Subgroups — C₅×#3563 #10619348

Order 640.

912 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#564	C₂	1	2	yes	maximal, complemented
2	C₅×#563	C₂	1	2	yes	maximal, complemented
3	C₅×#557	C₂	1	2	yes	maximal, complemented
4	C₅×#554	C₂	1	2	yes	maximal, complemented
5	C₅×#552	C₂	1	4	yes	maximal, complemented
6	C₅×#552	C₂	1	2	yes	maximal, complemented
7	C₅×#552	C₂	1	2	yes	maximal, complemented
8	C₅×#544	C₂	1	2	yes	maximal, complemented
9	C₅×#544	C₂	1	2	yes	maximal, complemented
10	C₅×#541	C₂	1	2	yes	maximal, complemented
11	C₅×#541	C₂	1	4	yes	maximal, complemented
12	C₅×#539	C₂	1	2	yes	maximal
13	C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#529	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₅×C₄⋊Q₈	C₂²	1	4	yes	—
19	C₅×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₅×C₄⋊Q₈	C₂²	1	4	yes	—
21	C₅×#126	C₂²	1	2	yes	—
22	C₅×#126	C₂²	1	4	yes	—
23	C₅×#126	C₂²	1	4	yes	—
24	C₅×#126	C₂²	1	4	yes	—
25	C₅×#126	C₂²	1	4	yes	—
26	C₅×#125	C₂²	1	2	yes	—
27	C₅×#125	C₂²	1	2	yes	—
28	C₅×#125	C₂²	1	2	yes	—
29	C₅×#125	C₂²	1	2	yes	—
30	C₅×#125	C₂²	1	1	yes	characteristic
31	C₅×#125	C₂²	1	2	yes	—
32	C₅×#125	C₂²	1	4	yes	—
33	C₅×#125	C₂²	1	4	yes	—
34	C₅×#125	C₂²	1	4	yes	—
35	C₅×#125	C₂²	1	4	yes	—
36	C₅×#125	C₂²	1	4	yes	—
37	C₅×#125	C₂²	1	4	yes	—
38	C₅×#125	C₂²	1	2	yes	—
39	C₅×#125	C₂²	1	4	yes	—
40	C₅×#125	C₂²	1	4	yes	—
41	C₅×#124	C₂²	1	1	yes	characteristic
42	C₅×#123	C₂²	1	2	yes	—
43	C₅×#123	C₂²	1	4	yes	—
44	C₅×#123	C₂²	1	4	yes	—
45	C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
47	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
48	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
49	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
52	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
53	C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
54	C₅×#121	C₂²	1	1	yes	characteristic
55	C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
56	C₄×C₅×Q₈	C₂²	1	2	yes	—
57	C₄×C₅×Q₈	C₂²	1	2	yes	—
58	C₄×C₅×Q₈	C₂²	1	4	yes	—
59	C₄×C₅×Q₈	C₂²	1	2	yes	—
60	C₄×C₅×Q₈	C₂²	1	2	yes	—
61	C₄×C₅×D₄	C₂²	1	1	yes	characteristic
62	C₄×C₅×D₄	C₂²	1	2	yes	—
63	C₄×C₅×D₄	C₂²	1	4	yes	—
64	C₅×#117	C₂²	1	2	yes	—
65	C₅×#117	C₂²	1	2	yes	—
66	C₅×#117	C₂²	1	4	yes	—
67	C₅×#117	C₂²	1	2	yes	—
68	C₅×#117	C₂²	1	4	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
72	C₂×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
73	C₂×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₂×C₄²×C₅	C₂²	1	1	yes	characteristic
75	#3563	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×C₅×Q₈	C₂³	1	2	yes	—
77	C₂×C₅×Q₈	C₂³	1	4	yes	—
78	C₂×C₅×Q₈	C₂³	1	2	yes	—
79	C₂×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₅×D₄	C₂³	1	2	yes	—
81	C₂×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂³	1	2	yes	—
85	C₂²×C₄×C₅	C₂³	1	2	yes	—
86	C₂²×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂³	1	2	yes	—
88	C₂²×C₄×C₅	C₂³	1	4	yes	—
89	C₅×C₄⋊C₄	C₂³	1	2	yes	—
90	C₅×C₄⋊C₄	C₂³	1	2	yes	—
91	C₅×C₄⋊C₄	C₂³	1	2	yes	—
92	C₅×C₄⋊C₄	C₂³	1	4	yes	—
93	C₅×C₄⋊C₄	C₂³	1	2	yes	—
