Subgroups — C₅×#35014 #11957734

Order 1280.

1978 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2848	C₂	1	2	yes	maximal
4	C₅×#2646	C₂	1	2	yes	maximal, complemented
5	C₅×#2626	C₂	1	2	yes	maximal
6	C₅×#2589	C₂	1	4	yes	maximal, complemented
7	C₅×#2587	C₂	1	4	yes	maximal, complemented
8	C₅×#2497	C₂	1	2	yes	maximal, complemented
9	C₅×#2492	C₂	1	2	yes	maximal, complemented
10	C₅×#2429	C₂	1	2	yes	maximal, complemented
11	C₅×#2423	C₂	1	2	yes	maximal, complemented
12	C₅×#2329	C₂	1	2	yes	maximal, complemented
13	C₅×#2312	C₂	1	2	yes	maximal
14	C₄×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₅×#400	C₂²	1	4	yes	complemented
29	C₅×#400	C₂²	1	4	yes	complemented
30	C₅×#399	C₂²	1	4	yes	—
31	C₅×#398	C₂²	1	4	yes	complemented
32	C₅×#398	C₂²	1	4	yes	complemented
33	C₅×#396	C₂²	1	4	yes	—
34	C₅×#396	C₂²	1	4	yes	—
35	C₅×#393	C₂²	1	4	yes	—
36	C₅×#391	C₂²	1	2	yes	complemented
37	C₅×#391	C₂²	1	4	yes	complemented
38	C₅×#391	C₂²	1	2	yes	complemented
39	C₅×#391	C₂²	1	2	yes	complemented
40	C₅×#389	C₂²	1	2	yes	complemented
41	C₅×#389	C₂²	1	2	yes	complemented
42	C₅×#389	C₂²	1	4	yes	complemented
43	C₅×#389	C₂²	1	2	yes	complemented
44	C₅×#389	C₂²	1	2	yes	complemented
45	C₅×#389	C₂²	1	2	yes	complemented
46	C₅×#388	C₂²	1	4	yes	—
47	C₅×#388	C₂²	1	4	yes	—
48	C₅×#388	C₂²	1	4	yes	—
49	C₅×#388	C₂²	1	4	yes	—
50	C₅×#387	C₂²	1	4	yes	complemented
51	C₅×#387	C₂²	1	4	yes	complemented
52	C₅×#387	C₂²	1	4	yes	complemented
53	C₅×#385	C₂²	1	4	yes	—
54	C₅×#385	C₂²	1	4	yes	—
55	C₅×#385	C₂²	1	4	yes	—
56	C₅×#385	C₂²	1	4	yes	—
57	C₅×#384	C₂²	1	1	yes	characteristic, complemented
58	C₅×#384	C₂²	1	1	yes	characteristic, complemented
59	C₅×#380	C₂²	1	2	yes	—
60	C₅×#380	C₂²	1	2	yes	—
61	C₅×#380	C₂²	1	2	yes	—
62	C₅×#380	C₂²	1	2	yes	—
63	C₅×#380	C₂²	1	2	yes	—
64	C₅×#380	C₂²	1	2	yes	—
65	C₅×#379	C₂²	1	4	yes	—
66	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
68	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₂×C₅×#95	C₂²	1	1	yes	characteristic
74	C₂×C₅×#95	C₂²	1	1	yes	characteristic
75	#35014	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁵×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Q₈	C₂³	1	2	yes	—
78	C₂²×C₅×Q₈	C₂³	1	2	yes	—
79	C₂³×C₄×C₅	—	2	4	no	—
80	C₂³×C₄×C₅	—	4	2	no	—
81	C₂³×C₄×C₅	—	4	2	no	—
82	C₂³×C₄×C₅	C₂³	1	2	yes	—
83	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂³	1	2	yes	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₅×C₄⋊Q₈	—	4	2	no	—
91	C₅×C₄⋊Q₈	—	4	2	no	—
92	C₅×C₂²⋊Q₈	—	2	8	no	—
93	C₅×C₂²⋊Q₈	—	2	8	no	—
94	C₅×C₂²⋊Q₈	—	4	4	no	—
95	C₅×C₂²⋊Q₈	—	4	4	no	—
96	C₄×C₅×Q₈	—	4	4	no	—
97	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	2	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	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
