Subgroups — C₂×#10618181 #13007199

Order 1280.

7738 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	#10618181	C₂	1	32	yes	maximal, direct product factor
3	C₂×#66064	C₂	1	2	yes	maximal, complemented
4	C₂×#66061	C₂	1	2	yes	maximal, complemented
5	C₂×#66024	C₂	1	4	yes	maximal, complemented
6	C₂×#65968	C₂	1	4	yes	maximal, complemented
7	C₂×D₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
8	C₂×#65913	C₂	1	4	yes	maximal, complemented
9	C₂×#65913	C₂	1	2	yes	maximal, complemented
10	C₂×Q₈×D₂₀	C₂	1	2	yes	maximal, complemented
11	C₂×#65855	C₂	1	2	yes	maximal
12	C₂×#65853	C₂	1	2	yes	maximal, complemented
13	C₂²×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
14	C₂×#65804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×Q₈×D₅	C₂²	1	4	yes	complemented
16	C₂³×D₂₀	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₅	C₂²	1	2	yes	—
18	C₅×#533	C₂²	1	16	yes	complemented
19	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×#125	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
25	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
26	C₂×C₅×#117	C₂²	1	2	yes	—
27	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×#4092	C₂²	1	4	yes	complemented
29	C₂×#4092	C₂²	1	8	yes	complemented
30	C₂²×#685	C₂²	1	2	yes	—
31	C₂×#4072	C₂²	1	2	yes	—
32	C₂²×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
33	C₂×#4070	C₂²	1	2	yes	—
34	C₂×#4070	C₂²	1	2	yes	—
35	#66064	C₂²	1	32	yes	complemented
36	#66061	C₂²	1	32	yes	complemented
37	#66024	C₂²	1	64	yes	complemented
38	#65968	C₂²	1	64	yes	complemented
39	D₅×C₂²⋊Q₈	C₂²	1	64	yes	complemented
40	#65913	C₂²	1	32	yes	complemented
41	#65913	C₂²	1	64	yes	complemented
42	Q₈×D₂₀	C₂²	1	32	yes	complemented
43	#65855	C₂²	1	32	yes	—
44	#65853	C₂²	1	32	yes	complemented
45	C₂×#4043	C₂²	1	4	yes	complemented
46	C₂×#4043	C₂²	1	8	yes	complemented
47	C₂×#4042	C₂²	1	8	yes	complemented
48	C₂×#4042	C₂²	1	8	yes	complemented
49	C₂×#4042	C₂²	1	8	yes	complemented
50	C₂×#4039	C₂²	1	4	yes	—
51	C₂×#4039	C₂²	1	4	yes	—
52	C₂×D₅×C₄⋊C₄	C₂²	1	4	yes	complemented
53	C₂×D₅×C₄⋊C₄	C₂²	1	8	yes	complemented
54	C₂×#4036	C₂²	1	4	yes	complemented
55	C₂×#4034	C₂²	1	4	yes	complemented
56	C₂×D₅×C₂²⋊C₄	C₂²	1	8	yes	—
57	C₂×#4024	C₂²	1	8	yes	—
58	C₂×C₄×D₂₀	C₂²	1	2	yes	—
59	C₂×C₄×D₂₀	C₂²	1	4	yes	—
60	C₂×C₄×D₂₀	C₂²	1	4	yes	—
61	C₂×C₄×D₂₀	C₂²	1	16	yes	—
62	C₂×C₄×D₂₀	C₂²	1	2	yes	—
63	C₂×C₄×D₂₀	C₂²	1	2	yes	—
64	C₂×C₄×D₂₀	C₂²	1	2	yes	—
65	#65804	C₂²	1	16	yes	complemented
66	C₂×#4016	C₂²	1	4	yes	complemented
67	C₂×#4016	C₂²	1	2	yes	complemented
68	C₂×#4015	C₂²	1	4	yes	complemented
69	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
70	C₂×#4015	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
72	C₂×C₄×Dic₁₀	C₂²	1	2	yes	complemented
73	C₂×#3501	—	5	1	no	maximal, Sylow
74	C₂⁴×D₅	C₂³	1	2	yes	—