94	C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₅×C₄⋊C₄	C₂³	1	4	yes	—
96	C₅×C₄⋊C₄	C₂³	1	4	yes	—
97	C₅×C₄⋊C₄	C₂³	1	4	yes	—
98	C₅×C₄⋊C₄	C₂³	1	2	yes	—
99	C₅×C₄⋊C₄	C₂³	1	4	yes	—
100	C₅×C₄⋊C₄	C₂³	1	2	yes	—
101	C₅×C₄⋊C₄	C₂³	1	4	yes	—
102	C₅×C₄⋊C₄	C₂³	1	2	yes	—
103	C₅×C₄⋊C₄	C₂³	1	4	yes	—
104	C₅×C₄⋊C₄	C₂³	1	2	yes	—
105	C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₅×C₄⋊C₄	C₂³	1	2	yes	—
110	C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₅×C₄⋊C₄	C₂³	1	4	yes	—
112	C₅×C₄⋊C₄	C₂³	1	4	yes	—
113	C₅×C₄⋊C₄	C₂³	1	4	yes	—
114	C₅×C₄⋊C₄	C₂³	1	4	yes	—
115	C₅×C₄⋊C₄	C₂³	1	2	yes	—
116	C₅×C₄⋊C₄	C₂³	1	4	yes	—
117	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₅×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₅×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₄²×C₅	C₂³	1	1	yes	characteristic
127	C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₄²×C₅	C₂³	1	1	yes	characteristic
129	C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₄²×C₅	C₂³	1	4	yes	—
131	C₄²×C₅	C₂³	1	4	yes	—
132	C₄²×C₅	C₂³	1	2	yes	—
133	C₄²×C₅	C₂³	1	4	yes	—
134	C₄²×C₅	C₂³	1	4	yes	—
135	#564	C₂×C₅	1	2	yes	complemented
136	#563	C₂×C₅	1	2	yes	complemented
137	#557	C₂×C₅	1	2	yes	complemented
138	#554	C₂×C₅	1	2	yes	complemented
139	#552	C₂×C₅	1	4	yes	complemented
140	#552	C₂×C₅	1	2	yes	complemented
141	#552	C₂×C₅	1	2	yes	complemented
142	#544	C₂×C₅	1	2	yes	complemented
143	#544	C₂×C₅	1	2	yes	complemented
144	#541	C₂×C₅	1	2	yes	complemented
145	#541	C₂×C₅	1	4	yes	complemented
146	#539	C₂×C₅	1	2	yes	—
147	#533	C₂×C₅	1	1	yes	characteristic, complemented
148	#529	C₂×C₅	1	1	yes	characteristic
149	C₂×#125	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂³×C₅	C₂⁴	1	2	yes	—
151	C₂³×C₅	C₂⁴	1	1	yes	characteristic
152	C₅×Q₈	—	2	4	no	—
153	C₅×Q₈	—	4	4	no	—
154	C₅×Q₈	—	4	1	no	—
155	C₅×Q₈	—	4	2	no	—
156	C₅×D₄	—	2	4	no	—
157	C₅×D₄	—	4	1	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	4	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	4	no	—
162	C₂×C₄×C₅	—	4	2	no	—
163	C₂×C₄×C₅	—	4	4	no	—
164	C₂×C₄×C₅	—	4	1	no	—
165	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₄×C₅	C₂⁴	1	2	yes	—
168	C₂×C₄×C₅	C₂⁴	1	2	yes	—
169	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂⁴	1	2	yes	—
172	C₂×C₄×C₅	C₂⁴	1	4	yes	—
173	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂⁴	1	4	yes	—
175	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂⁴	1	4	yes	—
177	C₂×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₄⋊Q₈	C₂²×C₅	1	4	yes	—
181	C₄⋊Q₈	C₂²×C₅	1	2	yes	—
182	C₄⋊Q₈	C₂²×C₅	1	4	yes	—
183	#126	C₂²×C₅	1	2	yes	—
184	#126	C₂²×C₅	1	4	yes	—
185	#126	C₂²×C₅	1	4	yes	—
186	#126	C₂²×C₅	1	4	yes	—
187	#126	C₂²×C₅	1	4	yes	—
188	#125	C₂²×C₅	1	2	yes	—
189	#125	C₂²×C₅	1	2	yes	—
190	#125	C₂²×C₅	1	2	yes	—
191	#125	C₂²×C₅	1	2	yes	—
192	#125	C₂²×C₅	1	1	yes	characteristic
193	#125	C₂²×C₅	1	2	yes	—
194	#125	C₂²×C₅	1	4	yes	—
195	#125	C₂²×C₅	1	4	yes	—
196	#125	C₂²×C₅	1	4	yes	—
197	#125	C₂²×C₅	1	4	yes	—
198	#125	C₂²×C₅	1	4	yes	—
199	#125	C₂²×C₅	1	4	yes	—
200	#125	C₂²×C₅	1	2	yes	—
201	#125	C₂²×C₅	1	4	yes	—
202	#125	C₂²×C₅	1	4	yes	—
