Subgroups — #72294193

Order 2048.

At least 7828 conjugacy classes of subgroups; only the 8328 normal subgroups are shown.

The subgroup lattice has 698 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72294137	C₂	1	2	yes	maximal, complemented
2	#72294130	C₂	1	8	yes	maximal, complemented
3	#72294116	C₂	1	4	yes	maximal, complemented
4	#72292051	C₂	1	4	yes	maximal, complemented
5	C₂×#6437621	C₂	1	4	yes	maximal, complemented
6	#72240108	C₂	1	16	yes	maximal, complemented
7	#72238029	C₂	1	8	yes	maximal, complemented
8	C₂²×#34980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#392109	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#6628892	C₂	1	2	yes	maximal, complemented
11	#72232804	C₂	1	2	yes	maximal, complemented
12	C₂³×#3484	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#359428	C₂	1	2	yes	maximal, complemented
14	#72214832	C₂	1	8	yes	maximal, complemented
15	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
16	C₂⁶×D₄	C₂²	1	1	yes	characteristic
17	C₂²×#3484	C₂²	1	8	yes	—
18	C₂²×#3484	C₂²	1	4	yes	—
19	C₂²×#3484	C₂²	1	4	yes	complemented
20	C₂²×#3484	C₂²	1	8	yes	complemented
21	C₂³×#534	C₂²	1	2	yes	complemented
22	C₂³×#534	C₂²	1	2	yes	complemented
23	C₂⁴×#120	C₂²	1	2	yes	—
24	C₂⁴×#120	C₂²	1	1	yes	characteristic, complemented
25	C₂³×#518	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#3026	C₂²	1	8	yes	complemented
27	C₂×#34980	C₂²	1	2	yes	—
28	C₂×#34980	C₂²	1	8	yes	complemented
29	C₂×#34980	C₂²	1	2	yes	complemented
30	C₂×#34980	C₂²	1	4	yes	complemented
31	C₂×#34980	C₂²	1	4	yes	complemented
32	C₂×#34980	C₂²	1	4	yes	complemented
33	C₂²×#2405	C₂²	1	4	yes	complemented
34	C₂²×#2403	C₂²	1	4	yes	complemented
35	C₂²×#2308	C₂²	1	2	yes	complemented
36	C₂³×#379	C₂²	1	1	yes	characteristic, complemented
37	C₂×#32900	C₂²	1	16	yes	complemented
38	C₂×#32898	C₂²	1	16	yes	complemented
39	C₂×#23903	C₂²	1	32	yes	complemented
40	C₂×#23901	C₂²	1	16	yes	complemented
41	C₂×#23900	C₂²	1	16	yes	complemented
42	C₂×#23444	C₂²	1	16	yes	complemented
43	C₂²×#1898	C₂²	1	8	yes	complemented
44	C₂×#20960	C₂²	1	8	yes	complemented
45	C₂×#20609	C₂²	1	8	yes	complemented
46	C₂²×#1781	C₂²	1	2	yes	complemented
47	C₂²×#1781	C₂²	1	4	yes	complemented
48	C₂²×#1781	C₂²	1	4	yes	complemented
49	C₂²×#1781	C₂²	1	4	yes	complemented
50	C₂²×#1781	C₂²	1	2	yes	complemented
51	#5955303	C₂²	1	8	yes	complemented
52	#635984	C₂²	1	16	yes	complemented
53	#612426	C₂²	1	8	yes	complemented
54	#612424	C₂²	1	8	yes	complemented
55	C₂×#14679	C₂²	1	2	yes	complemented
56	#516383	C₂²	1	4	yes	complemented
57	#516383	C₂²	1	4	yes	complemented
58	#394068	C₂²	1	64	yes	complemented
59	#394066	C₂²	1	64	yes	complemented
60	#393931	C₂²	1	32	yes	complemented
61	#393929	C₂²	1	32	yes	complemented
62	#392660	C₂²	1	16	yes	complemented
63	#392658	C₂²	1	16	yes	complemented
64	#392109	C₂²	1	8	yes	complemented
65	#392109	C₂²	1	8	yes	complemented
66	#359554	C₂²	1	32	yes	complemented
67	#359552	C₂²	1	32	yes	complemented
68	#359428	C₂²	1	16	yes	complemented
69	#359428	C₂²	1	16	yes	complemented
70	#357481	C₂²	1	16	yes	complemented
71	C₂×#10965	C₂²	1	8	yes	complemented
72	#353427	C₂²	1	8	yes	complemented
73	C₂×#10725	C₂²	1	4	yes	complemented
74	C₂⁸	D₄	1	1	yes	characteristic, complemented
75	C₂⁸	C₂³	1	1	yes	characteristic
76	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
77	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
78	C₂⁵×D₄	D₄	1	4	yes	complemented
79	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
80	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
81	C₂⁵×D₄	D₄	1	2	yes	complemented
82	C₂⁵×D₄	D₄	1	4	yes	complemented
83	C₂⁵×D₄	D₄	1	2	yes	complemented
84	C₂⁵×D₄	D₄	1	4	yes	complemented
85	C₂⁵×D₄	C₂³	1	1	yes	characteristic
86	C₂⁵×D₄	C₂³	1	1	yes	characteristic
87	C₂⁵×D₄	C₂³	1	2	yes	—
88	C₂⁵×D₄	C₂³	1	4	yes	—
89	C₂⁵×D₄	C₂³	1	4	yes	—
90	C₂⁵×D₄	C₂³	1	2	yes	—
91	C₂⁵×D₄	C₂³	1	2	yes	—
92	C₂⁵×D₄	C₂³	1	1	yes	characteristic, complemented
