Subgroups — #72261724

Order 2048.

Only the 2696 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 643 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261705	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#403939	C₂	1	1	yes	maximal, characteristic, complemented
3	#72261683	C₂	1	2	yes	maximal, complemented
4	C₂×#393934	C₂	1	1	yes	maximal, characteristic, complemented
5	#72261645	C₂	1	2	yes	maximal, complemented
6	C₂×#403952	C₂	1	2	yes	maximal, complemented
7	#72261626	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#403941	C₂	1	2	yes	maximal, complemented
9	#72261587	C₂	1	1	yes	maximal, characteristic, complemented
10	#72251005	C₂	1	1	yes	maximal, characteristic, complemented
11	#72240127	C₂	1	2	yes	maximal, complemented
12	C₂×#394066	C₂	1	4	yes	maximal, complemented
13	C₂×#393929	C₂	1	2	yes	maximal, complemented
14	C₂²×#62892	C₂	1	1	yes	maximal, characteristic, complemented
15	#72233926	C₂	1	2	yes	maximal, complemented
16	#72225622	C₂	1	4	yes	maximal, complemented
17	#72225621	C₂	1	2	yes	maximal, complemented
18	C₂²×#3505	C₂²	1	2	yes	—
19	C₂²×#3490	C₂²	1	2	yes	—
20	C₂²×#3496	C₂²	1	1	yes	characteristic
21	C₂²×#3484	C₂²	1	4	yes	—
22	C₂³×#546	C₂²	1	1	yes	characteristic
23	C₂³×D₄²	C₂²	1	2	yes	—
24	C₂²×#3459	C₂²	1	1	yes	characteristic
25	C₂³×#534	C₂²	1	2	yes	—
26	C₂³×B(4,𝔽₂)	C₂²	1	2	yes	complemented
27	C₂²×#2403	C₂²	1	4	yes	complemented
28	C₂³×#392	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#2029	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#2021	C₂²	1	2	yes	complemented
31	C₂²×#2021	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2021	C₂²	1	2	yes	complemented
33	C₂²×#2021	C₂²	1	4	yes	complemented
34	C₂²×#1889	C₂²	1	4	yes	complemented
35	C₂²×#1790	C₂²	1	2	yes	complemented
36	C₂²×#1790	C₂²	1	4	yes	complemented
37	C₂²×#1781	C₂²	1	4	yes	complemented
38	C₂²×#1781	C₂²	1	4	yes	complemented
39	C₂×#14717	C₂²	1	1	yes	characteristic, complemented
40	C₂×#14716	C₂²	1	2	yes	complemented
41	C₂×#14715	C₂²	1	4	yes	complemented
42	C₂×#14715	C₂²	1	2	yes	complemented
43	C₂×#13967	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13967	C₂²	1	2	yes	complemented
45	C₂×#13867	C₂²	1	2	yes	complemented
46	C₂×#13867	C₂²	1	4	yes	complemented
47	C₂×#11390	C₂²	1	2	yes	complemented
48	C₂×#11390	C₂²	1	1	yes	characteristic, complemented
49	C₂×#11381	C₂²	1	2	yes	complemented
50	C₂×#10995	C₂²	1	2	yes	complemented
51	C₂×#10995	C₂²	1	2	yes	complemented
52	C₂×#10995	C₂²	1	2	yes	complemented
53	C₂×#10995	C₂²	1	4	yes	complemented
54	C₂×#10995	C₂²	1	4	yes	complemented
55	C₂×#10995	C₂²	1	2	yes	complemented
56	C₂×#10995	C₂²	1	1	yes	characteristic, complemented
57	C₂×#10995	C₂²	1	4	yes	complemented
58	C₂×#10995	C₂²	1	4	yes	complemented
59	C₂×#10995	C₂²	1	2	yes	complemented
60	C₂×#10980	C₂²	1	2	yes	complemented
61	C₂×#10980	C₂²	1	2	yes	complemented
62	C₂×#10965	C₂²	1	4	yes	complemented
63	C₂×#10965	C₂²	1	4	yes	complemented
64	C₂×#10965	C₂²	1	4	yes	complemented
65	C₂×#10745	C₂²	1	4	yes	complemented
66	C₂×#10745	C₂²	1	4	yes	complemented
67	C₂×#10745	C₂²	1	4	yes	complemented
68	C₂×#10761	C₂²	1	1	yes	characteristic, complemented
69	C₂×#10761	C₂²	1	2	yes	complemented
70	C₂×#10761	C₂²	1	1	yes	characteristic, complemented
71	C₂×#10761	C₂²	1	2	yes	complemented
72	C₂×#10725	C₂²	1	2	yes	complemented
73	C₂×#10725	C₂²	1	2	yes	complemented