114	C₂×C₅×C₂²⋊C₄	Q₈	1	8	yes	complemented
115	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₄²×C₅	—	4	2	no	—
126	C₂×C₄²×C₅	—	4	2	no	—
127	C₂×C₄²×C₅	C₂³	1	2	yes	—
128	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₅	C₂³	1	2	yes	—
131	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₅	C₂³	1	4	yes	—
134	C₂×C₄²×C₅	C₂³	1	4	yes	—
135	C₅×#95	C₂³	1	2	yes	—
136	C₅×#95	C₂³	1	2	yes	—
137	C₅×#95	C₂³	1	2	yes	—
138	C₅×#95	C₂³	1	2	yes	—
139	C₅×#95	C₂³	1	4	yes	—
140	C₅×#95	C₂³	1	4	yes	—
141	C₅×#95	C₂³	1	4	yes	—
142	C₅×#95	C₂³	1	4	yes	—
143	C₅×#95	C₂³	1	4	yes	—
144	C₅×#95	C₂³	1	4	yes	—
145	C₅×#95	C₂³	1	4	yes	—
146	C₅×#95	C₂³	1	4	yes	—
147	C₅×#95	C₂³	1	4	yes	—
148	C₅×#95	C₂³	1	4	yes	—
149	#2857	C₂×C₅	1	1	yes	characteristic, complemented
150	#2857	C₂×C₅	1	1	yes	characteristic, complemented
151	#2848	C₂×C₅	1	2	yes	—
152	#2646	C₂×C₅	1	2	yes	complemented
153	#2626	C₂×C₅	1	2	yes	—
154	#2589	C₂×C₅	1	4	yes	complemented
155	#2587	C₂×C₅	1	4	yes	complemented
156	#2497	C₂×C₅	1	2	yes	complemented
157	#2492	C₂×C₅	1	2	yes	complemented
158	#2429	C₂×C₅	1	2	yes	complemented
159	#2423	C₂×C₅	1	2	yes	complemented
160	#2329	C₂×C₅	1	2	yes	complemented
161	#2312	C₂×C₅	1	2	yes	—
162	C₄×C₂²⋊Q₈	C₂×C₅	1	2	yes	complemented
163	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
164	C₂⁴×C₅	—	2	2	no	—
165	C₂⁴×C₅	—	2	2	no	—
166	C₂⁴×C₅	—	4	1	no	—
167	C₂⁴×C₅	—	4	1	no	—
168	C₂⁴×C₅	—	4	1	no	—
169	C₂⁴×C₅	—	4	1	no	—
170	C₂⁴×C₅	C₂×Q₈	1	4	yes	—
171	C₂⁴×C₅	C₂⁴	1	2	yes	—
172	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
173	C₂×C₅×Q₈	—	2	4	no	—
174	C₂×C₅×Q₈	—	2	4	no	—
175	C₂×C₅×Q₈	—	2	4	no	—
176	C₂×C₅×Q₈	—	2	4	no	—
177	C₂×C₅×Q₈	—	4	2	no	—
178	C₂×C₅×Q₈	—	4	2	no	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	2	4	no	—
184	C₂²×C₄×C₅	—	2	4	no	—
185	C₂²×C₄×C₅	—	2	4	no	—
186	C₂²×C₄×C₅	—	2	4	no	—
187	C₂²×C₄×C₅	—	4	1	no	—
188	C₂²×C₄×C₅	—	4	1	no	—
189	C₂²×C₄×C₅	—	4	1	no	—
190	C₂²×C₄×C₅	—	4	1	no	—
191	C₂²×C₄×C₅	—	4	2	no	—
192	C₂²×C₄×C₅	—	4	2	no	—
193	C₂²×C₄×C₅	—	4	1	no	—
194	C₂²×C₄×C₅	—	4	1	no	—
195	C₂²×C₄×C₅	—	4	1	no	—
196	C₂²×C₄×C₅	—	4	1	no	—
197	C₂²×C₄×C₅	—	4	1	no	—
198	C₂²×C₄×C₅	—	4	1	no	—
199	C₂²×C₄×C₅	—	4	16	no	—
200	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
201	C₂²×C₄×C₅	C₂×Q₈	1	4	yes	—
202	C₂²×C₄×C₅	#41	1	4	yes	—
203	C₂²×C₄×C₅	#41	1	4	yes	—
204	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
208	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
209	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₅×C₄⋊C₄	—	2	4	no	—
218	C₅×C₄⋊C₄	—	2	4	no	—
219	C₅×C₄⋊C₄	—	2	8	no	—
220	C₅×C₄⋊C₄	—	2	8	no	—
