂×D₄	1	4	yes	—
390	#2854	C₂⁴	1	8	yes	—
391	#2847	C₂×D₄	1	4	yes	—
392	#2847	C₂×D₄	1	4	yes	—
393	#2847	C₂⁴	1	8	yes	—
394	#2656	C₂⁴	1	16	yes	—
395	#2618	C₂⁴	1	8	yes	—
396	#2617	C₂⁴	1	8	yes	—
397	C₂×#400	C₂⁴	1	8	yes	—
398	C₂×#399	C₂⁴	1	8	yes	—
399	C₂×#394	C₂⁴	1	8	yes	—
400	C₂×#392	C₂⁴	1	8	yes	—
401	#2325	C₂⁴	1	16	yes	—
402	C₄×#121	C₂×D₄	1	8	yes	—
403	C₄×#121	C₂×D₄	1	8	yes	—
404	C₄×#121	C₂×D₄	1	8	yes	—
405	C₄×#121	C₂×D₄	1	8	yes	—
406	C₂×#391	C₂×D₄	1	2	yes	—
407	C₂×#390	C₂×D₄	1	4	yes	—
408	C₂×#390	C₂×D₄	1	2	yes	—
409	C₂×#389	C₂×D₄	1	4	yes	—
410	C₂×#389	C₂×D₄	1	2	yes	—
411	C₂×#389	C₂×D₄	1	2	yes	—
412	C₂×#388	C₂×D₄	1	4	yes	—
413	C₂×#388	C₂⁴	1	4	yes	—
414	C₂×#387	C₂×D₄	1	4	yes	—
415	C₂×#387	C₂⁴	1	4	yes	—
416	C₂×#386	C₂×D₄	1	2	yes	—
417	C₂×#386	C₂×D₄	1	2	yes	—
418	C₂×#386	C₂×D₄	1	4	yes	—
419	C₂×#386	C₂⁴	1	4	yes	—
420	C₂×#385	C₂×D₄	1	2	yes	—
421	C₂×#385	C₂×D₄	1	2	yes	—
422	C₂×#385	C₂×D₄	1	4	yes	—
423	C₂×#385	C₂⁴	1	4	yes	—
424	#2285	C₂×D₄	1	2	yes	—
425	#2285	C₂×D₄	1	2	yes	—
426	#2285	C₂⁴	1	2	yes	—
427	#2285	C₂⁴	1	2	yes	—
428	C₂×#384	C₂×D₄	1	2	yes	—
429	C₂×#383	C₂⁴	1	4	yes	—
430	C₂×#381	C₂×D₄	1	2	yes	—
431	C₂×#380	C₂×D₄	1	4	yes	—
432	C₂×#380	C₂×D₄	1	2	yes	—
433	C₂×#380	C₂×D₄	1	2	yes	—
434	C₂×#380	C₂⁴	1	4	yes	—
435	C₂×#380	C₂⁴	1	2	yes	—
436	C₂×#379	C₂×D₄	1	2	yes	—
437	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
438	C₂×C₄×C₄⋊C₄	C₂×D₄	1	4	yes	—
439	C₂×C₄×C₄⋊C₄	C₂×D₄	1	4	yes	—
440	C₂×C₄×C₄⋊C₄	C₂×D₄	1	2	yes	—
441	C₂×C₄×C₄⋊C₄	C₂×D₄	1	4	yes	—
442	C₂×C₄×C₄⋊C₄	C₂⁴	1	2	yes	—
443	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
444	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
445	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
446	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
447	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
448	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	—
449	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
450	C₂×C₄×C₂²⋊C₄	C₂⁴	1	2	yes	—
451	C₂×#376	C₂⁴	1	4	yes	—
452	C₂×#376	C₂⁴	1	2	yes	—
453	C₂×C₄³	C₂×D₄	1	2	yes	—
454	#1824	C₂⁴	1	16	yes	—
455	#1817	C₂⁴	1	8	yes	—
456	#1786	C₂⁴	1	16	yes	—
457	#1779	C₂⁴	1	8	yes	—
458	C₂×#327	C₂⁴	1	32	yes	—
459	C₂×#327	C₂⁴	1	32	yes	—
460	C₂×#327	C₂⁴	1	32	yes	—
461	C₂×#324	C₂⁴	1	16	yes	—
462	C₂×#323	C₂⁴	1	16	yes	—
463	#1445	C₂⁴	1	16	yes	—
464	#1438	C₂⁴	1	16	yes	—
465	#1434	C₂⁴	1	8	yes	—
466	C₂²⋊#95	C₂⁴	1	8	yes	—
467	#1294	C₂⁴	1	32	yes	—
468	#1280	C₂⁴	1	32	yes	—
469	C₂⁶	C₂²×D₄	1	1	yes	characteristic
470	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
471	C₂³×D₄	C₂²×D₄	1	2	yes	—
472	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
473	C₂³×D₄	C₂²×D₄	1	8	yes	—
474	C₂³×D₄	C₂²×D₄	1	2	yes	—
475	C₂³×D₄	C₂²×D₄	1	2	yes	—
476	C₂³×D₄	C₂²×D₄	1	4	yes	—
477	C₂³×D₄	C₂²×D₄	1	8	yes	—
478	C₂³×D₄	C₂²×D₄	1	2	yes	—
479	C₂³×D₄	C₂⁵	1	4	yes	—
480	C₂⁴×C₄	#120	1	1	yes	characteristic
481	C₂⁴×C₄	#120	1	1	yes	characteristic
482	C₂⁴×C₄	#120	1	2	yes	—
483	C₂⁴×C₄	#120	1	1	yes	characteristic
484	C₂⁴×C₄	#120	1	2	yes	—
485	C₂⁴×C₄	#120	1	2	yes	—
486	C₂⁴×C₄	#120	1	1	yes	characteristic
487	C₂⁴×C₄	#120	1	1	yes	characteristic
488	C₂⁴×C₄	#120	1	1	yes	characteristic
489	C₂⁴×C₄	#120	1	1	yes	characteristic
490	C₂⁴×C₄	#120	1	1	yes	characteristic
491	C₂⁴×C₄	#120	1	2	yes	—
492	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
