Subgroups — C₅×#34951 #11957671

Order 1280.

1692 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2585	C₂	1	4	yes	maximal
2	C₅×#2582	C₂	1	1	yes	maximal, characteristic
3	C₅×#2568	C₂	1	1	yes	maximal, characteristic
4	C₅×#2552	C₂	1	1	yes	maximal, characteristic
5	C₅×#2546	C₂	1	1	yes	maximal, characteristic
6	C₅×#2511	C₂	1	2	yes	maximal
7	C₅×#2509	C₂	1	2	yes	maximal
8	C₅×#2453	C₂	1	2	yes	maximal
9	C₅×#2446	C₂	1	2	yes	maximal
10	C₅×#2402	C₂	1	4	yes	maximal
11	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
12	C₄×C₅×C₄⋊Q₈	C₂	1	2	yes	maximal
13	C₄×C₅×#125	C₂	1	2	yes	maximal
14	C₅×#2295	C₂	1	2	yes	maximal
15	C₅×#2295	C₂	1	2	yes	maximal
16	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
17	C₄²×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
18	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₅×#125	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₅×#400	C₂²	1	4	yes	—
29	C₅×#400	C₂²	1	4	yes	—
30	C₅×#400	C₂²	1	4	yes	—
31	C₅×#400	C₂²	1	4	yes	—
32	C₅×#398	C₂²	1	4	yes	—
33	C₅×#398	C₂²	1	4	yes	—
34	C₅×#398	C₂²	1	4	yes	—
35	C₅×#398	C₂²	1	4	yes	—
36	C₅×#391	C₂²	1	2	yes	—
37	C₅×#391	C₂²	1	2	yes	—
38	C₅×#391	C₂²	1	2	yes	—
39	C₅×#391	C₂²	1	2	yes	—
40	C₅×#391	C₂²	1	2	yes	—
41	C₅×#391	C₂²	1	2	yes	—
42	C₅×#391	C₂²	1	2	yes	—
43	C₅×#389	C₂²	1	2	yes	—
44	C₅×#389	C₂²	1	2	yes	—
45	C₅×#389	C₂²	1	2	yes	—
46	C₅×#389	C₂²	1	4	yes	—
47	C₅×#389	C₂²	1	2	yes	—
48	C₅×#389	C₂²	1	2	yes	—
49	C₅×#389	C₂²	1	2	yes	—
50	C₅×#389	C₂²	1	2	yes	—
51	C₅×#389	C₂²	1	2	yes	—
52	C₅×#389	C₂²	1	4	yes	—
53	C₅×#387	C₂²	1	4	yes	—
54	C₅×#387	C₂²	1	4	yes	—
55	C₅×#387	C₂²	1	4	yes	—
56	C₅×#387	C₂²	1	4	yes	—
57	C₅×#387	C₂²	1	4	yes	—
58	C₅×#387	C₂²	1	4	yes	—
59	C₅×#384	C₂²	1	2	yes	—
60	C₅×#384	C₂²	1	1	yes	characteristic
61	C₅×#382	C₂²	1	2	yes	—
62	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
63	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
75	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
76	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
77	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
78	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
79	C₅×#376	C₂²	1	4	yes	—
80	C₄³×C₅	C₂²	1	1	yes	characteristic
81	C₄³×C₅	C₂²	1	2	yes	—
82	C₄³×C₅	C₂²	1	2	yes	—
83	#34951	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₅×Q₈	C₂³	1	2	yes	—
85	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	—	2	8	no	—
88	C₅×C₄⋊Q₈	—	2	4	no	—
89	C₅×#125	—	2	8	no	—
90	C₄×C₅×Q₈	—	2	4	no	—
91	C₄×C₅×Q₈	—	2	4	no	—
92	C₄×C₅×Q₈	—	2	4	no	—
93	C₄×C₅×Q₈	—	2	8	no	—
94	C₄×C₅×Q₈	—	2	4	no	—
95	C₄×C₅×Q₈	—	2	4	no	—
96	C₄×C₅×Q₈	Q₈	1	8	yes	complemented
97	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₅×C₄⋊C₄	C₂³	1	2	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	4	yes	—
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	4	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	2	yes	—
113	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅	C₂³	1	2	yes	—