93	C₂⁵×D₄	C₂³	1	2	yes	complemented
94	C₂⁶×C₄	D₄	1	1	yes	characteristic, complemented
95	C₂×#3484	D₄	1	64	yes	complemented
96	C₂×#3484	C₂³	1	32	yes	—
97	C₂×#3484	C₂³	1	16	yes	—
98	C₂×#3484	C₂³	1	16	yes	—
99	C₂²×#534	C₂³	1	16	yes	—
100	C₂²×#534	C₂³	1	8	yes	—
101	C₂²×#534	C₂³	1	4	yes	—
102	C₂²×#534	C₂³	1	4	yes	complemented
103	C₂²×#534	C₂³	1	8	yes	complemented
104	C₂²×#534	C₂³	1	8	yes	complemented
105	C₂³×#123	C₂³	1	4	yes	complemented
106	C₂³×#120	D₄	1	8	yes	complemented
107	C₂³×#120	D₄	1	16	yes	complemented
108	C₂³×#120	C₂³	1	8	yes	—
109	C₂³×#120	C₂³	1	4	yes	—
110	C₂³×#120	C₂³	1	8	yes	—
111	C₂³×#120	C₂³	1	4	yes	—
112	C₂³×#120	C₂³	1	2	yes	—
113	C₂³×#120	C₂³	1	4	yes	complemented
114	C₂³×#120	C₂³	1	4	yes	complemented
115	C₂³×#120	C₂³	1	2	yes	complemented
116	C₂²×#518	C₂³	1	8	yes	—
117	C₂²×#518	C₂³	1	4	yes	—
118	C₂⁴×C₂²⋊C₄	D₄	1	4	yes	complemented
119	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	complemented
121	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
122	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	complemented
123	C₂²×#458	C₂³	1	32	yes	complemented
124	C₂²×B(4,𝔽₂)	C₂³	1	32	yes	complemented
125	C₂³×#99	C₂³	1	8	yes	—
126	C₂³×#99	C₂³	1	16	yes	complemented
127	C₂³×#99	C₂³	1	8	yes	complemented
128	C₂×#2849	C₂³	1	8	yes	complemented
129	C₂×#2846	C₂³	1	8	yes	complemented
130	#34980	D₄	1	32	yes	complemented
131	C₂×#2405	C₂³	1	8	yes	—
132	C₂×#2405	C₂³	1	8	yes	complemented
133	C₂×#2405	C₂³	1	16	yes	complemented
134	C₂×#2405	C₂³	1	16	yes	complemented
135	C₂×#2403	C₂³	1	8	yes	—
136	C₂×#2403	C₂³	1	8	yes	complemented
137	C₂×#2403	C₂³	1	16	yes	complemented
138	C₂×#2403	C₂³	1	16	yes	complemented
139	C₂×#2613	C₂³	1	16	yes	complemented
140	C₂×#2308	C₂³	1	4	yes	—
141	C₂×#2308	C₂³	1	4	yes	complemented
142	C₂×#2308	C₂³	1	8	yes	complemented
143	C₂×#2308	C₂³	1	8	yes	complemented
144	C₂×#2308	C₂³	1	8	yes	complemented
145	C₂²×#386	C₂³	1	8	yes	complemented
146	C₂²×#379	C₂³	1	4	yes	—
147	C₂²×#379	C₂³	1	2	yes	—
148	C₂²×#379	C₂³	1	2	yes	complemented
149	C₂²×#379	C₂³	1	4	yes	complemented
150	C₂²×#379	C₂³	1	4	yes	complemented
151	C₂²×#379	C₂³	1	4	yes	complemented
152	C₂²×#379	C₂³	1	4	yes	complemented
153	C₂×#2022	C₂³	1	64	yes	complemented
154	C₂×#2021	C₂³	1	64	yes	complemented
155	C₂×#1898	C₂³	1	32	yes	complemented
156	C₂×#1898	C₂³	1	32	yes	complemented
157	C₂×#1890	C₂³	1	32	yes	complemented
158	C₂×#1889	C₂³	1	32	yes	complemented
159	C₂×#1790	C₂³	1	64	yes	complemented
160	C₂×#1781	C₂³	1	16	yes	—
161	C₂×#1781	C₂³	1	16	yes	complemented
162	C₂×#1781	C₂³	1	16	yes	complemented
163	C₂×#1781	C₂³	1	32	yes	complemented
164	C₂×#1781	C₂³	1	32	yes	complemented
165	C₂×#1781	C₂³	1	16	yes	complemented
166	C₂²×#342	C₂³	1	16	yes	complemented
167	#14911	C₂³	1	32	yes	complemented
168	#14715	C₂³	1	32	yes	complemented
169	#14694	C₂³	1	16	yes	complemented
170	#14679	C₂³	1	8	yes	complemented
171	#14679	C₂³	1	8	yes	complemented
172	#14255	C₂³	1	16	yes	complemented
173	#13869	C₂³	1	16	yes	complemented
174	#13867	C₂³	1	16	yes	complemented
175	#13794	C₂³	1	8	yes	complemented
176	#10995	C₂³	1	128	yes	complemented
177	#10965	C₂³	1	64	yes	complemented
178	#10745	C₂³	1	64	yes	complemented
179	#10725	C₂³	1	32	yes	complemented
180	C₂⁷	C₂×D₄	1	1	yes	characteristic
181	C₂⁷	C₂×D₄	1	1	yes	characteristic
182	C₂⁷	C₂×D₄	1	2	yes	—
183	C₂⁷	C₂×D₄	1	1	yes	characteristic
184	C₂⁷	C₂×D₄	1	4	yes	—
185	C₂⁷	C₂×D₄	1	4	yes	—
186	C₂⁷	C₂×D₄	1	2	yes	—
187	C₂⁷	C₂×D₄	1	8	yes	—
188	C₂⁷	C₂×D₄	1	4	yes	—
189	C₂⁷	C₂×D₄	1	4	yes	—
190	C₂⁷	C₂×D₄	1	1	yes	characteristic
191	C₂⁷	C₂×D₄	1	2	yes	—
192	C₂⁷	C₂×D₄	1	1	yes	characteristic
193	C₂⁷	C₂×D₄	1	1	yes	characteristic
194	C₂⁷	C₂×D₄	1	2	yes	—
195	C₂⁷	C₂×D₄	1	2	yes	complemented
196	C₂⁷	C₂⁴	1	1	yes	characteristic
197	C₂⁷	C₂⁴	1	2	yes	—
198	C₂⁷	C₂⁴	1	2	yes	—
199	C₂⁷	C₂⁴	1	1	yes	characteristic
200	C₂⁷	C₂⁴	1	1	yes	characteristic
201	C₂⁷	C₂⁴	1	1	yes	characteristic, complemented
