Subgroups — #72256093

Order 2048.

At least 11564 conjugacy classes of subgroups; only the 2224 normal subgroups are shown.

The subgroup lattice has 807 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72256085	C₂	1	4	yes	maximal, complemented
2	#72256081	C₂	1	4	yes	maximal, complemented
3	#72255932	C₂	1	4	yes	maximal, complemented
4	#72255890	C₂	1	4	yes	maximal, complemented
5	#72255852	C₂	1	2	yes	maximal, complemented
6	#72249537	C₂	1	1	yes	maximal, characteristic
7	#72238521	C₂	1	1	yes	maximal, characteristic, complemented
8	#72235188	C₂	1	2	yes	maximal, complemented
9	#72235168	C₂	1	4	yes	maximal, complemented
10	#72225783	C₂	1	1	yes	maximal, characteristic, complemented
11	#72218455	C₂	1	4	yes	maximal, complemented
12	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂×#62842	C₄	1	1	yes	characteristic, complemented
14	C₂×#62842	C₂²	1	1	yes	characteristic
15	C₂²×#3484	C₄	1	1	yes	characteristic, complemented
16	#7631032	C₄	1	2	yes	complemented
17	#7631032	C₂²	1	2	yes	—
18	#7630939	C₄	1	2	yes	complemented
19	#7630939	C₂²	1	2	yes	—
20	#7630668	C₄	1	2	yes	complemented
21	#7630668	C₄	1	2	yes	complemented
22	#7630668	C₂²	1	2	yes	—
23	#7630668	C₂²	1	2	yes	—
24	#7630502	C₄	1	2	yes	complemented
25	#7630502	C₂²	1	2	yes	—
26	#7628649	C₄	1	2	yes	complemented
27	#7628649	C₂²	1	2	yes	—
28	#7625680	C₄	1	1	yes	characteristic, complemented
29	#7625680	C₂²	1	1	yes	characteristic
30	C₂×#34171	C₄	1	1	yes	characteristic, complemented
31	C₂×#20592	C₂²	1	2	yes	complemented
32	C₂×#20592	C₂²	1	2	yes	complemented
33	C₂×#20585	C₂²	1	2	yes	complemented
34	C₂×#20585	C₂²	1	2	yes	complemented
35	#6370684	C₂²	1	2	yes	complemented
36	#517411	C₂²	1	2	yes	complemented
37	#392116	C₂²	1	2	yes	—
38	#392116	C₂²	1	2	yes	complemented
39	#392115	C₂²	1	2	yes	complemented
40	#392113	C₂²	1	2	yes	complemented
41	#392111	C₂²	1	2	yes	—
42	#392111	C₂²	1	2	yes	complemented
43	#392110	C₂²	1	2	yes	complemented
44	#392110	C₂²	1	2	yes	complemented
45	#201322	C₂²	1	16	yes	complemented
46	#201110	C₂²	1	16	yes	complemented
47	#190055	C₂²	1	8	yes	complemented
48	#187764	C₂²	1	8	yes	complemented
49	#186948	C₂²	1	8	yes	complemented
50	#186835	C₂²	1	8	yes	complemented
51	#113288	C₂²	1	16	yes	complemented
52	#112857	C₂²	1	16	yes	complemented
53	#108255	C₂²	1	8	yes	complemented
54	#108238	C₂²	1	8	yes	complemented
55	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
56	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
57	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
58	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
59	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
61	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
62	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
63	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
64	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
65	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
66	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
67	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
68	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
70	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
71	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
72	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic
73	C₂⁴×#41	C₂×C₄	1	1	yes	characteristic
74	C₂⁴×#41	D₄	1	1	yes	characteristic
75	C₂⁴×#41	D₄	1	1	yes	characteristic
76	C₂⁴×#41	C₂³	1	1	yes	characteristic
77	C₂⁴×#41	C₂³	1	1	yes	characteristic
78	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
79	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
80	C₂⁵×D₄	D₄	1	1	yes	characteristic
81	C₂⁵×D₄	D₄	1	1	yes	characteristic
82	C₂⁵×D₄	D₄	1	1	yes	characteristic
83	C₂⁵×D₄	D₄	1	1	yes	characteristic
84	C₂⁵×D₄	D₄	1	1	yes	characteristic
85	C₂⁵×D₄	D₄	1	1	yes	characteristic
86	C₂⁵×D₄	C₂³	1	1	yes	characteristic
87	C₂×#3485	C₂×C₄	1	2	yes	complemented
88	C₂×#3485	C₂×C₄	1	2	yes	complemented
89	C₂×#3485	C₂×C₄	1	2	yes	complemented
90	C₂×#3485	C₂³	1	2	yes	—
91	C₂×#3484	C₂×C₄	1	2	yes	—
92	C₂×#3484	C₂×C₄	1	2	yes	—
93	C₂×#3484	C₂×C₄	1	2	yes	—
94	C₂×#3484	C₂×C₄	1	2	yes	—
95	C₂×#3484	C₂×C₄	1	2	yes	complemented
96	C₂×#3484	C₂×C₄	1	2	yes	complemented
97	C₂×#3484	C₂×C₄	1	2	yes	complemented
98	C₂×#3484	C₂³	1	2	yes	—
99	C₂×#3449	C₂×C₄	1	2	yes	—
100	C₂×#3449	C₂×C₄	1	2	yes	complemented
101	C₂×#3449	C₂×C₄	1	2	yes	complemented
102	C₂×#3449	C₂³	1	2	yes	—
103	C₂²×#535	C₂×C₄	1	2	yes	—
104	C₂²×#525	C₂×C₄	1	2	yes	complemented
105	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
106	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
107	C₂²×#518	C₂×C₄	1	1	yes	characteristic, complemented
108	C₂×#2879	C₂³	1	4	yes	complemented
109	#36614	C₂×C₄	1	4	yes	complemented
110	#36614	C₂³	1	4	yes	—
111	#35616	D₄	1	8	yes	—
112	#35527	D₄	1	8	yes	—
113	#35513	D₄	1	16	yes	—