75	C₂²×C₅×Q₈	C₂³	1	2	yes	—
76	C₂²×C₅×Q₈	C₂³	1	2	yes	—
77	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂³×Dic₅	C₂³	1	2	yes	—
81	C₂×Q₈×D₅	—	4	16	no	—
82	C₂×Q₈×D₅	C₂³	1	32	yes	complemented
83	C₂²×D₂₀	Q₈	1	16	yes	complemented
84	C₂²×D₂₀	C₂³	1	2	yes	—
85	C₂²×D₂₀	C₂³	1	2	yes	—
86	C₂²×D₂₀	C₂³	1	8	yes	—
87	C₂²×C₄×D₅	—	4	8	no	—
88	C₂²×C₄×D₅	C₂³	1	4	yes	—
89	C₂²×C₄×D₅	C₂³	1	4	yes	—
90	C₂²×C₄×D₅	C₂³	1	16	yes	—
91	C₂²×C₄×D₅	C₂³	1	8	yes	—
92	C₂²×C₄×D₅	C₂³	1	8	yes	—
93	C₂²×Dic₁₀	C₂³	1	2	yes	—
94	C₂²×Dic₁₀	C₂³	1	2	yes	—
95	C₂²×Dic₁₀	C₂³	1	8	yes	—
96	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
97	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
98	C₅×#125	C₂³	1	16	yes	complemented
99	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
100	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
101	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
102	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
103	C₅×#117	C₂³	1	16	yes	—
104	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₅	C₂³	1	4	yes	—
115	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂³	1	8	yes	—
117	C₂×C₂²⋊Dic₅	C₂³	1	4	yes	—
118	#4092	C₂³	1	32	yes	complemented
119	#4092	C₂³	1	64	yes	complemented
120	C₂×#685	C₂³	1	4	yes	—
121	C₂×#685	C₂³	1	4	yes	—
122	C₂×#685	C₂³	1	16	yes	—
123	C₂×#685	C₂³	1	8	yes	—
124	C₂×#685	C₂³	1	8	yes	—
125	#4072	C₂³	1	16	yes	—
126	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
127	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
128	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
129	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
130	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
131	C₂×C₄⋊Dic₅	C₂³	1	8	yes	—
132	C₂×C₄⋊Dic₅	C₂³	1	2	yes	—
133	C₂×C₄⋊Dic₅	C₂³	1	8	yes	—
134	#4070	C₂³	1	16	yes	—
135	#4070	C₂³	1	16	yes	—
136	C₂×#683	C₂³	1	4	yes	—
137	C₂×#683	C₂³	1	4	yes	—
138	C₂×#683	C₂³	1	8	yes	—
139	C₂×#683	C₂³	1	8	yes	—
140	C₂×C₄×Dic₅	C₂³	1	4	yes	—
141	#4043	C₂³	1	32	yes	complemented
142	#4043	C₂³	1	64	yes	complemented
143	#4042	C₂³	1	64	yes	complemented
144	#4042	C₂³	1	64	yes	complemented
145	#4042	C₂³	1	64	yes	complemented
146	#4039	C₂³	1	32	yes	—
147	#4039	C₂³	1	32	yes	—
148	D₅×C₄⋊C₄	C₂³	1	32	yes	complemented
149	D₅×C₄⋊C₄	C₂³	1	64	yes	complemented
150	#4036	C₂³	1	32	yes	complemented
151	#4034	C₂³	1	32	yes	complemented
152	D₅×C₂²⋊C₄	C₂³	1	64	yes	—
153	#4024	C₂³	1	64	yes	—
154	C₄×D₂₀	C₂³	1	16	yes	—
155	C₄×D₂₀	C₂³	1	16	yes	—
156	C₄×D₂₀	C₂³	1	16	yes	—
157	C₄×D₂₀	C₂³	1	16	yes	—
158	C₄×D₂₀	C₂³	1	32	yes	—
159	C₄×D₂₀	C₂³	1	32	yes	—
160	#4016	C₂³	1	16	yes	complemented
161	#4016	C₂³	1	32	yes	complemented
162	#4015	C₂³	1	8	yes	complemented
163	#4015	C₂³	1	8	yes	complemented
164	#4015	C₂³	1	32	yes	complemented
165	C₄×Dic₁₀	C₂³	1	16	yes	complemented