493	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
494	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
495	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
496	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
497	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
498	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
499	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
500	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
501	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
502	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
503	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
504	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
505	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
506	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
507	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
508	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
509	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
510	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
511	C₂⁴×C₄	C₂⁵	1	2	yes	—
512	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
513	#532	#120	1	16	yes	complemented
514	#532	#120	1	16	yes	complemented
515	#532	C₂²×D₄	1	16	yes	—
516	#532	C₂²×D₄	1	16	yes	—
517	C₂×C₄⋊Q₈	#120	1	8	yes	complemented
518	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
519	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
520	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
521	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
522	C₂×C₄⋊Q₈	C₂²×D₄	1	8	yes	—
523	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
524	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	—
525	C₂×#127	#120	1	8	yes	complemented
526	C₂×#127	C₂²×D₄	1	2	yes	—
527	C₂×#127	C₂²×D₄	1	2	yes	—
528	C₂×#127	C₂²×D₄	1	2	yes	—
529	C₂×#127	C₂²×D₄	1	2	yes	—
530	C₂×#127	C₂²×D₄	1	8	yes	—
531	C₂×#127	C₂²×D₄	1	2	yes	—
532	C₂×#127	C₂²×D₄	1	2	yes	—
533	C₂×#121	C₂²×D₄	1	16	yes	—
534	C₂×#121	C₂²×D₄	1	4	yes	—
535	C₂×#121	C₂²×D₄	1	4	yes	—
536	C₂×#121	C₂²×D₄	1	8	yes	—
537	C₂×#121	C₂²×D₄	1	8	yes	—
538	C₂×#121	C₂²×D₄	1	4	yes	—
539	C₂×#121	C₂²×D₄	1	8	yes	—
540	C₂×#121	C₂²×D₄	1	8	yes	—
541	C₂×#121	C₂⁵	1	4	yes	—
542	C₂×#121	C₂⁵	1	4	yes	—
543	C₂×#121	C₂⁵	1	4	yes	—
544	C₂×#120	AGL(1,ℤ/8)	1	16	yes	—
545	C₂×C₄×D₄	#120	1	16	yes	complemented
546	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
547	C₂×C₄×D₄	C₂²×D₄	1	16	yes	—
548	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
549	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
550	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
551	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
552	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
553	C₂×C₄×D₄	C₂²×D₄	1	8	yes	—
554	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
555	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
556	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
557	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
558	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
559	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
560	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
561	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	—
562	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
