Subgroups — #72238084

Order 2048.

At least 10856 conjugacy classes of subgroups; only the 1660 normal subgroups are shown.

The subgroup lattice has 613 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72238082	C₂	1	1	yes	maximal, characteristic, complemented
2	#72238079	C₂	1	1	yes	maximal, characteristic, complemented
3	#72238049	C₂	1	2	yes	maximal, complemented
4	#72238046	C₂	1	4	yes	maximal, complemented
5	#72238022	C₂	1	4	yes	maximal, complemented
6	#72236483	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#233541	C₂	1	2	yes	maximal, complemented
9	#72234675	C₂	1	1	yes	maximal, characteristic, complemented
10	#72234629	C₂	1	2	yes	maximal, complemented
11	#72231815	C₂	1	4	yes	maximal, complemented
12	#72225801	C₂	1	2	yes	maximal, complemented
13	#72225665	C₂	1	1	yes	maximal, characteristic, complemented
14	#72219307	C₂	1	1	yes	maximal, characteristic, complemented
15	#72210600	C₂	1	4	yes	maximal, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic
17	C₂³×D₄²	C₂²	1	1	yes	characteristic
18	#7642273	C₂²	1	2	yes	complemented
19	#7642257	C₂²	1	2	yes	complemented
20	#7630945	C₂²	1	2	yes	complemented
21	#7630939	C₂²	1	2	yes	complemented
22	C₂×#34980	C₂²	1	2	yes	—
23	C₂×#34980	C₂²	1	1	yes	characteristic
24	C₂×#34980	C₂²	1	2	yes	—
25	C₂×#34980	C₂²	1	2	yes	complemented
26	C₂²×#2403	C₂²	1	1	yes	characteristic, complemented
27	C₂²×#2403	C₂²	1	1	yes	characteristic, complemented
28	#7626202	C₂²	1	1	yes	characteristic
29	#6477580	C₂²	1	4	yes	complemented
30	#6470225	C₂²	1	4	yes	complemented
31	C₂×#21746	C₂²	1	1	yes	characteristic
32	C₂×#21746	C₂²	1	1	yes	characteristic
33	C₂×#21746	C₂²	1	2	yes	complemented
34	C₂×#21746	C₂²	1	2	yes	complemented
35	C₂×#21746	C₂²	1	2	yes	complemented
36	C₂²×#1781	C₂²	1	2	yes	complemented
37	C₂²×#1781	C₂²	1	2	yes	complemented
38	#636791	C₂²	1	2	yes	complemented
39	#635984	C₂²	1	2	yes	complemented
40	#613191	C₂²	1	2	yes	complemented
41	#612424	C₂²	1	2	yes	complemented
42	#556752	C₂²	1	1	yes	characteristic
43	#517411	C₂²	1	1	yes	characteristic, complemented
44	#517411	C₂²	1	2	yes	complemented
45	#517411	C₂²	1	1	yes	characteristic, complemented
46	#405090	C₂²	1	8	yes	complemented
47	#394058	C₂²	1	8	yes	complemented
48	#392245	C₂²	1	2	yes	complemented
49	#392109	C₂²	1	2	yes	complemented
50	#382422	C₂²	1	2	yes	complemented
51	#382390	C₂²	1	2	yes	complemented
52	#355913	C₂²	1	2	yes	complemented
53	#233541	C₂²	1	8	yes	complemented
54	#233541	C₂²	1	8	yes	complemented
55	#201665	C₂²	1	4	yes	complemented
56	#201664	C₂²	1	4	yes	complemented
57	#187929	C₂²	1	4	yes	complemented
58	#187928	C₂²	1	4	yes	complemented
59	C₂×#8101	C₂²	1	2	yes	complemented
60	C₂×#8101	C₂²	1	2	yes	complemented
61	#115691	C₂²	1	8	yes	complemented
62	#115690	C₂²	1	8	yes	complemented
63	#115204	C₂²	1	8	yes	complemented
64	#115204	C₂²	1	8	yes	complemented
65	#106767	C₂²	1	4	yes	complemented
66	#106766	C₂²	1	4	yes	complemented
67	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
68	C₂⁵×D₄	C₂³	1	1	yes	characteristic
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂⁵×D₄	C₂³	1	1	yes	characteristic
