Subgroups — #72240620

Order 2048.

At least 6612 conjugacy classes of subgroups; only the 5392 normal subgroups are shown.

The subgroup lattice has 626 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240619	C₂	1	2	yes	maximal, complemented
2	#72240618	C₂	1	4	yes	maximal, complemented
3	#72240617	C₂	1	2	yes	maximal, complemented
4	#72240616	C₂	1	16	yes	maximal, complemented
5	#72238594	C₂	1	4	yes	maximal, complemented
6	#72237559	C₂	1	4	yes	maximal, complemented
7	#72234629	C₂	1	4	yes	maximal, complemented
8	#72233780	C₂	1	2	yes	maximal, complemented
9	#72219307	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#7631286	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#7631286	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#32898	C₂	1	2	yes	maximal, complemented
13	#72216660	C₂	1	16	yes	maximal, complemented
14	#72214832	C₂	1	4	yes	maximal, complemented
15	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
16	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3484	C₂²	1	2	yes	complemented
18	C₂³×D₄²	C₂²	1	1	yes	characteristic
19	C₂³×B(4,𝔽₂)	C₂²	1	8	yes	complemented
20	#7631286	C₂²	1	16	yes	complemented
21	C₂×#36212	C₂²	1	8	yes	complemented
22	C₂×D₄×#120	C₂²	1	8	yes	complemented
23	C₂×#35347	C₂²	1	2	yes	complemented
24	C₂×#35346	C₂²	1	2	yes	complemented
25	C₂×#35250	C₂²	1	2	yes	complemented
26	C₂×#34980	C₂²	1	2	yes	complemented
27	C₂×#34980	C₂²	1	2	yes	complemented
28	C₂×#34980	C₂²	1	2	yes	complemented
29	C₂×#34736	C₂²	1	2	yes	complemented
30	C₂²×#2403	C₂²	1	2	yes	—
31	C₂²×#2403	C₂²	1	2	yes	—
32	C₂²×#2403	C₂²	1	2	yes	complemented
33	C₂²×#2403	C₂²	1	4	yes	complemented
34	C₂×#34256	C₂²	1	2	yes	complemented
35	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
36	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
37	C₂×#32898	C₂²	1	8	yes	complemented
38	C₂×#32898	C₂²	1	8	yes	complemented
39	C₂×#32898	C₂²	1	16	yes	complemented
40	C₂×#23900	C₂²	1	16	yes	complemented
41	C₂×#21746	C₂²	1	2	yes	complemented
42	C₂²×#1790	C₂²	1	8	yes	complemented
43	C₂²×#1781	C₂²	1	2	yes	complemented
44	C₂²×#1781	C₂²	1	4	yes	complemented
45	#613188	C₂²	1	8	yes	complemented
46	#613188	C₂²	1	16	yes	complemented
47	#612424	C₂²	1	8	yes	complemented
48	#612424	C₂²	1	16	yes	complemented
49	#517411	C₂²	1	4	yes	complemented
50	#517411	C₂²	1	2	yes	complemented
51	#449501	C₂²	1	16	yes	complemented
52	#449475	C₂²	1	16	yes	complemented
53	#417898	C₂²	1	16	yes	complemented
54	#417821	C₂²	1	16	yes	complemented
55	#417526	C₂²	1	32	yes	complemented
56	#417508	C₂²	1	32	yes	complemented
57	#405104	C₂²	1	16	yes	complemented
58	#405090	C₂²	1	16	yes	complemented
59	#394419	C₂²	1	16	yes	complemented
60	#394267	C₂²	1	32	yes	complemented
61	#394174	C₂²	1	16	yes	complemented
62	#394066	C₂²	1	32	yes	complemented
63	#394058	C₂²	1	16	yes	complemented
64	#393929	C₂²	1	16	yes	complemented
65	#392658	C₂²	1	8	yes	complemented
66	#392245	C₂²	1	2	yes	complemented
67	#392109	C₂²	1	2	yes	complemented
68	#382422	C₂²	1	2	yes	complemented
69	#382390	C₂²	1	2	yes	complemented
70	#379754	C₂²	1	8	yes	complemented
71	#374038	C₂²	1	16	yes	complemented
72	#364513	C₂²	1	32	yes	complemented
73	#364471	C₂²	1	32	yes	complemented
74	#359863	C₂²	1	8	yes	complemented
75	#359695	C₂²	1	8	yes	complemented
76	#359579	C₂²	1	16	yes	complemented
77	#359552	C₂²	1	16	yes	complemented
78	#359501	C₂²	1	8	yes	complemented
79	#359428	C₂²	1	8	yes	complemented
80	#355913	C₂²	1	4	yes	complemented
81	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
82	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
83	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
84	C₂⁴×#41	C₂³	1	4	yes	complemented
85	C₂⁴×#41	C₂³	1	2	yes	complemented
86	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
87	C₂⁵×D₄	C₂³	1	1	yes	characteristic
88	C₂⁵×D₄	C₂³	1	2	yes	—
89	C₂⁵×D₄	C₂³	1	1	yes	characteristic
90	C₂⁵×D₄	C₂³	1	2	yes	—