563	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
564	C₂²×C₄⋊C₄	C₂²×D₄	1	8	yes	—
565	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
566	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
567	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
568	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
569	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
570	C₂²×C₄⋊C₄	C₂⁵	1	2	yes	—
571	C₂²×C₄⋊C₄	C₂⁵	1	4	yes	—
572	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
573	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
574	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
575	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
576	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
577	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
578	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
579	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
580	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
581	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
582	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
583	C₂²×C₄²	#120	1	2	yes	—
584	C₂²×C₄²	#120	1	2	yes	—
585	C₂²×C₄²	#120	1	2	yes	—
586	C₂²×C₄²	#120	1	2	yes	—
587	C₂²×C₄²	#120	1	1	yes	characteristic
588	C₂²×C₄²	#120	1	1	yes	characteristic
589	C₂²×C₄²	#120	1	1	yes	characteristic
590	C₂²×C₄²	#120	1	1	yes	characteristic
591	C₂²×C₄²	#120	1	2	yes	—
592	C₂²×C₄²	#120	1	2	yes	—
593	C₂²×C₄²	#120	1	2	yes	—
594	C₂²×C₄²	#120	1	2	yes	—
595	C₂²×C₄²	#120	1	2	yes	—
596	C₂²×C₄²	#120	1	2	yes	—
597	C₂²×C₄²	#120	1	1	yes	characteristic
598	C₂²×C₄²	#120	1	1	yes	characteristic
599	C₂²×C₄²	#120	1	1	yes	characteristic
600	C₂²×C₄²	#120	1	2	yes	—
601	C₂²×C₄²	#120	1	1	yes	characteristic
602	C₂²×C₄²	#120	1	2	yes	—
603	C₂²×C₄²	#120	1	2	yes	—
604	C₂²×C₄²	#120	1	2	yes	—
605	C₂²×C₄²	#120	1	2	yes	—
606	C₂²×C₄²	#120	1	2	yes	—
607	C₂²×C₄²	#120	1	2	yes	—
608	C₂²×C₄²	#120	1	2	yes	—
609	C₂²×C₄²	#120	1	2	yes	—
610	C₂²×C₄²	#120	1	2	yes	—
611	C₂²×C₄²	C₂²×D₄	1	2	yes	—
612	C₂²×C₄²	C₂²×D₄	1	2	yes	—
613	C₂²×C₄²	C₂²×D₄	1	2	yes	—
614	C₂²×C₄²	C₂²×D₄	1	2	yes	—
615	C₂²×C₄²	C₂²×D₄	1	2	yes	—
616	C₂²×C₄²	C₂²×D₄	1	2	yes	—
617	C₂²×C₄²	C₂²×D₄	1	2	yes	—
618	C₂²×C₄²	C₂²×D₄	1	2	yes	—
619	C₂²×C₄²	C₂²×D₄	1	2	yes	—
620	C₂²×C₄²	C₂²×D₄	1	2	yes	—
621	C₂²×C₄²	C₂²×D₄	1	2	yes	—
622	C₂²×C₄²	C₂²×D₄	1	2	yes	—
623	C₂²×C₄²	C₂²×D₄	1	2	yes	—
624	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
625	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
626	C₂²×C₄²	C₂²×D₄	1	2	yes	—
627	C₂²×C₄²	C₂²×D₄	1	2	yes	—
628	C₂²×C₄²	C₂²×D₄	1	2	yes	—
629	C₂²×C₄²	C₂²×D₄	1	2	yes	—
630	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
631	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
632	C₂²×C₄²	C₂²×D₄	1	2	yes	—
633	C₂²×C₄²	C₂²×D₄	1	2	yes	—
634	C₂²×C₄²	C₂²×D₄	1	2	yes	—
635	C₂²×C₄²	C₂²×D₄	1	2	yes	—
636	C₂²×C₄²	C₂²×D₄	1	2	yes	—
637	C₂²×C₄²	C₂²×D₄	1	2	yes	—
638	C₂²×C₄²	C₂²×D₄	1	2	yes	—
639	C₂²×C₄²	C₂²×D₄	1	2	yes	—
640	C₂²×C₄²	C₂²×D₄	1	2	yes	—
641	C₂²×C₄²	C₂²×D₄	1	2	yes	—
642	C₂²×C₄²	C₂²×D₄	1	4	yes	—
643	C₂²×C₄²	C₂²×D₄	1	4	yes	—
644	C₂²×C₄²	C₂²×D₄	1	2	yes	—
645	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
646	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
647	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