71	C₂⁵×D₄	C₂³	1	1	yes	characteristic
72	C₂×#3490	D₄	1	4	yes	complemented
73	C₂×#3490	C₂³	1	2	yes	—
74	C₂×#3484	D₄	1	4	yes	complemented
75	C₂×#3484	C₂³	1	2	yes	—
76	C₂³×#127	D₄	1	1	yes	characteristic, complemented
77	C₂³×#121	D₄	1	1	yes	characteristic, complemented
78	C₂³×#121	D₄	1	1	yes	characteristic, complemented
79	C₂³×#121	D₄	1	1	yes	characteristic, complemented
80	C₂³×#121	C₂³	1	1	yes	characteristic
81	C₂³×#120	D₄	1	1	yes	characteristic, complemented
82	C₂³×#120	D₄	1	1	yes	characteristic, complemented
83	C₂³×#120	C₂³	1	2	yes	—
84	C₂³×#120	C₂³	1	2	yes	—
85	C₂³×#120	C₂³	1	1	yes	characteristic
86	C₂³×#120	C₂³	1	1	yes	characteristic
87	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
88	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
89	C₂×#2849	D₄	1	2	yes	complemented
90	C₂×#2849	C₂³	1	4	yes	—
91	C₂×#2846	D₄	1	2	yes	complemented
92	C₂×#2846	C₂³	1	4	yes	—
93	#34980	D₄	1	8	yes	complemented
94	#34980	C₂³	1	4	yes	—
95	#34980	C₂³	1	4	yes	—
96	#34980	C₂³	1	8	yes	—
97	C₂×#2405	D₄	1	4	yes	complemented
98	C₂×#2405	D₄	1	4	yes	complemented
99	C₂×#2405	C₂³	1	2	yes	—
100	C₂×#2410	D₄	1	8	yes	complemented
101	C₂×#2410	D₄	1	4	yes	complemented
102	C₂×#2403	D₄	1	4	yes	complemented
103	C₂×#2403	D₄	1	4	yes	complemented
104	C₂×#2403	C₂³	1	2	yes	—
105	C₂×#2403	C₂³	1	2	yes	—
106	C₂×#2403	C₂³	1	2	yes	—
107	#34356	D₄	1	8	yes	complemented
108	#34176	C₂³	1	2	yes	—
109	#34171	C₂³	1	2	yes	—
110	C₂²×#386	C₂³	1	2	yes	—
111	C₂²×#379	C₂³	1	2	yes	—
112	C₂²×#379	C₂³	1	2	yes	—
113	C₂²×#379	C₂³	1	1	yes	characteristic
114	C₂²×#379	C₂³	1	1	yes	characteristic
115	C₂²×#379	C₂³	1	2	yes	—
116	C₂²×#379	C₂³	1	1	yes	characteristic
117	#21746	C₂³	1	8	yes	—
118	#21746	C₂³	1	8	yes	—
119	C₂×#1898	D₄	1	8	yes	complemented
120	C₂×#1898	C₂³	1	8	yes	—
121	C₂×#1819	C₂³	1	2	yes	—
122	C₂×#1819	C₂³	1	2	yes	—
123	C₂×#1781	C₂³	1	2	yes	—
124	C₂×#1781	C₂³	1	8	yes	—
125	C₂×#1781	C₂³	1	4	yes	—
126	C₂×#1781	C₂³	1	4	yes	—
127	C₂×#1781	C₂³	1	2	yes	—
128	#14681	C₂³	1	2	yes	—
129	#14681	C₂³	1	4	yes	—
130	#14679	C₂³	1	2	yes	—
131	#14679	C₂³	1	4	yes	—
132	#14657	D₄	1	4	yes	complemented
133	#14255	D₄	1	4	yes	complemented
134	#13869	C₂³	1	2	yes	—
135	#13867	C₂³	1	2	yes	—
136	#13867	C₂³	1	2	yes	—
137	#13867	C₂³	1	2	yes	—
138	#10735	C₂³	1	8	yes	—
139	#8101	C₂³	1	8	yes	—
140	#8101	C₂³	1	8	yes	—
141	C₂⁷	C₂×D₄	1	1	yes	characteristic
142	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
143	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
144	C₂⁷	C₂⁴	1	1	yes	characteristic
145	C₂⁷	C₂⁴	1	1	yes	characteristic
146	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
147	C₂⁴×D₄	C₂×D₄	1	4	yes	—
148	C₂⁴×D₄	C₂×D₄	1	4	yes	—
149	C₂⁴×D₄	C₂×D₄	1	2	yes	—
150	C₂⁴×D₄	C₂×D₄	1	2	yes	—
151	C₂⁴×D₄	C₂×D₄	1	2	yes	—
152	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂×D₄	1	4	yes	—
154	C₂⁴×D₄	C₂×D₄	1	4	yes	—
155	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
161	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
163	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
164	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