91	C₂⁵×D₄	C₂³	1	1	yes	characteristic
92	C₂⁵×D₄	C₂³	1	2	yes	complemented
93	C₂⁵×D₄	C₂³	1	4	yes	complemented
94	C₂×#3484	C₂³	1	16	yes	—
95	C₂²×D₄²	D₄	1	8	yes	complemented
96	C₂²×D₄²	C₂³	1	8	yes	—
97	C₂²×#534	C₂³	1	4	yes	—
98	C₂³×#127	D₄	1	1	yes	characteristic, complemented
99	C₂³×#121	D₄	1	1	yes	characteristic, complemented
100	C₂³×#121	D₄	1	1	yes	characteristic, complemented
101	C₂³×#121	D₄	1	1	yes	characteristic, complemented
102	C₂³×#121	C₂³	1	1	yes	characteristic
103	C₂³×#120	D₄	1	1	yes	characteristic, complemented
104	C₂³×#120	D₄	1	1	yes	characteristic, complemented
105	C₂³×#120	D₄	1	4	yes	complemented
106	C₂³×#120	C₂³	1	4	yes	—
107	C₂³×#120	C₂³	1	1	yes	characteristic
108	C₂³×#120	C₂³	1	1	yes	characteristic
109	C₂³×#120	C₂³	1	4	yes	—
110	C₂³×#120	C₂³	1	8	yes	complemented
111	C₂³×#120	C₂³	1	4	yes	complemented
112	C₂²×#518	C₂³	1	2	yes	—
113	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
114	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
115	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	—
116	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	complemented
117	C₂³×#99	C₂³	1	8	yes	—
118	C₂³×#99	C₂³	1	16	yes	complemented
119	C₂×#2849	C₂³	1	4	yes	complemented
120	C₂×#2849	C₂³	1	4	yes	complemented
121	C₂×#2847	C₂³	1	8	yes	complemented
122	C₂×#2846	C₂³	1	4	yes	complemented
123	C₂×#2846	C₂³	1	4	yes	complemented
124	C₂×#2846	C₂³	1	16	yes	complemented
125	#35347	C₂³	1	16	yes	—
126	#35346	C₂³	1	16	yes	—
127	#34980	C₂³	1	16	yes	—
128	C₂×#2436	C₂³	1	4	yes	complemented
129	C₂×#2409	C₂³	1	4	yes	complemented
130	C₂×#2433	C₂³	1	4	yes	complemented
131	C₂×#2408	C₂³	1	4	yes	complemented
132	C₂×#2405	C₂³	1	4	yes	complemented
133	C₂×#2410	C₂³	1	8	yes	complemented
134	C₂×#2410	C₂³	1	8	yes	complemented
135	C₂×#2403	D₄	1	32	yes	complemented
136	C₂×#2403	D₄	1	16	yes	complemented
137	C₂×#2403	C₂³	1	16	yes	—
138	C₂×#2403	C₂³	1	8	yes	—
139	C₂×#2403	C₂³	1	4	yes	—
140	C₂×#2403	C₂³	1	4	yes	—
141	C₂×#2403	C₂³	1	16	yes	—
142	C₂×#2403	C₂³	1	4	yes	complemented
143	C₂×#2403	C₂³	1	16	yes	complemented
144	C₂×#2403	C₂³	1	8	yes	complemented
145	C₂²×#392	D₄	1	8	yes	complemented
146	#34256	C₂³	1	16	yes	—
147	#34171	C₂³	1	8	yes	—
148	C₂×D₄×C₂²⋊C₄	C₂³	1	8	yes	complemented
149	C₂×#2308	C₂³	1	2	yes	—
150	C₂×#2308	C₂³	1	4	yes	—
151	C₂×C₄×#120	C₂³	1	8	yes	complemented
152	C₂²×#386	D₄	1	4	yes	complemented
153	C₂²×#386	C₂³	1	4	yes	—
154	C₂²×#386	C₂³	1	4	yes	—
155	C₂²×#386	C₂³	1	8	yes	complemented
156	C₂²×#386	C₂³	1	4	yes	complemented
157	C₂×#2280	C₂³	1	2	yes	complemented
158	C₂²×#379	C₂³	1	4	yes	—
159	C₂²×#379	C₂³	1	2	yes	—
160	C₂²×#379	C₂³	1	2	yes	—
161	C₂²×#379	C₂³	1	2	yes	complemented
162	C₂×#2021	C₂³	1	64	yes	complemented
163	C₂×#1898	C₂³	1	32	yes	complemented
164	C₂×#1898	C₂³	1	16	yes	complemented
165	C₂×#1889	C₂³	1	32	yes	complemented
166	C₂×#1819	C₂³	1	4	yes	complemented
167	C₂×#1790	C₂³	1	32	yes	—
168	C₂×#1790	C₂³	1	32	yes	complemented
169	C₂×#1781	C₂³	1	16	yes	—
170	C₂×#1781	C₂³	1	4	yes	—
171	C₂×#1781	C₂³	1	8	yes	—
172	C₂×#1781	C₂³	1	4	yes	—
173	C₂×#1781	C₂³	1	16	yes	complemented
174	C₂×#1781	C₂³	1	16	yes	complemented
175	C₂×#1781	C₂³	1	4	yes	complemented
176	#14873	C₂³	1	16	yes	complemented
177	#14715	C₂³	1	16	yes	complemented
178	#14715	C₂³	1	32	yes	complemented
179	#14694	C₂³	1	16	yes	complemented
180	#14694	C₂³	1	32	yes	complemented
181	#14681	C₂³	1	4	yes	complemented
182	#14681	C₂³	1	8	yes	complemented
183	#14679	C₂³	1	4	yes	complemented
184	#14679	C₂³	1	8	yes	complemented
185	#13867	C₂³	1	16	yes	complemented
186	#13867	C₂³	1	16	yes	complemented
187	#13867	C₂³	1	16	yes	complemented
188	#11174	C₂³	1	32	yes	complemented
189	#11087	C₂³	1	64	yes	complemented
190	#11043	C₂³	1	32	yes	complemented
191	#10995	C₂³	1	64	yes	complemented
192	#10991	C₂³	1	32	yes	complemented
193	#10991	C₂³	1	64	yes	complemented
194	#10980	C₂³	1	16	yes	complemented
195	#10965	C₂³	1	32	yes	complemented