166	C₄×Dic₁₀	C₂³	1	16	yes	complemented
167	#3501	—	5	32	no	—
168	C₂×#554	—	5	2	no	—
169	C₂×#554	—	5	4	no	—
170	C₂×#554	—	5	2	no	—
171	C₂×#554	—	5	4	no	—
172	C₂×D₄×Q₈	—	5	2	no	—
173	C₂×D₄×Q₈	—	5	2	no	—
174	C₂×#544	—	5	2	no	—
175	C₂×#543	—	5	4	no	—
176	C₂×#533	—	5	1	no	—
177	C₂×#533	D₅	1	1	yes	characteristic, complemented
178	C₂²×C₂²⋊Q₈	—	5	4	no	—
179	C₂×#518	—	5	2	no	—
180	C₂²×C₄×D₄	—	5	1	no	—
181	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
182	C₂³×D₅	—	4	4	no	—
183	C₂³×D₅	—	4	4	no	—
184	C₂³×D₅	C₂×Q₈	1	16	yes	complemented
185	C₂³×D₅	C₂⁴	1	4	yes	—
186	C₂³×D₅	C₂⁴	1	8	yes	—
187	C₂×C₅×Q₈	—	2	8	no	—
188	C₂×C₅×Q₈	—	4	4	no	—
189	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
190	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
191	C₂²×C₄×C₅	—	2	4	no	—
192	C₂²×C₄×C₅	—	4	2	no	—
193	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	complemented
194	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
198	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₂²×Dic₅	—	4	4	no	—
206	C₂²×Dic₅	C₂⁴	1	4	yes	—
207	C₂²×Dic₅	C₂⁴	1	4	yes	—
208	C₂²×Dic₅	C₂⁴	1	4	yes	—
209	C₂²×Dic₅	C₂⁴	1	8	yes	—
210	Q₈×D₅	—	4	64	no	—
211	C₂×D₂₀	C₂×Q₈	1	16	yes	complemented
212	C₂×D₂₀	C₂×Q₈	1	16	yes	complemented
213	C₂×D₂₀	C₂×Q₈	1	64	yes	complemented
214	C₂×D₂₀	C₂⁴	1	8	yes	—
215	C₂×D₂₀	C₂⁴	1	8	yes	—
216	C₂×C₄×D₅	—	2	16	no	—
217	C₂×C₄×D₅	—	4	32	no	—
218	C₂×C₄×D₅	—	4	8	no	—
219	C₂×C₄×D₅	—	4	16	no	—
220	C₂×C₄×D₅	—	4	16	no	—
221	C₂×C₄×D₅	C₂⁴	1	16	yes	—
222	C₂×C₄×D₅	C₂⁴	1	16	yes	—
223	C₂×C₄×D₅	C₂⁴	1	32	yes	—
224	C₂×C₄×D₅	C₂⁴	1	32	yes	—
225	C₂×Dic₁₀	—	2	8	no	—
226	C₂×Dic₁₀	—	4	4	no	—
227	C₂×Dic₁₀	—	4	16	no	—
228	C₂×Dic₁₀	C₂⁴	1	8	yes	—
229	C₂×Dic₁₀	C₂⁴	1	32	yes	—
230	C₂×Dic₁₀	C₂⁴	1	8	yes	—
231	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
233	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
234	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
235	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
236	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
237	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
238	C₄²×C₅	C₂⁴	1	4	yes	—
239	C₄²×C₅	C₂⁴	1	4	yes	—
240	C₄²×C₅	C₂⁴	1	4	yes	—
241	C₄²×C₅	C₂⁴	1	4	yes	—
242	C₄²×C₅	C₂⁴	1	16	yes	—
243	C₂²⋊Dic₅	C₂⁴	1	16	yes	—
244	#685	C₂⁴	1	16	yes	—
245	#685	C₂⁴	1	16	yes	—
246	#685	C₂⁴	1	32	yes	—
247	#685	C₂⁴	1	32	yes	—
248	C₄⋊Dic₅	C₂⁴	1	8	yes	—
249	C₄⋊Dic₅	C₂⁴	1	8	yes	—
250	C₄⋊Dic₅	C₂⁴	1	8	yes	—
251	C₄⋊Dic₅	C₂⁴	1	8	yes	—
252	C₄⋊Dic₅	C₂⁴	1	8	yes	—
253	C₄⋊Dic₅	C₂⁴	1	32	yes	—
254	C₄⋊Dic₅	C₂⁴	1	8	yes	—
255	#683	C₂⁴	1	16	yes	—
256	#683	C₂⁴	1	16	yes	—
257	#683	C₂⁴	1	32	yes	—
258	#683	C₂⁴	1	32	yes	—
259	C₄×Dic₅	C₂⁴	1	16	yes	—
260	C₂³×Q₈	—	5	4	no	—
261	C₂³×D₄	—	5	1	no	—
262	C₂⁴×C₄	—	5	2	no	—
263	#554	—	5	32	no	—
264	#554	—	5	64	no	—
265	#554	—	5	32	no	—