124	C₂×C₄²×C₅	C₂³	1	2	yes	—
125	C₂×C₄²×C₅	C₂³	1	2	yes	—
126	C₂×C₄²×C₅	C₂³	1	2	yes	—
127	C₂×C₄²×C₅	C₂³	1	2	yes	—
128	C₂×C₄²×C₅	C₂³	1	2	yes	—
129	C₂×C₄²×C₅	C₂³	1	2	yes	—
130	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₅	C₂³	1	2	yes	—
132	C₂×C₄²×C₅	C₂³	1	2	yes	—
133	C₂×C₄²×C₅	C₂³	1	4	yes	—
134	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₅	C₂³	1	2	yes	—
136	C₂×C₄²×C₅	C₂³	1	2	yes	—
137	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₅	C₂³	1	2	yes	—
139	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
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	2	yes	—
146	C₅×#95	C₂³	1	2	yes	—
147	C₅×#95	C₂³	1	2	yes	—
148	C₅×#95	C₂³	1	2	yes	—
149	C₅×#95	C₂³	1	2	yes	—
150	C₅×#95	C₂³	1	2	yes	—
151	C₅×#95	C₂³	1	4	yes	—
152	C₅×#95	C₂³	1	4	yes	—
153	C₅×#95	C₂³	1	4	yes	—
154	C₅×#95	C₂³	1	4	yes	—
155	C₅×#95	C₂³	1	4	yes	—
156	C₅×#95	C₂³	1	4	yes	—
157	C₅×#95	C₂³	1	4	yes	—
158	C₅×#95	C₂³	1	4	yes	—
159	#2585	C₂×C₅	1	4	yes	—
160	#2582	C₂×C₅	1	1	yes	characteristic
161	#2568	C₂×C₅	1	1	yes	characteristic
162	#2552	C₂×C₅	1	1	yes	characteristic
163	#2546	C₂×C₅	1	1	yes	characteristic
164	#2511	C₂×C₅	1	2	yes	—
165	#2509	C₂×C₅	1	2	yes	—
166	#2453	C₂×C₅	1	2	yes	—
167	#2446	C₂×C₅	1	2	yes	—
168	#2402	C₂×C₅	1	4	yes	—
169	C₄×C₄⋊Q₈	C₂×C₅	1	2	yes	—
170	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
171	C₄×#125	C₂×C₅	1	2	yes	—
172	#2295	C₂×C₅	1	2	yes	—
173	#2295	C₂×C₅	1	2	yes	—
174	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic
175	C₄²×Q₈	C₂×C₅	1	1	yes	characteristic
176	C₂×C₅×Q₈	—	2	2	no	—
177	C₂×C₅×Q₈	—	2	2	no	—
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	—	2	2	no	—
180	C₂×C₅×Q₈	—	2	4	no	—
181	C₂×C₅×Q₈	—	2	4	no	—
182	C₂×C₅×Q₈	—	2	4	no	—
183	C₂×C₅×Q₈	C₂×Q₈	1	4	yes	—
184	C₂×C₅×Q₈	#41	1	4	yes	—
185	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
202	C₅×C₄⋊C₄	—	2	4	no	—
203	C₅×C₄⋊C₄	—	2	4	no	—
204	C₅×C₄⋊C₄	—	2	4	no	—
205	C₅×C₄⋊C₄	—	2	4	no	—
206	C₅×C₄⋊C₄	—	2	4	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₄⋊C₄	—	2	2	no	—
212	C₅×C₄⋊C₄	—	2	8	no	—
213	C₅×C₄⋊C₄	—	2	8	no	—
214	C₅×C₄⋊C₄	—	2	8	no	—
215	C₅×C₄⋊C₄	—	2	4	no	—
216	C₅×C₄⋊C₄	—	2	8	no	—
217	C₅×C₄⋊C₄	—	2	8	no	—
218	C₅×C₄⋊C₄	—	2	4	no	—
219	C₅×C₄⋊C₄	—	2	4	no	—
220	C₅×C₄⋊C₄	—	4	4	no	—
221	C₅×C₄⋊C₄	—	4	2	no	—
222	C₅×C₄⋊C₄	—	4	4	no	—
223	C₅×C₄⋊C₄	C₂×Q₈	1	8	yes	—
224	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
225	C₅×C₄⋊C₄	#41	1	4	yes	—
226	C₄²×C₅	—	2	4	no	—
227	C₄²×C₅	—	2	4	no	—
228	C₄²×C₅	—	2	2	no	—
229	C₄²×C₅	—	2	2	no	—
230	C₄²×C₅	—	2	4	no	—
231	C₄²×C₅	—	2	4	no	—
232	C₄²×C₅	—	2	4	no	—
233	C₄²×C₅	—	2	8	no	—
234	C₄²×C₅	—	2	4	no	—
235	C₄²×C₅	—	2	4	no	—
236	C₄²×C₅	—	2	2	no	—
237	C₄²×C₅	—	2	4	no	—
238	C₄²×C₅	—	2	4	no	—
239	C₄²×C₅	—	4	1	no	—
240	C₄²×C₅	—	4	2	no	—
241	C₄²×C₅	—	4	2	no	—
242	C₄²×C₅	C₂×Q₈	1	8	yes	—
243	C₄²×C₅	C₂×Q₈	1	4	yes	—
244	C₄²×C₅	#41	1	4	yes	—
245	C₄²×C₅	#41	1	4	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