203	#124	C₂²×C₅	1	1	yes	characteristic
204	#123	C₂²×C₅	1	2	yes	—
205	#123	C₂²×C₅	1	4	yes	—
206	#123	C₂²×C₅	1	4	yes	—
207	C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
208	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
209	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
210	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
211	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
212	C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
213	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
214	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
215	C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
216	#121	C₂²×C₅	1	1	yes	characteristic
217	C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
218	C₄×Q₈	C₂²×C₅	1	2	yes	—
219	C₄×Q₈	C₂²×C₅	1	2	yes	—
220	C₄×Q₈	C₂²×C₅	1	4	yes	—
221	C₄×Q₈	C₂²×C₅	1	2	yes	—
222	C₄×Q₈	C₂²×C₅	1	2	yes	—
223	C₄×D₄	C₂²×C₅	1	1	yes	characteristic
224	C₄×D₄	C₂²×C₅	1	2	yes	—
225	C₄×D₄	C₂²×C₅	1	4	yes	—
226	#117	C₂²×C₅	1	2	yes	—
227	#117	C₂²×C₅	1	2	yes	—
228	#117	C₂²×C₅	1	4	yes	—
229	#117	C₂²×C₅	1	2	yes	—
230	#117	C₂²×C₅	1	4	yes	—
231	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
232	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
234	C₂×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂²×C₅	1	2	yes	—
236	C₂×C₄²	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₅	—	2	1	no	—
238	C₂²×C₅	—	2	1	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	2₋¹⁺⁴	1	2	yes	—
243	C₂²×C₅	C₂⁵	1	1	yes	characteristic
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	4	no	—
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	2	4	no	—
251	C₄×C₅	—	2	4	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	2₋¹⁺⁴	1	2	yes	—
257	C₂×Q₈	C₂³×C₅	1	2	yes	—
258	C₂×Q₈	C₂³×C₅	1	4	yes	—
259	C₂×Q₈	C₂³×C₅	1	2	yes	—
260	C₂×Q₈	C₂³×C₅	1	1	yes	characteristic
261	C₂×D₄	C₂³×C₅	1	2	yes	—
262	C₂×D₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₄	C₂³×C₅	1	2	yes	—
266	C₂²×C₄	C₂³×C₅	1	2	yes	—
267	C₂²×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₄	C₂³×C₅	1	2	yes	—
269	C₂²×C₄	C₂³×C₅	1	4	yes	—
270	C₄⋊C₄	C₂³×C₅	1	2	yes	—
271	C₄⋊C₄	C₂³×C₅	1	2	yes	—
272	C₄⋊C₄	C₂³×C₅	1	2	yes	—
273	C₄⋊C₄	C₂³×C₅	1	4	yes	—
274	C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₄⋊C₄	C₂³×C₅	1	4	yes	—
276	C₄⋊C₄	C₂³×C₅	1	4	yes	—
277	C₄⋊C₄	C₂³×C₅	1	4	yes	—
278	C₄⋊C₄	C₂³×C₅	1	4	yes	—
279	C₄⋊C₄	C₂³×C₅	1	2	yes	—
280	C₄⋊C₄	C₂³×C₅	1	4	yes	—
281	C₄⋊C₄	C₂³×C₅	1	2	yes	—
282	C₄⋊C₄	C₂³×C₅	1	4	yes	—
283	C₄⋊C₄	C₂³×C₅	1	2	yes	—
284	C₄⋊C₄	C₂³×C₅	1	4	yes	—
285	C₄⋊C₄	C₂³×C₅	1	2	yes	—
286	C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₄⋊C₄	C₂³×C₅	1	4	yes	—
289	C₄⋊C₄	C₂³×C₅	1	2	yes	—
290	C₄⋊C₄	C₂³×C₅	1	2	yes	—
291	C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
292	C₄⋊C₄	C₂³×C₅	1	4	yes	—
293	C₄⋊C₄	C₂³×C₅	1	4	yes	—
294	C₄⋊C₄	C₂³×C₅	1	4	yes	—
295	C₄⋊C₄	C₂³×C₅	1	4	yes	—
296	C₄⋊C₄	C₂³×C₅	1	2	yes	—
297	C₄⋊C₄	C₂³×C₅	1	4	yes	—
298	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
299	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