266	#554	—	5	64	no	—
267	D₄×Q₈	—	5	32	no	—
268	D₄×Q₈	—	5	32	no	—
269	#544	—	5	32	no	—
270	#543	—	5	64	no	—
271	#533	—	5	16	no	—
272	#533	C₂×D₅	1	16	yes	complemented
273	C₂×C₄⋊Q₈	—	5	4	no	—
274	C₂×C₄⋊Q₈	—	5	1	no	—
275	C₂×C₄⋊Q₈	—	5	1	no	—
276	C₂×C₄⋊Q₈	—	5	4	no	—
277	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
278	C₂×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
279	C₂×#125	—	5	4	no	—
280	C₂×#125	—	5	2	no	—
281	C₂×#125	—	5	4	no	—
282	C₂×#125	C₂×D₅	1	2	yes	complemented
283	C₂×C₂²⋊Q₈	—	5	4	no	—
284	C₂×C₂²⋊Q₈	—	5	8	no	—
285	C₂×C₂²⋊Q₈	—	5	2	no	—
286	C₂×C₂²⋊Q₈	—	5	2	no	—
287	C₂×C₂²⋊Q₈	—	5	64	no	—
288	C₂×C₂²⋊Q₈	—	5	8	no	—
289	C₂×C₂²⋊Q₈	—	5	8	no	—
290	C₂×C₂²⋊Q₈	—	5	8	no	—
291	C₂×C₂²⋊Q₈	—	5	4	no	—
292	C₂×C₂²⋊Q₈	—	5	8	no	—
293	C₂×C₂²⋊Q₈	—	5	8	no	—
294	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
295	C₂×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
296	#518	—	5	32	no	—
297	C₂×C₄×Q₈	—	5	2	no	—
298	C₂×C₄×Q₈	—	5	2	no	—
299	C₂×C₄×Q₈	C₂×D₅	1	2	yes	complemented
300	C₂×C₄×Q₈	C₂×D₅	1	2	yes	complemented
301	C₂×C₄×D₄	—	5	4	no	—
302	C₂×C₄×D₄	—	5	4	no	—
303	C₂×C₄×D₄	—	5	2	no	—
304	C₂×C₄×D₄	—	5	2	no	—
305	C₂×C₄×D₄	—	5	2	no	—
306	C₂×C₄×D₄	—	5	2	no	—
307	C₂×C₄×D₄	—	5	16	no	—
308	C₂×C₄×D₄	—	5	4	no	—
309	C₂×C₄×D₄	—	5	4	no	—
310	C₂×#117	—	5	2	no	—
311	C₂×#117	C₂×D₅	1	2	yes	—
312	C₂²×C₄⋊C₄	—	5	1	no	—
313	C₂²×C₄⋊C₄	—	5	8	no	—
314	C₂²×C₄⋊C₄	—	5	4	no	—
315	C₂²×C₂²⋊C₄	—	5	2	no	—
316	C₂²×C₂²⋊C₄	—	5	8	no	—
317	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
318	C₂³×C₅	—	2	2	no	—
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	C₂²×Q₈	1	4	yes	—
321	C₂³×C₅	C₂⁵	1	2	yes	—
322	C₂³×C₅	C₂⁵	1	1	yes	characteristic
323	C₂²×D₅	—	2	8	no	—
324	C₂²×D₅	—	2	8	no	—
325	C₂²×D₅	—	4	8	no	—
326	C₂²×D₅	—	4	32	no	—
327	C₂²×D₅	—	4	8	no	—
328	C₂²×D₅	C₂²×Q₈	1	16	yes	—
329	C₂²×D₅	C₂²×Q₈	1	32	yes	complemented
330	C₂²×D₅	C₂⁵	1	8	yes	—
331	C₅×Q₈	—	2	16	no	—
332	C₅×Q₈	—	4	8	no	—
333	C₂×C₄×C₅	—	2	8	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	8	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	8	no	—
339	C₂×C₄×C₅	—	4	4	no	—
340	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
341	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
342	C₂×C₄×C₅	C₂²×Q₈	1	16	yes	complemented
343	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
344	C₂×C₄×C₅	C₂⁵	1	2	yes	—
345	C₂×C₄×C₅	C₂⁵	1	2	yes	—
346	C₂×C₄×C₅	C₂⁵	1	8	yes	—
347	C₂×C₄×C₅	C₂⁵	1	8	yes	—
348	C₂×C₄×C₅	C₂⁵	1	2	yes	—
349	C₂×C₄×C₅	C₂⁵	1	2	yes	—
350	C₂×C₄×C₅	C₂⁵	1	2	yes	—
351	C₂×C₄×C₅	C₂⁵	1	2	yes	—
352	C₂×Dic₅	—	2	8	no	—
353	C₂×Dic₅	—	2	8	no	—
354	C₂×Dic₅	—	2	8	no	—
355	C₂×Dic₅	—	4	8	no	—
356	C₂×Dic₅	C₂⁵	1	8	yes	—
357	C₂×Dic₅	C₂⁵	1	8	yes	—
358	C₂×Dic₅	C₂⁵	1	8	yes	—
359	D₂₀	C₂²×Q₈	1	32	yes	complemented
360	D₂₀	C₂²×Q₈	1	32	yes	complemented
