Subgroups — #72260431

Order 2048.

At least 9357 conjugacy classes of subgroups; only the 1544 normal subgroups are shown.

The subgroup lattice has 508 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#115163	C₂	1	2	yes	maximal, complemented
2	#72238531	C₂	1	2	yes	maximal, complemented
3	C₂×#392109	C₂	1	2	yes	maximal, complemented
4	C₂×#106654	C₂	1	2	yes	maximal, complemented
5	C₂²×D₄×#120	C₂	1	1	yes	maximal, characteristic
6	C₂×#188035	C₂	1	1	yes	maximal, characteristic, complemented
7	#72219307	C₂	1	1	yes	maximal, characteristic, complemented
8	#72218451	C₂	1	2	yes	maximal, complemented
9	C₂×#115690	C₂	1	2	yes	maximal, complemented
10	C₂⁶×D₄	C₂²	1	1	yes	characteristic
11	C₂³×D₄²	C₂²	1	1	yes	characteristic
12	C₂⁴×#120	C₄	1	1	yes	characteristic, complemented
13	C₂⁴×#120	C₂²	1	1	yes	characteristic
14	C₂²×#2847	C₄	1	1	yes	characteristic, complemented
15	C₂²×#2846	C₄	1	1	yes	characteristic, complemented
16	C₂²×#2846	C₂²	1	1	yes	characteristic
17	C₂²×#2433	C₄	1	1	yes	characteristic, complemented
18	C₂²×#2408	C₄	1	1	yes	characteristic, complemented
19	C₂²×#2410	C₄	1	1	yes	characteristic, complemented
20	C₂²×#2410	C₂²	1	1	yes	characteristic
21	C₂²×#2403	C₄	1	1	yes	characteristic, complemented
22	C₂²×#2403	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₄×#120	C₄	1	1	yes	characteristic, complemented
25	C₂×#21746	C₂²	1	2	yes	complemented
26	C₂×#21746	C₂²	1	2	yes	complemented
27	C₂²×#1781	C₂²	1	2	yes	—
28	C₂²×#1781	C₂²	1	2	yes	—
29	C₂²×#1781	C₂²	1	4	yes	complemented
30	C₂²×#1781	C₂²	1	2	yes	complemented
31	C₂×#14679	C₂²	1	4	yes	complemented
32	#517411	C₂²	1	2	yes	complemented
33	C₂×#10735	C₂²	1	4	yes	complemented
34	C₂×#8101	C₂²	1	4	yes	complemented
35	C₂⁸	C₂×C₄	1	1	yes	characteristic
36	C₂⁸	C₂³	1	1	yes	characteristic
37	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
38	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
39	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic
40	C₂⁵×D₄	D₄	1	1	yes	characteristic
41	C₂⁵×D₄	D₄	1	8	yes	—
42	C₂⁵×D₄	C₂³	1	1	yes	characteristic
43	C₂⁵×D₄	C₂³	1	1	yes	characteristic
44	C₂⁵×D₄	C₂³	1	1	yes	characteristic
45	C₂⁶×C₄	C₂×C₄	1	1	yes	characteristic
46	C₂³×#127	D₄	1	1	yes	characteristic
47	C₂³×#121	C₂×C₄	1	1	yes	characteristic
48	C₂³×#121	D₄	1	1	yes	characteristic
49	C₂³×#121	D₄	1	1	yes	characteristic
50	C₂³×#121	D₄	1	1	yes	characteristic
51	C₂³×#120	C₂×C₄	1	1	yes	characteristic
52	C₂³×#120	C₂×C₄	1	1	yes	characteristic
53	C₂³×#120	C₂×C₄	1	1	yes	characteristic
54	C₂³×#120	C₂×C₄	1	1	yes	characteristic
55	C₂³×#120	C₂×C₄	1	1	yes	characteristic
56	C₂³×#120	C₂×C₄	1	1	yes	characteristic
57	C₂³×#120	C₂×C₄	1	1	yes	characteristic
58	C₂³×#120	C₂×C₄	1	1	yes	characteristic
59	C₂³×#120	C₂×C₄	1	1	yes	characteristic