202	C₂²×H(5,𝔽₂)	C₂×D₄	1	32	yes	complemented
203	C₂²×H(5,𝔽₂)	C₂⁴	1	16	yes	—
204	C₂⁴×D₄	C₂×D₄	1	16	yes	—
205	C₂⁴×D₄	C₂×D₄	1	32	yes	—
206	C₂⁴×D₄	C₂×D₄	1	4	yes	—
207	C₂⁴×D₄	C₂×D₄	1	2	yes	—
208	C₂⁴×D₄	C₂×D₄	1	8	yes	—
209	C₂⁴×D₄	C₂×D₄	1	4	yes	—
210	C₂⁴×D₄	C₂×D₄	1	2	yes	—
211	C₂⁴×D₄	C₂×D₄	1	2	yes	—
212	C₂⁴×D₄	C₂×D₄	1	2	yes	—
213	C₂⁴×D₄	C₂×D₄	1	8	yes	—
214	C₂⁴×D₄	C₂×D₄	1	8	yes	—
215	C₂⁴×D₄	C₂×D₄	1	8	yes	—
216	C₂⁴×D₄	C₂×D₄	1	8	yes	—
217	C₂⁴×D₄	C₂×D₄	1	4	yes	—
218	C₂⁴×D₄	C₂×D₄	1	4	yes	—
219	C₂⁴×D₄	C₂×D₄	1	4	yes	—
220	C₂⁴×D₄	C₂×D₄	1	4	yes	—
221	C₂⁴×D₄	C₂×D₄	1	4	yes	—
222	C₂⁴×D₄	C₂×D₄	1	4	yes	—
223	C₂⁴×D₄	C₂×D₄	1	2	yes	—
224	C₂⁴×D₄	C₂×D₄	1	2	yes	—
225	C₂⁴×D₄	C₂×D₄	1	16	yes	—
226	C₂⁴×D₄	C₂×D₄	1	8	yes	—
227	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
228	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
229	C₂⁴×D₄	C₂×D₄	1	16	yes	complemented
230	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
231	C₂⁴×D₄	C₂⁴	1	4	yes	—
232	C₂⁴×D₄	C₂⁴	1	2	yes	—
233	C₂⁴×D₄	C₂⁴	1	4	yes	—
234	C₂⁴×D₄	C₂⁴	1	8	yes	—
235	C₂⁴×D₄	C₂⁴	1	4	yes	—
236	C₂⁴×D₄	C₂⁴	1	8	yes	—
237	C₂⁴×D₄	C₂⁴	1	4	yes	—
238	C₂⁴×D₄	C₂⁴	1	4	yes	—
239	C₂⁴×D₄	C₂⁴	1	2	yes	—
240	C₂⁴×D₄	C₂⁴	1	2	yes	—
241	C₂⁴×D₄	C₂⁴	1	4	yes	—
242	C₂⁴×D₄	C₂⁴	1	2	yes	complemented
243	C₂⁴×D₄	C₂⁴	1	4	yes	complemented
244	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
245	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
246	C₂⁵×C₄	C₂×D₄	1	2	yes	—
247	C₂⁵×C₄	C₂×D₄	1	4	yes	—
248	C₂⁵×C₄	C₂×D₄	1	4	yes	—
249	C₂⁵×C₄	C₂×D₄	1	2	yes	—
250	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
251	C₂⁵×C₄	C₂×D₄	1	4	yes	complemented
252	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic, complemented
253	C₂⁵×C₄	C₂⁴	1	2	yes	complemented
254	#3484	C₂×D₄	1	128	yes	—
255	#3484	C₂×D₄	1	128	yes	complemented
256	C₂×#534	C₂×D₄	1	64	yes	complemented
257	C₂×#534	C₂×D₄	1	32	yes	complemented
258	C₂×#534	C₂⁴	1	32	yes	—
259	C₂²×#123	C₂⁴	1	8	yes	—
260	C₂²×#123	C₂⁴	1	8	yes	complemented
261	C₂²×#123	C₂⁴	1	16	yes	complemented
262	C₂²×#120	C₂×D₄	1	64	yes	—
263	C₂²×#120	C₂×D₄	1	32	yes	—
264	C₂²×#120	C₂×D₄	1	16	yes	—
265	C₂²×#120	C₂×D₄	1	32	yes	complemented
266	C₂²×#120	C₂×D₄	1	16	yes	complemented
267	C₂²×#120	C₂×D₄	1	16	yes	complemented
268	C₂²×#120	C₂⁴	1	8	yes	—
269	C₂²×#120	C₂⁴	1	16	yes	—
270	C₂²×#120	C₂⁴	1	8	yes	—
271	C₂²×#120	C₂⁴	1	8	yes	—
272	C₂²×#120	C₂⁴	1	8	yes	complemented
273	C₂²×#120	C₂⁴	1	16	yes	complemented
274	C₂×#518	C₂×D₄	1	32	yes	complemented
275	C₂×#518	C₂⁴	1	16	yes	—
276	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	—
277	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
278	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
279	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
280	C₂³×C₂²⋊C₄	C₂×D₄	1	16	yes	complemented
281	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
282	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
283	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
284	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
285	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
286	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
287	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
288	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
289	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	complemented
290	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
291	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
292	C₂²×#99	C₂⁴	1	32	yes	—
293	C₂²×#99	C₂⁴	1	64	yes	complemented
294	C₂²×#99	C₂⁴	1	32	yes	complemented
295	#2405	C₂×D₄	1	64	yes	complemented
296	#2403	C₂×D₄	1	64	yes	complemented
297	#2308	C₂×D₄	1	32	yes	complemented
298	C₂×#386	C₂⁴	1	16	yes	—
299	C₂×#386	C₂⁴	1	16	yes	complemented
300	C₂×#386	C₂⁴	1	32	yes	complemented
301	C₂×#381	C₂⁴	1	16	yes	complemented
302	C₂×#379	C₂×D₄	1	16	yes	complemented
303	C₂×#379	C₂⁴	1	16	yes	—
304	C₂×#379	C₂⁴	1	8	yes	—