361	C₄×D₅	—	2	32	no	—
362	C₄×D₅	—	4	16	no	—
363	C₄×D₅	—	4	32	no	—
364	C₄×D₅	—	4	32	no	—
365	Dic₁₀	—	2	16	no	—
366	Dic₁₀	—	4	8	no	—
367	Dic₁₀	—	4	32	no	—
368	C₂⁵	—	5	2	no	—
369	C₂²×Q₈	—	5	32	no	—
370	C₂²×Q₈	—	5	2	no	—
371	C₂²×Q₈	—	5	2	no	—
372	C₂²×Q₈	—	5	8	no	—
373	C₂²×Q₈	—	20	16	no	—
374	C₂²×Q₈	C₂²×D₅	1	2	yes	—
375	C₂²×Q₈	C₂²×D₅	1	2	yes	—
376	C₂²×D₄	—	5	16	no	—
377	C₂²×D₄	—	5	2	no	—
378	C₂²×D₄	—	5	2	no	—
379	C₂²×D₄	—	5	8	no	—
380	C₂³×C₄	—	5	2	no	—
381	C₂³×C₄	—	5	4	no	—
382	C₂³×C₄	—	5	8	no	—
383	C₂³×C₄	—	5	8	no	—
384	C₂³×C₄	—	5	4	no	—
385	C₂³×C₄	—	5	16	no	—
386	C₂³×C₄	—	20	8	no	—
387	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
388	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
389	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
390	C₄⋊Q₈	—	5	32	no	—
391	C₄⋊Q₈	—	5	8	no	—
392	C₄⋊Q₈	—	5	8	no	—
393	C₄⋊Q₈	—	5	32	no	—
394	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
395	C₄⋊Q₈	C₂²×D₅	1	8	yes	complemented
396	#125	—	5	32	no	—
397	#125	—	5	16	no	—
398	#125	—	5	32	no	—
399	#125	C₂²×D₅	1	16	yes	complemented
400	C₂²⋊Q₈	—	5	32	no	—
401	C₂²⋊Q₈	—	5	64	no	—
402	C₂²⋊Q₈	—	5	16	no	—
403	C₂²⋊Q₈	—	5	16	no	—
404	C₂²⋊Q₈	—	5	32	no	—
405	C₂²⋊Q₈	—	5	64	no	—
406	C₂²⋊Q₈	—	5	64	no	—
407	C₂²⋊Q₈	—	5	64	no	—
408	C₂²⋊Q₈	—	5	64	no	—
409	C₂²⋊Q₈	—	5	64	no	—
410	C₂²⋊Q₈	C₂²×D₅	1	16	yes	—
411	C₂²⋊Q₈	C₂²×D₅	1	16	yes	—
412	C₄×Q₈	—	5	16	no	—
413	C₄×Q₈	—	5	16	no	—
414	C₄×Q₈	C₂²×D₅	1	16	yes	complemented
415	C₄×Q₈	C₂²×D₅	1	16	yes	complemented
416	C₄×D₄	—	5	32	no	—
417	C₄×D₄	—	5	32	no	—
418	C₄×D₄	—	5	16	no	—
419	C₄×D₄	—	5	16	no	—
420	C₄×D₄	—	5	16	no	—
421	C₄×D₄	—	5	16	no	—
422	C₄×D₄	—	5	32	no	—
423	C₄×D₄	—	5	32	no	—
424	#117	—	5	16	no	—
425	#117	C₂²×D₅	1	16	yes	—
426	C₂×C₄⋊C₄	—	5	4	no	—
427	C₂×C₄⋊C₄	—	5	2	no	—
428	C₂×C₄⋊C₄	—	5	2	no	—
429	C₂×C₄⋊C₄	—	5	2	no	—
430	C₂×C₄⋊C₄	—	5	8	no	—
431	C₂×C₄⋊C₄	—	5	8	no	—
432	C₂×C₄⋊C₄	—	5	8	no	—
433	C₂×C₄⋊C₄	—	5	8	no	—
434	C₂×C₄⋊C₄	—	5	2	no	—
435	C₂×C₄⋊C₄	—	5	2	no	—
436	C₂×C₄⋊C₄	—	5	4	no	—
437	C₂×C₄⋊C₄	—	5	2	no	—
438	C₂×C₄⋊C₄	—	5	64	no	—
439	C₂×C₄⋊C₄	—	5	32	no	—
440	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
441	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
442	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
443	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
444	C₂×C₄⋊C₄	C₂²×D₅	1	4	yes	—
445	C₂×C₄⋊C₄	C₂²×D₅	1	2	yes	—
446	C₂×C₂²⋊C₄	—	5	4	no	—
447	C₂×C₂²⋊C₄	—	5	8	no	—
448	C₂×C₂²⋊C₄	—	5	8	no	—
449	C₂×C₂²⋊C₄	—	5	4	no	—
450	C₂×C₂²⋊C₄	—	5	4	no	—
451	C₂×C₂²⋊C₄	—	5	16	no	—
452	C₂×C₂²⋊C₄	—	5	64	no	—
453	C₂×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
454	C₂×C₄²	—	5	4	no	—
455	C₂×C₄²	C₂²×D₅	1	4	yes	—
456	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
457	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