300	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
301	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
302	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
303	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
304	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
305	C₂²⋊C₄	C₂³×C₅	1	4	yes	—
306	C₂²⋊C₄	C₂³×C₅	1	2	yes	—
307	C₄²	C₂³×C₅	1	1	yes	characteristic
308	C₄²	C₂³×C₅	1	1	yes	characteristic
309	C₄²	C₂³×C₅	1	1	yes	characteristic
310	C₄²	C₂³×C₅	1	1	yes	characteristic
311	C₄²	C₂³×C₅	1	4	yes	—
312	C₄²	C₂³×C₅	1	4	yes	—
313	C₄²	C₂³×C₅	1	2	yes	—
314	C₄²	C₂³×C₅	1	4	yes	—
315	C₄²	C₂³×C₅	1	4	yes	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	4	2	no	—
318	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
319	C₂×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
320	C₂×C₅	#585	1	1	yes	characteristic
321	C₂³	C₂⁴×C₅	1	2	yes	—
322	C₂³	C₂⁴×C₅	1	1	yes	characteristic
323	Q₈	—	2	4	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	1	no	—
326	Q₈	—	4	2	no	—
327	D₄	—	2	4	no	—
328	D₄	—	4	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×C₄	C₂⁴×C₅	1	4	yes	—
338	C₂×C₄	C₂⁴×C₅	1	2	yes	—
339	C₂×C₄	C₂⁴×C₅	1	2	yes	—
340	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
341	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₅	1	2	yes	—
343	C₂×C₄	C₂⁴×C₅	1	4	yes	—
344	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
345	C₂×C₄	C₂⁴×C₅	1	4	yes	—
346	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
347	C₂×C₄	C₂⁴×C₅	1	4	yes	—
348	C₂×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	C₅	#3563	1	1	yes	characteristic, direct product factor, Sylow
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	C₅×2₋¹⁺⁴	1	2	yes	—
356	C₂²	C₂⁵×C₅	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	4	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	C₅×2₋¹⁺⁴	1	2	yes	—
370	C₂	—	2	2	no	—
371	C₂	—	4	2	no	—
372	C₂	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
374	C₂	C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₅
prime radical	C₅×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#564	C₂	semidirect
2. C₅×#563	C₂	semidirect
3. C₅×#557	C₂	semidirect
4. C₅×#554	C₂	semidirect
5. C₅×#552	C₂	semidirect
6. C₅×#552	C₂	semidirect
7. C₅×#552	C₂	semidirect
8. C₅×#544	C₂	semidirect
9. C₅×#544	C₂	semidirect
10. C₅×#541	C₂	semidirect
11. C₅×#541	C₂	semidirect
13. C₅×#533	C₂	semidirect
15. C₂×C₅×#125	C₂	semidirect
75. #3563	C₅	direct (N × H)
135. #564	C₂×C₅	semidirect
136. #563	C₂×C₅	semidirect
137. #557	C₂×C₅	semidirect
138. #554	C₂×C₅	semidirect
139. #552	C₂×C₅	semidirect
140. #552	C₂×C₅	semidirect
141. #552	C₂×C₅	semidirect
142. #544	C₂×C₅	semidirect
143. #544	C₂×C₅	semidirect
144. #541	C₂×C₅	semidirect
145. #541	C₂×C₅	semidirect
147. #533	C₂×C₅	semidirect
149. C₂×#125	C₂×C₅	semidirect
349. C₅	#3563	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×#564	2
C₅×#563	2
C₅×#557	2
C₅×#554	2
C₅×#552	2
C₅×#544	2
C₅×#541	2
C₅×#539	2
C₅×#533	2
C₅×#529	2
C₂×C₅×#125	2
#3563	5

Subgroups — C5×#3563 #10619348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#3563 #10619348