165	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
166	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
167	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
168	C₂⁴×D₄	C₂⁴	1	2	yes	—
169	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
170	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
171	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
172	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
174	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
175	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
176	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
177	C₂×#543	C₂×D₄	1	2	yes	complemented
178	C₂×#534	C₂×D₄	1	4	yes	complemented
179	C₂×#534	C₂×D₄	1	2	yes	complemented
180	C₂²×#120	C₂×D₄	1	2	yes	—
181	C₂²×#120	C₂×D₄	1	4	yes	—
182	C₂²×#120	C₂×D₄	1	2	yes	—
183	C₂²×#120	C₂×D₄	1	4	yes	—
184	C₂²×#120	C₂×D₄	1	2	yes	—
185	C₂²×#120	C₂×D₄	1	2	yes	—
186	C₂²×#120	C₂×D₄	1	4	yes	—
187	C₂²×#120	C₂×D₄	1	4	yes	—
188	C₂²×#120	C₂×D₄	1	4	yes	—
189	C₂²×#120	C₂×D₄	1	4	yes	—
190	C₂²×#120	C₂×D₄	1	4	yes	complemented
191	C₂²×#120	C₂×D₄	1	8	yes	complemented
192	C₂²×#120	#41	1	4	yes	—
193	C₂²×#120	C₂⁴	1	4	yes	—
194	C₂×#518	C₂×D₄	1	4	yes	complemented
195	C₂×#518	C₂×D₄	1	2	yes	complemented
196	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
197	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
198	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
199	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
200	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
201	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
202	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
203	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
204	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
205	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
209	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
210	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
211	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
212	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
213	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
214	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
215	C₂²×#99	C₂×D₄	1	8	yes	complemented
216	#2405	C₂×D₄	1	8	yes	complemented
217	#2405	C₂×D₄	1	8	yes	complemented
218	#2403	C₂×D₄	1	8	yes	complemented
219	#2403	C₂×D₄	1	8	yes	complemented
220	#2312	C₂×D₄	1	4	yes	complemented
221	#2312	C₂×D₄	1	4	yes	complemented
222	#2309	C₂×D₄	1	4	yes	complemented
223	#2308	C₂×D₄	1	4	yes	complemented
224	C₂×#386	C₂×D₄	1	4	yes	complemented
225	C₂×#386	C₂×D₄	1	8	yes	complemented
226	C₂×#385	C₂×D₄	1	4	yes	complemented
227	C₂×#385	C₂×D₄	1	8	yes	complemented
228	C₂×#379	C₂×D₄	1	4	yes	—
229	C₂×#379	C₂×D₄	1	4	yes	—
230	C₂×#379	C₂×D₄	1	4	yes	—
231	C₂×#379	C₂×D₄	1	4	yes	—
232	C₂×#379	C₂×D₄	1	4	yes	—
233	C₂×#379	C₂×D₄	1	2	yes	complemented
234	C₂×#379	C₂×D₄	1	4	yes	complemented
235	C₂×#379	C₂×D₄	1	8	yes	complemented
236	C₂×#379	C₂×D₄	1	2	yes	complemented
237	C₂×#379	C₂×D₄	1	4	yes	complemented
238	C₂×#379	C₂×D₄	1	2	yes	complemented