248	C₂×#125	C₂²×C₅	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
256	#400	C₂²×C₅	1	4	yes	—
257	#400	C₂²×C₅	1	4	yes	—
258	#400	C₂²×C₅	1	4	yes	—
259	#400	C₂²×C₅	1	4	yes	—
260	#398	C₂²×C₅	1	4	yes	—
261	#398	C₂²×C₅	1	4	yes	—
262	#398	C₂²×C₅	1	4	yes	—
263	#398	C₂²×C₅	1	4	yes	—
264	#391	C₂²×C₅	1	2	yes	—
265	#391	C₂²×C₅	1	2	yes	—
266	#391	C₂²×C₅	1	2	yes	—
267	#391	C₂²×C₅	1	2	yes	—
268	#391	C₂²×C₅	1	2	yes	—
269	#391	C₂²×C₅	1	2	yes	—
270	#391	C₂²×C₅	1	2	yes	—
271	#389	C₂²×C₅	1	2	yes	—
272	#389	C₂²×C₅	1	2	yes	—
273	#389	C₂²×C₅	1	2	yes	—
274	#389	C₂²×C₅	1	4	yes	—
275	#389	C₂²×C₅	1	4	yes	—
276	#389	C₂²×C₅	1	2	yes	—
277	#389	C₂²×C₅	1	2	yes	—
278	#389	C₂²×C₅	1	2	yes	—
279	#389	C₂²×C₅	1	2	yes	—
280	#389	C₂²×C₅	1	2	yes	—
281	#387	C₂²×C₅	1	4	yes	—
282	#387	C₂²×C₅	1	4	yes	—
283	#387	C₂²×C₅	1	4	yes	—
284	#387	C₂²×C₅	1	4	yes	—
285	#387	C₂²×C₅	1	4	yes	—
286	#387	C₂²×C₅	1	4	yes	—
287	#384	C₂²×C₅	1	1	yes	characteristic
288	#384	C₂²×C₅	1	2	yes	—
289	#382	C₂²×C₅	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
292	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
293	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
294	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
295	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
296	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
298	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
299	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
301	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
303	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
304	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
307	#376	C₂²×C₅	1	4	yes	—
308	C₄³	C₂²×C₅	1	2	yes	—
309	C₄³	C₂²×C₅	1	1	yes	characteristic
310	C₄³	C₂²×C₅	1	2	yes	—
311	C₂³×C₅	C₂⁵	1	1	yes	characteristic
312	C₅×Q₈	—	2	8	no	—
313	C₅×Q₈	—	2	8	no	—
314	C₅×Q₈	—	4	8	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	4	no	—
333	C₂×C₄×C₅	—	2	2	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	2	no	—
338	C₂×C₄×C₅	—	2	4	no	—
339	C₂×C₄×C₅	—	2	4	no	—
340	C₂×C₄×C₅	—	2	4	no	—
341	C₂×C₄×C₅	—	2	4	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	2	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	2	4	no	—
350	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
351	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
352	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
353	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
354	C₂×C₄×C₅	C₂²×Q₈	1	2	yes	—
355	C₂×C₄×C₅	C₂×#41	1	4	yes	—
356	C₂×C₄×C₅	C₂×#41	1	4	yes	—
357	C₂×C₄×C₅	C₂×#41	1	2	yes	—
358	C₂×C₄×C₅	C₂×#41	1	2	yes	—
359	C₂×C₄×C₅	C₂×#41	1	2	yes	—
360	C₂×C₄×C₅	C₂×#41	1	2	yes	—
361	C₂×C₄×C₅	C₂×#41	1	2	yes	—
362	C₂×C₄×C₅	C₂×#41	1	2	yes	—
363	C₂×C₄×C₅	C₂×#41	1	2	yes	—
364	C₂×C₄×C₅	C₂×#41	1	2	yes	—
365	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
366	C₂²×Q₈	C₂³×C₅	1	2	yes	—
367	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