74	#154280	C₂²	1	1	yes	characteristic, complemented
75	#154255	C₂²	1	2	yes	complemented
76	#154195	C₂²	1	4	yes	complemented
77	#154195	C₂²	1	2	yes	complemented
78	#154094	C₂²	1	2	yes	complemented
79	#154094	C₂²	1	1	yes	characteristic, complemented
80	#153851	C₂²	1	2	yes	complemented
81	#153827	C₂²	1	2	yes	complemented
82	#153827	C₂²	1	1	yes	characteristic, complemented
83	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
84	C₂⁴×#41	D₄	1	1	yes	characteristic, complemented
85	C₂⁵×D₄	D₄	1	2	yes	complemented
86	C₂⁵×D₄	C₂³	1	4	yes	—
87	C₂⁵×D₄	C₂³	1	2	yes	—
88	C₂⁵×D₄	C₂³	1	1	yes	characteristic
89	C₂×#3505	D₄	1	16	yes	complemented
90	C₂×#3490	D₄	1	16	yes	complemented
91	C₂×#3496	D₄	1	8	yes	complemented
92	C₂×#3484	D₄	1	32	yes	complemented
93	C₂×#3459	D₄	1	8	yes	complemented
94	C₂²×#543	C₂³	1	1	yes	characteristic
95	C₂²×#534	D₄	1	16	yes	complemented
96	C₂²×#534	C₂³	1	1	yes	characteristic
97	C₂²×#534	C₂³	1	4	yes	—
98	C₂²×#534	C₂³	1	2	yes	—
99	C₂²×#534	C₂³	1	2	yes	—
100	C₂³×#127	D₄	1	2	yes	complemented
101	C₂³×#124	D₄	1	1	yes	characteristic, complemented
102	C₂³×#123	D₄	1	2	yes	complemented
103	C₂³×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
104	C₂³×#121	D₄	1	2	yes	complemented
105	C₂³×#121	D₄	1	4	yes	complemented
106	C₂³×#121	D₄	1	1	yes	characteristic, complemented
107	C₂³×#121	D₄	1	2	yes	complemented
108	C₂³×#121	C₂³	1	2	yes	—
109	C₂³×#120	D₄	1	4	yes	complemented
110	C₂³×#120	C₂³	1	4	yes	—
111	C₂³×#120	C₂³	1	2	yes	—
112	C₂³×#120	C₂³	1	1	yes	characteristic
113	C₂³×#120	C₂³	1	4	yes	—
114	C₂³×#120	C₂³	1	2	yes	—
115	C₂²×#518	C₂³	1	4	yes	—
116	C₂³×C₄×D₄	D₄	1	2	yes	complemented
117	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
118	C₂³×C₄×D₄	C₂³	1	2	yes	—
119	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
120	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
123	C₂³×#99	C₂³	1	2	yes	—
124	C₂³×#99	C₂³	1	4	yes	—
125	C₂³×#99	C₂³	1	2	yes	—
126	C₂³×#99	C₂³	1	4	yes	—
127	C₂³×#99	C₂³	1	4	yes	—
128	C₂³×#99	C₂³	1	4	yes	—
129	C₂³×#99	C₂³	1	2	yes	—
130	C₂³×#99	C₂³	1	4	yes	—
131	C₂³×#99	C₂³	1	2	yes	—
132	C₂²×#386	C₂³	1	4	yes	—
133	C₂²×#386	C₂³	1	4	yes	—
134	C₂²×#386	C₂³	1	1	yes	characteristic
135	C₂²×#386	C₂³	1	4	yes	—
136	C₂²×#386	C₂³	1	2	yes	—
137	C₂²×#386	C₂³	1	2	yes	—
138	C₂²×#386	C₂³	1	4	yes	—
139	C₂²×#379	C₂³	1	4	yes	—
140	C₂²×#379	C₂³	1	4	yes	—
141	C₂²×#379	C₂³	1	2	yes	—
142	C₂²×#379	C₂³	1	2	yes	—
143	C₂²×#379	C₂³	1	1	yes	characteristic
144	C₂²×#379	C₂³	1	2	yes	—
145	C₂²×#379	C₂³	1	2	yes	—
146	C₂³×#95	C₂³	1	1	yes	characteristic
147	C₂²×#342	C₂³	1	2	yes	—
148	C₂²×#342	C₂³	1	1	yes	characteristic
149	C₂²×#342	C₂³	1	1	yes	characteristic
150	C₂²×#342	C₂³	1	4	yes	—
151	C₂²×#342	C₂³	1	4	yes	—
152	C₂²×#342	C₂³	1	2	yes	—
153	C₂²×#342	C₂³	1	2	yes	—
154	C₂²×#342	C₂³	1	4	yes	—
155	C₂×C₂²⋊#95	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊#95	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊#95	C₂³	1	2	yes	—
158	C₂×C₂²⋊#95	C₂³	1	2	yes	—
159	C₂×C₂²⋊#95	C₂³	1	2	yes	—
160	C₂×C₂²⋊#95	C₂³	1	2	yes	—
161	C₂×C₂²⋊#95	C₂³	1	2	yes	—
162	C₂×C₂²⋊#95	C₂³	1	4	yes	—
163	C₂×C₂²⋊#95	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊#95	C₂³	1	2	yes	—
165	C₂×C₂²⋊#95	C₂³	1	2	yes	—
166	C₂⁷	C₂×D₄	1	4	yes	—
167	C₂⁷	C₂⁴	1	2	yes	—
168	C₂⁷	C₂⁴	1	1	yes	characteristic
169	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