239	C₂×#379	C₂×D₄	1	2	yes	complemented
240	C₂×#379	C₂⁴	1	4	yes	—
241	C₂×#379	C₂⁴	1	2	yes	—
242	C₂×#379	C₂⁴	1	2	yes	—
243	C₂×#379	C₂⁴	1	4	yes	—
244	C₂×#379	C₂⁴	1	4	yes	—
245	C₂×#342	C₂×D₄	1	8	yes	complemented
246	#1440	C₂×D₄	1	8	yes	complemented
247	#1438	C₂×D₄	1	8	yes	complemented
248	C₂⁶	#120	1	2	yes	—
249	C₂⁶	#120	1	2	yes	—
250	C₂⁶	#120	1	2	yes	complemented
251	C₂⁶	C₂²×D₄	1	2	yes	—
252	C₂⁶	C₂²×D₄	1	1	yes	characteristic
253	C₂⁶	C₂²×D₄	1	1	yes	characteristic
254	C₂⁶	C₂²×D₄	1	4	yes	—
255	C₂⁶	C₂²×D₄	1	1	yes	characteristic
256	C₂⁶	C₂²×D₄	1	1	yes	characteristic
257	C₂⁶	C₂²×D₄	1	1	yes	characteristic
258	C₂⁶	C₂²×D₄	1	1	yes	characteristic
259	C₂⁶	C₂²×D₄	1	1	yes	characteristic
260	C₂⁶	C₂²×D₄	1	2	yes	—
261	C₂⁶	C₂²×D₄	1	1	yes	characteristic
262	C₂⁶	C₂²×D₄	1	2	yes	—
263	C₂⁶	C₂²×D₄	1	2	yes	—
264	C₂⁶	C₂²×D₄	1	2	yes	—
265	C₂⁶	C₂²×D₄	1	1	yes	characteristic
266	C₂⁶	C₂²×D₄	1	1	yes	characteristic
267	C₂⁶	C₂²×D₄	1	2	yes	—
268	C₂⁶	C₂²×D₄	1	2	yes	—
269	C₂⁶	C₂²×D₄	1	2	yes	—
270	C₂⁶	C₂²×D₄	1	1	yes	characteristic
271	C₂⁶	C₂×#41	1	2	yes	—
272	C₂⁶	H(5,𝔽₂)	1	2	yes	—
273	C₂⁶	H(5,𝔽₂)	1	2	yes	—
274	C₂⁶	H(5,𝔽₂)	1	2	yes	—
275	C₂⁶	H(5,𝔽₂)	1	2	yes	—
276	C₂⁶	C₂⁵	1	1	yes	characteristic
277	C₂³×D₄	#120	1	4	yes	—
278	C₂³×D₄	#120	1	2	yes	—
279	C₂³×D₄	#120	1	2	yes	—
280	C₂³×D₄	#120	1	4	yes	—
281	C₂³×D₄	#120	1	4	yes	—
282	C₂³×D₄	#120	1	4	yes	—
283	C₂³×D₄	#120	1	2	yes	—
284	C₂³×D₄	#120	1	2	yes	—
285	C₂³×D₄	#120	1	2	yes	—
286	C₂³×D₄	#120	1	4	yes	—
287	C₂³×D₄	#120	1	2	yes	—
288	C₂³×D₄	#120	1	4	yes	—
289	C₂³×D₄	#120	1	2	yes	—
290	C₂³×D₄	#120	1	2	yes	—
291	C₂³×D₄	#120	1	4	yes	complemented
292	C₂³×D₄	#120	1	4	yes	complemented
293	C₂³×D₄	#120	1	4	yes	complemented
294	C₂³×D₄	#121	1	4	yes	—
295	C₂³×D₄	#121	1	4	yes	—
296	C₂³×D₄	C₂²×D₄	1	4	yes	—
297	C₂³×D₄	C₂²×D₄	1	4	yes	—
298	C₂³×D₄	C₂²×D₄	1	4	yes	—
299	C₂³×D₄	C₂²×D₄	1	4	yes	—
300	C₂³×D₄	C₂²×D₄	1	4	yes	—
301	C₂³×D₄	C₂²×D₄	1	2	yes	—
302	C₂³×D₄	C₂²×D₄	1	2	yes	—
303	C₂³×D₄	C₂²×D₄	1	2	yes	—
304	C₂³×D₄	C₂²×D₄	1	2	yes	—
305	C₂³×D₄	C₂²×D₄	1	2	yes	—
306	C₂³×D₄	C₂×#41	1	2	yes	—
307	C₂⁴×C₄	#120	1	2	yes	—
308	C₂⁴×C₄	#120	1	2	yes	—
309	C₂⁴×C₄	#120	1	2	yes	complemented
310	C₂⁴×C₄	#120	1	2	yes	complemented
311	C₂⁴×C₄	#120	1	2	yes	complemented
312	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
313	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
316	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂×#120	#120	1	8	yes	—
322	C₂×#120	#120	1	8	yes	—
323	C₂×#120	#121	1	8	yes	—
324	C₂×#120	#121	1	8	yes	—
325	C₂×#120	#121	1	8	yes	—
326	C₂×#120	#121	1	8	yes	—
327	C₂×#120	#127	1	8	yes	—
328	C₂×#120	#127	1	8	yes	—
329	C₂²×C₂²⋊C₄	#120	1	4	yes	—
330	C₂²×C₂²⋊C₄	#120	1	4	yes	—
331	C₂²×C₂²⋊C₄	#120	1	2	yes	—
332	C₂²×C₂²⋊C₄	#120	1	2	yes	—
333	C₂²×C₂²⋊C₄	#120	1	2	yes	—
334	C₂²×C₂²⋊C₄	#120	1	2	yes	—
335	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
336	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
337	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
338	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
339	C₂²×C₂²⋊C₄	#120	1	8	yes	complemented
340	C₂²×C₂²⋊C₄	#121	1	4	yes	—
