Subgroups — #72262760

Order 2048.

At least 7840 conjugacy classes of subgroups; only the 3352 normal subgroups are shown.

The subgroup lattice has 760 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262699	C₂	1	1	yes	maximal, characteristic, complemented
2	#72256427	C₂	1	1	yes	maximal, characteristic, complemented
3	#72256327	C₂	1	4	yes	maximal, complemented
4	#72256192	C₂	1	4	yes	maximal, complemented
5	#72255639	C₂	1	1	yes	maximal, characteristic, complemented
6	#72251326	C₂	1	1	yes	maximal, characteristic, complemented
7	#72251303	C₂	1	1	yes	maximal, characteristic, complemented
8	#72251260	C₂	1	1	yes	maximal, characteristic, complemented
9	#72251204	C₂	1	1	yes	maximal, characteristic, complemented
10	#72249558	C₂	1	1	yes	maximal, characteristic, complemented
11	#72237236	C₂	1	1	yes	maximal, characteristic, complemented
12	#72236747	C₂	1	1	yes	maximal, characteristic, complemented
13	#72235935	C₂	1	4	yes	maximal, complemented
14	C₂×#364592	C₂	1	4	yes	maximal, complemented
15	#72235090	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#359472	C₂	1	1	yes	maximal, characteristic, complemented
17	#72233876	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×#3003	C₂	1	1	yes	maximal, characteristic
19	#72231771	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁶×D₄	C₂²	1	1	yes	characteristic
21	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂⁴×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
23	C₂³×#525	C₂²	1	1	yes	characteristic
24	C₂²×#3003	C₄	1	16	yes	complemented
25	C₂²×#3003	C₂²	1	2	yes	—
26	C₂²×#3003	C₂²	1	2	yes	—
27	C₂²×#3003	C₂²	1	2	yes	—
28	C₂²×#3003	C₂²	1	2	yes	—
29	C₂×#60168	C₂²	1	2	yes	complemented
30	C₂³×#407	C₂²	1	1	yes	characteristic
31	C₂³×#418	C₂²	1	1	yes	characteristic
32	C₂³×#418	C₂²	1	1	yes	characteristic
33	#7625442	C₂²	1	1	yes	characteristic, complemented
34	C₂×#34171	C₂²	1	1	yes	characteristic
35	C₂×#34171	C₂²	1	1	yes	characteristic
36	C₂×#34171	C₂²	1	4	yes	complemented
37	#6372005	C₂²	1	2	yes	complemented
38	C₂²×#1904	C₂²	1	2	yes	complemented
39	C₂²×#1904	C₂²	1	2	yes	complemented
40	C₂×#20959	C₂²	1	4	yes	complemented
41	C₂×#20945	C₂²	1	4	yes	complemented
42	#6371425	C₂²	1	2	yes	complemented
43	#6371420	C₂²	1	2	yes	complemented
44	#6370810	C₂²	1	1	yes	characteristic, complemented
45	C₂×#20605	C₂²	1	1	yes	characteristic, complemented
46	#6370715	C₂²	1	1	yes	characteristic, complemented
47	C₂×#20598	C₂²	1	1	yes	characteristic
48	C₂×#20598	C₂²	1	1	yes	characteristic
49	C₂×#20598	C₂²	1	1	yes	characteristic
50	C₂×#20598	C₂²	1	1	yes	characteristic
51	C₂×#20598	C₂²	1	4	yes	complemented
52	C₂×#20598	C₂²	1	4	yes	complemented
53	C₂×#20584	C₂²	1	1	yes	characteristic, complemented
54	C₂×#20579	C₂²	1	1	yes	characteristic
55	#6369812	C₂²	1	1	yes	characteristic, complemented
56	#607558	C₂²	1	1	yes	characteristic
57	#607558	C₂²	1	1	yes	characteristic
58	#607558	C₂²	1	1	yes	characteristic
59	#517415	C₂²	1	1	yes	characteristic
60	#517415	C₂²	1	1	yes	characteristic
61	#517415	C₂²	1	4	yes	complemented
62	C₂×#11129	C₂²	1	4	yes	complemented
63	C₂×#11100	C₂²	1	4	yes	complemented
64	C₂×#11030	C₂²	1	4	yes	complemented
65	C₂×#11030	C₂²	1	4	yes	complemented
66	#357571	C₂²	1	4	yes	complemented
67	C₂×#11012	C₂²	1	2	yes	complemented
68	C₂×#11012	C₂²	1	2	yes	complemented
69	C₂×#10994	C₂²	1	4	yes	complemented
70	C₂×#10994	C₂²	1	4	yes	complemented
71	#357529	C₂²	1	4	yes	complemented
72	C₂×#10948	C₂²	1	4	yes	complemented
73	C₂×#10937	C₂²	1	4	yes	complemented
74	C₂×#10785	C₂²	1	4	yes	complemented
75	#353416	C₂²	1	1	yes	characteristic, complemented
76	C₂×#10737	C₂²	1	1	yes	characteristic, complemented
77	#353407	C₂²	1	1	yes	characteristic, complemented
78	#353407	C₂²	1	1	yes	characteristic, complemented
79	#353397	C₂²	1	1	yes	characteristic, complemented
80	#353397	C₂²	1	1	yes	characteristic, complemented
81	#353386	C₂²	1	1	yes	characteristic, complemented
82	C₂×#10776	C₂²	1	4	yes	complemented
83	C₂×#10729	C₂²	1	1	yes	characteristic, complemented
84	C₂×#10717	C₂²	1	1	yes	characteristic, complemented