170	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
171	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
172	C₂⁴×D₄	C₂×D₄	1	16	yes	—
173	C₂⁴×D₄	C₂×D₄	1	16	yes	—
174	C₂⁴×D₄	C₂×D₄	1	2	yes	—
175	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
176	C₂⁴×D₄	C₂×D₄	1	4	yes	—
177	C₂⁴×D₄	C₂×D₄	1	2	yes	—
178	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
179	C₂⁴×D₄	C₂×D₄	1	2	yes	—
180	C₂⁴×D₄	C₂×D₄	1	4	yes	—
181	C₂⁴×D₄	C₂×D₄	1	2	yes	—
182	C₂⁴×D₄	C₂×D₄	1	4	yes	—
183	C₂⁴×D₄	C₂×D₄	1	4	yes	—
184	C₂⁴×D₄	C₂×D₄	1	2	yes	—
185	C₂⁴×D₄	C₂×D₄	1	4	yes	—
186	C₂⁴×D₄	C₂×D₄	1	2	yes	—
187	C₂⁴×D₄	C₂⁴	1	2	yes	—
188	C₂⁴×D₄	C₂⁴	1	4	yes	—
189	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
190	C₂⁵×C₄	C₂×D₄	1	2	yes	—
191	C₂⁵×C₄	C₂×D₄	1	4	yes	—
192	C₂⁵×C₄	C₂×D₄	1	2	yes	—
193	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁵×C₄	C₂×D₄	1	2	yes	—
195	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
196	C₂⁵×C₄	C₂⁴	1	2	yes	—
197	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
198	C₂×#543	C₂×D₄	1	8	yes	—
199	C₂×#543	C₂×D₄	1	4	yes	—
200	C₂×#534	C₂×D₄	1	8	yes	—
201	C₂×#534	C₂×D₄	1	4	yes	—
202	C₂×#534	C₂×D₄	1	16	yes	—
203	C₂×#534	C₂×D₄	1	16	yes	—
204	C₂×#534	C₂×D₄	1	8	yes	—
205	C₂×#534	C₂×D₄	1	8	yes	—
206	C₂×#534	C₂×D₄	1	16	yes	—
207	C₂×#534	C₂×D₄	1	16	yes	—
208	C₂×#534	C₂×D₄	1	8	yes	—
209	C₂×#534	C₂×D₄	1	8	yes	—
210	C₂²×C₂²⋊Q₈	C₂×D₄	1	8	yes	—
211	C₂²×#121	C₂×D₄	1	8	yes	—
212	C₂²×#121	C₂×D₄	1	8	yes	—
213	C₂²×#120	C₂×D₄	1	16	yes	—
214	C₂²×#120	C₂×D₄	1	16	yes	—
215	C₂²×#120	C₂×D₄	1	16	yes	—
216	C₂×#518	C₂×D₄	1	16	yes	—
217	C₂×#518	C₂×D₄	1	16	yes	—
218	C₂×#518	C₂×D₄	1	16	yes	—
219	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
220	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
221	C₂²×C₄×D₄	C₂×D₄	1	8	yes	—
222	C₂²×C₄×D₄	C₂×D₄	1	4	yes	—
223	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
224	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
226	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
228	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
229	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
230	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
231	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
232	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
233	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
235	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
236	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
237	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
238	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
239	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
240	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
241	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
242	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
243	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
244	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
246	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
247	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
248	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
249	C₂³×C₄²	C₂×D₄	1	2	yes	—
250	C₂⁶	#120	1	16	yes	complemented
251	C₂⁶	C₂²×D₄	1	2	yes	—
252	C₂⁶	C₂²×D₄	1	1	yes	characteristic
253	C₂⁶	C₂²×D₄	1	4	yes	—
254	C₂⁶	C₂²×D₄	1	2	yes	—
255	C₂⁶	C₂²×D₄	1	4	yes	—
256	C₂⁶	C₂²×D₄	1	4	yes	—