196	#10965	C₂³	1	16	yes	complemented
197	#10960	C₂³	1	32	yes	complemented
198	#10761	C₂³	1	16	yes	complemented
199	#10745	C₂³	1	32	yes	complemented
200	#10735	C₂³	1	16	yes	complemented
201	#10735	C₂³	1	16	yes	complemented
202	#10725	C₂³	1	16	yes	complemented
203	C₂⁷	C₂×D₄	1	1	yes	characteristic
204	C₂⁷	C₂×D₄	1	2	yes	complemented
205	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂⁷	C₂⁴	1	2	yes	—
207	C₂⁷	C₂⁴	1	1	yes	characteristic
208	C₂⁷	C₂⁴	1	1	yes	characteristic
209	C₂⁷	C₂⁴	1	2	yes	complemented
210	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
211	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
212	C₂⁴×Q₈	C₂⁴	1	2	yes	complemented
213	C₂⁴×D₄	C₂×D₄	1	16	yes	—
214	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×D₄	C₂×D₄	1	4	yes	—
216	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
217	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂⁴×D₄	C₂×D₄	1	8	yes	—
219	C₂⁴×D₄	C₂×D₄	1	4	yes	—
220	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×D₄	C₂×D₄	1	4	yes	—
224	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
225	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
226	C₂⁴×D₄	C₂×D₄	1	4	yes	—
227	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
228	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
229	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
230	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
231	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
233	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
237	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
238	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
239	C₂⁴×D₄	C₂⁴	1	4	yes	—
240	C₂⁴×D₄	C₂⁴	1	8	yes	—
241	C₂⁴×D₄	C₂⁴	1	4	yes	—
242	C₂⁴×D₄	C₂⁴	1	4	yes	—
243	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
244	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
245	C₂⁴×D₄	C₂⁴	1	4	yes	—
246	C₂⁴×D₄	C₂⁴	1	4	yes	—
247	C₂⁴×D₄	C₂⁴	1	4	yes	—
248	C₂⁴×D₄	C₂⁴	1	4	yes	complemented
249	C₂⁴×D₄	C₂⁴	1	2	yes	complemented
250	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
251	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
252	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
254	C₂⁵×C₄	C₂⁴	1	2	yes	—
255	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
256	C₂⁵×C₄	C₂⁴	1	4	yes	complemented
257	C₂⁵×C₄	C₂⁴	1	2	yes	complemented
258	C₂×#534	C₂⁴	1	16	yes	—
259	C₂²×#127	C₂×D₄	1	8	yes	complemented
260	C₂²×#121	C₂×D₄	1	4	yes	complemented
261	C₂²×#121	C₂×D₄	1	8	yes	complemented
262	C₂²×#121	C₂×D₄	1	8	yes	complemented
263	C₂²×#121	C₂×D₄	1	8	yes	complemented
264	C₂²×#121	C₂⁴	1	4	yes	—
265	C₂²×#120	C₂×D₄	1	4	yes	—
266	C₂²×#120	C₂×D₄	1	32	yes	complemented
267	C₂²×#120	C₂×D₄	1	8	yes	complemented
268	C₂²×#120	C₂×D₄	1	4	yes	complemented
269	C₂²×#120	C₂×D₄	1	8	yes	complemented
270	C₂²×#120	C₂×D₄	1	16	yes	complemented
271	C₂²×#120	C₂×D₄	1	32	yes	complemented
272	C₂²×#120	C₂⁴	1	8	yes	—
273	C₂²×#120	C₂⁴	1	32	yes	—
274	C₂²×#120	C₂⁴	1	8	yes	—
275	C₂²×#120	C₂⁴	1	4	yes	—
276	C₂²×#120	C₂⁴	1	4	yes	—
277	C₂²×#120	C₂⁴	1	16	yes	—
278	C₂²×#120	C₂⁴	1	8	yes	complemented
279	C₂×#518	C₂⁴	1	8	yes	—
280	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
281	C₂²×C₄×D₄	C₂×D₄	1	4	yes	complemented
282	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
283	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
284	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
285	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
286	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
287	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
288	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
289	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
290	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
291	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
292	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
293	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