114	#35242	C₂×C₄	1	4	yes	complemented
115	#35222	C₂×C₄	1	4	yes	—
116	#35222	C₂×C₄	1	4	yes	—
117	#35222	C₂×C₄	1	4	yes	—
118	#35222	C₂×C₄	1	4	yes	complemented
119	#35222	C₂³	1	4	yes	—
120	#35149	C₂×C₄	1	4	yes	—
121	#35149	C₂×C₄	1	4	yes	—
122	#35149	C₂×C₄	1	4	yes	—
123	#35149	C₂×C₄	1	4	yes	complemented
124	#35149	C₂×C₄	1	4	yes	complemented
125	#35149	C₂³	1	4	yes	—
126	#34632	C₂×C₄	1	4	yes	complemented
127	#34632	C₂³	1	4	yes	—
128	#34172	C₂×C₄	1	2	yes	complemented
129	#34172	C₂×C₄	1	2	yes	complemented
130	#34172	C₂×C₄	1	2	yes	complemented
131	#34172	C₂³	1	2	yes	—
132	#34171	C₂×C₄	1	2	yes	—
133	#34171	C₂×C₄	1	2	yes	—
134	#34171	C₂×C₄	1	2	yes	—
135	#34171	C₂×C₄	1	2	yes	—
136	#34171	C₂×C₄	1	2	yes	complemented
137	#34171	C₂×C₄	1	2	yes	complemented
138	#34171	C₂×C₄	1	2	yes	complemented
139	#34171	C₂³	1	2	yes	—
140	#34044	C₂×C₄	1	2	yes	—
141	#34044	C₂×C₄	1	2	yes	complemented
142	#34044	C₂×C₄	1	2	yes	complemented
143	#34044	C₂³	1	2	yes	—
144	C₂×#2309	C₂×C₄	1	2	yes	—
145	C₂×#2308	C₂³	1	4	yes	complemented
146	C₂×#2280	C₂×C₄	1	2	yes	complemented
147	C₂×#1785	C₂³	1	4	yes	—
148	C₂×#1785	C₂³	1	4	yes	complemented
149	C₂×#1783	C₂³	1	4	yes	—
150	C₂×#1783	C₂³	1	4	yes	complemented
151	C₂×#1782	C₂³	1	4	yes	—
152	C₂×#1782	C₂³	1	4	yes	—
153	C₂×#1782	C₂³	1	4	yes	complemented
154	C₂×#1782	C₂³	1	4	yes	complemented
155	#20580	C₂³	1	4	yes	—
156	#20579	C₂³	1	4	yes	complemented
157	#17587	C₂³	1	32	yes	complemented
158	#14681	C₂³	1	4	yes	complemented
159	#14335	C₂³	1	4	yes	—
160	#7943	C₂³	1	32	yes	complemented
161	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
162	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
163	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁷	C₂×D₄	1	1	yes	characteristic
166	C₂⁷	C₂×D₄	1	1	yes	characteristic
167	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
168	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
169	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
170	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
171	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
175	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
176	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
177	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
178	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
179	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
180	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
181	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×#41	C₂²⋊C₄	1	1	yes	characteristic
187	C₂³×#41	C₂²×C₄	1	2	yes	—
188	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
189	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
190	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
191	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
192	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
193	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
194	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
195	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
196	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
197	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
198	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
199	C₂³×#41	C₂²×C₄	1	1	yes	characteristic
200	C₂³×#41	C₂×D₄	1	1	yes	characteristic
201	C₂³×#41	C₂×D₄	1	1	yes	characteristic
202	C₂³×#41	C₂×D₄	1	1	yes	characteristic
203	C₂³×#41	C₂×D₄	1	1	yes	characteristic
204	C₂³×#41	C₂×D₄	1	1	yes	characteristic
205	C₂³×#41	C₂×D₄	1	1	yes	characteristic
206	C₂³×#41	C₂×D₄	1	1	yes	characteristic
207	C₂³×#41	C₂×D₄	1	1	yes	characteristic
208	C₂³×#41	C₂×D₄	1	1	yes	characteristic
209	C₂³×#41	C₂×D₄	1	1	yes	characteristic
210	C₂³×#41	C₂×D₄	1	1	yes	characteristic
211	C₂³×#41	C₂×D₄	1	1	yes	characteristic
212	C₂³×#41	C₂×D₄	1	1	yes	characteristic
213	C₂³×#41	C₂×D₄	1	1	yes	characteristic
214	C₂³×#41	C₂×D₄	1	1	yes	characteristic
215	C₂³×#41	C₂×D₄	1	1	yes	characteristic
216	C₂³×#41	C₂⁴	1	1	yes	characteristic
217	C₂³×#41	C₂⁴	1	1	yes	characteristic
218	C₂³×#41	C₂⁴	1	1	yes	characteristic
219	C₂³×#41	C₂⁴	1	1	yes	characteristic
220	C₂⁴×Q₈	C₂²×C₄	1	1	yes	characteristic
221	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
223	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
224	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
225	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
226	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
227	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
228	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
229	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
230	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
231	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
232	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
233	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