305	C₂×#379	C₂⁴	1	8	yes	complemented
306	C₂×#379	C₂⁴	1	16	yes	complemented
307	C₂×#379	C₂⁴	1	8	yes	complemented
308	C₂×#379	C₂⁴	1	8	yes	complemented
309	C₂×#379	C₂⁴	1	16	yes	complemented
310	C₂×#342	C₂⁴	1	64	yes	complemented
311	C₂²⋊#95	C₂⁴	1	32	yes	complemented
312	C₂⁶	#120	1	2	yes	—
313	C₂⁶	#120	1	4	yes	—
314	C₂⁶	#120	1	8	yes	—
315	C₂⁶	#120	1	2	yes	—
316	C₂⁶	#120	1	2	yes	—
317	C₂⁶	#120	1	8	yes	—
318	C₂⁶	#120	1	8	yes	—
319	C₂⁶	#120	1	4	yes	—
320	C₂⁶	#120	1	4	yes	—
321	C₂⁶	#120	1	4	yes	—
322	C₂⁶	#120	1	4	yes	—
323	C₂⁶	#120	1	4	yes	—
324	C₂⁶	#120	1	8	yes	—
325	C₂⁶	#120	1	2	yes	—
326	C₂⁶	#120	1	8	yes	complemented
327	C₂⁶	#120	1	16	yes	complemented
328	C₂⁶	C₂²×D₄	1	2	yes	—
329	C₂⁶	C₂²×D₄	1	1	yes	characteristic
330	C₂⁶	C₂²×D₄	1	8	yes	—
331	C₂⁶	C₂²×D₄	1	4	yes	—
332	C₂⁶	C₂²×D₄	1	4	yes	—
333	C₂⁶	C₂²×D₄	1	4	yes	—
334	C₂⁶	C₂²×D₄	1	2	yes	—
335	C₂⁶	C₂²×D₄	1	1	yes	characteristic
336	C₂⁶	C₂²×D₄	1	2	yes	—
337	C₂⁶	C₂²×D₄	1	4	yes	—
338	C₂⁶	C₂²×D₄	1	8	yes	—
339	C₂⁶	C₂²×D₄	1	4	yes	—
340	C₂⁶	C₂²×D₄	1	8	yes	—
341	C₂⁶	C₂²×D₄	1	2	yes	—
342	C₂⁶	C₂²×D₄	1	2	yes	—
343	C₂⁶	C₂²×D₄	1	4	yes	—
344	C₂⁶	C₂²×D₄	1	8	yes	—
345	C₂⁶	C₂²×D₄	1	8	yes	—
346	C₂⁶	C₂²×D₄	1	1	yes	characteristic
347	C₂⁶	C₂²×D₄	1	1	yes	characteristic
348	C₂⁶	C₂²×D₄	1	1	yes	characteristic
349	C₂⁶	C₂²×D₄	1	2	yes	—
350	C₂⁶	C₂²×D₄	1	2	yes	—
351	C₂⁶	C₂²×D₄	1	2	yes	—
352	C₂⁶	C₂²×D₄	1	2	yes	—
353	C₂⁶	C₂²×D₄	1	2	yes	—
354	C₂⁶	C₂²×D₄	1	8	yes	—
355	C₂⁶	C₂²×D₄	1	4	yes	—
356	C₂⁶	C₂²×D₄	1	4	yes	—
357	C₂⁶	C₂²×D₄	1	2	yes	—
358	C₂⁶	C₂²×D₄	1	4	yes	—
359	C₂⁶	C₂²×D₄	1	2	yes	—
360	C₂⁶	C₂²×D₄	1	4	yes	—
361	C₂⁶	C₂²×D₄	1	16	yes	—
362	C₂⁶	C₂²×D₄	1	1	yes	characteristic
363	C₂⁶	C₂²×D₄	1	1	yes	characteristic
364	C₂⁶	C₂²×D₄	1	1	yes	characteristic
365	C₂⁶	C₂²×D₄	1	2	yes	—
366	C₂⁶	C₂²×D₄	1	8	yes	—
367	C₂⁶	C₂²×D₄	1	2	yes	—
368	C₂⁶	H(5,𝔽₂)	1	8	yes	—
369	C₂⁶	C₂⁵	1	2	yes	—
370	C₂⁶	C₂⁵	1	2	yes	—
371	C₂⁶	C₂⁵	1	1	yes	characteristic
372	C₂⁶	C₂⁵	1	2	yes	—
373	C₂⁶	C₂⁵	1	1	yes	characteristic
374	C₂⁶	C₂⁵	1	1	yes	characteristic
375	C₂×H(5,𝔽₂)	C₂²×D₄	1	64	yes	—
376	C₂³×D₄	#120	1	16	yes	complemented
377	C₂³×D₄	#120	1	32	yes	complemented
378	C₂³×D₄	#120	1	32	yes	complemented
379	C₂³×D₄	#120	1	16	yes	complemented
380	C₂³×D₄	#120	1	16	yes	complemented
381	C₂³×D₄	#120	1	32	yes	complemented
382	C₂³×D₄	#120	1	64	yes	complemented
383	C₂³×D₄	C₂²×D₄	1	32	yes	—
384	C₂³×D₄	C₂²×D₄	1	16	yes	—
385	C₂³×D₄	C₂²×D₄	1	32	yes	—
386	C₂³×D₄	C₂²×D₄	1	32	yes	—
387	C₂³×D₄	C₂²×D₄	1	16	yes	—
388	C₂³×D₄	C₂²×D₄	1	16	yes	—
389	C₂³×D₄	C₂²×D₄	1	32	yes	—
390	C₂³×D₄	C₂²×D₄	1	8	yes	—
391	C₂³×D₄	C₂²×D₄	1	4	yes	—
392	C₂³×D₄	C₂²×D₄	1	8	yes	—
393	C₂³×D₄	C₂²×D₄	1	8	yes	—
394	C₂³×D₄	C₂²×D₄	1	8	yes	—
395	C₂³×D₄	C₂²×D₄	1	8	yes	—
396	C₂³×D₄	C₂²×D₄	1	16	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	4	yes	—
401	C₂³×D₄	C₂²×D₄	1	4	yes	—
402	C₂³×D₄	C₂²×D₄	1	32	yes	—
403	C₂³×D₄	C₂²×D₄	1	16	yes	—
404	C₂³×D₄	C₂²×D₄	1	16	yes	—
405	C₂³×D₄	C₂²×D₄	1	8	yes	complemented
406	C₂³×D₄	C₂²×D₄	1	16	yes	complemented
407	C₂³×D₄	H(5,𝔽₂)	1	16	yes	—
408	C₂³×D₄	C₂⁵	1	4	yes	—
409	C₂³×D₄	C₂⁵	1	8	yes	—
410	C₂³×D₄	C₂⁵	1	4	yes	—
411	C₂⁴×C₄	#120	1	8	yes	complemented
412	C₂⁴×C₄	#120	1	16	yes	complemented
413	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
414	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
415	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
416	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
417	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
418	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
419	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
420	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
421	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
422	C₂⁴×C₄	C₂²×D₄	1	16	yes	—
423	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
424	C₂⁴×C₄	C₂⁵	1	2	yes	—
425	C₂⁴×C₄	C₂⁵	1	4	yes	—
426	#534	C₂²×D₄	1	128	yes	—
427	C₂×#123	C₂²×D₄	1	32	yes	complemented
428	C₂×#120	#120	1	128	yes	complemented