257	C₂⁶	C₂²×D₄	1	4	yes	—
258	C₂⁶	C₂²×D₄	1	2	yes	—
259	C₂⁶	C₂²×D₄	1	8	yes	—
260	C₂⁶	C₂²×D₄	1	4	yes	—
261	C₂⁶	H(5,𝔽₂)	1	2	yes	complemented
262	C₂⁶	C₂⁵	1	1	yes	characteristic
263	C₂×H(5,𝔽₂)	#120	1	32	yes	complemented
264	C₂³×Q₈	#120	1	4	yes	complemented
265	C₂³×D₄	#120	1	1	yes	characteristic
266	C₂³×D₄	#120	1	2	yes	—
267	C₂³×D₄	#120	1	1	yes	characteristic
268	C₂³×D₄	#120	1	2	yes	—
269	C₂³×D₄	#120	1	4	yes	—
270	C₂³×D₄	#120	1	4	yes	—
271	C₂³×D₄	#120	1	2	yes	—
272	C₂³×D₄	#120	1	16	yes	complemented
273	C₂³×D₄	#120	1	16	yes	complemented
274	C₂³×D₄	#120	1	16	yes	complemented
275	C₂³×D₄	#120	1	8	yes	complemented
276	C₂³×D₄	#120	1	16	yes	complemented
277	C₂³×D₄	#120	1	8	yes	complemented
278	C₂³×D₄	#120	1	8	yes	complemented
279	C₂³×D₄	C₂²×D₄	1	8	yes	—
280	C₂³×D₄	C₂²×D₄	1	8	yes	—
281	C₂³×D₄	C₂²×D₄	1	8	yes	—
282	C₂³×D₄	C₂²×D₄	1	8	yes	—
283	C₂³×D₄	C₂²×D₄	1	2	yes	—
284	C₂³×D₄	C₂²×D₄	1	8	yes	—
285	C₂³×D₄	C₂²×D₄	1	8	yes	—
286	C₂³×D₄	C₂²×D₄	1	8	yes	—
287	C₂³×D₄	C₂²×D₄	1	4	yes	—
288	C₂³×D₄	C₂²×D₄	1	4	yes	—
289	C₂³×D₄	C₂²×D₄	1	2	yes	—
290	C₂³×D₄	C₂²×D₄	1	8	yes	—
291	C₂³×D₄	C₂²×D₄	1	8	yes	—
292	C₂⁴×C₄	#120	1	16	yes	complemented
293	C₂⁴×C₄	#120	1	8	yes	complemented
294	C₂⁴×C₄	#120	1	8	yes	complemented
295	C₂⁴×C₄	#120	1	8	yes	complemented
296	C₂⁴×C₄	#120	1	4	yes	complemented
297	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
298	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
299	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
301	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
302	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
303	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
304	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
305	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
306	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
307	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
308	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
309	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
311	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
312	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×C₄	H(5,𝔽₂)	1	4	yes	complemented
314	#543	#120	1	16	yes	complemented
315	#534	#120	1	16	yes	—
316	#534	#120	1	32	yes	complemented
317	#534	#120	1	64	yes	complemented
318	#534	#120	1	32	yes	complemented
319	#518	#120	1	64	yes	complemented
320	C₂²×C₄⋊C₄	#120	1	8	yes	complemented
321	C₂²×C₄⋊C₄	#120	1	4	yes	complemented
322	C₂²×C₄⋊C₄	#120	1	8	yes	complemented
323	C₂²×C₄⋊C₄	#120	1	4	yes	complemented
324	C₂²×C₄⋊C₄	#120	1	8	yes	complemented
325	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
326	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
327	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
328	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
329	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
330	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
331	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
332	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
333	C₂²×C₂²⋊C₄	#120	1	16	yes	complemented
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
339	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
343	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
346	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	complemented