294	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
295	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
296	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
297	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
298	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
299	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
300	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
301	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
302	C₂²×#99	C₂⁴	1	16	yes	—
303	C₂²×#99	C₂⁴	1	64	yes	—
304	C₂²×#99	C₂⁴	1	16	yes	—
305	C₂²×#99	C₂⁴	1	16	yes	complemented
306	#2403	C₂×D₄	1	32	yes	complemented
307	#2403	C₂×D₄	1	64	yes	complemented
308	#2403	C₂×D₄	1	32	yes	complemented
309	C₂×#392	C₂×D₄	1	64	yes	complemented
310	#2308	C₂⁴	1	8	yes	—
311	#2308	C₂⁴	1	16	yes	—
312	C₂×#386	C₂×D₄	1	32	yes	complemented
313	C₂×#386	C₂×D₄	1	16	yes	complemented
314	C₂×#386	C₂×D₄	1	32	yes	complemented
315	C₂×#386	C₂⁴	1	32	yes	—
316	C₂×#386	C₂⁴	1	8	yes	—
317	C₂×#386	C₂⁴	1	8	yes	—
318	C₂×#386	C₂⁴	1	16	yes	—
319	C₂×#386	C₂⁴	1	8	yes	complemented
320	C₂×#385	C₂⁴	1	8	yes	complemented
321	C₂×#380	C₂⁴	1	4	yes	complemented
322	C₂×#379	C₂×D₄	1	16	yes	complemented
323	C₂×#379	C₂×D₄	1	8	yes	complemented
324	C₂×#379	C₂⁴	1	8	yes	—
325	C₂×#379	C₂⁴	1	8	yes	—
326	C₂×#379	C₂⁴	1	4	yes	—
327	C₂×#379	C₂⁴	1	4	yes	—
328	C₂×#379	C₂⁴	1	8	yes	—
329	C₂×#379	C₂⁴	1	8	yes	complemented
330	C₂×#379	C₂⁴	1	4	yes	complemented
331	C₂×#379	C₂⁴	1	16	yes	complemented
332	C₂×#379	C₂⁴	1	32	yes	complemented
333	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
334	C₂²×#95	C₂×D₄	1	8	yes	complemented
335	C₂×#342	C₂⁴	1	16	yes	complemented
336	C₂×#342	C₂⁴	1	64	yes	complemented
337	C₂²⋊#95	C₂⁴	1	16	yes	complemented
338	C₂²⋊#95	C₂⁴	1	32	yes	complemented
339	C₂⁶	#120	1	8	yes	complemented
340	C₂⁶	C₂²×D₄	1	1	yes	characteristic
341	C₂⁶	C₂²×D₄	1	1	yes	characteristic
342	C₂⁶	C₂²×D₄	1	8	yes	—
343	C₂⁶	C₂²×D₄	1	4	yes	—
344	C₂⁶	C₂²×D₄	1	4	yes	—
345	C₂⁶	C₂²×D₄	1	4	yes	—
346	C₂⁶	C₂²×D₄	1	4	yes	—
347	C₂⁶	C₂²×D₄	1	1	yes	characteristic
348	C₂⁶	C₂²×D₄	1	2	yes	—
349	C₂⁶	C₂²×D₄	1	1	yes	characteristic
350	C₂⁶	C₂²×D₄	1	4	yes	—
351	C₂⁶	C₂²×D₄	1	1	yes	characteristic
352	C₂⁶	C₂²×D₄	1	2	yes	—
353	C₂⁶	C₂²×D₄	1	1	yes	characteristic
354	C₂⁶	C₂²×D₄	1	1	yes	characteristic
355	C₂⁶	C₂²×D₄	1	2	yes	—
356	C₂⁶	C₂²×D₄	1	4	yes	—
357	C₂⁶	C₂²×D₄	1	2	yes	—
358	C₂⁶	C₂²×D₄	1	8	yes	—
359	C₂⁶	C₂²×D₄	1	8	yes	complemented
360	C₂⁶	H(5,𝔽₂)	1	8	yes	—
361	C₂⁶	C₂⁵	1	4	yes	—
362	C₂⁶	C₂⁵	1	2	yes	—
363	C₂⁶	C₂⁵	1	1	yes	characteristic
364	C₂⁶	C₂⁵	1	2	yes	—
365	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	32	yes	complemented
366	C₂³×D₄	#120	1	2	yes	—
367	C₂³×D₄	#120	1	4	yes	—
368	C₂³×D₄	#120	1	2	yes	—
369	C₂³×D₄	#120	1	4	yes	—
370	C₂³×D₄	#120	1	4	yes	—
371	C₂³×D₄	#120	1	16	yes	—
372	C₂³×D₄	#120	1	2	yes	—
373	C₂³×D₄	#120	1	2	yes	—
374	C₂³×D₄	#120	1	16	yes	—
375	C₂³×D₄	#120	1	4	yes	—
376	C₂³×D₄	#120	1	4	yes	—
377	C₂³×D₄	#120	1	4	yes	—
378	C₂³×D₄	#120	1	32	yes	complemented
379	C₂³×D₄	#120	1	8	yes	complemented
380	C₂³×D₄	#120	1	8	yes	complemented
381	C₂³×D₄	C₂²×D₄	1	8	yes	—
382	C₂³×D₄	C₂²×D₄	1	16	yes	—
383	C₂³×D₄	C₂²×D₄	1	16	yes	—
384	C₂³×D₄	C₂²×D₄	1	8	yes	—
385	C₂³×D₄	C₂²×D₄	1	4	yes	—
386	C₂³×D₄	C₂²×D₄	1	2	yes	—
387	C₂³×D₄	C₂²×D₄	1	8	yes	—
388	C₂³×D₄	C₂²×D₄	1	16	yes	—
389	C₂³×D₄	C₂²×D₄	1	4	yes	—
390	C₂³×D₄	C₂²×D₄	1	4	yes	—
391	C₂³×D₄	C₂²×D₄	1	4	yes	—
392	C₂³×D₄	C₂²×D₄	1	16	yes	—
393	C₂³×D₄	C₂²×D₄	1	4	yes	—
394	C₂³×D₄	C₂²×D₄	1	16	yes	—
395	C₂³×D₄	C₂²×D₄	1	4	yes	—
396	C₂³×D₄	C₂²×D₄	1	2	yes	—
397	C₂³×D₄	C₂²×D₄	1	4	yes	—
398	C₂³×D₄	C₂²×D₄	1	4	yes	—
399	C₂³×D₄	C₂²×D₄	1	4	yes	—
400	C₂³×D₄	C₂²×D₄	1	2	yes	—
401	C₂³×D₄	C₂²×D₄	1	16	yes	—
402	C₂³×D₄	C₂²×D₄	1	4	yes	—
403	C₂³×D₄	C₂²×D₄	1	4	yes	—
404	C₂³×D₄	C₂²×D₄	1	4	yes	—
405	C₂³×D₄	C₂²×D₄	1	32	yes	—
406	C₂³×D₄	C₂²×D₄	1	4	yes	—
407	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
408	C₂³×D₄	C₂⁵	1	2	yes	—