221	C₅×C₄⋊C₄	—	2	4	no	—
222	C₅×C₄⋊C₄	—	2	4	no	—
223	C₅×C₄⋊C₄	—	4	2	no	—
224	C₅×C₄⋊C₄	—	4	2	no	—
225	C₅×C₄⋊C₄	—	4	2	no	—
226	C₅×C₄⋊C₄	—	4	4	no	—
227	C₅×C₄⋊C₄	—	4	4	no	—
228	C₅×C₄⋊C₄	—	4	4	no	—
229	C₅×C₄⋊C₄	—	4	4	no	—
230	C₅×C₄⋊C₄	—	4	2	no	—
231	C₅×C₄⋊C₄	—	4	2	no	—
232	C₅×C₄⋊C₄	—	4	2	no	—
233	C₅×C₂²⋊C₄	—	2	8	no	—
234	C₅×C₂²⋊C₄	—	2	8	no	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	—	2	4	no	—
237	C₅×C₂²⋊C₄	—	4	4	no	—
238	C₅×C₂²⋊C₄	—	4	4	no	—
239	C₅×C₂²⋊C₄	—	4	4	no	—
240	C₅×C₂²⋊C₄	—	4	4	no	—
241	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
242	C₅×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
243	C₄²×C₅	—	2	4	no	—
244	C₄²×C₅	—	2	2	no	—
245	C₄²×C₅	—	2	2	no	—
246	C₄²×C₅	—	4	2	no	—
247	C₄²×C₅	—	4	1	no	—
248	C₄²×C₅	—	4	1	no	—
249	C₄²×C₅	—	4	4	no	—
250	C₄²×C₅	—	4	4	no	—
251	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
258	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
259	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
263	#400	C₂²×C₅	1	4	yes	complemented
264	#400	C₂²×C₅	1	4	yes	complemented
265	#399	C₂²×C₅	1	4	yes	—
266	#398	C₂²×C₅	1	4	yes	complemented
267	#398	C₂²×C₅	1	4	yes	complemented
268	#396	C₂²×C₅	1	4	yes	—
269	#396	C₂²×C₅	1	4	yes	—
270	#393	C₂²×C₅	1	4	yes	—
271	#391	C₂²×C₅	1	4	yes	complemented
272	#391	C₂²×C₅	1	2	yes	complemented
273	#391	C₂²×C₅	1	2	yes	complemented
274	#391	C₂²×C₅	1	2	yes	complemented
275	#389	C₂²×C₅	1	4	yes	complemented
276	#389	C₂²×C₅	1	2	yes	complemented
277	#389	C₂²×C₅	1	2	yes	complemented
278	#389	C₂²×C₅	1	2	yes	complemented
279	#389	C₂²×C₅	1	2	yes	complemented
280	#389	C₂²×C₅	1	2	yes	complemented
281	#388	C₂²×C₅	1	4	yes	—
282	#388	C₂²×C₅	1	4	yes	—
283	#388	C₂²×C₅	1	4	yes	—
284	#388	C₂²×C₅	1	4	yes	—
285	#387	C₂²×C₅	1	4	yes	complemented
286	#387	C₂²×C₅	1	4	yes	complemented
287	#387	C₂²×C₅	1	4	yes	complemented
288	#385	C₂²×C₅	1	4	yes	—
289	#385	C₂²×C₅	1	4	yes	—
290	#385	C₂²×C₅	1	4	yes	—
291	#385	C₂²×C₅	1	4	yes	—
292	#384	C₂²×C₅	1	1	yes	characteristic, complemented
293	#384	C₂²×C₅	1	1	yes	characteristic, complemented
294	#380	C₂²×C₅	1	2	yes	—
295	#380	C₂²×C₅	1	2	yes	—
296	#380	C₂²×C₅	1	2	yes	—
297	#380	C₂²×C₅	1	2	yes	—
298	#380	C₂²×C₅	1	2	yes	—
299	#380	C₂²×C₅	1	2	yes	—
300	#379	C₂²×C₅	1	4	yes	—
301	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
302	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
303	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
305	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
308	C₂×#95	C₂²×C₅	1	1	yes	characteristic
309	C₂×#95	C₂²×C₅	1	1	yes	characteristic
310	C₂³×C₅	—	2	1	no	—
311	C₂³×C₅	—	2	1	no	—
312	C₂³×C₅	—	2	1	no	—
313	C₂³×C₅	—	2	1	no	—