347	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	8	yes	complemented
348	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	2	yes	complemented
349	C₂²×C₄²	#120	1	4	yes	complemented
350	C₂²×C₄²	#120	1	8	yes	complemented
351	C₂⁵	C₂×#120	1	4	yes	—
352	C₂⁵	C₂×#120	1	2	yes	—
353	C₂⁵	C₂×#120	1	4	yes	—
354	C₂⁵	C₂×#120	1	8	yes	—
355	C₂⁵	C₂×#120	1	8	yes	—
356	C₂⁵	C₂×#120	1	4	yes	—
357	C₂⁵	C₂×#120	1	4	yes	—
358	C₂⁵	C₂×#120	1	8	yes	—
359	C₂⁵	C₂×#120	1	4	yes	—
360	C₂⁵	C₂×#120	1	8	yes	—
361	C₂⁵	C₂×#120	1	4	yes	—
362	C₂⁵	C₂×#120	1	8	yes	—
363	C₂⁵	C₂×#120	1	8	yes	—
364	C₂⁵	C₂×#120	1	8	yes	—
365	C₂⁵	C₂×#120	1	8	yes	—
366	C₂⁵	C₂×#120	1	2	yes	—
367	C₂⁵	C₂×#120	1	4	yes	—
368	C₂⁵	C₂×#120	1	2	yes	—
369	C₂⁵	C₂³×D₄	1	2	yes	—
370	C₂⁵	C₂³×D₄	1	4	yes	—
371	C₂⁵	C₂³×D₄	1	1	yes	characteristic
372	C₂⁵	C₂³×D₄	1	2	yes	—
373	C₂⁵	C₂³×D₄	1	1	yes	characteristic
374	C₂⁵	C₂³×D₄	1	2	yes	—
375	C₂⁵	C₂³×D₄	1	2	yes	—
376	C₂⁵	C₂³×D₄	1	1	yes	characteristic
377	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
379	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
380	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
381	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
382	C₂⁵	#585	1	1	yes	characteristic
383	C₂⁵	#585	1	2	yes	—
384	C₂⁵	#585	1	2	yes	—
385	C₂⁵	#585	1	1	yes	characteristic
386	C₂²×D₄	B(4,𝔽₂)	1	4	yes	complemented
387	C₂²×D₄	C₂×#120	1	16	yes	—
388	C₂²×D₄	C₂×#120	1	8	yes	—
389	C₂²×D₄	C₂×#120	1	8	yes	—
390	C₂²×D₄	C₂×#120	1	16	yes	—
391	C₂²×D₄	C₂×#120	1	16	yes	—
392	C₂²×D₄	C₂×#120	1	16	yes	—
393	C₂²×D₄	C₂×#120	1	8	yes	—
394	C₂²×D₄	C₂×#120	1	16	yes	—
395	C₂²×D₄	C₂×#120	1	8	yes	—
396	C₂³×C₄	C₂×#120	1	1	yes	characteristic
397	C₂³×C₄	C₂×#120	1	4	yes	—
398	C₂³×C₄	C₂×#120	1	8	yes	—
399	C₂³×C₄	C₂×#120	1	4	yes	—
400	C₂³×C₄	C₂×#120	1	4	yes	—
401	C₂³×C₄	C₂×#120	1	4	yes	—
402	C₂³×C₄	C₂×#120	1	4	yes	—
403	C₂³×C₄	C₂×#120	1	4	yes	—
404	C₂³×C₄	C₂×#120	1	4	yes	—
405	C₂³×C₄	C₂×#120	1	4	yes	—
406	C₂³×C₄	C₂×#120	1	8	yes	—
407	C₂³×C₄	C₂×#120	1	8	yes	—
408	C₂³×C₄	C₂×#120	1	4	yes	—
409	C₂³×C₄	C₂×#120	1	2	yes	—
410	C₂³×C₄	C₂×#120	1	4	yes	—
411	C₂³×C₄	C₂×#120	1	2	yes	—
412	C₂³×C₄	C₂×#120	1	8	yes	—
413	C₂³×C₄	C₂×#120	1	4	yes	—
414	C₂³×C₄	C₂×#120	1	4	yes	—
415	C₂³×C₄	C₂×#120	1	2	yes	—
416	C₂³×C₄	C₂×#120	1	4	yes	—
417	C₂³×C₄	C₂×#120	1	2	yes	—
418	C₂³×C₄	C₂×#120	1	4	yes	—
419	C₂³×C₄	C₂×#120	1	2	yes	—
420	C₂³×C₄	C₂×#120	1	4	yes	—
421	C₂³×C₄	C₂×#120	1	2	yes	—
422	C₂³×C₄	C₂×#120	1	4	yes	—
423	C₂³×C₄	C₂×#120	1	2	yes	—
424	C₂³×C₄	C₂×#120	1	8	yes	—
425	C₂³×C₄	C₂×#120	1	8	yes	—
426	C₂³×C₄	C₂×#120	1	2	yes	—
427	C₂³×C₄	C₂×#120	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
429	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
430	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
431	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
433	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
434	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
436	C₂⁴	#2846	1	16	yes	—
437	C₂⁴	#2846	1	8	yes	—
438	C₂⁴	#2846	1	4	yes	—
439	C₂⁴	#2846	1	8	yes	—
440	C₂⁴	#2846	1	4	yes	—
441	C₂⁴	#2846	1	4	yes	—
442	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
443	C₂⁴	#3026	1	4	yes	—
444	C₂⁴	C₂²×#120	1	4	yes	—
445	C₂⁴	C₂²×#120	1	2	yes	—
446	C₂⁴	C₂²×#120	1	1	yes	characteristic
447	C₂⁴	C₂²×#120	1	4	yes	—
448	C₂⁴	C₂²×#120	1	2	yes	—
449	C₂⁴	C₂²×#120	1	2	yes	—
450	C₂⁴	C₂²×#120	1	2	yes	—