60	C₂³×#120	C₂×C₄	1	1	yes	characteristic
61	C₂³×#120	D₄	1	8	yes	—
62	C₂³×#120	D₄	1	1	yes	characteristic
63	C₂³×#120	D₄	1	1	yes	characteristic
64	C₂³×#120	C₂³	1	1	yes	characteristic
65	C₂³×C₄×D₄	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×D₄	D₄	1	1	yes	characteristic
67	C₂⁴×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
69	C₂³×#99	D₄	1	8	yes	complemented
70	C₂×#2846	D₄	1	8	yes	—
71	C₂×#2410	D₄	1	8	yes	—
72	C₂×#2403	D₄	1	8	yes	—
73	C₂×D₄×C₂²⋊C₄	D₄	1	8	yes	—
74	C₂²×#386	C₂×C₄	1	1	yes	characteristic
75	C₂²×#386	C₂×C₄	1	1	yes	characteristic
76	C₂²×#386	C₂×C₄	1	1	yes	characteristic
77	C₂²×#385	C₂×C₄	1	1	yes	characteristic
78	C₂²×#380	C₂×C₄	1	1	yes	characteristic
79	C₂²×#379	C₂×C₄	1	1	yes	characteristic
80	C₂²×#379	C₂×C₄	1	1	yes	characteristic
81	C₂²×#379	C₂×C₄	1	1	yes	characteristic
82	C₂²×#379	C₂×C₄	1	1	yes	characteristic
83	C₂²×#379	C₂³	1	4	yes	—
84	C₂²×#379	C₂³	1	1	yes	characteristic
85	C₂²×#379	C₂³	1	4	yes	—
86	C₂²×C₄×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×#1781	D₄	1	8	yes	complemented
88	C₂⁷	C₂²⋊C₄	1	4	yes	complemented
89	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic, complemented
90	C₂⁷	C₂²×C₄	1	1	yes	characteristic
91	C₂⁷	C₂²×C₄	1	1	yes	characteristic
92	C₂⁷	C₂²×C₄	1	1	yes	characteristic
93	C₂⁷	C₂²×C₄	1	1	yes	characteristic
94	C₂⁷	C₂×D₄	1	4	yes	—
95	C₂⁷	C₂×D₄	1	4	yes	—
96	C₂⁷	C₂×D₄	1	4	yes	—
97	C₂⁷	C₂×D₄	1	1	yes	characteristic
98	C₂⁷	C₂⁴	1	1	yes	characteristic
99	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
100	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	complemented
101	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
102	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
103	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
105	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
106	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	4	yes	—
111	C₂⁴×D₄	C₂×D₄	1	4	yes	—
112	C₂⁴×D₄	C₂×D₄	1	4	yes	—
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
116	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
117	C₂⁴×D₄	C₂×D₄	1	4	yes	—
118	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
120	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×D₄	C₂×D₄	1	4	yes	—
122	C₂⁴×D₄	C₂×D₄	1	4	yes	—
123	C₂⁴×D₄	C₂×D₄	1	4	yes	—
124	C₂⁴×D₄	C₂×D₄	1	4	yes	—
125	C₂⁴×D₄	C₂×D₄	1	4	yes	—
126	C₂⁴×D₄	#41	1	4	yes	—
127	C₂⁴×D₄	#41	1	4	yes	—
128	C₂⁵×C₄	C₂²⋊C₄	1	4	yes	complemented
129	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
130	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
131	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
132	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
133	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