409	C₂³×D₄	C₂⁵	1	2	yes	—
410	C₂³×D₄	C₂⁵	1	8	yes	—
411	C₂³×D₄	C₂⁵	1	2	yes	—
412	C₂⁴×C₄	#120	1	8	yes	complemented
413	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
414	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
415	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
416	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
417	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
418	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
419	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
420	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
421	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
422	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
423	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
424	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
425	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
426	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
427	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
428	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
429	C₂⁴×C₄	C₂²×D₄	1	8	yes	complemented
430	C₂⁴×C₄	C₂⁵	1	4	yes	—
431	C₂⁴×C₄	C₂⁵	1	2	yes	—
432	C₂×#120	C₂²×D₄	1	32	yes	—
433	C₂×#120	C₂²×D₄	1	32	yes	complemented
434	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
435	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
436	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
437	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
438	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
439	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
440	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
441	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
442	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
443	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
444	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
445	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
446	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
447	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
448	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
449	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
450	C₂²×C₂²⋊C₄	C₂⁵	1	16	yes	—
451	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
452	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
453	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
454	C₂²×C₄²	C₂²×D₄	1	4	yes	—
455	#386	C₂²×D₄	1	32	yes	—
456	#386	C₂²×D₄	1	32	yes	complemented
457	#379	C₂²×D₄	1	16	yes	—
458	#379	C₂²×D₄	1	16	yes	complemented
459	C₂×#95	C₂²×D₄	1	32	yes	—
460	C₂⁵	C₂×#120	1	2	yes	—
461	C₂⁵	C₂×#120	1	2	yes	—
462	C₂⁵	C₂×#120	1	4	yes	—
463	C₂⁵	C₂×#120	1	8	yes	—
464	C₂⁵	C₂×#120	1	2	yes	—
465	C₂⁵	C₂×#120	1	1	yes	characteristic
466	C₂⁵	C₂×#120	1	4	yes	—
467	C₂⁵	C₂×#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	2	yes	—
469	C₂⁵	C₂×#120	1	16	yes	—
470	C₂⁵	C₂×#120	1	4	yes	—
471	C₂⁵	C₂×#120	1	2	yes	—
472	C₂⁵	C₂×#120	1	4	yes	—
473	C₂⁵	C₂×#120	1	4	yes	—
474	C₂⁵	C₂×#120	1	2	yes	—
475	C₂⁵	C₂×#120	1	8	yes	—
476	C₂⁵	C₂×#120	1	4	yes	—
477	C₂⁵	C₂×#120	1	1	yes	characteristic
478	C₂⁵	#534	1	4	yes	—
479	C₂⁵	#534	1	4	yes	—
480	C₂⁵	#534	1	8	yes	—
481	C₂⁵	D₄²	1	16	yes	—
482	C₂⁵	D₄²	1	16	yes	—
483	C₂⁵	D₄²	1	16	yes	—
484	C₂⁵	D₄²	1	16	yes	—
485	C₂⁵	C₂³×D₄	1	2	yes	—
486	C₂⁵	C₂³×D₄	1	8	yes	—
487	C₂⁵	C₂³×D₄	1	1	yes	characteristic
488	C₂⁵	C₂³×D₄	1	2	yes	—
489	C₂⁵	C₂³×D₄	1	2	yes	—
490	C₂⁵	C₂³×D₄	1	4	yes	—
491	C₂⁵	C₂³×D₄	1	2	yes	—
492	C₂⁵	C₂³×D₄	1	8	yes	—
493	C₂⁵	C₂³×D₄	1	2	yes	—
494	C₂⁵	C₂³×D₄	1	2	yes	—
495	C₂⁵	C₂³×D₄	1	8	yes	—
496	C₂⁵	C₂³×D₄	1	1	yes	characteristic
497	C₂⁵	C₂³×D₄	1	2	yes	—
498	C₂⁵	C₂³×D₄	1	2	yes	—
499	C₂⁵	C₂³×D₄	1	4	yes	—
500	C₂⁵	C₂³×D₄	1	2	yes	—
501	C₂⁵	C₂³×D₄	1	4	yes	—
502	C₂⁵	C₂³×D₄	1	4	yes	—
503	C₂⁵	C₂³×D₄	1	4	yes	—
504	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
505	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