368	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₄⋊Q₈	—	2	8	no	—
370	C₄⋊Q₈	—	2	4	no	—
371	#125	—	2	8	no	—
372	C₄×Q₈	—	2	4	no	—
373	C₄×Q₈	—	2	4	no	—
374	C₄×Q₈	—	2	4	no	—
375	C₄×Q₈	—	2	8	no	—
376	C₄×Q₈	—	2	4	no	—
377	C₄×Q₈	—	2	4	no	—
378	C₄×Q₈	C₅×Q₈	1	8	yes	complemented
379	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
395	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
397	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₅	1	2	yes	—
404	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
405	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₅	1	2	yes	—
407	C₂×C₄²	C₂³×C₅	1	2	yes	—
408	C₂×C₄²	C₂³×C₅	1	2	yes	—
409	C₂×C₄²	C₂³×C₅	1	2	yes	—
410	C₂×C₄²	C₂³×C₅	1	4	yes	—
411	C₂×C₄²	C₂³×C₅	1	2	yes	—
412	C₂×C₄²	C₂³×C₅	1	2	yes	—
413	C₂×C₄²	C₂³×C₅	1	2	yes	—
414	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₅	1	2	yes	—
416	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
417	C₂×C₄²	C₂³×C₅	1	2	yes	—
418	C₂×C₄²	C₂³×C₅	1	2	yes	—
419	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₅	1	2	yes	—
421	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
423	#95	C₂³×C₅	1	4	yes	—
424	#95	C₂³×C₅	1	4	yes	—
425	#95	C₂³×C₅	1	4	yes	—
426	#95	C₂³×C₅	1	4	yes	—
427	#95	C₂³×C₅	1	2	yes	—
428	#95	C₂³×C₅	1	2	yes	—
429	#95	C₂³×C₅	1	2	yes	—
430	#95	C₂³×C₅	1	2	yes	—
431	#95	C₂³×C₅	1	2	yes	—
432	#95	C₂³×C₅	1	2	yes	—
433	#95	C₂³×C₅	1	4	yes	—
434	#95	C₂³×C₅	1	4	yes	—
435	#95	C₂³×C₅	1	4	yes	—
436	#95	C₂³×C₅	1	4	yes	—
437	#95	C₂³×C₅	1	4	yes	—
438	#95	C₂³×C₅	1	4	yes	—
439	#95	C₂³×C₅	1	4	yes	—
440	#95	C₂³×C₅	1	4	yes	—
441	C₂²×C₅	C₂³×Q₈	1	1	yes	characteristic
442	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
443	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
444	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	C₂²×C₅	#585	1	1	yes	characteristic
448	C₄×C₅	—	2	4	no	—
449	C₄×C₅	—	2	4	no	—
450	C₄×C₅	—	2	2	no	—
451	C₄×C₅	—	2	2	no	—
452	C₄×C₅	—	2	4	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	4	no	—
455	C₄×C₅	—	4	4	no	—
456	C₄×C₅	—	4	2	no	—
457	C₄×C₅	—	4	2	no	—
458	C₄×C₅	—	4	2	no	—
459	C₄×C₅	—	4	4	no	—
460	C₄×C₅	—	4	1	no	—
461	C₄×C₅	—	4	2	no	—
462	C₄×C₅	#529	1	4	yes	—
463	C₄×C₅	#533	1	4	yes	—
464	C₄×C₅	#557	1	4	yes	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	4	no	—
470	C₂×Q₈	—	2	4	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	C₂×C₅×Q₈	1	4	yes	—
473	C₂×Q₈	C₅×#41	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
475	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	8	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	2	8	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	4	4	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	4	no	—
512	C₄⋊C₄	C₂×C₅×Q₈	1	8	yes	—
513	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
514	C₄⋊C₄	C₅×#41	1	4	yes	—
515	C₄²	—	2	4	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	4	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	8	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	4	1	no	—