134	C₂²×#120	C₂²⋊C₄	1	4	yes	—
135	C₂²×#120	C₂²⋊C₄	1	4	yes	—
136	C₂²×#120	C₂²⋊C₄	1	4	yes	—
137	C₂²×#120	C₂²⋊C₄	1	4	yes	—
138	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
139	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
140	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
141	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
142	C₂²×#120	C₂²⋊C₄	1	4	yes	complemented
143	C₂²×#120	C₂×D₄	1	4	yes	—
144	C₂²×#120	C₂×D₄	1	4	yes	—
145	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
146	C₂³×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
147	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
148	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
149	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
150	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
151	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
152	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
153	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
154	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
155	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
156	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
157	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
159	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
160	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
161	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
162	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
163	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	complemented
164	C₂³×C₄²	C₂²⋊C₄	1	1	yes	characteristic, complemented
165	C₂×#386	C₂²⋊C₄	1	4	yes	complemented
166	C₂×#386	C₂²⋊C₄	1	4	yes	complemented
167	C₂×#386	C₂²⋊C₄	1	4	yes	complemented
168	C₂×#385	C₂²⋊C₄	1	4	yes	complemented
169	C₂×#380	C₂²⋊C₄	1	4	yes	complemented
170	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
171	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
172	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
173	C₂×#379	C₂²⋊C₄	1	4	yes	complemented
174	C₂×#379	C₂×D₄	1	4	yes	—
175	C₂×#379	C₂×D₄	1	4	yes	—
176	C₂×#379	C₂×D₄	1	4	yes	—
177	C₂×#379	C₂×D₄	1	8	yes	complemented
178	C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	complemented
179	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂⁶	C₄×D₄	1	4	yes	—
196	C₂⁶	C₄×D₄	1	4	yes	—
197	C₂⁶	#120	1	4	yes	—
198	C₂⁶	#120	1	16	yes	—
199	C₂⁶	C₂³×C₄	1	1	yes	characteristic
200	C₂⁶	C₂²×D₄	1	1	yes	characteristic
201	C₂⁶	C₂²×D₄	1	2	yes	—
202	C₂⁶	C₂²×D₄	1	2	yes	—
203	C₂⁶	C₂²×D₄	1	1	yes	characteristic
204	C₂⁶	C₂²×D₄	1	2	yes	—
205	C₂⁶	C₂²×D₄	1	2	yes	—
206	C₂⁶	C₂²×D₄	1	2	yes	—
207	C₂⁶	C₂²×D₄	1	2	yes	—
208	C₂⁶	C₂²×D₄	1	2	yes	—
209	C₂⁶	C₂²×D₄	1	2	yes	—
210	C₂⁶	C₂×#41	1	2	yes	—
211	C₂⁶	C₂×#41	1	2	yes	—