314	C₂³×C₅	—	2	8	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	2	2	no	—
317	C₂³×C₅	—	2	2	no	—
318	C₂³×C₅	—	2	2	no	—
319	C₂³×C₅	—	2	2	no	—
320	C₂³×C₅	—	2	2	no	—
321	C₂³×C₅	—	4	4	no	—
322	C₂³×C₅	—	4	4	no	—
323	C₂³×C₅	—	4	4	no	—
324	C₂³×C₅	—	4	4	no	—
325	C₂³×C₅	—	4	4	no	—
326	C₂³×C₅	—	4	4	no	—
327	C₂³×C₅	C₂²×Q₈	1	4	yes	—
328	C₂³×C₅	C₂²×Q₈	1	2	yes	—
329	C₂³×C₅	C₂×#41	1	2	yes	—
330	C₂³×C₅	C₂×#41	1	2	yes	—
331	C₂³×C₅	C₂⁵	1	1	yes	characteristic
332	C₅×Q₈	—	4	8	no	—
333	C₅×Q₈	—	8	4	no	—
334	C₂×C₄×C₅	—	2	2	no	—
335	C₂×C₄×C₅	—	2	1	no	—
336	C₂×C₄×C₅	—	2	1	no	—
337	C₂×C₄×C₅	—	2	1	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	2	1	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	1	no	—
346	C₂×C₄×C₅	—	2	8	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	4	no	—
349	C₂×C₄×C₅	—	2	4	no	—
350	C₂×C₄×C₅	—	2	4	no	—
351	C₂×C₄×C₅	—	2	4	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	2	4	no	—
355	C₂×C₄×C₅	—	2	4	no	—
356	C₂×C₄×C₅	—	2	4	no	—
357	C₂×C₄×C₅	—	2	4	no	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	4	no	—
361	C₂×C₄×C₅	—	2	4	no	—
362	C₂×C₄×C₅	—	2	4	no	—
363	C₂×C₄×C₅	—	2	4	no	—
364	C₂×C₄×C₅	—	2	2	no	—
365	C₂×C₄×C₅	—	4	4	no	—
366	C₂×C₄×C₅	—	4	4	no	—
367	C₂×C₄×C₅	—	4	4	no	—
368	C₂×C₄×C₅	—	4	8	no	—
369	C₂×C₄×C₅	—	4	4	no	—
370	C₂×C₄×C₅	—	4	4	no	—
371	C₂×C₄×C₅	—	4	8	no	—
372	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
373	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
374	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
375	C₂×C₄×C₅	C₂×#41	1	2	yes	—
376	C₂×C₄×C₅	C₂×#41	1	2	yes	—
377	C₂×C₄×C₅	C₂×#41	1	2	yes	—
378	C₂×C₄×C₅	C₂×#41	1	2	yes	—
379	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
380	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
381	C₂⁵	C₂³×C₅	1	1	yes	characteristic
382	C₂²×Q₈	C₂³×C₅	1	2	yes	—
383	C₂²×Q₈	C₂³×C₅	1	2	yes	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	—	4	2	no	—
386	C₂³×C₄	—	4	2	no	—
387	C₂³×C₄	C₂³×C₅	1	2	yes	—
388	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₅	1	2	yes	—
392	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₄⋊Q₈	—	4	2	no	—
396	C₄⋊Q₈	—	4	2	no	—
397	C₂²⋊Q₈	—	2	8	no	—
398	C₂²⋊Q₈	—	2	8	no	—
399	C₂²⋊Q₈	—	4	4	no	—
400	C₂²⋊Q₈	—	4	4	no	—
401	C₄×Q₈	—	4	4	no	—
402	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
418	C₂×C₂²⋊C₄	—	2	4	no	—
419	C₂×C₂²⋊C₄	C₅×Q₈	1	8	yes	complemented
420	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
430	C₂×C₄²	—	4	2	no	—
431	C₂×C₄²	—	4	2	no	—
432	C₂×C₄²	C₂³×C₅	1	2	yes	—
433	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₅	1	4	yes	—
436	C₂×C₄²	C₂³×C₅	1	2	yes	—
437	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₅	1	4	yes	—