234	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
235	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
236	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
237	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
239	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
240	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
241	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
243	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
244	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
245	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
246	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
247	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
248	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
249	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
250	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
251	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
252	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
253	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
254	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
255	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
256	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
257	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
258	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
259	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
260	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
261	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
262	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
263	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
264	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
265	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
266	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
267	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
268	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
269	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
270	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
271	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
272	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
273	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
274	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
275	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
276	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
277	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
278	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
279	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
280	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
281	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
282	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
283	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
284	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
285	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
286	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
287	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
288	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
289	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
290	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
291	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
292	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
294	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
295	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
299	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
300	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
301	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
302	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
303	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
304	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
305	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
306	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
307	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
308	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
309	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
310	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
311	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
312	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
313	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
314	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
315	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
316	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
317	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
318	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
319	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
320	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
321	C₂×#537	C₂×D₄	1	8	yes	—
322	C₂×#536	C₂²⋊C₄	1	4	yes	complemented
323	C₂×#536	C₂²×C₄	1	4	yes	—
324	C₂×#536	C₂²×C₄	1	4	yes	—
325	C₂×#536	C₂×D₄	1	4	yes	—
326	C₂×#535	C₂²⋊C₄	1	8	yes	complemented
327	C₂×#535	C₂²⋊C₄	1	4	yes	complemented
328	C₂×#535	C₂²×C₄	1	4	yes	—
329	C₂×#535	C₂²×C₄	1	4	yes	—
330	C₂×#535	C₂²×C₄	1	4	yes	—
331	C₂×#535	C₂²×C₄	1	4	yes	—
332	C₂×#535	C₂×D₄	1	4	yes	—
333	C₂×#532	C₂²⋊C₄	1	8	yes	complemented
334	C₂²×#127	C₂²⋊C₄	1	4	yes	complemented
335	C₂²×#124	C₂²⋊C₄	1	4	yes	complemented
336	C₂×#525	C₂²×C₄	1	4	yes	—
337	C₂×#525	C₂²×C₄	1	4	yes	—
338	C₂×#525	C₂²×C₄	1	4	yes	—
339	C₂×#525	C₂²×C₄	1	4	yes	—
340	C₂×#525	C₂²×C₄	1	4	yes	—
341	C₂×#525	C₂⁴	1	4	yes	—
342	C₂×#518	C₂²×C₄	1	2	yes	—
343	C₂×#518	C₂²×C₄	1	2	yes	—
344	C₂×#518	C₂²×C₄	1	2	yes	—
345	C₂×#518	C₂²×C₄	1	2	yes	—
346	C₂×#518	C₂²×C₄	1	2	yes	—
347	C₂×#518	C₂²×C₄	1	2	yes	—
348	C₂²×#117	C₂²×C₄	1	2	yes	—
349	C₂²×#117	C₂²×C₄	1	2	yes	—
350	C₂²×#117	C₂²×C₄	1	2	yes	—
351	C₂×#407	C₂⁴	1	8	yes	—
352	#2435	C₂²⋊C₄	1	16	yes	complemented
353	#2435	C₂×D₄	1	16	yes	—
354	#2433	C₂²⋊C₄	1	16	yes	complemented
355	#2433	C₂×D₄	1	16	yes	—
356	#2432	C₂²⋊C₄	1	16	yes	complemented
357	#2432	C₂×D₄	1	16	yes	—
358	#2431	C₂²⋊C₄	1	16	yes	complemented
359	#2431	C₂×D₄	1	16	yes	—
360	#2311	C₂²⋊C₄	1	8	yes	complemented
361	#2310	C₂²×C₄	1	4	yes	—
362	#2310	C₂²×C₄	1	4	yes	—
363	#2309	C₂²⋊C₄	1	8	yes	complemented
364	#2309	C₂²×C₄	1	4	yes	—
365	#2309	C₂²×C₄	1	4	yes	—
366	#2309	C₂²×C₄	1	4	yes	—
367	#2309	C₂²×C₄	1	4	yes	—
368	#2297	C₂²⋊C₄	1	8	yes	complemented
369	#2297	C₂×D₄	1	8	yes	—
370	#2297	C₂×D₄	1	8	yes	—
371	C₂×#390	C₂²⋊C₄	1	8	yes	complemented
372	#2280	C₂²×C₄	1	4	yes	—
373	#2280	C₂²×C₄	1	4	yes	—
374	#2280	C₂²×C₄	1	4	yes	—
375	#2280	C₂²×C₄	1	4	yes	—
376	#2280	C₂²×C₄	1	4	yes	—
377	#2280	C₂⁴	1	4	yes	—
378	C₂×#381	C₂⁴	1	8	yes	—
379	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
380	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
381	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
382	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
383	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
384	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
385	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
386	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
387	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
388	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
389	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
390	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
391	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
392	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
393	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
394	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
395	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
396	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
397	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
398	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
399	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
400	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
401	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
402	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
403	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
404	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
405	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
406	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
407	C₂⁶	C₂²×D₄	1	1	yes	characteristic
408	C₂⁶	C₂²×D₄	1	1	yes	characteristic
409	C₂⁶	C₂²×D₄	1	1	yes	characteristic
410	C₂⁶	C₂²×D₄	1	1	yes	characteristic
411	C₂⁶	C₂²×D₄	1	1	yes	characteristic
412	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
413	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	—
414	C₂²×#41	C₂×C₂²⋊C₄	1	8	yes	—
415	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
416	C₂²×#41	#120	1	8	yes	—
417	C₂²×#41	#120	1	8	yes	—
418	C₂²×#41	C₂³×C₄	1	4	yes	—
419	C₂²×#41	C₂²×D₄	1	4	yes	—
420	C₂²×#41	C₂²×D₄	1	4	yes	—
421	C₂²×#41	C₂²×D₄	1	8	yes	—
422	C₂²×#41	H(5,𝔽₂)	1	8	yes	—
423	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
424	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
425	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
426	C₂³×Q₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	complemented
428	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
429	C₂³×Q₈	C₂³×C₄	1	1	yes	characteristic
430	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
431	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
432	C₂³×D₄	#99	1	8	yes	—
433	C₂³×D₄	#99	1	8	yes	—
434	C₂³×D₄	#99	1	8	yes	—
435	C₂³×D₄	#99	1	8	yes	—
436	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
437	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
438	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