458	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
459	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
460	C₂×C₄²	C₂²×D₅	1	8	yes	—
461	C₂²×C₅	—	2	2	no	—
462	C₂²×C₅	—	2	2	no	—
463	C₂²×C₅	—	2	8	no	—
464	C₂²×C₅	C₂³×Q₈	1	4	yes	—
465	C₂²×C₅	C₂³×Q₈	1	2	yes	—
466	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
467	C₂²×C₅	#585	1	2	yes	—
468	C₂²×C₅	C₂⁶	1	1	yes	characteristic
469	C₂×D₅	—	2	8	no	—
470	C₂×D₅	—	2	8	no	—
471	C₂×D₅	—	2	32	no	—
472	C₂×D₅	—	4	32	no	—
473	C₂×D₅	C₂³×Q₈	1	16	yes	—
474	C₄×C₅	—	2	8	no	—
475	C₄×C₅	—	2	2	no	—
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	2	8	no	—
478	C₄×C₅	—	2	2	no	—
479	C₄×C₅	C₂³×Q₈	1	4	yes	—
480	C₄×C₅	C₂³×Q₈	1	4	yes	—
481	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
482	Dic₅	—	2	8	no	—
483	Dic₅	—	2	8	no	—
484	Dic₅	—	2	8	no	—
485	C₂⁴	—	5	4	no	—
486	C₂⁴	—	5	16	no	—
487	C₂⁴	—	5	8	no	—
488	C₂⁴	—	20	4	no	—
489	C₂⁴	—	20	4	no	—
490	C₂⁴	C₂³×D₅	1	1	yes	characteristic
491	C₂×Q₈	—	2	8	no	—
492	C₂×Q₈	—	4	4	no	—
493	C₂×Q₈	—	5	8	no	—
494	C₂×Q₈	—	5	8	no	—
495	C₂×Q₈	—	5	32	no	—
496	C₂×Q₈	—	10	8	no	—
497	C₂×Q₈	—	20	16	no	—
498	C₂×Q₈	—	20	4	no	—
499	C₂×Q₈	—	20	64	no	—
500	C₂×Q₈	C₂³×D₅	1	8	yes	—
501	C₂×Q₈	C₂³×D₅	1	8	yes	—
502	C₂×D₄	—	5	16	no	—
503	C₂×D₄	—	5	16	no	—
504	C₂×D₄	—	5	64	no	—
505	C₂×D₄	—	5	8	no	—
506	C₂×D₄	—	5	8	no	—
507	C₂²×C₄	—	2	4	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	5	4	no	—
510	C₂²×C₄	—	5	4	no	—
511	C₂²×C₄	—	5	4	no	—
512	C₂²×C₄	—	5	8	no	—
513	C₂²×C₄	—	5	16	no	—
514	C₂²×C₄	—	5	32	no	—
515	C₂²×C₄	—	5	32	no	—
516	C₂²×C₄	—	5	16	no	—
517	C₂²×C₄	—	10	16	no	—
518	C₂²×C₄	—	20	32	no	—
519	C₂²×C₄	—	20	8	no	—
520	C₂²×C₄	—	20	16	no	—
521	C₂²×C₄	—	20	16	no	—
522	C₂²×C₄	—	20	4	no	—
523	C₂²×C₄	Q₈×D₅	1	8	yes	complemented
524	C₂²×C₄	C₂³×D₅	1	4	yes	—
525	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
526	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
527	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
528	C₂²×C₄	C₂³×D₅	1	4	yes	—
529	C₂²×C₄	C₂³×D₅	1	4	yes	—
530	C₂²×C₄	C₂³×D₅	1	4	yes	—
531	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
532	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
533	C₂²×C₄	C₂³×D₅	1	4	yes	—
534	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
535	C₄⋊C₄	—	5	16	no	—
536	C₄⋊C₄	—	5	8	no	—
537	C₄⋊C₄	—	5	8	no	—
538	C₄⋊C₄	—	5	8	no	—
539	C₄⋊C₄	—	5	32	no	—
540	C₄⋊C₄	—	5	32	no	—
541	C₄⋊C₄	—	5	32	no	—
542	C₄⋊C₄	—	5	8	no	—
543	C₄⋊C₄	—	5	8	no	—
544	C₄⋊C₄	—	5	16	no	—
545	C₄⋊C₄	—	5	8	no	—
546	C₄⋊C₄	C₂³×D₅	1	16	yes	—
547	C₄⋊C₄	C₂³×D₅	1	8	yes	—
548	C₄⋊C₄	C₂³×D₅	1	8	yes	—
549	C₄⋊C₄	C₂³×D₅	1	8	yes	—
550	C₄⋊C₄	C₂³×D₅	1	16	yes	—
551	C₄⋊C₄	C₂³×D₅	1	8	yes	—
552	C₂²⋊C₄	—	5	16	no	—
553	C₂²⋊C₄	—	5	32	no	—
554	C₂²⋊C₄	—	5	32	no	—
555	C₂²⋊C₄	—	5	16	no	—
556	C₂²⋊C₄	—	5	16	no	—
557	C₂²⋊C₄	C₂³×D₅	1	16	yes	—