429	C₂×#120	C₂²×D₄	1	64	yes	—
430	C₂×#120	C₂²×D₄	1	64	yes	—
431	C₂×#120	C₂²×D₄	1	32	yes	complemented
432	#518	C₂²×D₄	1	64	yes	—
433	C₂²×C₂²⋊C₄	#120	1	64	yes	complemented
434	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
435	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
436	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
437	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
438	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
439	C₂²×C₂²⋊C₄	C₂²×D₄	1	32	yes	—
440	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
441	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
442	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	complemented
443	C₂²×C₂²⋊C₄	C₂⁵	1	16	yes	—
444	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
445	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
446	#386	C₂²×D₄	1	64	yes	complemented
447	#379	C₂²×D₄	1	32	yes	complemented
448	C₂⁵	C₂×#120	1	1	yes	characteristic
449	C₂⁵	C₂×#120	1	2	yes	—
450	C₂⁵	C₂×#120	1	4	yes	—
451	C₂⁵	C₂×#120	1	4	yes	—
452	C₂⁵	C₂×#120	1	2	yes	—
453	C₂⁵	C₂×#120	1	4	yes	—
454	C₂⁵	C₂×#120	1	4	yes	—
455	C₂⁵	C₂×#120	1	8	yes	—
456	C₂⁵	C₂×#120	1	8	yes	—
457	C₂⁵	C₂×#120	1	2	yes	—
458	C₂⁵	C₂×#120	1	4	yes	—
459	C₂⁵	C₂×#120	1	2	yes	—
460	C₂⁵	C₂×#120	1	2	yes	—
461	C₂⁵	C₂×#120	1	4	yes	—
462	C₂⁵	C₂×#120	1	4	yes	—
463	C₂⁵	C₂×#120	1	2	yes	—
464	C₂⁵	C₂×#120	1	8	yes	—
465	C₂⁵	C₂×#120	1	8	yes	—
466	C₂⁵	C₂×#120	1	4	yes	—
467	C₂⁵	C₂×#120	1	2	yes	—
468	C₂⁵	C₂×#120	1	16	yes	—
469	C₂⁵	C₂×#120	1	8	yes	—
470	C₂⁵	C₂×#120	1	8	yes	—
471	C₂⁵	C₂×#120	1	4	yes	—
472	C₂⁵	C₂×#120	1	16	yes	—
473	C₂⁵	C₂×#120	1	4	yes	—
474	C₂⁵	C₂×#120	1	2	yes	—
475	C₂⁵	C₂×#120	1	4	yes	—
476	C₂⁵	C₂×#120	1	8	yes	—
477	C₂⁵	C₂×#120	1	2	yes	—
478	C₂⁵	C₂×#120	1	8	yes	—
479	C₂⁵	C₂×#120	1	1	yes	characteristic
480	C₂⁵	C₂×#120	1	4	yes	—
481	C₂⁵	C₂×#120	1	2	yes	—
482	C₂⁵	C₂×#120	1	2	yes	—
483	C₂⁵	C₂×#120	1	4	yes	—
484	C₂⁵	C₂×#120	1	32	yes	—
485	C₂⁵	C₂×#120	1	32	yes	—
486	C₂⁵	C₂×#120	1	8	yes	—
487	C₂⁵	C₂×#120	1	16	yes	—
488	C₂⁵	C₂×#120	1	8	yes	—
489	C₂⁵	C₂×#120	1	8	yes	—
490	C₂⁵	C₂×#120	1	4	yes	—
491	C₂⁵	C₂×#120	1	8	yes	—
492	C₂⁵	C₂×#120	1	8	yes	—
493	C₂⁵	C₂×#120	1	16	yes	complemented
494	C₂⁵	#534	1	4	yes	—
495	C₂⁵	#534	1	8	yes	—
496	C₂⁵	#534	1	4	yes	—
497	C₂⁵	#534	1	8	yes	—
498	C₂⁵	D₄²	1	16	yes	—
499	C₂⁵	D₄²	1	32	yes	—
500	C₂⁵	D₄²	1	16	yes	—
501	C₂⁵	C₂³×D₄	1	1	yes	characteristic
502	C₂⁵	C₂³×D₄	1	2	yes	—
503	C₂⁵	C₂³×D₄	1	8	yes	—
504	C₂⁵	C₂³×D₄	1	4	yes	—
505	C₂⁵	C₂³×D₄	1	2	yes	—
506	C₂⁵	C₂³×D₄	1	4	yes	—
507	C₂⁵	C₂³×D₄	1	2	yes	—
508	C₂⁵	C₂³×D₄	1	4	yes	—
509	C₂⁵	C₂³×D₄	1	8	yes	—
510	C₂⁵	C₂³×D₄	1	4	yes	—
511	C₂⁵	C₂³×D₄	1	1	yes	characteristic
512	C₂⁵	C₂³×D₄	1	1	yes	characteristic
513	C₂⁵	C₂³×D₄	1	1	yes	characteristic
514	C₂⁵	C₂³×D₄	1	8	yes	—
515	C₂⁵	C₂³×D₄	1	2	yes	—
516	C₂⁵	C₂³×D₄	1	4	yes	—
517	C₂⁵	C₂³×D₄	1	4	yes	—
518	C₂⁵	C₂³×D₄	1	8	yes	—
519	C₂⁵	C₂³×D₄	1	8	yes	—
520	C₂⁵	C₂³×D₄	1	1	yes	characteristic
521	C₂⁵	C₂³×D₄	1	1	yes	characteristic
522	C₂⁵	C₂³×D₄	1	2	yes	—
523	C₂⁵	C₂³×D₄	1	2	yes	—
524	C₂⁵	C₂³×D₄	1	8	yes	—
525	C₂⁵	C₂³×D₄	1	4	yes	—
526	C₂⁵	C₂³×D₄	1	4	yes	complemented
527	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
528	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
529	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
530	C₂⁵	C₂⁶	1	1	yes	characteristic
531	C₂²×D₄	C₂×#120	1	16	yes	—
532	C₂²×D₄	C₂×#120	1	32	yes	—
533	C₂²×D₄	C₂×#120	1	16	yes	—
534	C₂²×D₄	C₂×#120	1	16	yes	—
535	C₂²×D₄	C₂×#120	1	16	yes	—
536	C₂²×D₄	C₂×#120	1	16	yes	—
537	C₂²×D₄	C₂×#120	1	16	yes	—
538	C₂²×D₄	C₂×#120	1	16	yes	—
539	C₂²×D₄	C₂×#120	1	64	yes	—
540	C₂²×D₄	C₂×#120	1	32	yes	complemented
541	C₂²×D₄	C₂×#120	1	64	yes	complemented
542	C₂²×D₄	#534	1	16	yes	—
543	C₂²×D₄	D₄²	1	128	yes	—
544	C₂²×D₄	C₂³×D₄	1	32	yes	—
545	C₂²×D₄	C₂³×D₄	1	16	yes	—
546	C₂²×D₄	C₂³×D₄	1	16	yes	—
547	C₂²×D₄	C₂³×D₄	1	16	yes	—
548	C₂²×D₄	C₂×H(5,𝔽₂)	1	16	yes	—