439	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
440	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
441	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
442	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
443	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
444	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
445	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
446	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
447	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
448	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
449	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
458	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
459	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
460	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
461	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
462	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
463	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
464	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
465	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
466	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
467	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
468	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
469	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
470	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
471	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
472	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
473	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
474	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
475	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
476	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
477	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
478	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
479	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	—
480	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
481	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
482	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
483	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
484	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
485	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
486	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
487	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
488	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
489	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
490	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
491	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	complemented
492	C₂³×D₄	#120	1	4	yes	—
493	C₂³×D₄	#120	1	4	yes	—
494	C₂³×D₄	#120	1	4	yes	—
495	C₂³×D₄	#120	1	4	yes	—
496	C₂³×D₄	#120	1	4	yes	—
497	C₂³×D₄	#120	1	8	yes	—
498	C₂³×D₄	#120	1	4	yes	—
499	C₂³×D₄	#120	1	4	yes	—
500	C₂³×D₄	#120	1	8	yes	—
501	C₂³×D₄	#120	1	4	yes	—
502	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
503	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
504	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
505	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
506	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
507	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
508	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
509	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
510	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
511	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
512	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
513	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
514	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
515	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
516	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
517	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
518	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
519	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
520	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
521	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
522	C₂³×D₄	C₂²×D₄	1	8	yes	—
523	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
524	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
525	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
526	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
527	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
528	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
529	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
530	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
531	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
532	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
533	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