212	C₂⁶	H(5,𝔽₂)	1	4	yes	—
213	C₂⁶	H(5,𝔽₂)	1	4	yes	—
214	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
217	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
218	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
219	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂³×D₄	#120	1	4	yes	—
221	C₂³×D₄	#120	1	4	yes	—
222	C₂³×D₄	#120	1	4	yes	—
223	C₂³×D₄	#120	1	16	yes	—
224	C₂³×D₄	#120	1	4	yes	—
225	C₂³×D₄	#120	1	4	yes	—
226	C₂³×D₄	#120	1	4	yes	—
227	C₂³×D₄	#120	1	4	yes	—
228	C₂³×D₄	#120	1	4	yes	—
229	C₂³×D₄	#120	1	2	yes	—
230	C₂³×D₄	#120	1	8	yes	—
231	C₂³×D₄	#120	1	2	yes	—
232	C₂³×D₄	#120	1	2	yes	—
233	C₂³×D₄	#120	1	2	yes	—
234	C₂³×D₄	#121	1	4	yes	—
235	C₂³×D₄	#121	1	8	yes	—
236	C₂³×D₄	#121	1	4	yes	—
237	C₂³×D₄	#121	1	4	yes	—
238	C₂³×D₄	#121	1	8	yes	—
239	C₂³×D₄	#121	1	4	yes	—
240	C₂³×D₄	#121	1	8	yes	—
241	C₂³×D₄	#121	1	8	yes	—
242	C₂³×D₄	#123	1	2	yes	—
243	C₂³×D₄	#123	1	8	yes	—
244	C₂³×D₄	#123	1	2	yes	—
245	C₂³×D₄	#123	1	2	yes	—
246	C₂³×D₄	#123	1	2	yes	—
247	C₂³×D₄	#124	1	8	yes	—
248	C₂³×D₄	#127	1	8	yes	—
249	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
253	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
260	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂⁴×C₄	C₄×D₄	1	4	yes	—
262	C₂⁴×C₄	C₄×D₄	1	4	yes	—
263	C₂⁴×C₄	#120	1	4	yes	—
264	C₂×#120	#99	1	16	yes	complemented
265	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
274	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
276	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
279	C₂²×C₂²⋊C₄	#120	1	4	yes	—
280	C₂²×C₂²⋊C₄	#120	1	4	yes	—
281	C₂²×C₂²⋊C₄	#120	1	16	yes	—
282	#379	#120	1	16	yes	—
283	C₂⁵	#379	1	2	yes	—
284	C₂⁵	#379	1	4	yes	—
285	C₂⁵	#379	1	2	yes	—
286	C₂⁵	#379	1	2	yes	—
287	C₂⁵	#379	1	4	yes	—
288	C₂⁵	#379	1	2	yes	—
289	C₂⁵	#379	1	4	yes	—
290	C₂⁵	#379	1	2	yes	—
291	C₂⁵	#386	1	2	yes	—
292	C₂⁵	#386	1	2	yes	—
293	C₂⁵	#386	1	2	yes	—
294	C₂⁵	#386	1	8	yes	—
295	C₂⁵	#386	1	2	yes	—
296	C₂⁵	#390	1	8	yes	—
297	C₂⁵	C₂×#99	1	8	yes	—
298	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
300	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
301	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
302	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
304	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₂⁵	C₂×C₄×D₄	1	2	yes	—
306	C₂⁵	C₂×C₄×D₄	1	2	yes	—
307	C₂⁵	#518	1	2	yes	—
308	C₂⁵	#518	1	2	yes	—
309	C₂⁵	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×#120	1	2	yes	—
311	C₂⁵	C₂×#120	1	2	yes	—
312	C₂⁵	C₂×#120	1	2	yes	—
313	C₂⁵	C₂×#120	1	4	yes	—
314	C₂⁵	C₂×#120	1	4	yes	—
315	C₂⁵	C₂×#120	1	2	yes	—
316	C₂⁵	C₂×#120	1	2	yes	—
317	C₂⁵	C₂×#120	1	2	yes	—
318	C₂⁵	C₂×#120	1	1	yes	characteristic
319	C₂⁵	C₂×#120	1	4	yes	—
320	C₂⁵	C₂×#120	1	4	yes	—