529	C₄²	—	4	2	no	—
530	C₄²	—	4	2	no	—
531	C₄²	C₂×C₅×Q₈	1	8	yes	—
532	C₄²	C₂×C₅×Q₈	1	4	yes	—
533	C₄²	C₅×#41	1	4	yes	—
534	C₄²	C₅×#41	1	4	yes	—
535	C₂×C₅	C₂×#529	1	1	yes	characteristic
536	C₂×C₅	C₂×#533	1	1	yes	characteristic
537	C₂×C₅	#3461	1	1	yes	characteristic
538	C₂×C₅	C₂×#557	1	1	yes	characteristic
539	C₂×C₅	Q₈×#41	1	1	yes	characteristic
540	C₂×C₅	#3480	1	1	yes	characteristic
541	C₂×C₅	#3482	1	1	yes	characteristic
542	C₂³	C₂⁵×C₅	1	1	yes	characteristic
543	Q₈	—	2	8	no	—
544	Q₈	—	2	8	no	—
545	Q₈	—	4	8	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
582	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
583	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
584	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
585	C₂×C₄	C₂²×C₅×Q₈	1	2	yes	—
586	C₂×C₄	C₂×C₅×#41	1	4	yes	—
587	C₂×C₄	C₂×C₅×#41	1	4	yes	—
588	C₂×C₄	C₂×C₅×#41	1	2	yes	—
589	C₂×C₄	C₂×C₅×#41	1	2	yes	—
590	C₂×C₄	C₂×C₅×#41	1	2	yes	—
591	C₂×C₄	C₂×C₅×#41	1	2	yes	—
592	C₂×C₄	C₂×C₅×#41	1	2	yes	—
593	C₂×C₄	C₂×C₅×#41	1	2	yes	—
594	C₂×C₄	C₂×C₅×#41	1	2	yes	—
595	C₂×C₄	C₂×C₅×#41	1	2	yes	—
596	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
597	C₅	#34951	1	1	yes	characteristic, direct product factor, Sylow
598	C₂²	C₂³×C₅×Q₈	1	1	yes	characteristic
599	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
600	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
601	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
602	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
603	C₂²	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
604	C₂²	C₅×#585	1	1	yes	characteristic
605	C₄	—	2	4	no	—
606	C₄	—	2	4	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	4	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	4	no	—
612	C₄	—	4	4	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	2	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	4	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	2	no	—
619	C₄	C₅×#529	1	4	yes	—
620	C₄	C₅×#533	1	4	yes	—
621	C₄	C₅×#557	1	4	yes	—
622	C₂	C₂×C₅×#529	1	1	yes	characteristic
623	C₂	C₂×C₅×#533	1	1	yes	characteristic
624	C₂	C₅×#3461	1	1	yes	characteristic
625	C₂	C₂×C₅×#557	1	1	yes	characteristic
626	C₂	C₅×Q₈×#41	1	1	yes	characteristic
627	C₂	C₅×#3480	1	1	yes	characteristic
628	C₂	C₅×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
socle, prime radical	C₂³×C₅	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
83. #34951	C₅	direct (N × H)
96. C₄×C₅×Q₈	Q₈	semidirect
378. C₄×Q₈	C₅×Q₈	semidirect
597. C₅	#34951	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×#2585	2
C₅×#2582	2
C₅×#2568	2
C₅×#2552	2
C₅×#2546	2
C₅×#2511	2
C₅×#2509	2
C₅×#2453	2
C₅×#2446	2
C₅×#2402	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#125	2
C₅×#2295	2
C₄²×C₅×Q₈	2
#34951	5

Subgroups — C5×#34951 #11957671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34951 #11957671