558	C₄²	—	5	16	no	—
559	C₄²	C₂³×D₅	1	4	yes	—
560	C₄²	C₂³×D₅	1	4	yes	—
561	C₄²	C₂³×D₅	1	4	yes	—
562	C₄²	C₂³×D₅	1	4	yes	—
563	C₄²	C₂³×D₅	1	16	yes	—
564	C₂×C₅	—	2	4	no	—
565	C₂×C₅	#3501	1	4	yes	complemented
566	C₂×C₅	C₂⁴×Q₈	1	1	yes	characteristic
567	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂×C₅	C₂×#585	1	1	yes	characteristic
569	D₅	—	2	16	no	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	5	16	no	—
573	C₂³	—	5	8	no	—
574	C₂³	—	5	32	no	—
575	C₂³	—	10	8	no	—
576	C₂³	—	10	8	no	—
577	C₂³	—	20	8	no	—
578	C₂³	—	20	8	no	—
579	C₂³	—	20	32	no	—
580	C₂³	C₂×Q₈×D₅	1	4	yes	—
581	C₂³	C₂⁴×D₅	1	2	yes	—
582	C₂³	C₂⁴×D₅	1	1	yes	characteristic
583	Q₈	—	2	16	no	—
584	Q₈	—	4	8	no	—
585	Q₈	—	10	16	no	—
586	Q₈	—	20	32	no	—
587	Q₈	—	20	8	no	—
588	D₄	—	5	32	no	—
589	D₄	—	5	32	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	5	8	no	—
598	C₂×C₄	—	5	8	no	—
599	C₂×C₄	—	5	8	no	—
600	C₂×C₄	—	10	8	no	—
601	C₂×C₄	—	10	8	no	—
602	C₂×C₄	—	10	8	no	—
603	C₂×C₄	—	10	32	no	—
604	C₂×C₄	—	20	16	no	—
605	C₂×C₄	—	20	32	no	—
606	C₂×C₄	—	20	32	no	—
607	C₂×C₄	—	20	8	no	—
608	C₂×C₄	C₂×Q₈×D₅	1	4	yes	—
609	C₂×C₄	C₂×Q₈×D₅	1	4	yes	—
610	C₂×C₄	C₂×Q₈×D₅	1	16	yes	complemented
611	C₂×C₄	#4149	1	4	yes	—
612	C₂×C₄	C₂⁴×D₅	1	2	yes	—
613	C₂×C₄	C₂⁴×D₅	1	2	yes	—
614	C₂×C₄	C₂⁴×D₅	1	2	yes	—
615	C₂×C₄	C₂⁴×D₅	1	8	yes	—
616	C₂×C₄	C₂⁴×D₅	1	8	yes	—
617	C₂×C₄	C₂⁴×D₅	1	2	yes	—
618	C₂×C₄	C₂⁴×D₅	1	2	yes	—
619	C₂×C₄	C₂⁴×D₅	1	2	yes	—
620	C₅	C₂×#3501	1	1	yes	characteristic, complemented, Sylow
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	8	no	—
624	C₂²	—	5	16	no	—
625	C₂²	—	10	8	no	—
626	C₂²	—	10	8	no	—
627	C₂²	—	10	32	no	—
628	C₂²	—	20	32	no	—
629	C₂²	C₂²×Q₈×D₅	1	4	yes	—
630	C₂²	C₂²×Q₈×D₅	1	2	yes	—
631	C₂²	C₂×#4149	1	2	yes	—
632	C₂²	#66283	1	2	yes	—
633	C₂²	C₂⁵×D₅	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	8	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	8	no	—
639	C₄	—	10	8	no	—
640	C₄	—	10	8	no	—
641	C₄	—	10	8	no	—
642	C₄	C₂²×Q₈×D₅	1	4	yes	—
643	C₄	C₂²×Q₈×D₅	1	4	yes	—
644	C₄	C₂×#4149	1	4	yes	—
645	C₂	—	2	4	no	—
646	C₂	—	10	16	no	—
647	C₂	#10618181	1	4	yes	direct product factor
648	C₂	C₂³×Q₈×D₅	1	1	yes	characteristic
649	C₂	C₂²×#4149	1	1	yes	characteristic
650	C₂	C₂×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁶
Frattini	C₂²	C₂⁵×D₅
Fitting	C₂×C₅×#533	C₂
socle	C₂³×C₅	C₂⁵
prime radical	C₂³×D₂₀	C₂²
hypercenter	C₂×#533	D₅
hypocenter	C₅	C₂×#3501
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#533	C₂	semidirect
2. #10618181	C₂	direct (N × H)
3. C₂×#66064	C₂	semidirect
4. C₂×#66061	C₂	semidirect
5. C₂×#66024	C₂	semidirect
6. C₂×#65968	C₂	semidirect
7. C₂×D₅×C₂²⋊Q₈	C₂	semidirect
8. C₂×#65913	C₂	semidirect
9. C₂×#65913	C₂	semidirect
10. C₂×Q₈×D₂₀	C₂	semidirect
12. C₂×#65853	C₂	semidirect
14. C₂×#65804	C₂	semidirect