549	C₂³×C₄	C₂×#120	1	8	yes	—
550	C₂³×C₄	C₂×#120	1	16	yes	—
551	C₂³×C₄	C₂×#120	1	16	yes	—
552	C₂³×C₄	C₂×#120	1	16	yes	—
553	C₂³×C₄	C₂×#120	1	8	yes	—
554	C₂³×C₄	C₂×#120	1	8	yes	—
555	C₂³×C₄	C₂×#120	1	16	yes	complemented
556	C₂³×C₄	C₂×#120	1	32	yes	complemented
557	C₂³×C₄	#534	1	8	yes	—
558	C₂³×C₄	C₂³×D₄	1	8	yes	—
559	C₂³×C₄	C₂³×D₄	1	4	yes	—
560	C₂³×C₄	C₂³×D₄	1	4	yes	—
561	C₂³×C₄	C₂³×D₄	1	16	yes	—
562	C₂³×C₄	C₂³×D₄	1	4	yes	complemented
563	C₂³×C₄	C₂³×D₄	1	8	yes	complemented
564	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	—
565	C₂×C₂²⋊C₄	C₂×#120	1	64	yes	complemented
566	C₂×C₂²⋊C₄	C₂×#120	1	32	yes	complemented
567	C₂×C₂²⋊C₄	C₂³×D₄	1	32	yes	—
568	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	complemented
569	C₂⁴	#2403	1	4	yes	—
570	C₂⁴	#2403	1	8	yes	—
571	C₂⁴	#2403	1	16	yes	—
572	C₂⁴	#2403	1	4	yes	—
573	C₂⁴	#2403	1	8	yes	—
574	C₂⁴	#2403	1	16	yes	—
575	C₂⁴	#2403	1	8	yes	—
576	C₂⁴	#2403	1	32	yes	complemented
577	C₂⁴	#2846	1	8	yes	—
578	C₂⁴	#2846	1	16	yes	—
579	C₂⁴	#2846	1	8	yes	—
580	C₂⁴	#2846	1	8	yes	—
581	C₂⁴	#2846	1	16	yes	—
582	C₂⁴	#2846	1	8	yes	—
583	C₂⁴	#3026	1	16	yes	complemented
584	C₂⁴	C₂²×#120	1	4	yes	—
585	C₂⁴	C₂²×#120	1	4	yes	—
586	C₂⁴	C₂²×#120	1	2	yes	—
587	C₂⁴	C₂²×#120	1	2	yes	—
588	C₂⁴	C₂²×#120	1	2	yes	—
589	C₂⁴	C₂²×#120	1	2	yes	—
590	C₂⁴	C₂²×#120	1	4	yes	—
591	C₂⁴	C₂²×#120	1	4	yes	—
592	C₂⁴	C₂²×#120	1	16	yes	—
593	C₂⁴	C₂²×#120	1	4	yes	—
594	C₂⁴	C₂²×#120	1	1	yes	characteristic
595	C₂⁴	C₂²×#120	1	2	yes	—
596	C₂⁴	C₂²×#120	1	1	yes	characteristic
597	C₂⁴	C₂²×#120	1	2	yes	—
598	C₂⁴	C₂²×#120	1	2	yes	—
599	C₂⁴	C₂²×#120	1	8	yes	—
600	C₂⁴	C₂²×#120	1	16	yes	—
601	C₂⁴	C₂²×#120	1	16	yes	—
602	C₂⁴	C₂²×#120	1	4	yes	—
603	C₂⁴	C₂²×#120	1	4	yes	—
604	C₂⁴	C₂²×#120	1	4	yes	—
605	C₂⁴	C₂²×#120	1	4	yes	—
606	C₂⁴	C₂²×#120	1	8	yes	—
607	C₂⁴	C₂²×#120	1	8	yes	—
608	C₂⁴	C₂²×#120	1	4	yes	—
609	C₂⁴	C₂²×#120	1	4	yes	—
610	C₂⁴	C₂²×#120	1	8	yes	—
611	C₂⁴	C₂²×#120	1	8	yes	—
612	C₂⁴	C₂²×#120	1	2	yes	—
613	C₂⁴	C₂²×#120	1	2	yes	—
614	C₂⁴	C₂×#534	1	4	yes	—
615	C₂⁴	C₂×#534	1	4	yes	—
616	C₂⁴	C₂×#534	1	8	yes	—
617	C₂⁴	C₂×#534	1	2	yes	—
618	C₂⁴	C₂×#534	1	4	yes	—
619	C₂⁴	C₂×#534	1	2	yes	—
620	C₂⁴	C₂×#534	1	4	yes	—
621	C₂⁴	C₂×D₄²	1	16	yes	—
622	C₂⁴	C₂×D₄²	1	16	yes	—
623	C₂⁴	C₂×D₄²	1	8	yes	—
624	C₂⁴	C₂×D₄²	1	8	yes	—
625	C₂⁴	C₂×D₄²	1	32	yes	—
626	C₂⁴	#3484	1	8	yes	—
627	C₂⁴	#3484	1	8	yes	—
628	C₂⁴	#3484	1	32	yes	—
629	C₂⁴	C₂⁴×D₄	1	2	yes	—
630	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
631	C₂⁴	C₂⁴×D₄	1	4	yes	—
632	C₂⁴	C₂⁴×D₄	1	2	yes	—
633	C₂⁴	C₂²×H(5,𝔽₂)	1	4	yes	—
634	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
635	C₂×D₄	#2403	1	64	yes	complemented
636	C₂×D₄	C₂×D₄²	1	64	yes	—
637	C₂²×C₄	#2403	1	32	yes	complemented
638	C₂²×C₄	C₂²×#120	1	16	yes	—
639	C₂²×C₄	C₂²×#120	1	8	yes	—
640	C₂²×C₄	C₂²×#120	1	8	yes	—
641	C₂²×C₄	C₂²×#120	1	8	yes	—
642	C₂²×C₄	C₂²×#120	1	32	yes	—
643	C₂²×C₄	C₂×#534	1	8	yes	—
644	C₂³	C₂×#2403	1	4	yes	—
645	C₂³	C₂×#2403	1	8	yes	—
646	C₂³	C₂×#2403	1	2	yes	—
647	C₂³	C₂×#2403	1	2	yes	—
648	C₂³	C₂×#2403	1	4	yes	—
649	C₂³	C₂×#2403	1	4	yes	—
650	C₂³	C₂×#2403	1	16	yes	—
651	C₂³	C₂×#2403	1	8	yes	—
652	C₂³	C₂×#2403	1	8	yes	—
653	C₂³	#34980	1	2	yes	—
654	C₂³	#34980	1	2	yes	—
655	C₂³	#34980	1	4	yes	—
656	C₂³	#34980	1	8	yes	—
657	C₂³	#34980	1	8	yes	—
658	C₂³	D₄×#120	1	32	yes	—
659	C₂³	D₄×#120	1	32	yes	—
660	C₂³	C₂×#2846	1	4	yes	—
661	C₂³	C₂×#2846	1	4	yes	—
662	C₂³	C₂×#2846	1	4	yes	—
663	C₂³	C₂×#2846	1	4	yes	—
664	C₂³	C₂×#2846	1	2	yes	—
665	C₂³	C₂×#2846	1	4	yes	—
666	C₂³	C₂×#2846	1	2	yes	—
667	C₂³	C₂×#3026	1	8	yes	—
668	C₂³	C₂×#3026	1	8	yes	—
669	C₂³	C₂×#3026	1	8	yes	—
670	C₂³	C₂³×#120	1	1	yes	characteristic
671	C₂³	C₂³×#120	1	2	yes	—
672	C₂³	C₂³×#120	1	4	yes	—
673	C₂³	C₂³×#120	1	1	yes	characteristic
674	C₂³	C₂²×#534	1	1	yes	characteristic
675	C₂³	C₂²×#534	1	2	yes	—
676	C₂³	C₂²×D₄²	1	4	yes	—
677	C₂³	C₂²×D₄²	1	8	yes	—
678	C₂³	C₂×#3484	1	4	yes	—
679	C₂³	C₂×#3484	1	8	yes	—