534	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
535	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
536	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
537	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
538	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
539	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
540	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
541	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
542	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
543	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
544	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
545	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
546	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
547	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
548	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
549	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
550	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
551	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
552	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
553	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
554	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
555	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
556	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
557	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
558	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
559	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
560	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
561	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
562	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
563	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
564	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
565	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
566	C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
567	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
568	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	—
569	C₂×#127	C₂×C₂²⋊C₄	1	8	yes	complemented
570	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	—
571	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	—
572	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	complemented
573	C₂×#124	C₂×C₂²⋊C₄	1	8	yes	complemented
574	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	8	yes	complemented
575	C₂×C₂²⋊Q₈	C₂²×D₄	1	8	yes	—
576	C₂×#121	C₂×C₂²⋊C₄	1	8	yes	complemented
577	C₂×#121	C₂²×D₄	1	8	yes	—
578	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
579	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
580	C₂×#117	C₂×C₂²⋊C₄	1	4	yes	complemented
581	C₂×#117	C₂³×C₄	1	4	yes	—
582	C₂×#117	C₂³×C₄	1	4	yes	—
583	C₂×#117	C₂³×C₄	1	4	yes	—
584	C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	1	4	yes	complemented
585	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	complemented
586	C₂²×C₄²	C₂×C₂²⋊C₄	1	4	yes	complemented
587	#391	C₂×C₂²⋊C₄	1	16	yes	complemented
588	#390	C₂×C₂²⋊C₄	1	16	yes	—
589	#390	C₂×C₂²⋊C₄	1	16	yes	—
590	#390	C₂×C₂²⋊C₄	1	16	yes	complemented
591	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	16	yes	complemented
592	C₄×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
593	C₂⁵	#379	1	2	yes	—
594	C₂⁵	#379	1	2	yes	—
595	C₂⁵	#379	1	2	yes	—
596	C₂⁵	#379	1	2	yes	—
597	C₂⁵	#379	1	4	yes	—
598	C₂⁵	#379	1	4	yes	—
599	C₂⁵	C₂×#99	1	4	yes	—
600	C₂⁵	C₂×#99	1	4	yes	—
601	C₂⁵	C₂×#99	1	4	yes	—
602	C₂⁵	C₂×#99	1	4	yes	—
603	C₂⁵	C₂×#99	1	4	yes	—
604	C₂⁵	C₂×#99	1	4	yes	—
605	C₂⁵	C₂×#99	1	4	yes	—
606	C₂⁵	C₂×#99	1	4	yes	—
607	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
608	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
609	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
610	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
611	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
612	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
613	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
614	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
615	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
616	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
617	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
618	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
619	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
620	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
621	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
622	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
623	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
624	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
625	C₂⁵	C₂×#120	1	4	yes	—
626	C₂⁵	C₂×#120	1	4	yes	—
627	C₂⁵	#534	1	4	yes	—
628	C₂⁵	#534	1	4	yes	—