341	C₂²×C₂²⋊C₄	#121	1	4	yes	—
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
343	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
355	C₂²×C₂²⋊C₄	C₂×#41	1	2	yes	—
356	#379	#120	1	8	yes	complemented
357	#379	#120	1	8	yes	complemented
358	#379	C₂²×D₄	1	8	yes	—
359	#379	C₂²×D₄	1	8	yes	—
360	C₂⁵	C₂×#120	1	2	yes	—
361	C₂⁵	C₂×#120	1	2	yes	—
362	C₂⁵	C₂×#120	1	1	yes	characteristic
363	C₂⁵	C₂×#120	1	1	yes	characteristic
364	C₂⁵	C₂×#120	1	2	yes	—
365	C₂⁵	C₂×#120	1	2	yes	—
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	C₂×#120	1	1	yes	characteristic
368	C₂⁵	C₂×#120	1	2	yes	—
369	C₂⁵	C₂×#120	1	2	yes	—
370	C₂⁵	C₂×#120	1	4	yes	—
371	C₂⁵	C₂×#120	1	2	yes	—
372	C₂⁵	C₂×#120	1	2	yes	—
373	C₂⁵	C₂×#120	1	2	yes	—
374	C₂⁵	C₂×#120	1	2	yes	—
375	C₂⁵	C₂×#120	1	2	yes	—
376	C₂⁵	C₂×#120	1	2	yes	—
377	C₂⁵	C₂×#120	1	1	yes	characteristic
378	C₂⁵	C₂×#120	1	1	yes	characteristic
379	C₂⁵	C₂×#120	1	1	yes	characteristic
380	C₂⁵	C₂×#120	1	2	yes	—
381	C₂⁵	C₂×#120	1	2	yes	—
382	C₂⁵	C₂×#120	1	2	yes	—
383	C₂⁵	C₂×#120	1	2	yes	—
384	C₂⁵	C₂×#120	1	1	yes	characteristic
385	C₂⁵	C₂×#120	1	2	yes	—
386	C₂⁵	C₂×#120	1	2	yes	—
387	C₂⁵	C₂×#120	1	2	yes	—
388	C₂⁵	C₂×#120	1	2	yes	—
389	C₂⁵	C₂×#121	1	2	yes	—
390	C₂⁵	C₂×#121	1	2	yes	—
391	C₂⁵	C₂×#121	1	2	yes	—
392	C₂⁵	C₂×#121	1	2	yes	—
393	C₂⁵	C₂×#121	1	2	yes	—
394	C₂⁵	C₂×#121	1	2	yes	—
395	C₂⁵	C₂×#121	1	2	yes	—
396	C₂⁵	C₂×#127	1	2	yes	—
397	C₂⁵	C₂×#127	1	2	yes	—
398	C₂⁵	#534	1	1	yes	characteristic
399	C₂⁵	#534	1	2	yes	—
400	C₂⁵	#534	1	2	yes	—
401	C₂⁵	#534	1	1	yes	characteristic
402	C₂⁵	#534	1	2	yes	—
403	C₂⁵	#534	1	2	yes	—
404	C₂⁵	#534	1	2	yes	—
405	C₂⁵	#534	1	2	yes	—
406	C₂⁵	#534	1	1	yes	characteristic
407	C₂⁵	#534	1	1	yes	characteristic
408	C₂⁵	#535	1	2	yes	—
409	C₂⁵	#535	1	2	yes	—
410	C₂⁵	#535	1	2	yes	—
411	C₂⁵	#535	1	2	yes	—
412	C₂⁵	D₄²	1	2	yes	—
413	C₂⁵	D₄²	1	2	yes	—
414	C₂⁵	D₄²	1	2	yes	—
415	C₂⁵	D₄²	1	2	yes	—
416	C₂⁵	D₄²	1	2	yes	—
417	C₂⁵	D₄²	1	2	yes	—
418	C₂⁵	D₄²	1	2	yes	—
419	C₂⁵	D₄²	1	2	yes	—
420	C₂⁵	D₄²	1	2	yes	—
421	C₂⁵	D₄²	1	2	yes	—
422	C₂⁵	D₄²	1	2	yes	—
423	C₂⁵	D₄²	1	2	yes	—
424	C₂⁵	D₄²	1	2	yes	—
425	C₂⁵	D₄²	1	2	yes	—
426	C₂⁵	D₄²	1	2	yes	—
427	C₂⁵	D₄²	1	2	yes	—
428	C₂⁵	D₄²	1	2	yes	—
429	C₂⁵	D₄²	1	2	yes	—
430	C₂⁵	D₄²	1	2	yes	—
431	C₂⁵	D₄²	1	2	yes	—
432	C₂⁵	D₄²	1	2	yes	—
433	C₂⁵	D₄²	1	2	yes	—
434	C₂⁵	D₄²	1	2	yes	—
435	C₂⁵	D₄²	1	2	yes	—
436	C₂⁵	#546	1	2	yes	—
437	C₂⁵	#546	1	2	yes	—
438	C₂⁵	#546	1	2	yes	—
439	C₂⁵	#546	1	2	yes	—
440	C₂⁵	#546	1	2	yes	—
441	C₂⁵	#546	1	2	yes	—
442	C₂⁵	#546	1	2	yes	—
443	C₂⁵	#546	1	2	yes	—
444	C₂⁵	C₂³×D₄	1	1	yes	characteristic
445	C₂⁵	C₂³×D₄	1	1	yes	characteristic
446	C₂⁵	C₂³×D₄	1	1	yes	characteristic
447	C₂⁵	C₂³×D₄	1	2	yes	—
448	C₂⁵	C₂³×D₄	1	1	yes	characteristic
449	C₂⁵	C₂³×D₄	1	2	yes	—
450	C₂⁵	C₂³×D₄	1	1	yes	characteristic
451	C₂⁵	C₂³×D₄	1	1	yes	characteristic
452	C₂⁵	C₂²×#41	1	1	yes	characteristic
453	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
454	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
455	C₂²×D₄	#392	1	8	yes	—
456	C₂²×D₄	#392	1	8	yes	—
457	C₂²×D₄	#392	1	8	yes	—
458	C₂²×D₄	#392	1	8	yes	—
459	C₂²×D₄	C₂×#120	1	4	yes	—