451	C₂⁴	C₂²×#120	1	2	yes	—
452	C₂⁴	C₂²×#120	1	4	yes	—
453	C₂⁴	C₂²×#120	1	4	yes	—
454	C₂⁴	C₂²×#120	1	1	yes	characteristic
455	C₂⁴	C₂²×#120	1	2	yes	—
456	C₂⁴	C₂²×#120	1	2	yes	—
457	C₂⁴	C₂²×#120	1	1	yes	characteristic
458	C₂⁴	C₂²×#120	1	1	yes	characteristic
459	C₂⁴	C₂²×#120	1	1	yes	characteristic
460	C₂⁴	#3484	1	2	yes	—
461	C₂⁴	#3484	1	4	yes	—
462	C₂⁴	#3484	1	2	yes	—
463	C₂⁴	#3484	1	1	yes	characteristic
464	C₂⁴	#3484	1	4	yes	—
465	C₂⁴	#3484	1	4	yes	—
466	C₂⁴	#3484	1	4	yes	—
467	C₂⁴	#3484	1	4	yes	—
468	C₂⁴	#3484	1	2	yes	—
469	C₂⁴	#3485	1	2	yes	—
470	C₂⁴	#3485	1	4	yes	—
471	C₂⁴	#3485	1	2	yes	—
472	C₂⁴	#3485	1	1	yes	characteristic
473	C₂⁴	#3488	1	1	yes	characteristic
474	C₂⁴	#3488	1	2	yes	—
475	C₂⁴	#3488	1	1	yes	characteristic
476	C₂⁴	#3488	1	2	yes	—
477	C₂⁴	#3488	1	2	yes	—
478	C₂⁴	#3488	1	1	yes	characteristic
479	C₂⁴	#3488	1	4	yes	—
480	C₂⁴	#3488	1	2	yes	—
481	C₂⁴	#3488	1	4	yes	—
482	C₂⁴	#3488	1	2	yes	—
483	C₂⁴	#3488	1	1	yes	characteristic
484	C₂⁴	#3488	1	2	yes	—
485	C₂⁴	#3496	1	2	yes	—
486	C₂⁴	#3496	1	4	yes	—
487	C₂⁴	#3496	1	2	yes	—
488	C₂⁴	#3496	1	4	yes	—
489	C₂⁴	#3496	1	2	yes	—
490	C₂⁴	#3496	1	4	yes	—
491	C₂⁴	#3496	1	4	yes	—
492	C₂⁴	#3496	1	4	yes	—
493	C₂⁴	#3496	1	2	yes	—
494	C₂⁴	#3496	1	4	yes	—
495	C₂⁴	#3496	1	2	yes	—
496	C₂⁴	#3496	1	2	yes	—
497	C₂⁴	#3498	1	1	yes	characteristic
498	C₂⁴	#3498	1	2	yes	—
499	C₂⁴	#3498	1	4	yes	—
500	C₂⁴	#3498	1	2	yes	—
501	C₂⁴	#3498	1	2	yes	—
502	C₂⁴	#3498	1	2	yes	—
503	C₂⁴	#3498	1	4	yes	—
504	C₂⁴	#3498	1	1	yes	characteristic
505	C₂⁴	#3500	1	1	yes	characteristic
506	C₂⁴	#3500	1	2	yes	—
507	C₂⁴	#3500	1	1	yes	characteristic
508	C₂⁴	#3500	1	2	yes	—
509	C₂²×C₄	#2846	1	2	yes	—
510	C₂²×C₄	#2846	1	8	yes	—
511	C₂²×C₄	#2846	1	8	yes	—
512	C₂²×C₄	#2846	1	8	yes	—
513	C₂²×C₄	#2846	1	8	yes	—
514	C₂²×C₄	#2846	1	4	yes	—
515	C₂²×C₄	#2846	1	4	yes	—
516	C₂²×C₄	#2846	1	2	yes	—
517	C₂²×C₄	#2846	1	4	yes	—
518	C₂²×C₄	#2846	1	4	yes	—
519	C₂²×C₄	#2846	1	16	yes	—
520	C₂²×C₄	#2846	1	8	yes	—
521	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
522	C₂²×C₄	#3026	1	2	yes	—
523	C₂³	#32898	1	8	yes	—
524	C₂³	#35346	1	2	yes	—
525	C₂³	#35346	1	4	yes	—
526	C₂³	#35347	1	4	yes	—
527	C₂³	#35347	1	4	yes	—
528	C₂³	#35347	1	4	yes	—
529	C₂³	#35347	1	2	yes	—
530	C₂³	#35347	1	4	yes	—
531	C₂³	#35512	1	4	yes	—
532	C₂³	#35512	1	2	yes	—
533	C₂³	#35512	1	1	yes	characteristic
534	C₂³	#35512	1	2	yes	—
535	C₂³	#35513	1	1	yes	characteristic
536	C₂³	#35513	1	2	yes	—
537	C₂³	#35513	1	2	yes	—
538	C₂³	#35513	1	2	yes	—
539	C₂³	#35513	1	4	yes	—
540	C₂³	#35513	1	4	yes	—
541	C₂³	#35513	1	1	yes	characteristic
542	C₂³	#35513	1	2	yes	—
543	C₂³	#35527	1	1	yes	characteristic
544	C₂³	#35527	1	2	yes	—
545	C₂³	#35527	1	4	yes	—
546	C₂³	#35527	1	2	yes	—
547	C₂³	#35680	1	1	yes	characteristic
548	C₂³	#35680	1	2	yes	—
549	C₂³	#35680	1	4	yes	—
550	C₂³	#35680	1	2	yes	—
551	C₂³	#35680	1	4	yes	—
552	C₂³	#35680	1	2	yes	—
553	C₂³	#35680	1	4	yes	—
554	C₂³	#35680	1	2	yes	—
555	C₂³	#35680	1	4	yes	—
556	C₂³	#35680	1	2	yes	—
557	C₂³	#35680	1	4	yes	—
558	C₂³	#35680	1	2	yes	—
559	C₂³	#35680	1	4	yes	—
560	C₂³	#35680	1	1	yes	characteristic
561	C₂³	#35680	1	2	yes	—
562	C₂³	#35680	1	4	yes	—
563	C₂³	#35680	1	2	yes	—
564	C₂³	#35680	1	2	yes	—
565	C₂³	#35680	1	4	yes	—
566	C₂³	#35680	1	2	yes	—
567	C₂³	#35750	1	1	yes	characteristic
568	C₂³	#35750	1	2	yes	—
569	C₂³	#35750	1	4	yes	—