321	C₂⁵	C₂×#120	1	1	yes	characteristic
322	C₂⁵	C₂×#121	1	2	yes	—
323	C₂⁵	C₂×#121	1	2	yes	—
324	C₂⁵	C₂×#121	1	2	yes	—
325	C₂⁵	C₂×#121	1	2	yes	—
326	C₂⁵	C₂×#121	1	2	yes	—
327	C₂⁵	C₂×#121	1	2	yes	—
328	C₂⁵	C₂×#123	1	1	yes	characteristic
329	C₂⁵	C₂×#123	1	1	yes	characteristic
330	C₂⁵	C₂×#123	1	2	yes	—
331	C₂⁵	C₂×#124	1	2	yes	—
332	C₂⁵	C₂×#127	1	2	yes	—
333	C₂⁵	#534	1	2	yes	—
334	C₂⁵	#534	1	2	yes	—
335	C₂⁵	#534	1	2	yes	—
336	C₂⁵	#534	1	2	yes	—
337	C₂⁵	#534	1	4	yes	—
338	C₂⁵	#534	1	4	yes	—
339	C₂⁵	#535	1	4	yes	—
340	C₂⁵	#535	1	4	yes	—
341	C₂⁵	D₄²	1	4	yes	—
342	C₂⁵	D₄²	1	4	yes	—
343	C₂⁵	D₄²	1	4	yes	—
344	C₂⁵	D₄²	1	4	yes	—
345	C₂⁵	D₄²	1	4	yes	—
346	C₂⁵	D₄²	1	4	yes	—
347	C₂⁵	D₄²	1	4	yes	—
348	C₂⁵	D₄²	1	4	yes	—
349	C₂⁵	#546	1	4	yes	—
350	C₂⁵	#546	1	4	yes	—
351	C₂⁵	#546	1	4	yes	—
352	C₂⁵	#546	1	4	yes	—
353	C₂⁵	#546	1	4	yes	—
354	C₂⁵	#546	1	4	yes	—
355	C₂⁵	#546	1	4	yes	—
356	C₂⁵	#546	1	4	yes	—
357	C₂²×D₄	#392	1	8	yes	—
358	C₂²×D₄	#392	1	8	yes	—
359	C₂²×D₄	#392	1	8	yes	—
360	C₂²×D₄	#392	1	8	yes	—
361	C₂²×D₄	#394	1	8	yes	—
362	C₂²×D₄	#394	1	8	yes	—
363	C₂²×D₄	#394	1	8	yes	—
364	C₂²×D₄	#394	1	8	yes	—
365	C₂²×D₄	C₂×#99	1	8	yes	—
366	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
367	C₂³×C₄	#379	1	2	yes	—
368	C₂³×C₄	#379	1	2	yes	—
369	C₂³×C₄	#379	1	2	yes	—
370	C₂³×C₄	#379	1	2	yes	—
371	C₂³×C₄	#379	1	2	yes	—
372	C₂³×C₄	#379	1	2	yes	—
373	C₂³×C₄	#379	1	4	yes	—
374	C₂³×C₄	#379	1	2	yes	—
375	C₂³×C₄	#386	1	2	yes	—
376	C₂³×C₄	#386	1	2	yes	—
377	C₂³×C₄	#386	1	8	yes	—
378	C₂³×C₄	#386	1	2	yes	—
379	C₂³×C₄	#386	1	2	yes	—
380	C₂³×C₄	#390	1	8	yes	—
381	C₂×C₂²⋊C₄	#379	1	4	yes	—
382	C₂×C₂²⋊C₄	#379	1	4	yes	—
383	C₂×C₂²⋊C₄	#379	1	4	yes	—
384	C₂×C₂²⋊C₄	#379	1	4	yes	—
385	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	—
386	C₂⁴	#1438	1	4	yes	—
387	C₂⁴	#1438	1	4	yes	—
388	C₂⁴	#1781	1	8	yes	complemented
389	C₂⁴	#1781	1	4	yes	complemented
390	C₂⁴	#1889	1	8	yes	—
391	C₂⁴	C₂×#379	1	1	yes	characteristic
392	C₂⁴	C₂×#379	1	1	yes	characteristic
393	C₂⁴	C₂×#379	1	1	yes	characteristic
394	C₂⁴	C₂×#379	1	1	yes	characteristic
395	C₂⁴	C₂×#379	1	1	yes	characteristic
396	C₂⁴	C₂×#379	1	1	yes	characteristic
397	C₂⁴	C₂×#379	1	1	yes	characteristic
398	C₂⁴	C₂×#386	1	1	yes	characteristic
399	C₂⁴	C₂×#386	1	2	yes	—
400	C₂⁴	C₂×#386	1	1	yes	characteristic
401	C₂⁴	C₂×#390	1	2	yes	—
402	C₂⁴	#2308	1	1	yes	characteristic
403	C₂⁴	#2308	1	2	yes	—
404	C₂⁴	#2308	1	1	yes	characteristic
405	C₂⁴	#2309	1	2	yes	—
406	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
407	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
408	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
409	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
410	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