440	#95	C₂³×C₅	1	2	yes	—
441	#95	C₂³×C₅	1	2	yes	—
442	#95	C₂³×C₅	1	2	yes	—
443	#95	C₂³×C₅	1	2	yes	—
444	#95	C₂³×C₅	1	4	yes	—
445	#95	C₂³×C₅	1	4	yes	—
446	#95	C₂³×C₅	1	4	yes	—
447	#95	C₂³×C₅	1	4	yes	—
448	#95	C₂³×C₅	1	4	yes	—
449	#95	C₂³×C₅	1	4	yes	—
450	#95	C₂³×C₅	1	4	yes	—
451	#95	C₂³×C₅	1	4	yes	—
452	#95	C₂³×C₅	1	4	yes	—
453	#95	C₂³×C₅	1	4	yes	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	2	2	no	—
456	C₂²×C₅	—	2	2	no	—
457	C₂²×C₅	—	2	2	no	—
458	C₂²×C₅	—	2	2	no	—
459	C₂²×C₅	—	2	2	no	—
460	C₂²×C₅	—	2	4	no	—
461	C₂²×C₅	—	2	4	no	—
462	C₂²×C₅	—	2	4	no	—
463	C₂²×C₅	—	4	16	no	—
464	C₂²×C₅	—	4	2	no	—
465	C₂²×C₅	—	4	2	no	—
466	C₂²×C₅	—	4	2	no	—
467	C₂²×C₅	—	4	2	no	—
468	C₂²×C₅	#533	1	4	yes	—
469	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
470	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
471	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
472	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
473	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
474	C₂²×C₅	#585	1	1	yes	characteristic
475	C₂²×C₅	#585	1	1	yes	characteristic
476	C₄×C₅	—	2	2	no	—
477	C₄×C₅	—	2	4	no	—
478	C₄×C₅	—	2	2	no	—
479	C₄×C₅	—	2	2	no	—
480	C₄×C₅	—	2	2	no	—
481	C₄×C₅	—	2	2	no	—
482	C₄×C₅	—	4	2	no	—
483	C₄×C₅	—	4	4	no	—
484	C₄×C₅	—	4	4	no	—
485	C₄×C₅	—	4	4	no	—
486	C₄×C₅	—	4	4	no	—
487	C₄×C₅	—	4	2	no	—
488	C₄×C₅	#538	1	4	yes	—
489	C₂⁴	—	2	2	no	—
490	C₂⁴	—	2	2	no	—
491	C₂⁴	—	4	1	no	—
492	C₂⁴	—	4	1	no	—
493	C₂⁴	—	4	1	no	—
494	C₂⁴	—	4	1	no	—
495	C₂⁴	C₂×C₅×Q₈	1	4	yes	—
496	C₂⁴	C₂⁴×C₅	1	2	yes	—
497	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	—	2	4	no	—
500	C₂×Q₈	—	2	4	no	—
501	C₂×Q₈	—	2	4	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	2	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	4	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	—	4	1	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	—	4	1	no	—
519	C₂²×C₄	—	4	1	no	—
520	C₂²×C₄	—	4	1	no	—
521	C₂²×C₄	—	4	1	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	—	4	16	no	—
525	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
526	C₂²×C₄	C₂×C₅×Q₈	1	4	yes	—
527	C₂²×C₄	C₅×#41	1	4	yes	—
528	C₂²×C₄	C₅×#41	1	4	yes	—
529	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
533	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
534	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
535	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	8	no	—
545	C₄⋊C₄	—	2	8	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	2	no	—
553	C₄⋊C₄	—	4	2	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	4	2	no	—
556	C₄⋊C₄	—	4	2	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	2	4	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	4	4	no	—