629	C₂⁵	C₂³×D₄	1	1	yes	characteristic
630	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
631	C₂²×Q₈	C₂²×C₂²⋊C₄	1	4	yes	—
632	C₂²×Q₈	#518	1	4	yes	—
633	C₂²×Q₈	C₂×#120	1	4	yes	—
634	C₂²×D₄	#379	1	2	yes	—
635	C₂²×D₄	#379	1	2	yes	—
636	C₂²×D₄	#379	1	4	yes	—
637	C₂²×D₄	#379	1	4	yes	—
638	C₂²×D₄	#379	1	4	yes	—
639	C₂²×D₄	#379	1	4	yes	—
640	C₂²×D₄	#379	1	4	yes	—
641	C₂²×D₄	#379	1	2	yes	—
642	C₂²×D₄	#379	1	2	yes	—
643	C₂²×D₄	#379	1	4	yes	—
644	C₂²×D₄	C₂×#99	1	4	yes	—
645	C₂²×D₄	C₂×#99	1	4	yes	—
646	C₂²×D₄	C₂×#99	1	4	yes	—
647	C₂²×D₄	C₂×#99	1	4	yes	—
648	C₂²×D₄	C₂×#99	1	4	yes	—
649	C₂²×D₄	C₂×#99	1	4	yes	—
650	C₂²×D₄	C₂×#99	1	4	yes	—
651	C₂²×D₄	C₂×#99	1	4	yes	—
652	C₂²×D₄	C₂×#99	1	4	yes	—
653	C₂²×D₄	C₂×#99	1	4	yes	—
654	C₂²×D₄	C₂×#99	1	4	yes	—
655	C₂²×D₄	C₂×#99	1	4	yes	—
656	C₂²×D₄	C₂×#99	1	4	yes	—
657	C₂²×D₄	C₂×#99	1	4	yes	—
658	C₂²×D₄	C₂×#99	1	4	yes	—
659	C₂²×D₄	C₂×#99	1	4	yes	—
660	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
661	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
662	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
663	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
664	C₂²×D₄	#518	1	4	yes	—
665	C₂²×D₄	#518	1	4	yes	—
666	C₂²×D₄	#518	1	4	yes	—
667	C₂²×D₄	C₂×#120	1	2	yes	—
668	C₂²×D₄	C₂×#120	1	2	yes	—
669	C₂²×D₄	C₂×#120	1	4	yes	—
670	C₂²×D₄	C₂×#120	1	4	yes	—
671	C₂²×D₄	C₂×#120	1	2	yes	—
672	C₂²×D₄	C₂×#120	1	2	yes	—
673	C₂²×D₄	C₂×#120	1	4	yes	—
674	C₂²×D₄	C₂×#120	1	4	yes	—
675	C₂²×D₄	C₂×#120	1	4	yes	—
676	C₂²×D₄	#534	1	4	yes	—
677	C₂²×D₄	#534	1	4	yes	—
678	C₂²×D₄	#534	1	4	yes	—
679	C₂²×D₄	#534	1	4	yes	—
680	C₂³×C₄	#379	1	4	yes	—
681	C₂³×C₄	#379	1	4	yes	—
682	C₂³×C₄	#379	1	4	yes	—
683	C₂³×C₄	#379	1	4	yes	—
684	C₂³×C₄	C₂×#99	1	4	yes	—
685	C₂³×C₄	C₂×#99	1	4	yes	—
686	C₂³×C₄	C₂×#99	1	4	yes	—
687	C₂³×C₄	C₂×#99	1	4	yes	—
688	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
689	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
690	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
691	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
692	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
693	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
694	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
695	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
696	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
697	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
698	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
699	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
700	C₂³×C₄	C₂²×C₂²⋊C₄	1	4	yes	—
701	C₂³×C₄	C₂×#120	1	4	yes	—
702	C₂³×C₄	C₂×#120	1	4	yes	—
703	C₂³×C₄	#534	1	4	yes	—
704	C₂³×C₄	#534	1	4	yes	—
705	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
706	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
707	C₂³×C₄	C₂³×D₄	1	4	yes	—
708	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
709	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
710	C₂×C₄⋊C₄	C₂²×C₂²⋊C₄	1	8	yes	—
711	C₂×C₄²	C₂²×C₂²⋊C₄	1	8	yes	—
712	C₂×C₄²	C₂²×C₂²⋊C₄	1	8	yes	—
713	C₂⁴	C₂×#379	1	2	yes	—
714	C₂⁴	C₂×#379	1	2	yes	—
715	C₂⁴	C₂×#379	1	2	yes	—
716	C₂⁴	C₂×#379	1	2	yes	—
717	C₂⁴	C₂×#379	1	2	yes	—
718	C₂⁴	C₂×#379	1	2	yes	—
719	C₂⁴	C₂×#379	1	2	yes	—
720	C₂⁴	C₂×#379	1	1	yes	characteristic
721	C₂⁴	C₂×#379	1	1	yes	characteristic
722	C₂⁴	#2308	1	2	yes	—
723	C₂⁴	#2308	1	2	yes	—
724	C₂⁴	#2308	1	2	yes	—
725	C₂⁴	#2308	1	2	yes	—
726	C₂⁴	#2308	1	2	yes	—
727	C₂⁴	#2308	1	2	yes	—
728	C₂⁴	C₂²×#99	1	2	yes	—
729	C₂⁴	C₂²×#99	1	2	yes	—
730	C₂⁴	C₂²×#99	1	2	yes	—
731	C₂⁴	C₂²×#99	1	2	yes	—
732	C₂⁴	C₂²×#99	1	2	yes	—
733	C₂⁴	C₂²×#99	1	2	yes	—
734	C₂⁴	C₂²×#99	1	2	yes	—
735	C₂⁴	C₂²×#99	1	2	yes	—
736	C₂⁴	C₂²×#99	1	2	yes	—
737	C₂⁴	C₂²×#99	1	2	yes	—
738	C₂⁴	C₂²×#99	1	2	yes	—
739	C₂⁴	C₂²×#99	1	2	yes	—
740	C₂⁴	C₂²×#99	1	2	yes	—
741	C₂⁴	C₂²×#99	1	2	yes	—
742	C₂⁴	C₂²×#99	1	2	yes	—
743	C₂⁴	C₂²×#99	1	2	yes	—
744	C₂⁴	C₂²×#99	1	2	yes	—
745	C₂⁴	C₂²×#99	1	2	yes	—
746	C₂⁴	C₂²×#99	1	2	yes	—
747	C₂⁴	C₂²×#99	1	2	yes	—
748	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
749	C₂⁴	C₂²×#120	1	2	yes	—
750	C₂⁴	C₂×#534	1	2	yes	—
751	C₂⁴	C₂×#534	1	2	yes	—
752	C₂×D₄	#1781	1	8	yes	—
753	C₂×D₄	#1781	1	8	yes	—
754	C₂×D₄	#1781	1	16	yes	—
755	C₂²×C₄	C₂×#379	1	2	yes	—
756	C₂²×C₄	C₂×#379	1	2	yes	—
757	C₂²×C₄	C₂×#379	1	2	yes	—
758	C₂²×C₄	C₂×#379	1	2	yes	—
759	C₂²×C₄	#2308	1	2	yes	—
760	C₂²×C₄	#2308	1	2	yes	—
761	C₂²×C₄	C₂²×#99	1	2	yes	—
762	C₂²×C₄	C₂²×#99	1	2	yes	—
763	C₂²×C₄	C₂²×#99	1	2	yes	—
764	C₂²×C₄	C₂²×#99	1	2	yes	—
765	C₂²×C₄	C₂²×#99	1	2	yes	—
766	C₂²×C₄	C₂²×#99	1	2	yes	—
767	C₂²×C₄	C₂²×#99	1	2	yes	—
768	C₂²×C₄	C₂²×#99	1	2	yes	—
769	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
770	C₂²×C₄	C₂×#518	1	2	yes	—
771	C₂²×C₄	C₂×#518	1	2	yes	—
772	C₂²×C₄	C₂²×#120	1	2	yes	—
773	C₂²×C₄	C₂×#534	1	2	yes	—
774	C₂²×C₄	C₂×#534	1	2	yes	—