680	C₂×C₄	C₂×#2403	1	16	yes	—
681	C₂²	#612424	1	4	yes	—
682	C₂²	#612424	1	4	yes	—
683	C₂²	#612424	1	8	yes	—
684	C₂²	#6437621	1	8	yes	complemented
685	C₂²	#6628892	1	8	yes	complemented
686	C₂²	C₂²×#2403	1	2	yes	—
687	C₂²	C₂²×#2403	1	1	yes	characteristic
688	C₂²	C₂×#34980	1	2	yes	—
689	C₂²	C₂×#34980	1	1	yes	characteristic
690	C₂²	C₂×D₄×#120	1	8	yes	—
691	C₂²	C₂²×#2846	1	1	yes	characteristic
692	C₂²	C₂²×#3026	1	4	yes	—
693	C₂	C₂×#612424	1	1	yes	characteristic
694	C₂	C₂×#6628892	1	2	yes	—
695	C₂	#72234661	1	2	yes	—
696	C₂	C₂×#6437621	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂³×#120
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁸ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72294137	C₂	semidirect
2. #72294130	C₂	semidirect
3. #72294116	C₂	semidirect
4. #72292051	C₂	semidirect
5. C₂×#6437621	C₂	semidirect
6. #72240108	C₂	semidirect
7. #72238029	C₂	semidirect
8. C₂²×#34980	C₂	semidirect
9. C₂×#392109	C₂	semidirect
10. C₂×#6628892	C₂	semidirect
11. #72232804	C₂	semidirect
12. C₂³×#3484	C₂	semidirect
13. C₂×#359428	C₂	semidirect
14. #72214832	C₂	semidirect
15. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
19. C₂²×#3484	C₂²	semidirect
20. C₂²×#3484	C₂²	semidirect
21. C₂³×#534	C₂²	semidirect
22. C₂³×#534	C₂²	semidirect
24. C₂⁴×#120	C₂²	semidirect
25. C₂³×#518	C₂²	semidirect
26. C₂²×#3026	C₂²	semidirect
28. C₂×#34980	C₂²	semidirect
29. C₂×#34980	C₂²	semidirect
30. C₂×#34980	C₂²	semidirect
31. C₂×#34980	C₂²	semidirect
32. C₂×#34980	C₂²	semidirect
33. C₂²×#2405	C₂²	semidirect
34. C₂²×#2403	C₂²	semidirect
35. C₂²×#2308	C₂²	semidirect
36. C₂³×#379	C₂²	semidirect
37. C₂×#32900	C₂²	semidirect
38. C₂×#32898	C₂²	semidirect
39. C₂×#23903	C₂²	semidirect
40. C₂×#23901	C₂²	semidirect
41. C₂×#23900	C₂²	semidirect
42. C₂×#23444	C₂²	semidirect
43. C₂²×#1898	C₂²	semidirect
44. C₂×#20960	C₂²	semidirect
45. C₂×#20609	C₂²	semidirect
46. C₂²×#1781	C₂²	semidirect
47. C₂²×#1781	C₂²	semidirect
48. C₂²×#1781	C₂²	semidirect
49. C₂²×#1781	C₂²	semidirect
50. C₂²×#1781	C₂²	semidirect
51. #5955303	C₂²	semidirect
52. #635984	C₂²	semidirect
53. #612426	C₂²	semidirect
54. #612424	C₂²	semidirect
55. C₂×#14679	C₂²	semidirect
56. #516383	C₂²	semidirect
57. #516383	C₂²	semidirect
58. #394068	C₂²	semidirect
59. #394066	C₂²	semidirect
60. #393931	C₂²	semidirect
61. #393929	C₂²	semidirect
62. #392660	C₂²	semidirect
63. #392658	C₂²	semidirect
64. #392109	C₂²	semidirect
65. #392109	C₂²	semidirect
66. #359554	C₂²	semidirect
67. #359552	C₂²	semidirect
68. #359428	C₂²	semidirect
69. #359428	C₂²	semidirect
70. #357481	C₂²	semidirect
71. C₂×#10965	C₂²	semidirect
72. #353427	C₂²	semidirect
73. C₂×#10725	C₂²	semidirect
74. C₂⁸	D₄	semidirect
78. C₂⁵×D₄	D₄	semidirect
79. C₂⁵×D₄	D₄	semidirect
80. C₂⁵×D₄	D₄	semidirect
81. C₂⁵×D₄	D₄	semidirect
82. C₂⁵×D₄	D₄	semidirect
83. C₂⁵×D₄	D₄	semidirect
84. C₂⁵×D₄	D₄	semidirect
92. C₂⁵×D₄	C₂³	semidirect
93. C₂⁵×D₄	C₂³	semidirect
94. C₂⁶×C₄	D₄	semidirect
95. C₂×#3484	D₄	semidirect
102. C₂²×#534	C₂³	semidirect
103. C₂²×#534	C₂³	semidirect
104. C₂²×#534	C₂³	semidirect
105. C₂³×#123	C₂³	semidirect
106. C₂³×#120	D₄	semidirect
107. C₂³×#120	D₄	semidirect
113. C₂³×#120	C₂³	semidirect
114. C₂³×#120	C₂³	semidirect
115. C₂³×#120	C₂³	semidirect
118. C₂⁴×C₂²⋊C₄	D₄	semidirect
120. C₂⁴×C₂²⋊C₄	C₂³	semidirect
121. C₂⁴×C₂²⋊C₄	C₂³	semidirect
122. C₂⁴×C₂²⋊C₄	C₂³	semidirect
123. C₂²×#458	C₂³	semidirect
124. C₂²×B(4,𝔽₂)	C₂³	semidirect
126. C₂³×#99	C₂³	semidirect
127. C₂³×#99	C₂³	semidirect
128. C₂×#2849	C₂³	semidirect
129. C₂×#2846	C₂³	semidirect
130. #34980	D₄	semidirect
132. C₂×#2405	C₂³	semidirect
133. C₂×#2405	C₂³	semidirect
134. C₂×#2405	C₂³	semidirect
136. C₂×#2403	C₂³	semidirect
137. C₂×#2403	C₂³	semidirect
138. C₂×#2403	C₂³	semidirect
139. C₂×#2613	C₂³	semidirect
141. C₂×#2308	C₂³	semidirect
142. C₂×#2308	C₂³	semidirect
143. C₂×#2308	C₂³	semidirect