563	C₂²⋊C₄	—	4	4	no	—
564	C₂²⋊C₄	—	4	4	no	—
565	C₂²⋊C₄	—	4	4	no	—
566	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
567	C₂²⋊C₄	C₂×C₅×Q₈	1	8	yes	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	2	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	4	2	no	—
572	C₄²	—	4	1	no	—
573	C₄²	—	4	1	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	4	no	—
576	C₂×C₅	—	2	4	no	—
577	C₂×C₅	—	4	4	no	—
578	C₂×C₅	C₂×#533	1	1	yes	characteristic
579	C₂×C₅	C₂×#538	1	1	yes	characteristic
580	C₂×C₅	#3455	1	1	yes	characteristic
581	C₂×C₅	#3501	1	1	yes	characteristic
582	C₂×C₅	#3501	1	1	yes	characteristic
583	C₂×C₅	#3505	1	1	yes	characteristic
584	C₂×C₅	#3506	1	1	yes	characteristic
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	8	no	—
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	4	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	4	no	—
602	C₂³	C₂²×C₅×Q₈	1	4	yes	—
603	C₂³	C₂²×C₅×Q₈	1	2	yes	—
604	C₂³	C₂×C₅×#41	1	2	yes	—
605	C₂³	C₂×C₅×#41	1	2	yes	—
606	C₂³	C₂⁵×C₅	1	1	yes	characteristic
607	Q₈	—	4	8	no	—
608	Q₈	—	8	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	4	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	4	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	4	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	8	no	—
647	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
648	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
649	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
650	C₂×C₄	C₂×C₅×#41	1	2	yes	—
651	C₂×C₄	C₂×C₅×#41	1	2	yes	—
652	C₂×C₄	C₂×C₅×#41	1	2	yes	—
653	C₂×C₄	C₂×C₅×#41	1	2	yes	—
654	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
655	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
656	C₅	#35014	1	1	yes	characteristic, direct product factor, Sylow
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	4	16	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	C₅×#533	1	4	yes	—
672	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
673	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
674	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
675	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂²	C₅×#585	1	1	yes	characteristic
678	C₂²	C₅×#585	1	1	yes	characteristic
679	C₄	—	2	2	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	4	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	4	no	—
691	C₄	C₅×#538	1	4	yes	—
692	C₂	—	2	4	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂×C₅×#533	1	1	yes	characteristic
695	C₂	C₂×C₅×#538	1	1	yes	characteristic
696	C₂	C₅×#3455	1	1	yes	characteristic
697	C₂	C₅×#3501	1	1	yes	characteristic