85	C₂×#10716	C₂²	1	1	yes	characteristic, complemented
86	#123605	C₂²	1	4	yes	complemented
87	#123600	C₂²	1	4	yes	complemented
88	#123560	C₂²	1	4	yes	complemented
89	#123547	C₂²	1	4	yes	complemented
90	#123535	C₂²	1	4	yes	complemented
91	#123531	C₂²	1	4	yes	complemented
92	C₂⁴×#41	C₂³	1	1	yes	characteristic
93	C₂⁵×D₄	C₂×C₄	1	8	yes	complemented
94	C₂⁵×D₄	C₂³	1	2	yes	—
95	C₂⁵×D₄	C₂³	1	2	yes	—
96	C₂⁵×D₄	C₂³	1	1	yes	characteristic
97	C₂⁵×D₄	C₂³	1	1	yes	characteristic
98	C₂⁶×C₄	C₂³	1	1	yes	characteristic
99	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	—
100	C₂³×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
101	C₂³×AGL(1,ℤ/8)	D₄	1	8	yes	—
102	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	—
103	C₂³×AGL(1,ℤ/8)	D₄	1	2	yes	—
104	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
105	C₂³×AGL(1,ℤ/8)	C₂³	1	2	yes	—
106	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
107	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
108	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
109	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
110	C₂⁴×SD₁₆	D₄	1	2	yes	—
111	C₂⁴×D₈	D₄	1	2	yes	—
112	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
113	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
114	C₂²×#525	C₂×C₄	1	8	yes	complemented
115	C₂²×#525	C₂³	1	2	yes	—
116	C₂²×#525	C₂³	1	2	yes	—
117	C₂×#3428	C₂³	1	2	yes	complemented
118	C₂²×#518	C₂³	1	2	yes	—
119	C₂²×#518	C₂³	1	2	yes	—
120	C₂³×#117	C₂³	1	1	yes	characteristic
121	C₂×#3003	C₂×C₄	1	16	yes	—
122	C₂×#3003	C₂×C₄	1	16	yes	complemented
123	C₂×#3003	C₂×C₄	1	16	yes	complemented
124	C₂×#3003	C₂×C₄	1	16	yes	complemented
125	C₂×#3003	D₄	1	32	yes	—
126	C₂×#2911	C₂³	1	2	yes	complemented
127	C₂²×#421	C₂³	1	2	yes	complemented
128	C₂²×#421	C₂³	1	2	yes	complemented
129	C₂×#2896	C₂³	1	2	yes	complemented
130	C₂×#2896	C₂³	1	2	yes	complemented
131	C₂²×#418	C₂×C₄	1	8	yes	complemented
132	C₂²×#418	C₂×C₄	1	8	yes	complemented
133	C₂²×#418	C₂³	1	2	yes	—
134	C₂²×#418	C₂³	1	2	yes	—
135	C₂²×#418	C₂³	1	2	yes	—
136	C₂²×#418	C₂³	1	4	yes	—
137	C₂²×#418	C₂³	1	4	yes	—
138	C₂²×#418	C₂³	1	2	yes	—
139	C₂²×#418	C₂³	1	2	yes	—
140	C₂²×#418	C₂³	1	2	yes	—
141	C₂²×#418	C₂³	1	2	yes	—
142	C₂²×#418	C₂³	1	2	yes	—
143	C₂²×#410	C₂³	1	2	yes	complemented
144	C₂²×#410	C₂³	1	2	yes	complemented
145	C₂²×#407	C₂×C₄	1	8	yes	complemented
146	C₂²×#407	C₂³	1	2	yes	—
147	C₂²×#407	C₂³	1	4	yes	—
148	C₂²×#407	C₂³	1	2	yes	—
149	C₂²×#407	C₂³	1	1	yes	characteristic
150	C₂²×#407	C₂³	1	1	yes	characteristic
151	C₂×#2873	C₂³	1	2	yes	complemented
152	C₂×D₄×C₂²⋊C₄	D₄	1	8	yes	complemented
153	#34044	C₂³	1	2	yes	complemented
154	C₂×#2309	C₂³	1	4	yes	—
155	C₂×#2309	C₂³	1	2	yes	—
156	C₂×#2309	C₂³	1	4	yes	—
157	C₂×#2309	C₂³	1	2	yes	—
158	C₂×#2280	C₂³	1	4	yes	—
159	C₂×#2280	C₂³	1	4	yes	—
160	C₂×#2280	C₂³	1	4	yes	—
161	C₂×#2280	C₂³	1	1	yes	characteristic
162	C₂×#2280	C₂³	1	1	yes	characteristic
163	C₂×#2280	C₂³	1	1	yes	characteristic
164	C₂×#2280	C₂³	1	1	yes	characteristic
165	C₂×#2280	C₂³	1	1	yes	characteristic
166	C₂×#2280	C₂³	1	1	yes	characteristic
167	C₂×#1786	D₄	1	8	yes	complemented
168	C₂²×#344	C₂³	1	2	yes	complemented
169	C₂²×#344	C₂³	1	2	yes	complemented
170	C₂²×#344	C₂³	1	4	yes	complemented
171	C₂×#1742	C₂³	1	4	yes	complemented
172	C₂×#1740	C₂³	1	4	yes	complemented
173	C₂×#1740	C₂³	1	4	yes	complemented
174	#20347	C₂³	1	2	yes	complemented
175	C₂×#1733	C₂³	1	4	yes	complemented
176	C₂×#1733	C₂³	1	4	yes	complemented
177	C₂×#1733	C₂³	1	4	yes	complemented
178	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
179	C₂²×H(3,ℤ/4)	C₂³	1	4	yes	complemented
180	C₂²×H(3,ℤ/4)	C₂³	1	2	yes	complemented
181	#20335	C₂³	1	2	yes	complemented
182	#14681	D₄	1	2	yes	—
183	#14681	D₄	1	4	yes	—
184	#14679	D₄	1	2	yes	—
185	#13902	D₄	1	8	yes	complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂³×#41	C₂²×C₄	1	4	yes	—
188	C₂³×#41	C₂×D₄	1	4	yes	—
189	C₂³×#41	C₂×D₄	1	1	yes	characteristic
190	C₂³×#41	C₂×D₄	1	1	yes	characteristic
191	C₂³×#41	C₂⁴	1	1	yes	characteristic
192	C₂³×#41	C₂⁴	1	1	yes	characteristic
193	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂²×C₄	1	8	yes	—