506	C₂⁵	C₂⁶	1	1	yes	characteristic
507	C₂²×D₄	B(4,𝔽₂)	1	16	yes	complemented
508	C₂²×D₄	C₂×#120	1	8	yes	—
509	C₂²×D₄	C₂×#120	1	8	yes	—
510	C₂²×D₄	C₂×#120	1	8	yes	—
511	C₂²×D₄	C₂×#120	1	16	yes	—
512	C₂²×D₄	C₂×#120	1	16	yes	—
513	C₂²×D₄	C₂×#120	1	16	yes	—
514	C₂²×D₄	C₂×#120	1	16	yes	—
515	C₂²×D₄	C₂×#120	1	8	yes	—
516	C₂²×D₄	C₂×#120	1	8	yes	—
517	C₂²×D₄	C₂×#120	1	8	yes	—
518	C₂²×D₄	C₂³×D₄	1	8	yes	—
519	C₂²×D₄	C₂³×D₄	1	8	yes	—
520	C₂²×D₄	C₂×H(5,𝔽₂)	1	16	yes	—
521	C₂²×D₄	C₂×H(5,𝔽₂)	1	32	yes	—
522	C₂³×C₄	C₂×#120	1	2	yes	—
523	C₂³×C₄	C₂×#120	1	4	yes	—
524	C₂³×C₄	C₂×#120	1	2	yes	—
525	C₂³×C₄	C₂×#120	1	16	yes	—
526	C₂³×C₄	C₂×#120	1	8	yes	—
527	C₂³×C₄	C₂×#120	1	2	yes	—
528	C₂³×C₄	C₂×#120	1	4	yes	—
529	C₂³×C₄	C₂×#120	1	2	yes	—
530	C₂³×C₄	C₂³×D₄	1	2	yes	—
531	C₂³×C₄	C₂³×D₄	1	2	yes	—
532	C₂³×C₄	C₂³×D₄	1	2	yes	—
533	C₂³×C₄	C₂³×D₄	1	8	yes	—
534	C₂³×C₄	C₂³×D₄	1	8	yes	—
535	C₂³×C₄	C₂³×D₄	1	2	yes	—
536	C₂³×C₄	C₂³×D₄	1	16	yes	—
537	C₂³×C₄	C₂³×D₄	1	2	yes	—
538	C₂³×C₄	C₂³×D₄	1	2	yes	—
539	C₂³×C₄	C₂³×D₄	1	8	yes	—
540	C₂³×C₄	C₂³×D₄	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
542	C₂⁴	#2403	1	4	yes	—
543	C₂⁴	#2403	1	8	yes	—
544	C₂⁴	#2403	1	8	yes	—
545	C₂⁴	#2403	1	16	yes	—
546	C₂⁴	#2403	1	8	yes	—
547	C₂⁴	#2403	1	16	yes	—
548	C₂⁴	#2403	1	4	yes	—
549	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
550	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	complemented
551	C₂⁴	C₂²×#120	1	4	yes	—
552	C₂⁴	C₂²×#120	1	4	yes	—
553	C₂⁴	C₂²×#120	1	2	yes	—
554	C₂⁴	C₂²×#120	1	1	yes	characteristic
555	C₂⁴	C₂²×#120	1	2	yes	—
556	C₂⁴	C₂²×#120	1	4	yes	—
557	C₂⁴	C₂²×#120	1	2	yes	—
558	C₂⁴	C₂²×#120	1	4	yes	—
559	C₂⁴	C₂²×#120	1	2	yes	—
560	C₂⁴	C₂²×#120	1	1	yes	characteristic
561	C₂⁴	C₂²×#120	1	4	yes	—
562	C₂⁴	C₂²×#120	1	4	yes	—
563	C₂⁴	C₂²×#120	1	4	yes	—
564	C₂⁴	C₂²×#120	1	2	yes	—
565	C₂⁴	C₂×#534	1	4	yes	—
566	C₂⁴	C₂×#534	1	2	yes	—
567	C₂⁴	C₂×#534	1	2	yes	—
568	C₂⁴	C₂×#534	1	4	yes	—
569	C₂⁴	C₂×D₄²	1	8	yes	—
570	C₂⁴	C₂×D₄²	1	8	yes	—
571	C₂⁴	C₂×D₄²	1	8	yes	—
572	C₂⁴	C₂×D₄²	1	8	yes	—
573	C₂⁴	C₂×D₄²	1	8	yes	—
574	C₂⁴	C₂×D₄²	1	8	yes	—
575	C₂⁴	#3484	1	8	yes	—
576	C₂⁴	#3484	1	16	yes	complemented
577	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
578	C₂⁴	C₂⁴×D₄	1	2	yes	—
579	C₂⁴	C₂⁴×D₄	1	2	yes	—
580	C₂⁴	C₂²×H(5,𝔽₂)	1	8	yes	—
581	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
582	C₂×D₄	C₂×B(4,𝔽₂)	1	32	yes	complemented
583	C₂×D₄	#3484	1	32	yes	—
584	C₂²×C₄	C₂×B(4,𝔽₂)	1	8	yes	complemented
585	C₂²×C₄	C₂²×#120	1	4	yes	—
586	C₂²×C₄	C₂²×#120	1	4	yes	—
587	C₂²×C₄	C₂²×#120	1	4	yes	—
588	C₂²×C₄	C₂²×#120	1	4	yes	—
589	C₂²×C₄	#3484	1	8	yes	—
590	C₂²×C₄	#3484	1	16	yes	complemented
591	C₂³	#23900	1	16	yes	complemented
592	C₂³	C₂×#2403	1	4	yes	—
593	C₂³	C₂×#2403	1	4	yes	—
594	C₂³	C₂×#2403	1	8	yes	—
595	C₂³	C₂×#2403	1	2	yes	—
596	C₂³	C₂×#2403	1	4	yes	—
597	C₂³	C₂×#2403	1	2	yes	—
598	C₂³	#35346	1	8	yes	complemented
599	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
600	C₂³	C₂²×B(4,𝔽₂)	1	8	yes	—
601	C₂³	C₂²×B(4,𝔽₂)	1	4	yes	—
602	C₂³	C₂³×#120	1	1	yes	characteristic
603	C₂³	C₂³×#120	1	1	yes	characteristic
604	C₂³	C₂²×#534	1	1	yes	characteristic
605	C₂³	C₂²×D₄²	1	4	yes	—
606	C₂³	C₂×#3484	1	4	yes	—
607	C₂³	C₂×#3484	1	8	yes	—
608	C₂³	C₂×#3484	1	8	yes	—
609	C₂³	#62817	1	8	yes	—
610	C₂×C₄	#35346	1	8	yes	complemented
611	C₂×C₄	C₂²×B(4,𝔽₂)	1	8	yes	—
612	C₂²	C₂×#23900	1	4	yes	—
613	C₂²	C₂×#23900	1	8	yes	—
614	C₂²	C₂²×#2403	1	1	yes	characteristic
615	C₂²	C₂×#35346	1	2	yes	—
616	C₂²	#7630939	1	2	yes	—
617	C₂²	#7642244	1	2	yes	—
618	C₂²	#7670203	1	8	yes	—
619	C₂²	C₂³×B(4,𝔽₂)	1	2	yes	—
620	C₂²	#10574873	1	2	yes	—
621	C₂	#72217875	1	1	yes	characteristic
622	C₂	C₂²×#23900	1	1	yes	characteristic
623	C₂	#72234135	1	4	yes	—
624	C₂	#72240571	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂³×#120
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72240619	C₂	semidirect
2. #72240618	C₂	semidirect