698	C₂	C₅×#3501	1	1	yes	characteristic
699	C₂	C₅×#3505	1	1	yes	characteristic
700	C₂	C₅×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂⁵×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#2857	C₂	semidirect
2. C₅×#2857	C₂	semidirect
4. C₅×#2646	C₂	semidirect
6. C₅×#2589	C₂	semidirect
7. C₅×#2587	C₂	semidirect
8. C₅×#2497	C₂	semidirect
9. C₅×#2492	C₂	semidirect
10. C₅×#2429	C₂	semidirect
11. C₅×#2423	C₂	semidirect
12. C₅×#2329	C₂	semidirect
14. C₄×C₅×C₂²⋊Q₈	C₂	semidirect
17. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₄×C₅×Q₈	C₂²	semidirect
28. C₅×#400	C₂²	semidirect
29. C₅×#400	C₂²	semidirect
31. C₅×#398	C₂²	semidirect
32. C₅×#398	C₂²	semidirect
36. C₅×#391	C₂²	semidirect
37. C₅×#391	C₂²	semidirect
38. C₅×#391	C₂²	semidirect
39. C₅×#391	C₂²	semidirect
40. C₅×#389	C₂²	semidirect
41. C₅×#389	C₂²	semidirect
42. C₅×#389	C₂²	semidirect
43. C₅×#389	C₂²	semidirect
44. C₅×#389	C₂²	semidirect
45. C₅×#389	C₂²	semidirect
50. C₅×#387	C₂²	semidirect
51. C₅×#387	C₂²	semidirect
52. C₅×#387	C₂²	semidirect
57. C₅×#384	C₂²	semidirect
58. C₅×#384	C₂²	semidirect
66. C₄×C₅×C₄⋊C₄	C₂²	semidirect
67. C₄×C₅×C₄⋊C₄	C₂²	semidirect
75. #35014	C₅	direct (N × H)
114. C₂×C₅×C₂²⋊C₄	Q₈	semidirect
149. #2857	C₂×C₅	semidirect
150. #2857	C₂×C₅	semidirect
152. #2646	C₂×C₅	semidirect
154. #2589	C₂×C₅	semidirect
155. #2587	C₂×C₅	semidirect
156. #2497	C₂×C₅	semidirect
157. #2492	C₂×C₅	semidirect
158. #2429	C₂×C₅	semidirect
159. #2423	C₂×C₅	semidirect
160. #2329	C₂×C₅	semidirect
162. C₄×C₂²⋊Q₈	C₂×C₅	semidirect
252. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
253. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
258. C₂×C₄×Q₈	C₂²×C₅	semidirect
263. #400	C₂²×C₅	semidirect
264. #400	C₂²×C₅	semidirect
266. #398	C₂²×C₅	semidirect
267. #398	C₂²×C₅	semidirect
271. #391	C₂²×C₅	semidirect
272. #391	C₂²×C₅	semidirect
273. #391	C₂²×C₅	semidirect
274. #391	C₂²×C₅	semidirect
275. #389	C₂²×C₅	semidirect
276. #389	C₂²×C₅	semidirect
277. #389	C₂²×C₅	semidirect
278. #389	C₂²×C₅	semidirect
279. #389	C₂²×C₅	semidirect
280. #389	C₂²×C₅	semidirect
285. #387	C₂²×C₅	semidirect
286. #387	C₂²×C₅	semidirect
287. #387	C₂²×C₅	semidirect
292. #384	C₂²×C₅	semidirect
293. #384	C₂²×C₅	semidirect
301. C₄×C₄⋊C₄	C₂²×C₅	semidirect
302. C₄×C₄⋊C₄	C₂²×C₅	semidirect
419. C₂×C₂²⋊C₄	C₅×Q₈	semidirect
656. C₅	#35014	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2857	2
C₅×#2848	2
C₅×#2646	2
C₅×#2626	2
C₅×#2589	2
C₅×#2587	2
C₅×#2497	2
C₅×#2492	2
C₅×#2429	2
C₅×#2423	2
C₅×#2329	2
C₅×#2312	2
C₄×C₅×C₂²⋊Q₈	2
C₂×C₄×C₅×C₂²⋊C₄	2
#35014	5

Subgroups — C5×#35014 #11957734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35014 #11957734