460	C₂²×D₄	C₂×#121	1	4	yes	—
461	C₂²×D₄	C₂×#121	1	4	yes	—
462	C₂²×D₄	C₂×#127	1	4	yes	—
463	C₂³×C₄	C₂×#120	1	4	yes	—
464	C₂³×C₄	C₂×#120	1	4	yes	—
465	C₂³×C₄	C₂×#120	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	4	yes	—
470	C₂³×C₄	C₂×#120	1	2	yes	—
471	C₂³×C₄	C₂×#120	1	2	yes	—
472	C₂³×C₄	C₂×#120	1	2	yes	—
473	C₂³×C₄	C₂×#120	1	2	yes	—
474	C₂³×C₄	C₂×#120	1	2	yes	—
475	C₂³×C₄	C₂×#120	1	2	yes	—
476	C₂³×C₄	C₂×#121	1	2	yes	—
477	C₂³×C₄	C₂×#121	1	2	yes	—
478	C₂³×C₄	C₂×#121	1	2	yes	—
479	C₂×C₂²⋊C₄	#392	1	8	yes	—
480	C₂×C₂²⋊C₄	#392	1	8	yes	—
481	C₂×C₂²⋊C₄	#392	1	8	yes	—
482	C₂×C₂²⋊C₄	#392	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	—
484	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
485	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂×#121	1	4	yes	—
487	C₂×C₂²⋊C₄	C₂×#127	1	4	yes	—
488	C₂⁴	C₂×#392	1	2	yes	—
489	C₂⁴	C₂×#392	1	4	yes	—
490	C₂⁴	C₂×#392	1	2	yes	—
491	C₂⁴	C₂×#392	1	2	yes	—
492	C₂⁴	C₂×#392	1	2	yes	—
493	C₂⁴	#2403	1	2	yes	—
494	C₂⁴	#2403	1	2	yes	—
495	C₂⁴	#2403	1	2	yes	—
496	C₂⁴	#2403	1	1	yes	characteristic
497	C₂⁴	#2403	1	1	yes	characteristic
498	C₂⁴	#2403	1	1	yes	characteristic
499	C₂⁴	#2403	1	2	yes	—
500	C₂⁴	#2403	1	2	yes	—
501	C₂⁴	#2403	1	2	yes	—
502	C₂⁴	#2403	1	2	yes	—
503	C₂⁴	#2403	1	2	yes	—
504	C₂⁴	#2403	1	2	yes	—
505	C₂⁴	#2403	1	2	yes	—
506	C₂⁴	#2403	1	1	yes	characteristic
507	C₂⁴	#2403	1	1	yes	characteristic
508	C₂⁴	#2403	1	1	yes	characteristic
509	C₂⁴	#2403	1	2	yes	—
510	C₂⁴	#2403	1	1	yes	characteristic
511	C₂⁴	#2403	1	2	yes	—
512	C₂⁴	#2403	1	1	yes	characteristic
513	C₂⁴	#2408	1	2	yes	—
514	C₂⁴	#2408	1	2	yes	—
515	C₂⁴	#2408	1	2	yes	—
516	C₂⁴	#2408	1	2	yes	—
517	C₂⁴	#2408	1	2	yes	—
518	C₂⁴	#2408	1	2	yes	—
519	C₂⁴	#2408	1	2	yes	—
520	C₂⁴	#2408	1	2	yes	—
521	C₂⁴	#2410	1	2	yes	—
522	C₂⁴	#2410	1	2	yes	—
523	C₂⁴	#2410	1	2	yes	—
524	C₂⁴	#2410	1	2	yes	—
525	C₂⁴	#2410	1	2	yes	—
526	C₂⁴	#2410	1	2	yes	—
527	C₂⁴	#2410	1	2	yes	—
528	C₂⁴	#2410	1	2	yes	—
529	C₂⁴	#2410	1	2	yes	—
530	C₂⁴	#2410	1	2	yes	—
531	C₂⁴	#2410	1	2	yes	—
532	C₂⁴	#2410	1	2	yes	—
533	C₂⁴	#2410	1	2	yes	—
534	C₂⁴	#2410	1	2	yes	—
535	C₂⁴	#2410	1	2	yes	—
536	C₂⁴	#2410	1	2	yes	—
537	C₂⁴	#2433	1	2	yes	—
538	C₂⁴	#2433	1	2	yes	—
539	C₂⁴	#2433	1	2	yes	—
540	C₂⁴	#2433	1	2	yes	—
541	C₂⁴	#2433	1	2	yes	—
542	C₂⁴	#2433	1	2	yes	—
543	C₂⁴	#2433	1	2	yes	—
544	C₂⁴	#2433	1	2	yes	—
545	C₂⁴	#2613	1	2	yes	—
546	C₂⁴	#2613	1	2	yes	—
547	C₂⁴	#2613	1	2	yes	—
548	C₂⁴	#2613	1	2	yes	—
549	C₂⁴	#2846	1	2	yes	—
550	C₂⁴	#2846	1	2	yes	—
551	C₂⁴	#2846	1	2	yes	—
552	C₂⁴	#2846	1	2	yes	—
553	C₂⁴	C₂²×#120	1	1	yes	characteristic
554	C₂⁴	C₂²×#120	1	1	yes	characteristic
555	C₂⁴	C₂²×#120	1	2	yes	—
556	C₂⁴	C₂²×#120	1	1	yes	characteristic
557	C₂⁴	C₂²×#120	1	2	yes	—
558	C₂⁴	C₂²×#120	1	1	yes	characteristic
559	C₂⁴	C₂²×#120	1	1	yes	characteristic
560	C₂⁴	C₂²×#121	1	1	yes	characteristic
561	C₂⁴	C₂²×#121	1	1	yes	characteristic
562	C₂⁴	C₂²×#121	1	1	yes	characteristic
563	C₂⁴	C₂²×#127	1	1	yes	characteristic
564	C₂⁴	C₂×#534	1	1	yes	characteristic
565	C₂⁴	C₂×#534	1	2	yes	—
566	C₂⁴	C₂×#534	1	1	yes	characteristic
567	C₂⁴	C₂×#535	1	2	yes	—