195	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
196	C₂⁴×D₄	C₂²×C₄	1	8	yes	—
197	C₂⁴×D₄	C₂²×C₄	1	4	yes	—
198	C₂⁴×D₄	C₂×D₄	1	16	yes	—
199	C₂⁴×D₄	C₂×D₄	1	4	yes	—
200	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×D₄	C₂×D₄	1	2	yes	—
202	C₂⁴×D₄	C₂×D₄	1	2	yes	—
203	C₂⁴×D₄	C₂×D₄	1	4	yes	—
204	C₂⁴×D₄	C₂×D₄	1	4	yes	—
205	C₂⁴×D₄	C₂×D₄	1	4	yes	—
206	C₂⁴×D₄	#41	1	4	yes	—
207	C₂⁴×D₄	#41	1	4	yes	—
208	C₂⁴×D₄	#41	1	4	yes	—
209	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
210	C₂⁴×D₄	C₂⁴	1	2	yes	—
211	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
212	C₂⁵×C₄	C₂²×C₄	1	4	yes	—
213	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
214	C₂⁵×C₄	C₂×D₄	1	2	yes	—
215	C₂⁵×C₄	#41	1	4	yes	—
216	C₂⁵×C₄	C₂⁴	1	2	yes	—
217	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
218	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	16	yes	complemented
219	C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	1	16	yes	complemented
220	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	8	yes	—
221	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	8	yes	—
222	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
223	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
224	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
225	C₂²×AGL(1,ℤ/8)	C₂²×C₄	1	4	yes	—
226	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
227	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
228	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
229	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
230	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	4	yes	—
231	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	16	yes	—
232	C₂³×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
233	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
234	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
235	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
236	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
237	C₂³×D₈	C₂²⋊C₄	1	16	yes	complemented
238	C₂³×D₈	C₂×D₄	1	2	yes	—
239	C₂³×D₈	C₂×D₄	1	2	yes	—
240	C₂³×D₈	C₂×D₄	1	2	yes	—
241	C₂³×D₈	C₂×D₄	1	2	yes	—
242	C₂³×M₁₆	C₂²×C₄	1	4	yes	—
243	C₂³×M₁₆	C₂²×C₄	1	4	yes	—
244	C₂³×M₁₆	C₂×D₄	1	4	yes	—
245	C₂³×M₁₆	C₂×D₄	1	2	yes	—
246	C₂³×M₁₆	C₂⁴	1	2	yes	—
247	C₂³×M₁₆	C₂⁴	1	2	yes	—
248	C₂³×M₁₆	C₂⁴	1	2	yes	—
249	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
250	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₈	C₂×D₄	1	2	yes	—
252	C₂×#525	C₂²×C₄	1	8	yes	—
253	C₂×#525	C₂²×C₄	1	8	yes	—
254	C₂×#525	C₂×D₄	1	16	yes	—
255	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
256	C₂²×#117	C₂²×C₄	1	4	yes	—
257	C₂²×#117	C₂⁴	1	2	yes	—
258	C₂²×#117	C₂⁴	1	2	yes	—
259	C₂²×#117	C₂⁴	1	2	yes	—
260	C₂²×#117	C₂⁴	1	2	yes	—
261	C₂²×#117	C₂⁴	1	2	yes	—
262	C₂²×#117	C₂⁴	1	2	yes	—
263	C₂²×#117	C₂⁴	1	2	yes	—
264	#3003	C₂²⋊C₄	1	128	yes	complemented
265	C₂×#418	C₂²×C₄	1	8	yes	—
266	C₂×#418	C₂²×C₄	1	8	yes	—
267	C₂×#418	C₂²×C₄	1	8	yes	—
268	C₂×#418	C₂²×C₄	1	8	yes	—
269	C₂×#418	C₂×D₄	1	16	yes	—
270	C₂×#418	C₂×D₄	1	16	yes	—
271	C₂²×#102	C₂×D₄	1	8	yes	complemented
272	C₂²×#102	C₂×D₄	1	8	yes	complemented
273	C₂×#407	C₂²×C₄	1	8	yes	—
274	C₂×#407	C₂²×C₄	1	8	yes	—
275	C₂×#407	C₂×D₄	1	16	yes	—
276	C₂²×C₂²⋊C₈	C₂×D₄	1	4	yes	—
277	C₂×#390	C₂×D₄	1	16	yes	complemented
278	C₂×#390	C₂×D₄	1	8	yes	complemented
279	C₂×#381	C₂×D₄	1	2	yes	—
280	C₂×#381	C₂×D₄	1	8	yes	—
281	C₂×#381	C₂×D₄	1	2	yes	—
282	C₂×#380	C₂×D₄	1	4	yes	—
283	C₂×#380	C₂×D₄	1	4	yes	—
284	C₂×#380	C₂×D₄	1	4	yes	—
285	C₂×#379	C₂×D₄	1	2	yes	—
286	C₂×#379	C₂×D₄	1	8	yes	—
287	C₂×#379	C₂×D₄	1	2	yes	—
288	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
289	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	4	yes	—
290	C₂⁶	C₄×D₄	1	4	yes	—
291	C₂⁶	C₂²×D₄	1	2	yes	—
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
294	C₂²×#41	C₂×C₂²⋊C₄	1	4	yes	complemented
295	C₂²×#41	C₂³×C₄	1	2	yes	—
296	C₂²×#41	C₂³×C₄	1	2	yes	—
297	C₂²×#41	C₂²×D₄	1	2	yes	—
298	C₂²×#41	C₂²×D₄	1	2	yes	—
299	C₂²×#41	C₂²×D₄	1	8	yes	—
300	C₂³×Q₈	C₂×C₂²⋊C₄	1	4	yes	complemented