3. #72240617	C₂	semidirect
4. #72240616	C₂	semidirect
5. #72238594	C₂	semidirect
6. #72237559	C₂	semidirect
7. #72234629	C₂	semidirect
8. #72233780	C₂	semidirect
9. #72219307	C₂	semidirect
10. C₂×#7631286	C₂	semidirect
11. C₂×#7631286	C₂	semidirect
12. C₂²×#32898	C₂	semidirect
13. #72216660	C₂	semidirect
14. #72214832	C₂	semidirect
15. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
16. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#3484	C₂²	semidirect
19. C₂³×B(4,𝔽₂)	C₂²	semidirect
20. #7631286	C₂²	semidirect
21. C₂×#36212	C₂²	semidirect
22. C₂×D₄×#120	C₂²	semidirect
23. C₂×#35347	C₂²	semidirect
24. C₂×#35346	C₂²	semidirect
25. C₂×#35250	C₂²	semidirect
26. C₂×#34980	C₂²	semidirect
27. C₂×#34980	C₂²	semidirect
28. C₂×#34980	C₂²	semidirect
29. C₂×#34736	C₂²	semidirect
32. C₂²×#2403	C₂²	semidirect
33. C₂²×#2403	C₂²	semidirect
34. C₂×#34256	C₂²	semidirect
35. C₂×#34171	C₂²	semidirect
36. C₂×#34171	C₂²	semidirect
37. C₂×#32898	C₂²	semidirect
38. C₂×#32898	C₂²	semidirect
39. C₂×#32898	C₂²	semidirect
40. C₂×#23900	C₂²	semidirect
41. C₂×#21746	C₂²	semidirect
42. C₂²×#1790	C₂²	semidirect
43. C₂²×#1781	C₂²	semidirect
44. C₂²×#1781	C₂²	semidirect
45. #613188	C₂²	semidirect
46. #613188	C₂²	semidirect
47. #612424	C₂²	semidirect
48. #612424	C₂²	semidirect
49. #517411	C₂²	semidirect
50. #517411	C₂²	semidirect
51. #449501	C₂²	semidirect
52. #449475	C₂²	semidirect
53. #417898	C₂²	semidirect
54. #417821	C₂²	semidirect
55. #417526	C₂²	semidirect
56. #417508	C₂²	semidirect
57. #405104	C₂²	semidirect
58. #405090	C₂²	semidirect
59. #394419	C₂²	semidirect
60. #394267	C₂²	semidirect
61. #394174	C₂²	semidirect
62. #394066	C₂²	semidirect
63. #394058	C₂²	semidirect
64. #393929	C₂²	semidirect
65. #392658	C₂²	semidirect
66. #392245	C₂²	semidirect
67. #392109	C₂²	semidirect
68. #382422	C₂²	semidirect
69. #382390	C₂²	semidirect
70. #379754	C₂²	semidirect
71. #374038	C₂²	semidirect
72. #364513	C₂²	semidirect
73. #364471	C₂²	semidirect
74. #359863	C₂²	semidirect
75. #359695	C₂²	semidirect
76. #359579	C₂²	semidirect
77. #359552	C₂²	semidirect
78. #359501	C₂²	semidirect
79. #359428	C₂²	semidirect
80. #355913	C₂²	semidirect
84. C₂⁴×#41	C₂³	semidirect
85. C₂⁴×#41	C₂³	semidirect
86. C₂⁵×D₄	D₄	semidirect
92. C₂⁵×D₄	C₂³	semidirect
93. C₂⁵×D₄	C₂³	semidirect
95. C₂²×D₄²	D₄	semidirect
98. C₂³×#127	D₄	semidirect
99. C₂³×#121	D₄	semidirect
100. C₂³×#121	D₄	semidirect
101. C₂³×#121	D₄	semidirect
103. C₂³×#120	D₄	semidirect
104. C₂³×#120	D₄	semidirect
105. C₂³×#120	D₄	semidirect
110. C₂³×#120	C₂³	semidirect
111. C₂³×#120	C₂³	semidirect
113. C₂³×C₄×D₄	D₄	semidirect
116. C₂²×B(4,𝔽₂)	C₂³	semidirect
118. C₂³×#99	C₂³	semidirect
119. C₂×#2849	C₂³	semidirect
120. C₂×#2849	C₂³	semidirect
121. C₂×#2847	C₂³	semidirect
122. C₂×#2846	C₂³	semidirect
123. C₂×#2846	C₂³	semidirect
124. C₂×#2846	C₂³	semidirect
128. C₂×#2436	C₂³	semidirect
129. C₂×#2409	C₂³	semidirect
130. C₂×#2433	C₂³	semidirect
131. C₂×#2408	C₂³	semidirect
132. C₂×#2405	C₂³	semidirect
133. C₂×#2410	C₂³	semidirect
134. C₂×#2410	C₂³	semidirect
135. C₂×#2403	D₄	semidirect
136. C₂×#2403	D₄	semidirect
142. C₂×#2403	C₂³	semidirect
143. C₂×#2403	C₂³	semidirect
144. C₂×#2403	C₂³	semidirect
145. C₂²×#392	D₄	semidirect
148. C₂×D₄×C₂²⋊C₄	C₂³	semidirect
151. C₂×C₄×#120	C₂³	semidirect
152. C₂²×#386	D₄	semidirect
155. C₂²×#386	C₂³	semidirect
156. C₂²×#386	C₂³	semidirect
157. C₂×#2280	C₂³	semidirect
161. C₂²×#379	C₂³	semidirect
162. C₂×#2021	C₂³	semidirect
163. C₂×#1898	C₂³	semidirect
164. C₂×#1898	C₂³	semidirect
165. C₂×#1889	C₂³	semidirect
166. C₂×#1819	C₂³	semidirect
168. C₂×#1790	C₂³	semidirect
173. C₂×#1781	C₂³	semidirect
174. C₂×#1781	C₂³	semidirect
175. C₂×#1781	C₂³	semidirect
176. #14873	C₂³	semidirect
177. #14715	C₂³	semidirect
178. #14715	C₂³	semidirect
179. #14694	C₂³	semidirect
180. #14694	C₂³	semidirect
181. #14681	C₂³	semidirect
182. #14681	C₂³	semidirect