144. C₂×#2308	C₂³	semidirect
145. C₂²×#386	C₂³	semidirect
148. C₂²×#379	C₂³	semidirect
149. C₂²×#379	C₂³	semidirect
150. C₂²×#379	C₂³	semidirect
151. C₂²×#379	C₂³	semidirect
152. C₂²×#379	C₂³	semidirect
153. C₂×#2022	C₂³	semidirect
154. C₂×#2021	C₂³	semidirect
155. C₂×#1898	C₂³	semidirect
156. C₂×#1898	C₂³	semidirect
157. C₂×#1890	C₂³	semidirect
158. C₂×#1889	C₂³	semidirect
159. C₂×#1790	C₂³	semidirect
161. C₂×#1781	C₂³	semidirect
162. C₂×#1781	C₂³	semidirect
163. C₂×#1781	C₂³	semidirect
164. C₂×#1781	C₂³	semidirect
165. C₂×#1781	C₂³	semidirect
166. C₂²×#342	C₂³	semidirect
167. #14911	C₂³	semidirect
168. #14715	C₂³	semidirect
169. #14694	C₂³	semidirect
170. #14679	C₂³	semidirect
171. #14679	C₂³	semidirect
172. #14255	C₂³	semidirect
173. #13869	C₂³	semidirect
174. #13867	C₂³	semidirect
175. #13794	C₂³	semidirect
176. #10995	C₂³	semidirect
177. #10965	C₂³	semidirect
178. #10745	C₂³	semidirect
179. #10725	C₂³	semidirect
195. C₂⁷	C₂×D₄	semidirect
201. C₂⁷	C₂⁴	semidirect
202. C₂²×H(5,𝔽₂)	C₂×D₄	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
242. C₂⁴×D₄	C₂⁴	semidirect
243. C₂⁴×D₄	C₂⁴	semidirect
250. C₂⁵×C₄	C₂×D₄	semidirect
251. C₂⁵×C₄	C₂×D₄	semidirect
252. C₂⁵×C₄	C₂⁴	semidirect
253. C₂⁵×C₄	C₂⁴	semidirect
255. #3484	C₂×D₄	semidirect
256. C₂×#534	C₂×D₄	semidirect
257. C₂×#534	C₂×D₄	semidirect
260. C₂²×#123	C₂⁴	semidirect
261. C₂²×#123	C₂⁴	semidirect
265. C₂²×#120	C₂×D₄	semidirect
266. C₂²×#120	C₂×D₄	semidirect
267. C₂²×#120	C₂×D₄	semidirect
272. C₂²×#120	C₂⁴	semidirect
273. C₂²×#120	C₂⁴	semidirect
274. C₂×#518	C₂×D₄	semidirect
278. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
279. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
280. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
281. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
288. C₂³×C₂²⋊C₄	C₂⁴	semidirect
289. C₂³×C₂²⋊C₄	C₂⁴	semidirect
290. C₂³×C₂²⋊C₄	C₂⁴	semidirect
291. C₂³×C₂²⋊C₄	C₂⁴	semidirect
293. C₂²×#99	C₂⁴	semidirect
294. C₂²×#99	C₂⁴	semidirect
295. #2405	C₂×D₄	semidirect
296. #2403	C₂×D₄	semidirect
297. #2308	C₂×D₄	semidirect
299. C₂×#386	C₂⁴	semidirect
300. C₂×#386	C₂⁴	semidirect
301. C₂×#381	C₂⁴	semidirect
302. C₂×#379	C₂×D₄	semidirect
305. C₂×#379	C₂⁴	semidirect
306. C₂×#379	C₂⁴	semidirect
307. C₂×#379	C₂⁴	semidirect
308. C₂×#379	C₂⁴	semidirect
309. C₂×#379	C₂⁴	semidirect
310. C₂×#342	C₂⁴	semidirect
311. C₂²⋊#95	C₂⁴	semidirect
326. C₂⁶	#120	semidirect
327. C₂⁶	#120	semidirect
376. C₂³×D₄	#120	semidirect
377. C₂³×D₄	#120	semidirect
378. C₂³×D₄	#120	semidirect
379. C₂³×D₄	#120	semidirect
380. C₂³×D₄	#120	semidirect
381. C₂³×D₄	#120	semidirect
382. C₂³×D₄	#120	semidirect
405. C₂³×D₄	C₂²×D₄	semidirect
406. C₂³×D₄	C₂²×D₄	semidirect
411. C₂⁴×C₄	#120	semidirect
412. C₂⁴×C₄	#120	semidirect
427. C₂×#123	C₂²×D₄	semidirect
428. C₂×#120	#120	semidirect
431. C₂×#120	C₂²×D₄	semidirect
433. C₂²×C₂²⋊C₄	#120	semidirect
440. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
441. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
442. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
446. #386	C₂²×D₄	semidirect
447. #379	C₂²×D₄	semidirect
493. C₂⁵	C₂×#120	semidirect
526. C₂⁵	C₂³×D₄	semidirect
540. C₂²×D₄	C₂×#120	semidirect
541. C₂²×D₄	C₂×#120	semidirect
555. C₂³×C₄	C₂×#120	semidirect
556. C₂³×C₄	C₂×#120	semidirect
562. C₂³×C₄	C₂³×D₄	semidirect
563. C₂³×C₄	C₂³×D₄	semidirect
565. C₂×C₂²⋊C₄	C₂×#120	semidirect
566. C₂×C₂²⋊C₄	C₂×#120	semidirect
568. C₂×C₂²⋊C₄	C₂³×D₄	semidirect
576. C₂⁴	#2403	semidirect
583. C₂⁴	#3026	semidirect
635. C₂×D₄	#2403	semidirect
637. C₂²×C₄	#2403	semidirect
684. C₂²	#6437621	semidirect
685. C₂²	#6628892	semidirect

Maximal subgroups

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

subgroup	index
#72294137	2
#72294130	2
#72294116	2
#72292051	2
C₂×#6437621	2
#72240108	2
#72238029	2
C₂²×#34980	2
C₂×#392109	2
C₂×#6628892	2
#72232804	2
C₂³×#3484	2
C₂×#359428	2
#72214832	2