301	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
302	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
304	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
305	C₂³×D₄	C₂×C₂²⋊C₄	1	32	yes	complemented
306	C₂³×D₄	C₂×C₂²⋊C₄	1	4	yes	complemented
307	C₂³×D₄	C₄×D₄	1	16	yes	—
308	C₂³×D₄	C₄×D₄	1	16	yes	—
309	C₂³×D₄	C₄×D₄	1	16	yes	—
310	C₂³×D₄	#120	1	8	yes	—
311	C₂³×D₄	#120	1	8	yes	—
312	C₂³×D₄	#121	1	16	yes	—
313	C₂³×D₄	#121	1	16	yes	—
314	C₂³×D₄	#123	1	8	yes	—
315	C₂³×D₄	#123	1	8	yes	—
316	C₂³×D₄	C₂³×C₄	1	2	yes	—
317	C₂³×D₄	C₂³×C₄	1	4	yes	—
318	C₂³×D₄	C₂³×C₄	1	2	yes	—
319	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	C₂²×D₄	1	2	yes	—
322	C₂³×D₄	C₂²×D₄	1	2	yes	—
323	C₂³×D₄	C₂²×D₄	1	8	yes	—
324	C₂³×D₄	C₂²×D₄	1	2	yes	—
325	C₂³×D₄	C₂²×D₄	1	2	yes	—
326	C₂³×D₄	C₂²×D₄	1	4	yes	—
327	C₂³×D₄	C₂²×D₄	1	2	yes	—
328	C₂³×D₄	C₂²×D₄	1	2	yes	—
329	C₂³×D₄	C₂²×D₄	1	8	yes	—
330	C₂³×D₄	C₂²×D₄	1	2	yes	—
331	C₂³×D₄	C₂²×D₄	1	2	yes	—
332	C₂³×D₄	C₂×#41	1	2	yes	—
333	C₂³×D₄	C₂×#41	1	2	yes	—
334	C₂³×D₄	C₂×#41	1	4	yes	—
335	C₂³×D₄	C₂×#41	1	2	yes	—
336	C₂³×D₄	C₂×#41	1	2	yes	—
337	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
338	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
339	C₂⁴×C₄	C₄×D₄	1	4	yes	—
340	C₂⁴×C₄	C₄×D₄	1	8	yes	—
341	C₂⁴×C₄	C₂³×C₄	1	4	yes	—
342	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
343	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
344	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
345	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
348	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
349	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
350	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
352	C₂⁴×C₄	C₂×#41	1	4	yes	—
353	C₂⁴×C₄	C₂×#41	1	2	yes	—
354	C₂⁴×C₄	C₂×#41	1	2	yes	—
355	C₂⁴×C₄	C₂×#41	1	2	yes	—
356	C₂⁴×C₄	C₂×#41	1	2	yes	—
357	C₂⁴×C₄	H(5,𝔽₂)	1	8	yes	—
358	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
359	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
360	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
361	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
362	C₂⁴×C₄	H(5,𝔽₂)	1	2	yes	—
363	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
364	C₂×AGL(1,ℤ/8)	C₂×C₂²⋊C₄	1	32	yes	—
365	C₂×AGL(1,ℤ/8)	C₂×C₂²⋊C₄	1	32	yes	complemented
366	C₂×AGL(1,ℤ/8)	#120	1	32	yes	—
367	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
368	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	—
369	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	complemented
370	C₂²×SD₁₆	C₂×C₂²⋊C₄	1	8	yes	complemented
371	C₂²×SD₁₆	#120	1	16	yes	—
372	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
373	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	—
374	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	complemented
375	C₂²×D₈	C₂×C₂²⋊C₄	1	8	yes	complemented
376	C₂²×D₈	#120	1	16	yes	—
377	C₂²×M₁₆	C₂×C₂²⋊C₄	1	8	yes	complemented
378	C₂²×M₁₆	C₂³×C₄	1	4	yes	—
379	C₂²×M₁₆	C₂³×C₄	1	2	yes	—
380	C₂²×M₁₆	C₂³×C₄	1	2	yes	—
381	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
382	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
383	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
384	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
385	C₂³×C₈	C₂×C₂²⋊C₄	1	8	yes	complemented
386	C₂³×C₈	C₂²×D₄	1	4	yes	—
387	C₂³×C₈	C₂²×D₄	1	2	yes	—
388	C₂³×C₈	C₂²×D₄	1	2	yes	—
389	#525	C₂×C₂²⋊C₄	1	32	yes	complemented
390	C₂×#117	C₂³×C₄	1	4	yes	—
391	C₂×#117	C₂²×D₄	1	8	yes	—
392	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
393	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
394	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
395	C₂²×C₂²⋊C₄	#120	1	8	yes	—
396	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
397	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
398	C₂²×C₄²	C₂²×D₄	1	4	yes	—
399	C₂²×C₄²	C₂²×D₄	1	4	yes	—
400	#418	C₂×C₂²⋊C₄	1	32	yes	complemented
401	#418	C₂×C₂²⋊C₄	1	32	yes	complemented
402	#407	C₂×C₂²⋊C₄	1	32	yes	complemented
403	C₂×#95	#120	1	8	yes	—
404	C₂⁵	C₂×C₄×D₄	1	4	yes	—
405	C₂⁵	C₂×C₄×D₄	1	2	yes	—