648	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
649	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
650	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
651	C₂²×C₄²	C₂²×D₄	1	8	yes	—
652	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
653	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
654	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
655	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
656	C₂²×C₄²	H(5,𝔽₂)	1	8	yes	—
657	C₂²×C₄²	C₂⁵	1	2	yes	—
658	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
659	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
660	#481	C₂²×D₄	1	64	yes	—
661	#447	C₂²×D₄	1	64	yes	—
662	#432	C₂²×D₄	1	16	yes	—
663	#432	C₂²×D₄	1	16	yes	—
664	C₂×C₂²⋊C₈	C₂²×D₄	1	16	yes	—
665	C₂×C₂²⋊C₈	C₂⁵	1	8	yes	—
666	C₂×C₂²⋊C₈	C₂⁵	1	8	yes	—
667	#390	C₂²×D₄	1	8	yes	—
668	#390	C₂²×D₄	1	8	yes	—
669	#389	C₂²×D₄	1	8	yes	—
670	#389	C₂²×D₄	1	8	yes	—
671	#384	C₂²×D₄	1	4	yes	—
672	#384	C₂²×D₄	1	4	yes	—
673	#380	C₂²×D₄	1	4	yes	—
674	#380	C₂²×D₄	1	8	yes	—
675	#380	C₂²×D₄	1	8	yes	—
676	#380	C₂⁵	1	4	yes	—
677	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
678	C₄×C₄⋊C₄	C₂²×D₄	1	4	yes	—
679	C₂×#95	C₂²×D₄	1	4	yes	—
680	C₂×#95	C₂²×D₄	1	4	yes	—
681	C₂×#95	C₂²×D₄	1	4	yes	—
682	C₂×#95	C₂²×D₄	1	4	yes	—
683	C₂×#95	C₂²×D₄	1	4	yes	—
684	C₂×#95	C₂²×D₄	1	4	yes	—
685	C₂×#95	C₂²×D₄	1	4	yes	—
686	C₂×#95	C₂⁵	1	8	yes	—
687	C₂×#95	C₂⁵	1	4	yes	—
688	C₂⁵	C₂×#120	1	1	yes	characteristic
689	C₂⁵	C₂×#120	1	2	yes	—
690	C₂⁵	C₂×#120	1	1	yes	characteristic
691	C₂⁵	C₂×AGL(1,ℤ/8)	1	8	yes	—
692	C₂⁵	C₂³×D₄	1	2	yes	—
693	C₂⁵	C₂³×D₄	1	2	yes	—
694	C₂⁵	C₂³×D₄	1	1	yes	characteristic
695	C₂²×D₄	C₂×#120	1	8	yes	—
696	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
697	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	16	yes	—
698	C₂²×D₄	C₂³×D₄	1	8	yes	—
699	C₂²×D₄	C₂³×D₄	1	4	yes	—
700	C₂²×D₄	C₂³×D₄	1	4	yes	—
701	C₂²×D₄	C₂³×D₄	1	4	yes	—
702	C₂³×C₄	C₂×#120	1	2	yes	—
703	C₂³×C₄	C₂×#120	1	1	yes	characteristic
704	C₂³×C₄	C₂×#120	1	1	yes	characteristic
705	C₂³×C₄	C₂×#120	1	1	yes	characteristic
706	C₂³×C₄	C₂×#120	1	1	yes	characteristic
707	C₂³×C₄	C₂×#120	1	2	yes	—
708	C₂³×C₄	C₂×#120	1	2	yes	—
709	C₂³×C₄	C₂×#120	1	2	yes	—
710	C₂³×C₄	C₂×#120	1	2	yes	—
711	C₂³×C₄	C₂×#120	1	2	yes	—
712	C₂³×C₄	C₂×#120	1	2	yes	—
713	C₂³×C₄	C₂×#120	1	2	yes	—
714	C₂³×C₄	C₂×#120	1	2	yes	—
715	C₂³×C₄	C₂×#120	1	2	yes	—
716	C₂³×C₄	C₂×#120	1	2	yes	—
717	C₂³×C₄	C₂×#120	1	2	yes	—
718	C₂³×C₄	C₂×#120	1	2	yes	—
719	C₂³×C₄	C₂×#120	1	2	yes	—
720	C₂³×C₄	C₂×#120	1	2	yes	—
721	C₂³×C₄	C₂×#120	1	2	yes	—
722	C₂³×C₄	C₂×#120	1	2	yes	—
723	C₂³×C₄	C₂×#120	1	2	yes	—
724	C₂³×C₄	C₂×#120	1	2	yes	—
725	C₂³×C₄	C₂×#120	1	2	yes	—
726	C₂³×C₄	C₂×#120	1	1	yes	characteristic
727	C₂³×C₄	C₂×#120	1	1	yes	characteristic
728	C₂³×C₄	C₂×#120	1	1	yes	characteristic
729	C₂³×C₄	C₂×#120	1	1	yes	characteristic
730	C₂³×C₄	C₂×#120	1	1	yes	characteristic
731	C₂³×C₄	C₂×#120	1	1	yes	characteristic
732	C₂³×C₄	C₂×#120	1	2	yes	—
733	C₂³×C₄	C₂×#120	1	2	yes	—
734	C₂³×C₄	C₂×#120	1	1	yes	characteristic
735	C₂³×C₄	C₂×#120	1	1	yes	characteristic
736	C₂³×C₄	C₂×#120	1	2	yes	—
737	C₂³×C₄	C₂×#120	1	1	yes	characteristic
738	C₂³×C₄	C₂×#120	1	1	yes	characteristic
739	C₂³×C₄	D₄²	1	8	yes	—
740	C₂³×C₄	D₄²	1	8	yes	—
741	C₂³×C₄	C₂³×D₄	1	2	yes	—
742	C₂³×C₄	C₂³×D₄	1	2	yes	—
743	C₂³×C₄	C₂³×D₄	1	2	yes	—