570	C₂³	#35750	1	1	yes	characteristic
571	C₂³	#35750	1	4	yes	—
572	C₂³	#35750	1	2	yes	—
573	C₂³	#35750	1	2	yes	—
574	C₂³	#35750	1	2	yes	—
575	C₂³	#36082	1	1	yes	characteristic
576	C₂³	#36082	1	1	yes	characteristic
577	C₂³	#36091	1	2	yes	—
578	C₂³	#36091	1	2	yes	—
579	C₂³	#36091	1	1	yes	characteristic
580	C₂³	#36091	1	1	yes	characteristic
581	C₂³	C₂×#2846	1	2	yes	—
582	C₂³	C₂×#2846	1	1	yes	characteristic
583	C₂³	C₂×#2846	1	1	yes	characteristic
584	C₂³	C₂×#2846	1	2	yes	—
585	C₂³	C₂×#2846	1	2	yes	—
586	C₂³	C₂×#2846	1	2	yes	—
587	C₂³	C₂×#2846	1	4	yes	—
588	C₂³	C₂×#2846	1	1	yes	characteristic
589	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
590	C₂³	C₂×#3026	1	1	yes	characteristic
591	C₂³	C₂×#3026	1	2	yes	—
592	C₂³	#60399	1	2	yes	—
593	C₂³	#60399	1	1	yes	characteristic
594	C₂³	#60401	1	1	yes	characteristic
595	C₂×C₄	#32898	1	4	yes	—
596	C₂²	#4928938	1	2	yes	—
597	C₂²	#4928938	1	4	yes	—
598	C₂²	#4928938	1	1	yes	characteristic
599	C₂²	#4928938	1	2	yes	—
600	C₂²	#4929082	1	1	yes	characteristic
601	C₂²	#4929082	1	2	yes	—
602	C₂²	#4929082	1	2	yes	—
603	C₂²	#4929082	1	1	yes	characteristic
604	C₂²	#4930494	1	2	yes	—
605	C₂²	#4930494	1	2	yes	—
606	C₂²	#4930494	1	4	yes	—
607	C₂²	#4930494	1	1	yes	characteristic
608	C₂²	#4930608	1	1	yes	characteristic
609	C₂²	#4930608	1	1	yes	characteristic
610	C₂²	#4930608	1	2	yes	—
611	C₂²	#4930608	1	2	yes	—
612	C₂²	#6342371	1	1	yes	characteristic
613	C₂²	#6533135	1	2	yes	—
614	C₂²	#6533135	1	1	yes	characteristic
615	C₂²	#6533141	1	1	yes	characteristic
616	C₂²	#6533144	1	2	yes	—
617	C₂²	#6533339	1	2	yes	—
618	C₂²	#6533339	1	2	yes	—
619	C₂²	#6533343	1	2	yes	—
620	C₂²	#6542240	1	1	yes	characteristic
621	C₂²	#6542246	1	1	yes	characteristic
622	C₂²	#6542409	1	2	yes	—
623	C₂²	C₂×#32898	1	2	yes	—
624	C₂²	C₂×#32898	1	1	yes	characteristic
625	C₂²	#6628892	1	2	yes	—
626	C₂²	#6628892	1	1	yes	characteristic
627	C₂²	#6628896	1	2	yes	—
628	C₂²	#6628898	1	1	yes	characteristic
629	C₂²	#6628900	1	2	yes	—
630	C₂²	#6628901	1	1	yes	characteristic
631	C₂	#72219118	1	1	yes	characteristic
632	C₂	#72233203	1	2	yes	—
633	C₂	#72241173	1	1	yes	characteristic
634	C₂	#72250267	1	1	yes	characteristic
635	C₂	#72260908	1	2	yes	—
636	C₂	#72261090	1	2	yes	—
637	C₂	#72261197	1	2	yes	—
638	C₂	#72261515	1	1	yes	characteristic
639	C₂	#72261531	1	1	yes	characteristic
640	C₂	#72261540	1	1	yes	characteristic
641	C₂	#72261562	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂²×#120
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261705	C₂	semidirect
2. C₂×#403939	C₂	semidirect
3. #72261683	C₂	semidirect
4. C₂×#393934	C₂	semidirect
5. #72261645	C₂	semidirect
6. C₂×#403952	C₂	semidirect
7. #72261626	C₂	semidirect
8. C₂×#403941	C₂	semidirect
9. #72261587	C₂	semidirect
10. #72251005	C₂	semidirect
11. #72240127	C₂	semidirect
12. C₂×#394066	C₂	semidirect
13. C₂×#393929	C₂	semidirect
14. C₂²×#62892	C₂	semidirect
15. #72233926	C₂	semidirect
16. #72225622	C₂	semidirect
17. #72225621	C₂	semidirect
26. C₂³×B(4,𝔽₂)	C₂²	semidirect
27. C₂²×#2403	C₂²	semidirect
28. C₂³×#392	C₂²	semidirect
29. C₂²×#2029	C₂²	semidirect
30. C₂²×#2021	C₂²	semidirect
31. C₂²×#2021	C₂²	semidirect
32. C₂²×#2021	C₂²	semidirect
33. C₂²×#2021	C₂²	semidirect
34. C₂²×#1889	C₂²	semidirect
35. C₂²×#1790	C₂²	semidirect
36. C₂²×#1790	C₂²	semidirect
37. C₂²×#1781	C₂²	semidirect