411	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
412	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
413	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
414	C₂⁴	C₂×#392	1	2	yes	—
415	C₂⁴	C₂×#392	1	2	yes	—
416	C₂⁴	C₂×#394	1	2	yes	—
417	C₂⁴	C₂×#394	1	2	yes	—
418	C₂⁴	#2403	1	4	yes	—
419	C₂⁴	#2403	1	2	yes	—
420	C₂⁴	#2403	1	2	yes	—
421	C₂⁴	#2403	1	2	yes	—
422	C₂⁴	#2403	1	4	yes	—
423	C₂⁴	#2403	1	2	yes	—
424	C₂⁴	#2405	1	2	yes	—
425	C₂⁴	#2405	1	2	yes	—
426	C₂⁴	#2405	1	2	yes	—
427	C₂⁴	#2405	1	2	yes	—
428	C₂⁴	#2405	1	4	yes	—
429	C₂⁴	#2405	1	4	yes	—
430	C₂⁴	#2408	1	4	yes	—
431	C₂⁴	#2408	1	4	yes	—
432	C₂⁴	#2408	1	4	yes	—
433	C₂⁴	#2408	1	4	yes	—
434	C₂⁴	#2410	1	4	yes	—
435	C₂⁴	#2410	1	4	yes	—
436	C₂⁴	#2410	1	4	yes	—
437	C₂⁴	#2410	1	4	yes	—
438	C₂⁴	#2410	1	4	yes	—
439	C₂⁴	#2410	1	4	yes	—
440	C₂⁴	#2410	1	4	yes	—
441	C₂⁴	#2410	1	4	yes	—
442	C₂⁴	#2433	1	4	yes	—
443	C₂⁴	#2433	1	4	yes	—
444	C₂⁴	#2435	1	4	yes	—
445	C₂⁴	#2435	1	4	yes	—
446	C₂⁴	#2613	1	4	yes	—
447	C₂⁴	#2613	1	4	yes	—
448	C₂⁴	#2846	1	4	yes	—
449	C₂⁴	#2846	1	4	yes	—
450	C₂⁴	C₂²×#99	1	4	yes	—
451	C₂⁴	#2883	1	4	yes	—
452	C₂⁴	C₂×B(4,𝔽₂)	1	8	yes	—
453	C₂×D₄	#2021	1	32	yes	—
454	C₂²×C₄	#1438	1	4	yes	—
455	C₂²×C₄	#1438	1	4	yes	—
456	C₂²×C₄	#1781	1	4	yes	complemented
457	C₂²×C₄	#1889	1	8	yes	—
458	C₂²⋊C₄	#1781	1	8	yes	complemented
459	C₂³	#10991	1	8	yes	complemented
460	C₂³	C₂×#1438	1	1	yes	characteristic
461	C₂³	#13867	1	2	yes	—
462	C₂³	#13867	1	1	yes	characteristic
463	C₂³	#13867	1	2	yes	—
464	C₂³	#13867	1	1	yes	characteristic
465	C₂³	#13867	1	1	yes	characteristic
466	C₂³	#13867	1	1	yes	characteristic
467	C₂³	#13902	1	2	yes	—
468	C₂³	#13902	1	2	yes	—
469	C₂³	#14335	1	1	yes	characteristic
470	C₂³	#14679	1	1	yes	characteristic
471	C₂³	#14715	1	4	yes	—
472	C₂³	#14715	1	4	yes	—
473	C₂³	#14724	1	4	yes	—
474	C₂³	#14724	1	4	yes	—
475	C₂³	C₂×#1781	1	2	yes	—
476	C₂³	C₂×#1781	1	2	yes	—
477	C₂³	C₂×#1781	1	2	yes	—
478	C₂³	#20585	1	2	yes	—
479	C₂³	#20585	1	2	yes	—
480	C₂³	#20586	1	2	yes	—
481	C₂³	C₂×#1889	1	4	yes	—
482	C₂³	#21776	1	4	yes	—
483	C₂³	D₄×#99	1	8	yes	—
484	C₂³	D₄×#99	1	8	yes	—
485	C₂³	C₂×#2021	1	8	yes	—
486	C₂³	#23900	1	8	yes	—
487	C₂³	#23900	1	8	yes	—
488	C₂×C₄	#10991	1	8	yes	complemented
489	C₂²	#154094	1	1	yes	characteristic
490	C₂²	C₂×#10991	1	2	yes	—
491	C₂²	#359501	1	2	yes	—
492	C₂²	#359501	1	2	yes	—
493	C₂²	#359579	1	2	yes	—
494	C₂²	#359579	1	4	yes	—
495	C₂²	#359579	1	2	yes	—
496	C₂²	#359591	1	2	yes	—
497	C₂²	#359591	1	2	yes	—
498	C₂²	#361622	1	4	yes	—
499	C₂²	#382434	1	2	yes	—
500	C₂²	#392109	1	1	yes	characteristic
501	C₂²	#392111	1	1	yes	characteristic
502	C₂²	#394058	1	8	yes	—
503	C₂	#72216625	1	4	yes	—
504	C₂	#72218451	1	1	yes	characteristic
505	C₂	#72225621	1	1	yes	characteristic