744	C₂³×C₄	C₂³×D₄	1	2	yes	—
745	C₂³×C₄	C₂³×D₄	1	2	yes	—
746	C₂³×C₄	C₂³×D₄	1	2	yes	—
747	C₂³×C₄	C₂³×D₄	1	2	yes	—
748	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
749	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
750	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
751	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
752	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
753	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
754	C₂³×C₄	C₂³×D₄	1	4	yes	—
755	C₂³×C₄	C₂³×D₄	1	2	yes	—
756	C₂³×C₄	C₂³×D₄	1	2	yes	—
757	C₂³×C₄	C₂³×D₄	1	2	yes	—
758	C₂³×C₄	C₂³×D₄	1	4	yes	—
759	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
760	C₂³×C₄	C₂³×D₄	1	4	yes	—
761	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
762	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
763	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
764	C₂³×C₄	C₂⁶	1	1	yes	characteristic
765	C₄⋊Q₈	C₂×#120	1	8	yes	—
766	C₄⋊Q₈	C₂×#120	1	8	yes	—
767	#127	C₂×#120	1	8	yes	—
768	#127	C₂×#120	1	8	yes	—
769	#121	C₂×#120	1	16	yes	—
770	#121	C₂³×D₄	1	16	yes	—
771	C₄×D₄	C₂×#120	1	16	yes	—
772	C₄×D₄	C₂×#120	1	16	yes	—
773	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
774	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
775	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
776	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
777	C₂×C₄⋊C₄	C₂³×D₄	1	4	yes	—
778	C₂×C₄⋊C₄	C₂³×D₄	1	8	yes	—
779	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	8	yes	—
780	C₂×C₂²⋊C₄	C₂×AGL(1,ℤ/8)	1	16	yes	—
781	C₂×C₄²	C₂×#120	1	2	yes	—
782	C₂×C₄²	C₂×#120	1	2	yes	—
783	C₂×C₄²	C₂×#120	1	2	yes	—
784	C₂×C₄²	C₂×#120	1	2	yes	—
785	C₂×C₄²	C₂×#120	1	2	yes	—
786	C₂×C₄²	C₂×#120	1	2	yes	—
787	C₂×C₄²	C₂×#120	1	2	yes	—
788	C₂×C₄²	C₂×#120	1	2	yes	—
789	C₂×C₄²	C₂×#120	1	2	yes	—
790	C₂×C₄²	C₂×#120	1	2	yes	—
791	C₂×C₄²	C₂×#120	1	2	yes	—
792	C₂×C₄²	C₂×#120	1	2	yes	—
793	C₂×C₄²	C₂×#120	1	2	yes	—
794	C₂×C₄²	C₂×#120	1	2	yes	—
795	C₂×C₄²	C₂×#120	1	2	yes	—
796	C₂×C₄²	C₂×#120	1	2	yes	—
797	C₂×C₄²	C₂×#120	1	2	yes	—
798	C₂×C₄²	C₂×#120	1	2	yes	—
799	C₂×C₄²	C₂×#120	1	2	yes	—
800	C₂×C₄²	C₂×#120	1	2	yes	—
801	C₂×C₄²	C₂×#120	1	1	yes	characteristic
802	C₂×C₄²	C₂×#120	1	1	yes	characteristic
803	C₂×C₄²	C₂×#120	1	1	yes	characteristic
804	C₂×C₄²	C₂×#120	1	1	yes	characteristic
805	C₂×C₄²	C₂×#120	1	1	yes	characteristic
806	C₂×C₄²	C₂×#120	1	1	yes	characteristic
807	C₂×C₄²	C₂×#120	1	1	yes	characteristic
808	C₂×C₄²	C₂×#120	1	1	yes	characteristic
809	C₂×C₄²	C₂×#120	1	4	yes	—
810	C₂×C₄²	C₂×#120	1	4	yes	—
811	C₂×C₄²	C₂×#120	1	4	yes	—
812	C₂×C₄²	C₂×#120	1	4	yes	—
813	C₂×C₄²	#534	1	4	yes	—
814	C₂×C₄²	#534	1	4	yes	—
815	C₂×C₄²	#534	1	4	yes	—
816	C₂×C₄²	#534	1	4	yes	—
817	C₂×C₄²	D₄²	1	8	yes	—
818	C₂×C₄²	D₄²	1	8	yes	—
819	C₂×C₄²	D₄²	1	8	yes	—
820	C₂×C₄²	D₄²	1	8	yes	—
821	C₂×C₄²	D₄²	1	8	yes	—
822	C₂×C₄²	D₄²	1	8	yes	—
823	C₂×C₄²	C₂³×D₄	1	2	yes	—
824	C₂×C₄²	C₂³×D₄	1	2	yes	—
825	C₂×C₄²	C₂³×D₄	1	2	yes	—
826	C₂×C₄²	C₂³×D₄	1	2	yes	—
827	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
828	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
829	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
830	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
831	C₂×C₄²	C₂³×D₄	1	4	yes	—
832	C₂×C₄²	C₂³×D₄	1	4	yes	—