775	C₂²×C₄	#3484	1	16	yes	—
776	C₂³	C₂×#1781	1	2	yes	—
777	C₂³	C₂×#1781	1	4	yes	—
778	C₂³	C₂×#1781	1	4	yes	—
779	C₂³	C₂×#1781	1	4	yes	—
780	C₂³	C₂×#1781	1	2	yes	—
781	C₂³	#21746	1	4	yes	—
782	C₂³	#21746	1	4	yes	—
783	C₂³	#21746	1	4	yes	—
784	C₂³	#21746	1	4	yes	—
785	C₂³	C₂²×#379	1	1	yes	characteristic
786	C₂³	C₂×#2308	1	1	yes	characteristic
787	C₂³	C₂×#2308	1	1	yes	characteristic
788	C₂³	#34980	1	4	yes	—
789	C₂³	C₂³×#99	1	1	yes	characteristic
790	C₂³	C₂³×#99	1	1	yes	characteristic
791	C₂³	C₂³×#99	1	1	yes	characteristic
792	C₂³	C₂³×#99	1	1	yes	characteristic
793	C₂×C₄	C₂×#1781	1	4	yes	—
794	C₂×C₄	C₂×#1781	1	4	yes	—
795	C₂×C₄	#34171	1	4	yes	—
796	C₂×C₄	#34980	1	4	yes	—
797	C₂²	#517411	1	1	yes	characteristic
798	C₂²	C₂²×#1781	1	1	yes	characteristic
799	C₂²	C₂²×#1781	1	1	yes	characteristic
800	C₂²	C₂×#21746	1	1	yes	characteristic
801	C₂²	C₂×#21746	1	1	yes	characteristic
802	C₂²	C₂×#21746	1	1	yes	characteristic
803	C₂²	C₂×#21746	1	1	yes	characteristic
804	C₂	#72217789	1	1	yes	characteristic
805	C₂	#72251416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²	#517411
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	#72249537	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72256085	C₂	semidirect
2. #72256081	C₂	semidirect
3. #72255932	C₂	semidirect
4. #72255890	C₂	semidirect
5. #72255852	C₂	semidirect
7. #72238521	C₂	semidirect
8. #72235188	C₂	semidirect
9. #72235168	C₂	semidirect
10. #72225783	C₂	semidirect
11. #72218455	C₂	semidirect
13. C₂×#62842	C₄	semidirect
15. C₂²×#3484	C₄	semidirect
16. #7631032	C₄	semidirect
18. #7630939	C₄	semidirect
20. #7630668	C₄	semidirect
21. #7630668	C₄	semidirect
24. #7630502	C₄	semidirect
26. #7628649	C₄	semidirect
28. #7625680	C₄	semidirect
30. C₂×#34171	C₄	semidirect
31. C₂×#20592	C₂²	semidirect
32. C₂×#20592	C₂²	semidirect
33. C₂×#20585	C₂²	semidirect
34. C₂×#20585	C₂²	semidirect
35. #6370684	C₂²	semidirect
36. #517411	C₂²	semidirect
38. #392116	C₂²	semidirect
39. #392115	C₂²	semidirect
40. #392113	C₂²	semidirect
42. #392111	C₂²	semidirect
43. #392110	C₂²	semidirect
44. #392110	C₂²	semidirect
45. #201322	C₂²	semidirect
46. #201110	C₂²	semidirect
47. #190055	C₂²	semidirect
48. #187764	C₂²	semidirect
49. #186948	C₂²	semidirect
50. #186835	C₂²	semidirect
51. #113288	C₂²	semidirect
52. #112857	C₂²	semidirect
53. #108255	C₂²	semidirect
54. #108238	C₂²	semidirect
59. C₂³×H(5,𝔽₂)	C₂×C₄	semidirect
87. C₂×#3485	C₂×C₄	semidirect
88. C₂×#3485	C₂×C₄	semidirect
89. C₂×#3485	C₂×C₄	semidirect
95. C₂×#3484	C₂×C₄	semidirect
96. C₂×#3484	C₂×C₄	semidirect
97. C₂×#3484	C₂×C₄	semidirect
100. C₂×#3449	C₂×C₄	semidirect
101. C₂×#3449	C₂×C₄	semidirect
104. C₂²×#525	C₂×C₄	semidirect
105. C₂²×#518	C₂×C₄	semidirect
106. C₂²×#518	C₂×C₄	semidirect
107. C₂²×#518	C₂×C₄	semidirect
108. C₂×#2879	C₂³	semidirect
109. #36614	C₂×C₄	semidirect
114. #35242	C₂×C₄	semidirect
118. #35222	C₂×C₄	semidirect
123. #35149	C₂×C₄	semidirect
124. #35149	C₂×C₄	semidirect
126. #34632	C₂×C₄	semidirect
128. #34172	C₂×C₄	semidirect
129. #34172	C₂×C₄	semidirect
130. #34172	C₂×C₄	semidirect
136. #34171	C₂×C₄	semidirect
137. #34171	C₂×C₄	semidirect
138. #34171	C₂×C₄	semidirect
141. #34044	C₂×C₄	semidirect
142. #34044	C₂×C₄	semidirect
145. C₂×#2308	C₂³	semidirect
146. C₂×#2280	C₂×C₄	semidirect
148. C₂×#1785	C₂³	semidirect
150. C₂×#1783	C₂³	semidirect
153. C₂×#1782	C₂³	semidirect
154. C₂×#1782	C₂³	semidirect
156. #20579	C₂³	semidirect
157. #17587	C₂³	semidirect
158. #14681	C₂³	semidirect
160. #7943	C₂³	semidirect
322. C₂×#536	C₂²⋊C₄	semidirect
326. C₂×#535	C₂²⋊C₄	semidirect
327. C₂×#535	C₂²⋊C₄	semidirect
333. C₂×#532	C₂²⋊C₄	semidirect
334. C₂²×#127	C₂²⋊C₄	semidirect
335. C₂²×#124	C₂²⋊C₄	semidirect
352. #2435	C₂²⋊C₄	semidirect
354. #2433	C₂²⋊C₄	semidirect
356. #2432	C₂²⋊C₄	semidirect
358. #2431	C₂²⋊C₄	semidirect
360. #2311	C₂²⋊C₄	semidirect
363. #2309	C₂²⋊C₄	semidirect
368. #2297	C₂²⋊C₄	semidirect
371. C₂×#390	C₂²⋊C₄	semidirect
415. C₂²×#41	C₂×C₂²⋊C₄	semidirect
427. C₂³×Q₈	C₂×C₂²⋊C₄	semidirect
491. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
566. C₂×C₄⋊Q₈	C₂×C₂²⋊C₄	semidirect
569. C₂×#127	C₂×C₂²⋊C₄	semidirect
572. C₂×#124	C₂×C₂²⋊C₄	semidirect
573. C₂×#124	C₂×C₂²⋊C₄	semidirect
574. C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	semidirect
576. C₂×#121	C₂×C₂²⋊C₄	semidirect
578. C₂×#117	C₂×C₂²⋊C₄	semidirect
579. C₂×#117	C₂×C₂²⋊C₄	semidirect
580. C₂×#117	C₂×C₂²⋊C₄	semidirect
584. C₂²×C₄⋊C₄	C₂×C₂²⋊C₄	semidirect
585. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
586. C₂²×C₄²	C₂×C₂²⋊C₄	semidirect
587. #391	C₂×C₂²⋊C₄	semidirect
590. #390	C₂×C₂²⋊C₄	semidirect
591. C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72256085	2
#72256081	2
#72255932	2
#72255890	2
#72255852	2
#72249537	2
#72238521	2
#72235188	2
#72235168	2
#72225783	2
#72218455	2