15. C₂²×Q₈×D₅	C₂²	semidirect
18. C₅×#533	C₂²	semidirect
19. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₅×#125	C₂²	semidirect
24. C₂×C₄×C₅×Q₈	C₂²	semidirect
25. C₂×C₄×C₅×Q₈	C₂²	semidirect
28. C₂×#4092	C₂²	semidirect
29. C₂×#4092	C₂²	semidirect
35. #66064	C₂²	semidirect
36. #66061	C₂²	semidirect
37. #66024	C₂²	semidirect
38. #65968	C₂²	semidirect
39. D₅×C₂²⋊Q₈	C₂²	semidirect
40. #65913	C₂²	semidirect
41. #65913	C₂²	semidirect
42. Q₈×D₂₀	C₂²	semidirect
44. #65853	C₂²	semidirect
45. C₂×#4043	C₂²	semidirect
46. C₂×#4043	C₂²	semidirect
47. C₂×#4042	C₂²	semidirect
48. C₂×#4042	C₂²	semidirect
49. C₂×#4042	C₂²	semidirect
52. C₂×D₅×C₄⋊C₄	C₂²	semidirect
53. C₂×D₅×C₄⋊C₄	C₂²	semidirect
54. C₂×#4036	C₂²	semidirect
55. C₂×#4034	C₂²	semidirect
65. #65804	C₂²	semidirect
66. C₂×#4016	C₂²	semidirect
67. C₂×#4016	C₂²	semidirect
68. C₂×#4015	C₂²	semidirect
69. C₂×#4015	C₂²	semidirect
70. C₂×#4015	C₂²	semidirect
71. C₂×C₄×Dic₁₀	C₂²	semidirect
72. C₂×C₄×Dic₁₀	C₂²	semidirect
82. C₂×Q₈×D₅	C₂³	semidirect
83. C₂²×D₂₀	Q₈	semidirect
96. C₅×C₄⋊Q₈	C₂³	semidirect
97. C₅×C₄⋊Q₈	C₂³	semidirect
98. C₅×#125	C₂³	semidirect
101. C₄×C₅×Q₈	C₂³	semidirect
102. C₄×C₅×Q₈	C₂³	semidirect
118. #4092	C₂³	semidirect
119. #4092	C₂³	semidirect
141. #4043	C₂³	semidirect
142. #4043	C₂³	semidirect
143. #4042	C₂³	semidirect
144. #4042	C₂³	semidirect
145. #4042	C₂³	semidirect
148. D₅×C₄⋊C₄	C₂³	semidirect
149. D₅×C₄⋊C₄	C₂³	semidirect
150. #4036	C₂³	semidirect
151. #4034	C₂³	semidirect
160. #4016	C₂³	semidirect
161. #4016	C₂³	semidirect
162. #4015	C₂³	semidirect
163. #4015	C₂³	semidirect
164. #4015	C₂³	semidirect
165. C₄×Dic₁₀	C₂³	semidirect
166. C₄×Dic₁₀	C₂³	semidirect
177. C₂×#533	D₅	semidirect
184. C₂³×D₅	C₂×Q₈	semidirect
193. C₂²×C₄×C₅	C₂×Q₈	semidirect
211. C₂×D₂₀	C₂×Q₈	semidirect
212. C₂×D₂₀	C₂×Q₈	semidirect
213. C₂×D₂₀	C₂×Q₈	semidirect
272. #533	C₂×D₅	semidirect
277. C₂×C₄⋊Q₈	C₂×D₅	semidirect
278. C₂×C₄⋊Q₈	C₂×D₅	semidirect
282. C₂×#125	C₂×D₅	semidirect
299. C₂×C₄×Q₈	C₂×D₅	semidirect
300. C₂×C₄×Q₈	C₂×D₅	semidirect
329. C₂²×D₅	C₂²×Q₈	semidirect
342. C₂×C₄×C₅	C₂²×Q₈	semidirect
359. D₂₀	C₂²×Q₈	semidirect
360. D₂₀	C₂²×Q₈	semidirect
394. C₄⋊Q₈	C₂²×D₅	semidirect
395. C₄⋊Q₈	C₂²×D₅	semidirect
399. #125	C₂²×D₅	semidirect
414. C₄×Q₈	C₂²×D₅	semidirect
415. C₄×Q₈	C₂²×D₅	semidirect
523. C₂²×C₄	Q₈×D₅	semidirect
565. C₂×C₅	#3501	semidirect
610. C₂×C₄	C₂×Q₈×D₅	semidirect
620. C₅	C₂×#3501	semidirect
647. C₂	#10618181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#533	2
#10618181	2
C₂×#66064	2
C₂×#66061	2
C₂×#66024	2
C₂×#65968	2
C₂×D₅×C₂²⋊Q₈	2
C₂×#65913	2
C₂×Q₈×D₂₀	2
C₂×#65855	2
C₂×#65853	2
C₂²×C₄×D₂₀	2
C₂×#65804	2
C₂×#3501	5

Subgroups — C2×#10618181 #13007199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10618181 #13007199