833	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
834	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
835	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
836	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
837	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
838	C₂×C₄²	C₂×H(5,𝔽₂)	1	4	yes	—
839	C₂²⋊C₈	C₂³×D₄	1	16	yes	—
840	C₂⁴	#3003	1	4	yes	—
841	C₂⁴	#3003	1	8	yes	—
842	C₂⁴	#3003	1	4	yes	—
843	C₂⁴	C₂²×#120	1	2	yes	—
844	C₂⁴	C₂²×#120	1	1	yes	characteristic
845	C₂⁴	C₂²×#120	1	1	yes	characteristic
846	C₂⁴	C₂²×#120	1	2	yes	—
847	C₂⁴	C₂×D₄²	1	4	yes	—
848	C₂⁴	C₂²×AGL(1,ℤ/8)	1	8	yes	—
849	C₂⁴	C₂²×AGL(1,ℤ/8)	1	4	yes	—
850	C₂⁴	C₂²×AGL(1,ℤ/8)	1	4	yes	—
851	C₂⁴	#3585	1	4	yes	—
852	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
853	C₂×D₄	C₂²×#120	1	8	yes	—
854	C₂²×C₄	#2403	1	4	yes	—
855	C₂²×C₄	#2403	1	4	yes	—
856	C₂²×C₄	#2403	1	4	yes	—
857	C₂²×C₄	#2403	1	4	yes	—
858	C₂²×C₄	#2403	1	4	yes	—
859	C₂²×C₄	#2403	1	4	yes	—
860	C₂²×C₄	#2403	1	4	yes	—
861	C₂²×C₄	#2403	1	4	yes	—
862	C₂²×C₄	#3021	1	8	yes	—
863	C₂²×C₄	#3025	1	8	yes	—
864	C₂²×C₄	C₂²×#120	1	2	yes	—
865	C₂²×C₄	C₂²×#120	1	2	yes	—
866	C₂²×C₄	C₂²×#120	1	2	yes	—
867	C₂²×C₄	C₂²×#120	1	2	yes	—
868	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
869	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
870	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
871	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
872	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
873	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
874	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
875	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
876	C₂²×C₄	C₂²×#120	1	2	yes	—
877	C₂²×C₄	C₂²×#120	1	2	yes	—
878	C₂²×C₄	C₂²×#120	1	2	yes	—
879	C₂²×C₄	C₂²×#120	1	2	yes	—
880	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
881	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
882	C₂²×C₄	C₂×#534	1	2	yes	—
883	C₂²×C₄	C₂×#534	1	2	yes	—
884	C₂²×C₄	C₂×D₄²	1	4	yes	—
885	C₂²×C₄	C₂×D₄²	1	4	yes	—
886	C₂²×C₄	C₂×D₄²	1	4	yes	—
887	C₂²×C₄	C₂×D₄²	1	4	yes	—
888	C₂²×C₄	C₂×D₄²	1	4	yes	—
889	C₂²×C₄	C₂×D₄²	1	4	yes	—
890	C₂²×C₄	C₂×D₄²	1	4	yes	—
891	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	4	yes	—
892	C₂²×C₄	C₂²×AGL(1,ℤ/8)	1	8	yes	—
893	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
894	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
895	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
896	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
897	C₄⋊C₄	C₂²×#120	1	8	yes	—
898	C₄²	#2403	1	4	yes	—
899	C₄²	#2403	1	4	yes	—
900	C₄²	#2403	1	4	yes	—
901	C₄²	#2403	1	4	yes	—
902	C₄²	#2403	1	4	yes	—
903	C₄²	#2403	1	4	yes	—
904	C₄²	#2403	1	4	yes	—
905	C₄²	#2403	1	4	yes	—
906	C₄²	C₂²×#120	1	2	yes	—
907	C₄²	C₂²×#120	1	2	yes	—
908	C₄²	C₂²×#120	1	2	yes	—
909	C₄²	C₂²×#120	1	2	yes	—
910	C₄²	C₂×#534	1	2	yes	—
911	C₄²	C₂×#534	1	2	yes	—
912	C₄²	C₂×#534	1	2	yes	—
913	C₄²	C₂×#534	1	2	yes	—
914	C₄²	C₂×D₄²	1	4	yes	—
915	C₄²	C₂×D₄²	1	4	yes	—
916	C₄²	C₂×D₄²	1	4	yes	—
917	C₄²	C₂×D₄²	1	4	yes	—
918	C₂³	C₂×#2403	1	2	yes	—
919	C₂³	C₂×#2403	1	2	yes	—
920	C₂³	C₂×#3003	1	4	yes	—
921	C₂³	C₂×#3003	1	2	yes	—
922	C₂³	C₂×#3003	1	2	yes	—
923	C₂³	C₂×#3003	1	4	yes	—
924	C₂³	#60367	1	2	yes	—
925	C₂³	#60367	1	2	yes	—
926	C₂³	C₂×#3021	1	4	yes	—
927	C₂³	C₂×#3025	1	4	yes	—