406	C₂⁵	C₂×#120	1	2	yes	—
407	C₂⁵	#525	1	2	yes	—
408	C₂⁵	D₄²	1	1	yes	characteristic
409	C₂⁵	D₄²	1	2	yes	—
410	C₂⁵	D₄²	1	8	yes	—
411	C₂⁵	D₄²	1	1	yes	characteristic
412	C₂⁵	D₄²	1	2	yes	—
413	C₂⁵	#546	1	2	yes	—
414	C₂⁵	C₂³×D₄	1	1	yes	characteristic
415	C₂×#41	C₂²×C₂²⋊C₄	1	8	yes	—
416	C₂×#41	C₂×#120	1	8	yes	—
417	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
418	C₂²×Q₈	C₂²×C₂²⋊C₄	1	2	yes	—
419	C₂²×Q₈	C₂×#120	1	4	yes	—
420	C₂²×D₄	#386	1	32	yes	—
421	C₂²×D₄	#386	1	32	yes	—
422	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
423	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
424	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
425	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
426	C₂²×D₄	C₂²×C₂²⋊C₄	1	4	yes	—
427	C₂²×D₄	C₂²×C₂²⋊C₄	1	8	yes	—
428	C₂²×D₄	C₂×C₄×D₄	1	8	yes	—
429	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
430	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
431	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
432	C₂²×D₄	C₂×C₄×D₄	1	4	yes	—
433	C₂²×D₄	#518	1	8	yes	—
434	C₂²×D₄	#518	1	8	yes	—
435	C₂²×D₄	C₂×#120	1	4	yes	—
436	C₂²×D₄	C₂×#120	1	4	yes	—
437	C₂²×D₄	C₂×#120	1	4	yes	—
438	C₂²×D₄	C₂×#120	1	8	yes	—
439	C₂²×D₄	C₂×#120	1	8	yes	—
440	C₂²×D₄	C₂×#121	1	4	yes	—
441	C₂²×D₄	C₂×#121	1	4	yes	—
442	C₂²×D₄	C₂×#121	1	4	yes	—
443	C₂²×D₄	C₂×#121	1	4	yes	—
444	C₂²×D₄	C₂×#123	1	4	yes	—
445	C₂²×D₄	C₂×#123	1	4	yes	—
446	C₂²×D₄	#534	1	8	yes	—
447	C₂²×D₄	#534	1	8	yes	—
448	C₂²×D₄	D₄²	1	16	yes	—
449	C₂²×D₄	D₄²	1	16	yes	—
450	C₂²×D₄	D₄²	1	16	yes	—
451	C₂²×D₄	#546	1	16	yes	—
452	C₂²×D₄	#546	1	16	yes	—
453	C₂²×D₄	#546	1	16	yes	—
454	C₂³×C₄	C₂²×C₂²⋊C₄	1	8	yes	—
455	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
456	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
457	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
458	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
459	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
460	C₂³×C₄	C₂×C₄×D₄	1	2	yes	—
461	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
462	C₂³×C₄	#518	1	8	yes	—
463	C₂³×C₄	#518	1	4	yes	—
464	C₂³×C₄	#518	1	2	yes	—
465	C₂³×C₄	#518	1	2	yes	—
466	C₂³×C₄	C₂×#120	1	2	yes	—
467	C₂³×C₄	C₂×#120	1	2	yes	—
468	C₂³×C₄	C₂×#120	1	2	yes	—
469	C₂³×C₄	C₂×#120	1	8	yes	—
470	C₂³×C₄	C₂×#121	1	4	yes	—
471	C₂³×C₄	C₂×#121	1	4	yes	—
472	C₂³×C₄	C₂×#123	1	2	yes	—
473	C₂³×C₄	C₂×#123	1	2	yes	—
474	C₂³×C₄	#525	1	4	yes	—
475	C₂³×C₄	#525	1	4	yes	—
476	C₂³×C₄	#525	1	2	yes	—
477	C₂³×C₄	#534	1	2	yes	—
478	C₂³×C₄	#534	1	2	yes	—
479	C₂³×C₄	#535	1	4	yes	—
480	C₂³×C₄	#538	1	4	yes	—
481	C₂³×C₄	#538	1	2	yes	—
482	C₂³×C₄	#538	1	2	yes	—
483	C₂³×C₄	D₄²	1	8	yes	—
484	C₂³×C₄	D₄²	1	1	yes	characteristic
485	C₂³×C₄	D₄²	1	1	yes	characteristic
486	C₂³×C₄	D₄²	1	2	yes	—
487	C₂³×C₄	D₄²	1	2	yes	—
488	C₂³×C₄	D₄²	1	2	yes	—
489	C₂³×C₄	D₄²	1	4	yes	—
490	C₂³×C₄	D₄²	1	2	yes	—
491	C₂³×C₄	D₄²	1	2	yes	—
492	C₂³×C₄	D₄²	1	2	yes	—
493	C₂³×C₄	#546	1	16	yes	—
494	C₂³×C₄	#546	1	2	yes	—
495	C₂³×C₄	#546	1	2	yes	—
496	C₂³×C₄	#546	1	4	yes	—
497	C₂³×C₄	#546	1	2	yes	—
498	C₂³×C₄	#546	1	2	yes	—
499	C₂³×C₄	#546	1	2	yes	—
500	C₂³×C₄	#546	1	2	yes	—
501	C₂³×C₄	#546	1	4	yes	—
502	C₂³×C₄	#546	1	2	yes	—
503	C₂³×C₄	#546	1	4	yes	—
504	C₂³×C₄	#546	1	4	yes	—
505	C₂³×C₄	#551	1	2	yes	—
506	C₂³×C₄	#551	1	2	yes	—
507	C₂³×C₄	#551	1	4	yes	—
508	C₂³×C₄	C₂⁴×C₄	1	1	yes	characteristic
509	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
510	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
511	C₂³×C₄	C₂³×D₄	1	4	yes	—
512	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
515	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
516	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
517	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
518	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
519	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
520	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
521	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
525	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
526	C₂×SD₁₆	#379	1	32	yes	complemented