183. #14679	C₂³	semidirect
184. #14679	C₂³	semidirect
185. #13867	C₂³	semidirect
186. #13867	C₂³	semidirect
187. #13867	C₂³	semidirect
188. #11174	C₂³	semidirect
189. #11087	C₂³	semidirect
190. #11043	C₂³	semidirect
191. #10995	C₂³	semidirect
192. #10991	C₂³	semidirect
193. #10991	C₂³	semidirect
194. #10980	C₂³	semidirect
195. #10965	C₂³	semidirect
196. #10965	C₂³	semidirect
197. #10960	C₂³	semidirect
198. #10761	C₂³	semidirect
199. #10745	C₂³	semidirect
200. #10735	C₂³	semidirect
201. #10735	C₂³	semidirect
202. #10725	C₂³	semidirect
204. C₂⁷	C₂×D₄	semidirect
205. C₂⁷	C₂×D₄	semidirect
209. C₂⁷	C₂⁴	semidirect
212. C₂⁴×Q₈	C₂⁴	semidirect
227. C₂⁴×D₄	C₂×D₄	semidirect
228. C₂⁴×D₄	C₂×D₄	semidirect
229. C₂⁴×D₄	C₂×D₄	semidirect
230. C₂⁴×D₄	C₂×D₄	semidirect
231. C₂⁴×D₄	C₂×D₄	semidirect
232. C₂⁴×D₄	C₂×D₄	semidirect
233. C₂⁴×D₄	C₂×D₄	semidirect
234. C₂⁴×D₄	C₂×D₄	semidirect
235. C₂⁴×D₄	C₂×D₄	semidirect
236. C₂⁴×D₄	C₂×D₄	semidirect
237. C₂⁴×D₄	C₂×D₄	semidirect
248. C₂⁴×D₄	C₂⁴	semidirect
249. C₂⁴×D₄	C₂⁴	semidirect
251. C₂⁵×C₄	C₂×D₄	semidirect
252. C₂⁵×C₄	C₂×D₄	semidirect
253. C₂⁵×C₄	C₂×D₄	semidirect
256. C₂⁵×C₄	C₂⁴	semidirect
257. C₂⁵×C₄	C₂⁴	semidirect
259. C₂²×#127	C₂×D₄	semidirect
260. C₂²×#121	C₂×D₄	semidirect
261. C₂²×#121	C₂×D₄	semidirect
262. C₂²×#121	C₂×D₄	semidirect
263. C₂²×#121	C₂×D₄	semidirect
266. C₂²×#120	C₂×D₄	semidirect
267. C₂²×#120	C₂×D₄	semidirect
268. C₂²×#120	C₂×D₄	semidirect
269. C₂²×#120	C₂×D₄	semidirect
270. C₂²×#120	C₂×D₄	semidirect
271. C₂²×#120	C₂×D₄	semidirect
278. C₂²×#120	C₂⁴	semidirect
280. C₂²×C₄×D₄	C₂×D₄	semidirect
281. C₂²×C₄×D₄	C₂×D₄	semidirect
283. C₂³×C₄⋊C₄	C₂×D₄	semidirect
284. C₂³×C₄⋊C₄	C₂×D₄	semidirect
287. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
288. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
289. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
290. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
291. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
292. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
293. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
294. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
295. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
300. C₂³×C₂²⋊C₄	C₂⁴	semidirect
301. C₂³×C₄²	C₂×D₄	semidirect
305. C₂²×#99	C₂⁴	semidirect
306. #2403	C₂×D₄	semidirect
307. #2403	C₂×D₄	semidirect
308. #2403	C₂×D₄	semidirect
309. C₂×#392	C₂×D₄	semidirect
312. C₂×#386	C₂×D₄	semidirect
313. C₂×#386	C₂×D₄	semidirect
314. C₂×#386	C₂×D₄	semidirect
319. C₂×#386	C₂⁴	semidirect
320. C₂×#385	C₂⁴	semidirect
321. C₂×#380	C₂⁴	semidirect
322. C₂×#379	C₂×D₄	semidirect
323. C₂×#379	C₂×D₄	semidirect
329. C₂×#379	C₂⁴	semidirect
330. C₂×#379	C₂⁴	semidirect
331. C₂×#379	C₂⁴	semidirect
332. C₂×#379	C₂⁴	semidirect
333. C₂×C₄×C₂²⋊C₄	C₂⁴	semidirect
334. C₂²×#95	C₂×D₄	semidirect
335. C₂×#342	C₂⁴	semidirect
336. C₂×#342	C₂⁴	semidirect
337. C₂²⋊#95	C₂⁴	semidirect
338. C₂²⋊#95	C₂⁴	semidirect
339. C₂⁶	#120	semidirect
359. C₂⁶	C₂²×D₄	semidirect
365. C₂×H(5,𝔽₂)	H(5,𝔽₂)	semidirect
378. C₂³×D₄	#120	semidirect
379. C₂³×D₄	#120	semidirect
380. C₂³×D₄	#120	semidirect
407. C₂³×D₄	C₂²×D₄	semidirect
412. C₂⁴×C₄	#120	semidirect
429. C₂⁴×C₄	C₂²×D₄	semidirect
433. C₂×#120	C₂²×D₄	semidirect
449. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
456. #386	C₂²×D₄	semidirect
458. #379	C₂²×D₄	semidirect
507. C₂²×D₄	B(4,𝔽₂)	semidirect
550. C₂⁴	C₂×B(4,𝔽₂)	semidirect
576. C₂⁴	#3484	semidirect
582. C₂×D₄	C₂×B(4,𝔽₂)	semidirect
584. C₂²×C₄	C₂×B(4,𝔽₂)	semidirect
590. C₂²×C₄	#3484	semidirect
591. C₂³	#23900	semidirect
598. C₂³	#35346	semidirect
610. C₂×C₄	#35346	semidirect

Maximal subgroups

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

subgroup	index
#72240619	2
#72240618	2
#72240617	2
#72240616	2
#72238594	2
#72237559	2
#72234629	2
#72233780	2
#72219307	2
C₂×#7631286	2
C₂²×#32898	2
#72216660	2
#72214832	2