928	C₂³	D₄×AGL(1,ℤ/8)	1	16	yes	—
929	C₂³	C₂³×#120	1	1	yes	characteristic
930	C₂³	C₂²×D₄²	1	2	yes	—
931	C₂³	C₂³×AGL(1,ℤ/8)	1	2	yes	—
932	C₂³	C₂×#3585	1	2	yes	—
933	C₂×C₄	C₂×#2403	1	2	yes	—
934	C₂×C₄	C₂×#2403	1	2	yes	—
935	C₂×C₄	C₂×#2403	1	2	yes	—
936	C₂×C₄	C₂×#2403	1	2	yes	—
937	C₂×C₄	C₂×#2403	1	2	yes	—
938	C₂×C₄	C₂×#2403	1	2	yes	—
939	C₂×C₄	C₂×#2403	1	2	yes	—
940	C₂×C₄	C₂×#2403	1	2	yes	—
941	C₂×C₄	C₂×#2403	1	2	yes	—
942	C₂×C₄	C₂×#2403	1	2	yes	—
943	C₂×C₄	C₂×#3021	1	4	yes	—
944	C₂×C₄	C₂×#3021	1	4	yes	—
945	C₂×C₄	C₂×#3025	1	4	yes	—
946	C₂×C₄	C₂×#3025	1	4	yes	—
947	C₂×C₄	C₂³×#120	1	1	yes	characteristic
948	C₂×C₄	C₂²×#534	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄²	1	2	yes	—
950	C₂²	#6346637	1	8	yes	complemented
951	C₂²	#6437510	1	4	yes	—
952	C₂²	#6437510	1	4	yes	—
953	C₂²	C₂²×#2403	1	1	yes	characteristic
954	C₂²	C₂²×#3003	1	1	yes	characteristic
955	C₂²	C₂²×#3021	1	2	yes	—
956	C₂²	C₂×#60367	1	1	yes	characteristic
957	C₂²	C₂²×#3025	1	2	yes	—
958	C₂²	C₂×D₄×AGL(1,ℤ/8)	1	4	yes	—
959	C₄	#6437475	1	4	yes	—
960	C₄	#6437616	1	4	yes	—
961	C₂	C₂×#6437510	1	1	yes	characteristic
962	C₂	C₂×#6437616	1	1	yes	characteristic
963	C₂	C₂×#6437475	1	1	yes	characteristic
964	C₂	C₂×#6346637	1	2	yes	—
965	C₂	#72307970	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂³×#120
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72311704	C₂	semidirect
2. #72311701	C₂	semidirect
3. #72311691	C₂	semidirect
4. #72311678	C₂	semidirect
5. #72311661	C₂	semidirect
6. #72311653	C₂	semidirect
7. #72311641	C₂	semidirect
8. #72311631	C₂	semidirect
9. #72308125	C₂	semidirect
10. C₂³×#3109	C₂	semidirect
11. #72264565	C₂	semidirect
12. C₂×#6346637	C₂	semidirect
13. #72250438	C₂	semidirect
14. #72249998	C₂	semidirect
15. #72249980	C₂	semidirect
16. C₂×#6629283	C₂	semidirect
17. #72237121	C₂	semidirect
18. C₂×#62812	C₂²	semidirect
20. C₂⁴×C₄×D₄	C₂²	semidirect
22. C₂²×#3109	C₂²	semidirect
23. C₂²×#3109	C₂²	semidirect
24. C₂²×#3109	C₂²	semidirect
25. C₂²×#3109	C₂²	semidirect
26. C₂²×#3109	C₂²	semidirect
27. C₂³×#481	C₂²	semidirect
28. C₂³×#447	C₂²	semidirect
29. C₂³×#432	C₂²	semidirect
30. #7672136	C₂²	semidirect
31. #7671479	C₂²	semidirect
32. #7670725	C₂²	semidirect
34. #7635132	C₂²	semidirect
36. #7628666	C₂²	semidirect
37. #7628665	C₂²	semidirect
38. C₂×#34963	C₂²	semidirect
39. #7625531	C₂²	semidirect
41. #6629283	C₂²	semidirect
42. #6629283	C₂²	semidirect
43. C₂×#33004	C₂²	semidirect
44. C₂×#32979	C₂²	semidirect
45. C₂×#32878	C₂²	semidirect
46. C₂×#20738	C₂²	semidirect
47. C₂×#20715	C₂²	semidirect
48. C₂×#18203	C₂²	semidirect
49. C₂×#18194	C₂²	semidirect
50. C₂×#18186	C₂²	semidirect
51. C₂×#18178	C₂²	semidirect
52. C₂×#18152	C₂²	semidirect
53. C₂×#17595	C₂²	semidirect
54. C₂×#17595	C₂²	semidirect
55. C₂×#17595	C₂²	semidirect
56. C₂×#17363	C₂²	semidirect
57. #613868	C₂²	semidirect
58. #613437	C₂²	semidirect
59. #613009	C₂²	semidirect
60. #612792	C₂²	semidirect
61. #607843	C₂²	semidirect
62. #607767	C₂²	semidirect
63. #607563	C₂²	semidirect
64. #514210	C₂²	semidirect
65. #246143	C₂²	semidirect
66. #246103	C₂²	semidirect
67. #246052	C₂²	semidirect
68. #246039	C₂²	semidirect
69. #246012	C₂²	semidirect
70. #245999	C₂²	semidirect
71. #234605	C₂²	semidirect
72. #234601	C₂²	semidirect