506	C₂	#72225808	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	#13867
commutator	C₂⁶	C₂³×C₄
Frattini, cosocle	C₂⁷	C₂⁴
prime radical	C₂²×D₄×#120	C₂
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#115163	C₂	semidirect
2. #72238531	C₂	semidirect
3. C₂×#392109	C₂	semidirect
4. C₂×#106654	C₂	semidirect
6. C₂×#188035	C₂	semidirect
7. #72219307	C₂	semidirect
8. #72218451	C₂	semidirect
9. C₂×#115690	C₂	semidirect
12. C₂⁴×#120	C₄	semidirect
14. C₂²×#2847	C₄	semidirect
15. C₂²×#2846	C₄	semidirect
17. C₂²×#2433	C₄	semidirect
18. C₂²×#2408	C₄	semidirect
19. C₂²×#2410	C₄	semidirect
21. C₂²×#2403	C₄	semidirect
24. C₂²×C₄×#120	C₄	semidirect
25. C₂×#21746	C₂²	semidirect
26. C₂×#21746	C₂²	semidirect
29. C₂²×#1781	C₂²	semidirect
30. C₂²×#1781	C₂²	semidirect
31. C₂×#14679	C₂²	semidirect
32. #517411	C₂²	semidirect
33. C₂×#10735	C₂²	semidirect
34. C₂×#8101	C₂²	semidirect
69. C₂³×#99	D₄	semidirect
87. C₂×#1781	D₄	semidirect
88. C₂⁷	C₂²⋊C₄	semidirect
89. C₂⁷	C₂²⋊C₄	semidirect
99. C₂⁴×D₄	C₂²⋊C₄	semidirect
100. C₂⁴×D₄	C₂²⋊C₄	semidirect
101. C₂⁴×D₄	C₂²⋊C₄	semidirect
102. C₂⁴×D₄	C₂²⋊C₄	semidirect
103. C₂⁴×D₄	C₂²⋊C₄	semidirect
104. C₂⁴×D₄	C₂²⋊C₄	semidirect
105. C₂⁴×D₄	C₂²⋊C₄	semidirect
128. C₂⁵×C₄	C₂²⋊C₄	semidirect
129. C₂⁵×C₄	C₂²⋊C₄	semidirect
130. C₂⁵×C₄	C₂²⋊C₄	semidirect
138. C₂²×#120	C₂²⋊C₄	semidirect
139. C₂²×#120	C₂²⋊C₄	semidirect
140. C₂²×#120	C₂²⋊C₄	semidirect
141. C₂²×#120	C₂²⋊C₄	semidirect
142. C₂²×#120	C₂²⋊C₄	semidirect
145. C₂³×C₄⋊C₄	C₂²⋊C₄	semidirect
146. C₂³×C₄⋊C₄	C₂²⋊C₄	semidirect
147. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
148. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
149. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
150. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
151. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
152. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
163. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
164. C₂³×C₄²	C₂²⋊C₄	semidirect
165. C₂×#386	C₂²⋊C₄	semidirect
166. C₂×#386	C₂²⋊C₄	semidirect
167. C₂×#386	C₂²⋊C₄	semidirect
168. C₂×#385	C₂²⋊C₄	semidirect
169. C₂×#380	C₂²⋊C₄	semidirect
170. C₂×#379	C₂²⋊C₄	semidirect
171. C₂×#379	C₂²⋊C₄	semidirect
172. C₂×#379	C₂²⋊C₄	semidirect
173. C₂×#379	C₂²⋊C₄	semidirect
177. C₂×#379	C₂×D₄	semidirect
178. C₂×C₄×C₂²⋊C₄	C₂²⋊C₄	semidirect
264. C₂×#120	#99	semidirect
388. C₂⁴	#1781	semidirect
389. C₂⁴	#1781	semidirect
456. C₂²×C₄	#1781	semidirect
458. C₂²⋊C₄	#1781	semidirect
459. C₂³	#10991	semidirect
488. C₂×C₄	#10991	semidirect

Maximal subgroups

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

subgroup	index
C₂×#115163	2
#72238531	2
C₂×#392109	2
C₂×#106654	2
C₂²×D₄×#120	2
C₂×#188035	2
#72219307	2
#72218451	2
C₂×#115690	2