527	C₂×D₈	#379	1	32	yes	complemented
528	C₂×M₁₆	C₂²×C₂²⋊C₄	1	8	yes	—
529	C₂×M₁₆	C₂²×C₂²⋊C₄	1	8	yes	—
530	C₂×M₁₆	C₂×#120	1	8	yes	—
531	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
532	C₂²×C₈	C₂²×C₂²⋊C₄	1	4	yes	—
533	C₂²×C₈	C₂×#120	1	8	yes	—
534	#117	C₂²×C₂²⋊C₄	1	8	yes	—
535	C₂⁴	C₄×#120	1	4	yes	—
536	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
537	C₂⁴	D₄×C₂²⋊C₄	1	8	yes	—
538	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
539	C₂⁴	#2358	1	4	yes	—
540	C₂⁴	#2403	1	2	yes	—
541	C₂⁴	#2403	1	2	yes	—
542	C₂⁴	#2408	1	4	yes	—
543	C₂⁴	#2418	1	2	yes	—
544	C₂⁴	#2418	1	2	yes	—
545	C₂⁴	#2424	1	4	yes	—
546	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
547	C₂⁴	C₂²×#120	1	1	yes	characteristic
548	C₂⁴	C₂×#525	1	1	yes	characteristic
549	C₂⁴	C₂×D₄²	1	1	yes	characteristic
550	C₂⁴	C₂×D₄²	1	1	yes	characteristic
551	C₂⁴	C₂×D₄²	1	4	yes	—
552	C₂⁴	C₂×D₄²	1	1	yes	characteristic
553	C₂⁴	C₂×#546	1	1	yes	characteristic
554	C₂⁴	#3484	1	4	yes	—
555	C₂×Q₈	C₂×#379	1	4	yes	complemented
556	C₂×D₄	C₂×#379	1	8	yes	—
557	C₂×D₄	C₂×#379	1	4	yes	complemented
558	C₂×D₄	C₂×#386	1	8	yes	—
559	C₂×D₄	C₂×#386	1	8	yes	—
560	C₂×D₄	#2308	1	8	yes	—
561	C₂×D₄	D₄×C₂²⋊C₄	1	16	yes	—
562	C₂×D₄	D₄×C₂²⋊C₄	1	16	yes	—
563	C₂×D₄	D₄×C₂²⋊C₄	1	16	yes	—
564	C₂×D₄	#2403	1	16	yes	—
565	C₂×D₄	#2405	1	16	yes	—
566	C₂×D₄	#2410	1	16	yes	—
567	C₂×D₄	#2410	1	16	yes	—
568	C₂²×C₄	C₂×#386	1	4	yes	—
569	C₂²×C₄	C₂×#386	1	4	yes	—
570	C₂²×C₄	C₄×#120	1	4	yes	—
571	C₂²×C₄	#2321	1	4	yes	—
572	C₂²×C₄	#2321	1	4	yes	—
573	C₂²×C₄	D₄×C₂²⋊C₄	1	8	yes	—
574	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
575	C₂²×C₄	D₄×C₂²⋊C₄	1	4	yes	—
576	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
577	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
578	C₂²×C₄	#2358	1	4	yes	—
579	C₂²×C₄	#2358	1	4	yes	—
580	C₂²×C₄	#2358	1	4	yes	—
581	C₂²×C₄	#2403	1	2	yes	—
582	C₂²×C₄	#2403	1	2	yes	—
583	C₂²×C₄	#2404	1	4	yes	—
584	C₂²×C₄	#2404	1	4	yes	—
585	C₂²×C₄	#2408	1	4	yes	—
586	C₂²×C₄	#2418	1	4	yes	—
587	C₂²×C₄	#2418	1	4	yes	—
588	C₂²×C₄	#2418	1	2	yes	—
589	C₂²×C₄	#2418	1	2	yes	—
590	C₂²×C₄	#2424	1	4	yes	—
591	C₂²×C₄	#2424	1	4	yes	—
592	C₂²×C₄	#2424	1	4	yes	—
593	C₂²×C₄	#2534	1	4	yes	—
594	C₂²×C₄	#2534	1	4	yes	—
595	C₂²×C₄	C₂³×C₂²⋊C₄	1	2	yes	—
596	C₂²×C₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
600	C₂²×C₄	C₂×#518	1	1	yes	characteristic
601	C₂²×C₄	C₂×#518	1	1	yes	characteristic
602	C₂²×C₄	C₂×#518	1	2	yes	—
603	C₂²×C₄	C₂×#518	1	2	yes	—
604	C₂²×C₄	C₂×#518	1	2	yes	—
605	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
606	C₂²×C₄	C₂²×#120	1	2	yes	—
607	C₂²×C₄	C₂²×#120	1	2	yes	—
608	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
609	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
610	C₂²×C₄	C₂²×#123	1	1	yes	characteristic
611	C₂²×C₄	C₂×#525	1	1	yes	characteristic
612	C₂²×C₄	C₂×#525	1	1	yes	characteristic
613	C₂²×C₄	C₂×#534	1	1	yes	characteristic
614	C₂²×C₄	C₂×#534	1	2	yes	—
615	C₂²×C₄	C₂×#534	1	2	yes	—
616	C₂²×C₄	C₂×#535	1	1	yes	characteristic
617	C₂²×C₄	C₂×#538	1	1	yes	characteristic
618	C₂²×C₄	C₂×#538	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄²	1	4	yes	—
620	C₂²×C₄	C₂×D₄²	1	4	yes	—
621	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄²	1	4	yes	—
624	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
625	C₂²×C₄	C₂×#546	1	1	yes	characteristic
626	C₂²×C₄	C₂×#546	1	1	yes	characteristic
627	C₂²×C₄	C₂×#546	1	4	yes	—
628	C₂²×C₄	C₂×#546	1	4	yes	—
629	C₂²×C₄	C₂×#546	1	4	yes	—
630	C₂²×C₄	C₂×#546	1	1	yes	characteristic
631	C₂²×C₄	C₂×#546	1	4	yes	—
632	C₂²×C₄	C₂×#546	1	1	yes	characteristic
633	C₂²×C₄	C₂×#546	1	1	yes	characteristic
634	C₂²×C₄	C₂×#546	1	1	yes	characteristic
635	C₂²×C₄	C₂×#546	1	1	yes	characteristic
636	C₂²×C₄	C₂×#551	1	1	yes	characteristic
637	C₂²×C₄	C₂×#551	1	1	yes	characteristic
638	C₂²×C₄	#3484	1	4	yes	—
639	C₂²×C₄	#3484	1	4	yes	—
640	C₂²×C₄	#3484	1	2	yes	—
641	C₂²×C₄	#3484	1	2	yes	—
642	C₂²×C₄	#3484	1	4	yes	—
643	C₂²×C₄	#3484	1	4	yes	—
644	C₂²×C₄	#3484	1	4	yes	—
645	C₂²×C₄	#3484	1	4	yes	—
646	C₂²×C₄	#3484	1	4	yes	—
647	C₂²×C₄	#3484	1	2	yes	—