73. #234559	C₂²	semidirect
74. #234507	C₂²	semidirect
75. #234499	C₂²	semidirect
76. #232299	C₂²	semidirect
77. #232292	C₂²	semidirect
78. #232283	C₂²	semidirect
79. #232247	C₂²	semidirect
80. #196416	C₂²	semidirect
81. #196407	C₂²	semidirect
82. #196396	C₂²	semidirect
83. #196377	C₂²	semidirect
84. #196023	C₂²	semidirect
85. #196022	C₂²	semidirect
86. #196018	C₂²	semidirect
87. #195942	C₂²	semidirect
88. #195923	C₂²	semidirect
89. #195225	C₂²	semidirect
90. #195207	C₂²	semidirect
91. #195202	C₂²	semidirect
92. #195137	C₂²	semidirect
93. #185051	C₂²	semidirect
94. #185046	C₂²	semidirect
95. #185043	C₂²	semidirect
96. #185024	C₂²	semidirect
97. #181754	C₂²	semidirect
98. #181008	C₂²	semidirect
100. C₂×#3497	C₂³	semidirect
102. C₂×#3496	C₂³	semidirect
103. C₂×#3449	C₂³	semidirect
104. C₂²×#532	D₄	semidirect
105. C₂²×#532	D₄	semidirect
106. C₂²×#532	D₄	semidirect
107. C₂²×#532	D₄	semidirect
108. C₂²×#532	D₄	semidirect
115. C₂³×C₄⋊Q₈	D₄	semidirect
116. C₂³×#127	D₄	semidirect
120. C₂³×C₄×D₄	D₄	semidirect
127. C₂×#3109	D₄	semidirect
133. C₂×#3109	C₂³	semidirect
134. C₂×#3109	C₂³	semidirect
149. #37679	C₂³	semidirect
150. #37678	C₂³	semidirect
153. #36624	D₄	semidirect
154. #36624	D₄	semidirect
155. #36624	D₄	semidirect
156. #36624	D₄	semidirect
159. C₂×#2857	D₄	semidirect
160. C₂×#2856	D₄	semidirect
163. #35178	C₂³	semidirect
164. #35166	C₂³	semidirect
165. #35165	C₂³	semidirect
168. C₂×#2598	C₂³	semidirect
171. #34641	C₂³	semidirect
172. #34633	C₂³	semidirect
173. C₂×#2398	C₂³	semidirect
174. C₂×#2397	C₂³	semidirect
175. #34206	C₂³	semidirect
177. #34070	C₂³	semidirect
183. C₂×C₄×#121	D₄	semidirect
195. #33004	C₂³	semidirect
198. #20738	C₂³	semidirect
199. #20738	C₂³	semidirect
206. C₂×#1616	C₂³	semidirect
207. C₂×#1598	C₂³	semidirect
208. C₂×#1613	C₂³	semidirect
209. C₂×#1595	C₂³	semidirect
213. C₂×#1514	C₂³	semidirect
214. C₂×#1514	C₂³	semidirect
215. C₂×#1514	C₂³	semidirect
216. C₂×#1505	C₂³	semidirect
217. C₂×#1505	C₂³	semidirect
218. C₂×#1505	C₂³	semidirect
219. C₂×#1467	C₂³	semidirect
220. C₂×#1466	C₂³	semidirect
221. C₂×#1464	C₂³	semidirect
223. #14860	C₂³	semidirect
225. #14796	C₂³	semidirect
232. #13959	C₂³	semidirect
235. #13847	C₂³	semidirect
237. #9968	C₂³	semidirect
238. #9962	C₂³	semidirect
239. #9921	C₂³	semidirect
240. #9920	C₂³	semidirect
241. #9915	C₂³	semidirect
242. #9914	C₂³	semidirect
243. #9118	C₂³	semidirect
245. #9086	C₂³	semidirect
246. #9084	C₂³	semidirect
249. #9045	C₂³	semidirect
250. #9041	C₂³	semidirect
251. #8332	C₂³	semidirect
254. #8022	C₂³	semidirect
255. #8018	C₂³	semidirect
256. #7912	C₂³	semidirect
257. #7910	C₂³	semidirect
327. C₂²×C₄×D₄	C₂×D₄	semidirect
361. #3109	C₂×D₄	semidirect
362. #3109	C₂×D₄	semidirect
363. C₂×#481	C₂×D₄	semidirect
367. C₂×#447	C₂×D₄	semidirect
371. C₂×#432	C₂×D₄	semidirect
513. #532	#120	semidirect
514. #532	#120	semidirect
517. C₂×C₄⋊Q₈	#120	semidirect
525. C₂×#127	#120	semidirect
545. C₂×C₄×D₄	#120	semidirect
950. C₂²	#6346637	semidirect

Maximal subgroups

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

subgroup	index
#72311704	2
#72311701	2
#72311691	2
#72311678	2
#72311661	2
#72311653	2
#72311641	2
#72311631	2
#72308125	2
C₂³×#3109	2
#72264565	2
C₂×#6346637	2
#72250438	2
#72249998	2
#72249980	2
C₂×#6629283	2
#72237121	2