568	C₂⁴	C₂×D₄²	1	2	yes	—
569	C₂⁴	C₂×D₄²	1	2	yes	—
570	C₂⁴	C₂×D₄²	1	2	yes	—
571	C₂⁴	C₂×D₄²	1	2	yes	—
572	C₂⁴	C₂×D₄²	1	2	yes	—
573	C₂⁴	C₂×D₄²	1	2	yes	—
574	C₂⁴	C₂×#546	1	2	yes	—
575	C₂⁴	C₂×#546	1	2	yes	—
576	C₂²×C₄	C₂×#392	1	4	yes	—
577	C₂²×C₄	C₂×#392	1	4	yes	—
578	C₂²×C₄	C₂×#392	1	4	yes	—
579	C₂³	#14715	1	2	yes	—
580	C₂³	#14715	1	2	yes	—
581	C₂³	#14715	1	2	yes	—
582	C₂³	#14715	1	2	yes	—
583	C₂³	#14715	1	2	yes	—
584	C₂³	#14715	1	2	yes	—
585	C₂³	#14715	1	2	yes	—
586	C₂³	#14715	1	2	yes	—
587	C₂³	#23895	1	4	yes	—
588	C₂³	C₂²×#392	1	1	yes	characteristic
589	C₂³	C₂×#2613	1	1	yes	characteristic
590	C₂³	C₂×#2403	1	2	yes	—
591	C₂³	C₂×#2403	1	1	yes	characteristic
592	C₂³	C₂×#2403	1	1	yes	characteristic
593	C₂³	C₂×#2410	1	2	yes	—
594	C₂³	C₂×#2410	1	1	yes	characteristic
595	C₂³	C₂×#2410	1	1	yes	characteristic
596	C₂³	C₂×#2408	1	2	yes	—
597	C₂³	C₂×#2433	1	2	yes	—
598	C₂³	C₂×#2846	1	1	yes	characteristic
599	C₂³	#60399	1	4	yes	—
600	C₂³	#60399	1	4	yes	—
601	C₂²	#394064	1	4	yes	—
602	C₂²	C₂×#14715	1	1	yes	characteristic
603	C₂²	#6431795	1	2	yes	—
604	C₂²	C₂×#23895	1	2	yes	—
605	C₂²	#6437632	1	4	yes	—
606	C₂²	#6437632	1	2	yes	—
607	C₂²	#6437999	1	2	yes	—
608	C₂²	#6628896	1	2	yes	—
609	C₂	C₂×#394064	1	1	yes	characteristic
610	C₂	#72236375	1	1	yes	characteristic
611	C₂	#72238078	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#14715
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72238082	C₂	semidirect
2. #72238079	C₂	semidirect
3. #72238049	C₂	semidirect
4. #72238046	C₂	semidirect
5. #72238022	C₂	semidirect
6. #72236483	C₂	semidirect
7. #72236467	C₂	semidirect
8. C₂×#233541	C₂	semidirect
9. #72234675	C₂	semidirect
10. #72234629	C₂	semidirect
11. #72231815	C₂	semidirect
12. #72225801	C₂	semidirect
13. #72225665	C₂	semidirect
14. #72219307	C₂	semidirect
15. #72210600	C₂	semidirect
18. #7642273	C₂²	semidirect
19. #7642257	C₂²	semidirect
20. #7630945	C₂²	semidirect
21. #7630939	C₂²	semidirect
25. C₂×#34980	C₂²	semidirect
26. C₂²×#2403	C₂²	semidirect
27. C₂²×#2403	C₂²	semidirect
29. #6477580	C₂²	semidirect
30. #6470225	C₂²	semidirect
33. C₂×#21746	C₂²	semidirect
34. C₂×#21746	C₂²	semidirect
35. C₂×#21746	C₂²	semidirect
36. C₂²×#1781	C₂²	semidirect
37. C₂²×#1781	C₂²	semidirect
38. #636791	C₂²	semidirect
39. #635984	C₂²	semidirect
40. #613191	C₂²	semidirect
41. #612424	C₂²	semidirect
43. #517411	C₂²	semidirect
44. #517411	C₂²	semidirect
45. #517411	C₂²	semidirect
46. #405090	C₂²	semidirect
47. #394058	C₂²	semidirect
48. #392245	C₂²	semidirect
49. #392109	C₂²	semidirect
50. #382422	C₂²	semidirect
51. #382390	C₂²	semidirect
52. #355913	C₂²	semidirect
53. #233541	C₂²	semidirect
54. #233541	C₂²	semidirect
55. #201665	C₂²	semidirect
56. #201664	C₂²	semidirect
57. #187929	C₂²	semidirect
58. #187928	C₂²	semidirect
59. C₂×#8101	C₂²	semidirect
60. C₂×#8101	C₂²	semidirect
61. #115691	C₂²	semidirect
62. #115690	C₂²	semidirect
63. #115204	C₂²	semidirect
64. #115204	C₂²	semidirect
65. #106767	C₂²	semidirect
66. #106766	C₂²	semidirect
67. C₂⁵×D₄	D₄	semidirect
72. C₂×#3490	D₄	semidirect
74. C₂×#3484	D₄	semidirect