648	C₂²×C₄	#3484	1	2	yes	—
649	C₂²×C₄	#3490	1	4	yes	—
650	C₂²×C₄	#3490	1	4	yes	—
651	C₂²×C₄	#3490	1	4	yes	—
652	C₂²×C₄	#3490	1	4	yes	—
653	C₂²×C₄	#3532	1	4	yes	—
654	C₂²×C₄	#3532	1	4	yes	—
655	C₂²×C₄	#3532	1	4	yes	—
656	C₂²×C₄	#3532	1	4	yes	—
657	C₂×C₈	C₂×#379	1	8	yes	complemented
658	C₂³	#13967	1	4	yes	—
659	C₂³	#13967	1	4	yes	—
660	C₂³	#23882	1	8	yes	—
661	C₂³	C₂×C₄×#120	1	1	yes	characteristic
662	C₂³	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
663	C₂³	C₂×D₄×C₂²⋊C₄	1	2	yes	—
664	C₂³	C₂×#2358	1	1	yes	characteristic
665	C₂³	#34198	1	2	yes	—
666	C₂³	C₂×#2403	1	1	yes	characteristic
667	C₂³	C₂×#2418	1	1	yes	characteristic
668	C₂³	C₂×#2424	1	1	yes	characteristic
669	C₂³	C₂×#2408	1	1	yes	characteristic
670	C₂³	D₄×#120	1	2	yes	—
671	C₂³	D₄×#120	1	4	yes	—
672	C₂³	D₄×#120	1	2	yes	—
673	C₂³	#36098	1	4	yes	—
674	C₂³	#37644	1	2	yes	—
675	C₂³	#37644	1	2	yes	—
676	C₂³	#58990	1	4	yes	—
677	C₂³	#58991	1	4	yes	—
678	D₄	#13867	1	16	yes	—
679	C₂×C₄	#13967	1	4	yes	—
680	C₂×C₄	#13967	1	4	yes	—
681	C₂×C₄	C₂²×#379	1	1	yes	characteristic
682	C₂×C₄	C₂²×#386	1	1	yes	characteristic
683	C₂×C₄	C₂×#2308	1	1	yes	characteristic
684	C₂×C₄	C₂×#2321	1	1	yes	characteristic
685	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
686	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
687	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
688	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	2	yes	—
689	C₂×C₄	C₂×#2358	1	1	yes	characteristic
690	C₂×C₄	#34171	1	2	yes	—
691	C₂×C₄	#34171	1	1	yes	characteristic
692	C₂×C₄	#34171	1	2	yes	—
693	C₂×C₄	#34171	1	1	yes	characteristic
694	C₂×C₄	#34198	1	2	yes	—
695	C₂×C₄	#34198	1	2	yes	—
696	C₂×C₄	#34198	1	2	yes	—
697	C₂×C₄	#34356	1	2	yes	—
698	C₂×C₄	#34356	1	2	yes	—
699	C₂×C₄	C₂×#2403	1	2	yes	—
700	C₂×C₄	C₂×#2410	1	2	yes	—
701	C₂×C₄	C₂×#2410	1	2	yes	—
702	C₂×C₄	C₂×#2418	1	1	yes	characteristic
703	C₂×C₄	C₂×#2424	1	1	yes	characteristic
704	C₂×C₄	C₂×#2405	1	2	yes	—
705	C₂×C₄	C₂×#2404	1	1	yes	characteristic
706	C₂×C₄	C₂×#2534	1	1	yes	characteristic
707	C₂×C₄	#35346	1	2	yes	—
708	C₂×C₄	#35348	1	2	yes	—
709	C₂×C₄	#35348	1	2	yes	—
710	C₂×C₄	#35350	1	2	yes	—
711	C₂×C₄	D₄×#120	1	2	yes	—
712	C₂×C₄	D₄×#120	1	2	yes	—
713	C₂×C₄	#36098	1	4	yes	—
714	C₂×C₄	#36098	1	4	yes	—
715	C₂×C₄	#36152	1	2	yes	—
716	C₂×C₄	#36152	1	2	yes	—
717	C₂×C₄	#36152	1	2	yes	—
718	C₂×C₄	#36152	1	2	yes	—
719	C₂×C₄	#37644	1	2	yes	—
720	C₂×C₄	#37644	1	4	yes	—
721	C₂×C₄	#37644	1	2	yes	—
722	C₂×C₄	#37645	1	4	yes	—
723	C₂×C₄	#37660	1	4	yes	—
724	C₂×C₄	#37660	1	4	yes	—
725	C₂×C₄	#37832	1	2	yes	—
726	C₂×C₄	#37832	1	2	yes	—
727	C₂×C₄	#37832	1	2	yes	—
728	C₂×C₄	#37832	1	2	yes	—
729	C₂×C₄	#58990	1	4	yes	—
730	C₂×C₄	#58991	1	4	yes	—
731	C₂×C₄	#58991	1	4	yes	—
732	C₂×C₄	#58991	1	4	yes	—
733	C₂×C₄	#59006	1	4	yes	—
734	C₂×C₄	#59006	1	4	yes	—
735	C₂²	#364592	1	8	yes	complemented
736	C₂²	C₂×#13967	1	1	yes	characteristic
737	C₂²	C₂²⋊C₄×#120	1	2	yes	—
738	C₂²	D₄×#379	1	1	yes	characteristic
739	C₂²	#521311	1	1	yes	characteristic
740	C₂²	#531607	1	2	yes	—
741	C₂²	#647656	1	2	yes	—
742	C₂²	#647670	1	2	yes	—
743	C₂²	#647682	1	2	yes	—
744	C₂²	#648042	1	2	yes	—
745	C₂²	C₂×#23882	1	4	yes	—
746	C₄	C₂×#13867	1	1	yes	characteristic
747	C₄	#515285	1	1	yes	characteristic
748	C₄	D₄×#379	1	1	yes	characteristic
749	C₄	#521311	1	1	yes	characteristic
750	C₄	#530231	1	2	yes	—
751	C₄	#531607	1	2	yes	—
752	C₄	#647657	1	2	yes	—
753	C₄	#647671	1	2	yes	—
754	C₄	#647682	1	2	yes	—
755	C₄	#648042	1	2	yes	—
756	C₂	#72214076	1	4	yes	—
757	C₂	C₂×#364592	1	2	yes	—
758	C₂	#72251015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator	C₂³×C₄	C₂⁴×C₄
Frattini, cosocle	C₂⁴×C₄	C₂⁵
prime radical	C₂³×#3003	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262699	C₂	semidirect
2. #72256427	C₂	semidirect
3. #72256327	C₂	semidirect
4. #72256192	C₂	semidirect
5. #72255639	C₂	semidirect
6. #72251326	C₂	semidirect
7. #72251303	C₂	semidirect
8. #72251260	C₂	semidirect
9. #72251204	C₂	semidirect
10. #72249558	C₂	semidirect
11. #72237236	C₂	semidirect
12. #72236747	C₂	semidirect
13. #72235935	C₂	semidirect