38. C₂²×#1781	C₂²	semidirect
39. C₂×#14717	C₂²	semidirect
40. C₂×#14716	C₂²	semidirect
41. C₂×#14715	C₂²	semidirect
42. C₂×#14715	C₂²	semidirect
43. C₂×#13967	C₂²	semidirect
44. C₂×#13967	C₂²	semidirect
45. C₂×#13867	C₂²	semidirect
46. C₂×#13867	C₂²	semidirect
47. C₂×#11390	C₂²	semidirect
48. C₂×#11390	C₂²	semidirect
49. C₂×#11381	C₂²	semidirect
50. C₂×#10995	C₂²	semidirect
51. C₂×#10995	C₂²	semidirect
52. C₂×#10995	C₂²	semidirect
53. C₂×#10995	C₂²	semidirect
54. C₂×#10995	C₂²	semidirect
55. C₂×#10995	C₂²	semidirect
56. C₂×#10995	C₂²	semidirect
57. C₂×#10995	C₂²	semidirect
58. C₂×#10995	C₂²	semidirect
59. C₂×#10995	C₂²	semidirect
60. C₂×#10980	C₂²	semidirect
61. C₂×#10980	C₂²	semidirect
62. C₂×#10965	C₂²	semidirect
63. C₂×#10965	C₂²	semidirect
64. C₂×#10965	C₂²	semidirect
65. C₂×#10745	C₂²	semidirect
66. C₂×#10745	C₂²	semidirect
67. C₂×#10745	C₂²	semidirect
68. C₂×#10761	C₂²	semidirect
69. C₂×#10761	C₂²	semidirect
70. C₂×#10761	C₂²	semidirect
71. C₂×#10761	C₂²	semidirect
72. C₂×#10725	C₂²	semidirect
73. C₂×#10725	C₂²	semidirect
74. #154280	C₂²	semidirect
75. #154255	C₂²	semidirect
76. #154195	C₂²	semidirect
77. #154195	C₂²	semidirect
78. #154094	C₂²	semidirect
79. #154094	C₂²	semidirect
80. #153851	C₂²	semidirect
81. #153827	C₂²	semidirect
82. #153827	C₂²	semidirect
84. C₂⁴×#41	D₄	semidirect
85. C₂⁵×D₄	D₄	semidirect
89. C₂×#3505	D₄	semidirect
90. C₂×#3490	D₄	semidirect
91. C₂×#3496	D₄	semidirect
92. C₂×#3484	D₄	semidirect
93. C₂×#3459	D₄	semidirect
95. C₂²×#534	D₄	semidirect
100. C₂³×#127	D₄	semidirect
101. C₂³×#124	D₄	semidirect
102. C₂³×#123	D₄	semidirect
104. C₂³×#121	D₄	semidirect
105. C₂³×#121	D₄	semidirect
106. C₂³×#121	D₄	semidirect
107. C₂³×#121	D₄	semidirect
109. C₂³×#120	D₄	semidirect
116. C₂³×C₄×D₄	D₄	semidirect
117. C₂³×C₄×D₄	D₄	semidirect
250. C₂⁶	#120	semidirect
261. C₂⁶	H(5,𝔽₂)	semidirect
263. C₂×H(5,𝔽₂)	#120	semidirect
264. C₂³×Q₈	#120	semidirect
272. C₂³×D₄	#120	semidirect
273. C₂³×D₄	#120	semidirect
274. C₂³×D₄	#120	semidirect
275. C₂³×D₄	#120	semidirect
276. C₂³×D₄	#120	semidirect
277. C₂³×D₄	#120	semidirect
278. C₂³×D₄	#120	semidirect
292. C₂⁴×C₄	#120	semidirect
293. C₂⁴×C₄	#120	semidirect
294. C₂⁴×C₄	#120	semidirect
295. C₂⁴×C₄	#120	semidirect
296. C₂⁴×C₄	#120	semidirect
313. C₂⁴×C₄	H(5,𝔽₂)	semidirect
314. #543	#120	semidirect
316. #534	#120	semidirect
317. #534	#120	semidirect
318. #534	#120	semidirect
319. #518	#120	semidirect
320. C₂²×C₄⋊C₄	#120	semidirect
321. C₂²×C₄⋊C₄	#120	semidirect
322. C₂²×C₄⋊C₄	#120	semidirect
323. C₂²×C₄⋊C₄	#120	semidirect
324. C₂²×C₄⋊C₄	#120	semidirect
325. C₂²×C₂²⋊C₄	#120	semidirect
326. C₂²×C₂²⋊C₄	#120	semidirect
327. C₂²×C₂²⋊C₄	#120	semidirect
328. C₂²×C₂²⋊C₄	#120	semidirect
329. C₂²×C₂²⋊C₄	#120	semidirect
330. C₂²×C₂²⋊C₄	#120	semidirect
331. C₂²×C₂²⋊C₄	#120	semidirect
332. C₂²×C₂²⋊C₄	#120	semidirect
333. C₂²×C₂²⋊C₄	#120	semidirect
346. C₂²×C₂²⋊C₄	H(5,𝔽₂)	semidirect
347. C₂²×C₂²⋊C₄	H(5,𝔽₂)	semidirect
348. C₂²×C₂²⋊C₄	H(5,𝔽₂)	semidirect
349. C₂²×C₄²	#120	semidirect
350. C₂²×C₄²	#120	semidirect
386. C₂²×D₄	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72261705	2
C₂×#403939	2
#72261683	2
C₂×#393934	2
#72261645	2
C₂×#403952	2
#72261626	2
C₂×#403941	2
#72261587	2
#72251005	2
#72240127	2
C₂×#394066	2
C₂×#393929	2
C₂²×#62892	2
#72233926	2
#72225622	2
#72225621	2