76. C₂³×#127	D₄	semidirect
77. C₂³×#121	D₄	semidirect
78. C₂³×#121	D₄	semidirect
79. C₂³×#121	D₄	semidirect
81. C₂³×#120	D₄	semidirect
82. C₂³×#120	D₄	semidirect
87. C₂³×C₄×D₄	D₄	semidirect
89. C₂×#2849	D₄	semidirect
91. C₂×#2846	D₄	semidirect
93. #34980	D₄	semidirect
97. C₂×#2405	D₄	semidirect
98. C₂×#2405	D₄	semidirect
100. C₂×#2410	D₄	semidirect
101. C₂×#2410	D₄	semidirect
102. C₂×#2403	D₄	semidirect
103. C₂×#2403	D₄	semidirect
107. #34356	D₄	semidirect
119. C₂×#1898	D₄	semidirect
132. #14657	D₄	semidirect
133. #14255	D₄	semidirect
142. C₂⁷	C₂×D₄	semidirect
143. C₂⁷	C₂×D₄	semidirect
146. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
162. C₂⁴×D₄	C₂×D₄	semidirect
163. C₂⁴×D₄	C₂×D₄	semidirect
164. C₂⁴×D₄	C₂×D₄	semidirect
165. C₂⁴×D₄	C₂×D₄	semidirect
166. C₂⁴×D₄	C₂×D₄	semidirect
167. C₂⁴×D₄	C₂×D₄	semidirect
173. C₂⁵×C₄	C₂×D₄	semidirect
174. C₂⁵×C₄	C₂×D₄	semidirect
175. C₂⁵×C₄	C₂×D₄	semidirect
177. C₂×#543	C₂×D₄	semidirect
178. C₂×#534	C₂×D₄	semidirect
179. C₂×#534	C₂×D₄	semidirect
190. C₂²×#120	C₂×D₄	semidirect
191. C₂²×#120	C₂×D₄	semidirect
194. C₂×#518	C₂×D₄	semidirect
195. C₂×#518	C₂×D₄	semidirect
196. C₂³×C₄⋊C₄	C₂×D₄	semidirect
197. C₂³×C₄⋊C₄	C₂×D₄	semidirect
204. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
205. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
206. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
207. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
208. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
209. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
210. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
211. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
214. C₂³×C₄²	C₂×D₄	semidirect
215. C₂²×#99	C₂×D₄	semidirect
216. #2405	C₂×D₄	semidirect
217. #2405	C₂×D₄	semidirect
218. #2403	C₂×D₄	semidirect
219. #2403	C₂×D₄	semidirect
220. #2312	C₂×D₄	semidirect
221. #2312	C₂×D₄	semidirect
222. #2309	C₂×D₄	semidirect
223. #2308	C₂×D₄	semidirect
224. C₂×#386	C₂×D₄	semidirect
225. C₂×#386	C₂×D₄	semidirect
226. C₂×#385	C₂×D₄	semidirect
227. C₂×#385	C₂×D₄	semidirect
233. C₂×#379	C₂×D₄	semidirect
234. C₂×#379	C₂×D₄	semidirect
235. C₂×#379	C₂×D₄	semidirect
236. C₂×#379	C₂×D₄	semidirect
237. C₂×#379	C₂×D₄	semidirect
238. C₂×#379	C₂×D₄	semidirect
239. C₂×#379	C₂×D₄	semidirect
245. C₂×#342	C₂×D₄	semidirect
246. #1440	C₂×D₄	semidirect
247. #1438	C₂×D₄	semidirect
250. C₂⁶	#120	semidirect
291. C₂³×D₄	#120	semidirect
292. C₂³×D₄	#120	semidirect
293. C₂³×D₄	#120	semidirect
309. C₂⁴×C₄	#120	semidirect
310. C₂⁴×C₄	#120	semidirect
311. C₂⁴×C₄	#120	semidirect
335. C₂²×C₂²⋊C₄	#120	semidirect
336. C₂²×C₂²⋊C₄	#120	semidirect
337. C₂²×C₂²⋊C₄	#120	semidirect
338. C₂²×C₂²⋊C₄	#120	semidirect
339. C₂²×C₂²⋊C₄	#120	semidirect
356. #379	#120	semidirect
357. #379	#120	semidirect

Maximal subgroups

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

subgroup	index
#72238082	2
#72238079	2
#72238049	2
#72238046	2
#72238022	2
#72236483	2
#72236467	2
C₂×#233541	2
#72234675	2
#72234629	2
#72231815	2
#72225801	2
#72225665	2
#72219307	2
#72210600	2