14. C₂×#364592	C₂	semidirect
15. #72235090	C₂	semidirect
16. C₂×#359472	C₂	semidirect
17. #72233876	C₂	semidirect
19. #72231771	C₂	semidirect
24. C₂²×#3003	C₄	semidirect
29. C₂×#60168	C₂²	semidirect
33. #7625442	C₂²	semidirect
36. C₂×#34171	C₂²	semidirect
37. #6372005	C₂²	semidirect
38. C₂²×#1904	C₂²	semidirect
39. C₂²×#1904	C₂²	semidirect
40. C₂×#20959	C₂²	semidirect
41. C₂×#20945	C₂²	semidirect
42. #6371425	C₂²	semidirect
43. #6371420	C₂²	semidirect
44. #6370810	C₂²	semidirect
45. C₂×#20605	C₂²	semidirect
46. #6370715	C₂²	semidirect
51. C₂×#20598	C₂²	semidirect
52. C₂×#20598	C₂²	semidirect
53. C₂×#20584	C₂²	semidirect
55. #6369812	C₂²	semidirect
61. #517415	C₂²	semidirect
62. C₂×#11129	C₂²	semidirect
63. C₂×#11100	C₂²	semidirect
64. C₂×#11030	C₂²	semidirect
65. C₂×#11030	C₂²	semidirect
66. #357571	C₂²	semidirect
67. C₂×#11012	C₂²	semidirect
68. C₂×#11012	C₂²	semidirect
69. C₂×#10994	C₂²	semidirect
70. C₂×#10994	C₂²	semidirect
71. #357529	C₂²	semidirect
72. C₂×#10948	C₂²	semidirect
73. C₂×#10937	C₂²	semidirect
74. C₂×#10785	C₂²	semidirect
75. #353416	C₂²	semidirect
76. C₂×#10737	C₂²	semidirect
77. #353407	C₂²	semidirect
78. #353407	C₂²	semidirect
79. #353397	C₂²	semidirect
80. #353397	C₂²	semidirect
81. #353386	C₂²	semidirect
82. C₂×#10776	C₂²	semidirect
83. C₂×#10729	C₂²	semidirect
84. C₂×#10717	C₂²	semidirect
85. C₂×#10716	C₂²	semidirect
86. #123605	C₂²	semidirect
87. #123600	C₂²	semidirect
88. #123560	C₂²	semidirect
89. #123547	C₂²	semidirect
90. #123535	C₂²	semidirect
91. #123531	C₂²	semidirect
93. C₂⁵×D₄	C₂×C₄	semidirect
100. C₂³×AGL(1,ℤ/8)	C₂×C₄	semidirect
114. C₂²×#525	C₂×C₄	semidirect
117. C₂×#3428	C₂³	semidirect
122. C₂×#3003	C₂×C₄	semidirect
123. C₂×#3003	C₂×C₄	semidirect
124. C₂×#3003	C₂×C₄	semidirect
126. C₂×#2911	C₂³	semidirect
127. C₂²×#421	C₂³	semidirect
128. C₂²×#421	C₂³	semidirect
129. C₂×#2896	C₂³	semidirect
130. C₂×#2896	C₂³	semidirect
131. C₂²×#418	C₂×C₄	semidirect
132. C₂²×#418	C₂×C₄	semidirect
143. C₂²×#410	C₂³	semidirect
144. C₂²×#410	C₂³	semidirect
145. C₂²×#407	C₂×C₄	semidirect
151. C₂×#2873	C₂³	semidirect
152. C₂×D₄×C₂²⋊C₄	D₄	semidirect
153. #34044	C₂³	semidirect
167. C₂×#1786	D₄	semidirect
168. C₂²×#344	C₂³	semidirect
169. C₂²×#344	C₂³	semidirect
170. C₂²×#344	C₂³	semidirect
171. C₂×#1742	C₂³	semidirect
172. C₂×#1740	C₂³	semidirect
173. C₂×#1740	C₂³	semidirect
174. #20347	C₂³	semidirect
175. C₂×#1733	C₂³	semidirect
176. C₂×#1733	C₂³	semidirect
177. C₂×#1733	C₂³	semidirect
178. C₂²×H(3,ℤ/4)	C₂³	semidirect
179. C₂²×H(3,ℤ/4)	C₂³	semidirect
180. C₂²×H(3,ℤ/4)	C₂³	semidirect
181. #20335	C₂³	semidirect
185. #13902	D₄	semidirect
218. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
219. C₂²×AGL(1,ℤ/8)	C₂²⋊C₄	semidirect
232. C₂³×SD₁₆	C₂²⋊C₄	semidirect
237. C₂³×D₈	C₂²⋊C₄	semidirect
255. C₂²×C₄×D₄	C₂×D₄	semidirect
264. #3003	C₂²⋊C₄	semidirect
271. C₂²×#102	C₂×D₄	semidirect
272. C₂²×#102	C₂×D₄	semidirect
277. C₂×#390	C₂×D₄	semidirect
278. C₂×#390	C₂×D₄	semidirect
293. C₂²×#41	C₂×C₂²⋊C₄	semidirect
294. C₂²×#41	C₂×C₂²⋊C₄	semidirect
300. C₂³×Q₈	C₂×C₂²⋊C₄	semidirect
305. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
306. C₂³×D₄	C₂×C₂²⋊C₄	semidirect
365. C₂×AGL(1,ℤ/8)	C₂×C₂²⋊C₄	semidirect
369. C₂²×SD₁₆	C₂×C₂²⋊C₄	semidirect
370. C₂²×SD₁₆	C₂×C₂²⋊C₄	semidirect
374. C₂²×D₈	C₂×C₂²⋊C₄	semidirect
375. C₂²×D₈	C₂×C₂²⋊C₄	semidirect
377. C₂²×M₁₆	C₂×C₂²⋊C₄	semidirect
385. C₂³×C₈	C₂×C₂²⋊C₄	semidirect
389. #525	C₂×C₂²⋊C₄	semidirect
400. #418	C₂×C₂²⋊C₄	semidirect
401. #418	C₂×C₂²⋊C₄	semidirect
402. #407	C₂×C₂²⋊C₄	semidirect
526. C₂×SD₁₆	#379	semidirect
527. C₂×D₈	#379	semidirect
555. C₂×Q₈	C₂×#379	semidirect
557. C₂×D₄	C₂×#379	semidirect
657. C₂×C₈	C₂×#379	semidirect
735. C₂²	#364592	semidirect

Maximal subgroups

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

subgroup	index
#72262699	2
#72256427	2
#72256327	2
#72256192	2
#72255639	2
#72251326	2
#72251303	2
#72251260	2
#72251204	2
#72249558	2
#72237236	2
#72236747	2
#72235935	2
C₂×#364592	2
#72235090	2
C₂×#359472	2
#72233876	2
C₂³×#3003	2
#72231771	2