Subgroups — C₅×#22839 #11945559

Order 1280.

876 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#1954	C₂	1	2	yes	maximal
3	C₅×#1924	C₂	1	4	yes	maximal, complemented
4	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1817	C₂	1	2	yes	maximal, complemented
6	C₅×#1770	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1749	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
10	C₂×C₄×C₅×D₄	C₄	1	1	yes	characteristic
11	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₅×#97	C₂²	1	4	yes	—
18	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
19	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
23	C₄×C₅×C₂²⋊C₄	C₄	1	2	yes	—
24	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₄³×C₅	C₂²	1	1	yes	characteristic
26	C₅×#336	C₂²	1	1	yes	characteristic
27	C₅×#336	C₂²	1	1	yes	characteristic
28	C₅×#336	C₂²	1	4	yes	—
29	C₅×#336	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	#22839	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₅	C₂³	1	2	yes	—
36	C₂²×C₅×C₈	C₂³	1	2	yes	—
37	C₂²×C₅×C₈	C₂³	1	4	yes	—
38	C₂²×C₅×C₈	C₂³	1	2	yes	—
39	C₄×C₅×D₄	—	2	4	no	—
40	C₄×C₅×D₄	—	2	4	no	—
41	C₄×C₅×D₄	—	2	2	no	—
42	C₄×C₅×D₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₅	—	4	4	no	—
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂³	1	2	yes	—
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×C₄⋊C₈	—	2	4	no	—
61	C₅×C₄⋊C₈	—	2	4	no	—
62	C₅×C₂²⋊C₈	—	2	8	no	—
63	C₅×C₂²⋊C₈	—	4	4	no	—
64	C₅×#97	—	4	4	no	—
65	C₄×C₅×C₈	—	2	4	no	—
66	C₅×#95	C₂×C₄	1	2	yes	—
67	C₅×#95	C₂×C₄	1	2	yes	—
68	C₅×#95	C₂×C₄	1	2	yes	—
69	C₄²×D₄	C₂×C₅	1	1	yes	characteristic
70	#1954	C₂×C₅	1	2	yes	—
71	#1924	C₂×C₅	1	4	yes	complemented
72	#1831	C₂×C₅	1	1	yes	characteristic, complemented
73	#1817	C₂×C₅	1	2	yes	complemented
74	#1770	C₂×C₅	1	2	yes	complemented
75	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
76	#1749	C₂×C₅	1	2	yes	complemented
77	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
78	C₂×C₅×D₄	—	2	2	no	—
79	C₂×C₅×D₄	—	2	2	no	—
80	C₂×C₅×D₄	M₁₆	1	4	yes	—
81	C₂²×C₄×C₅	—	2	4	no	—
82	C₂²×C₄×C₅	—	2	4	no	—
83	C₂²×C₄×C₅	—	2	4	no	—
84	C₂²×C₄×C₅	—	2	2	no	—
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	—	4	2	no	—
89	C₂²×C₄×C₅	—	4	2	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	4	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	—	2	4	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	#41	1	4	yes	—
110	C₅×C₄⋊C₄	—	2	2	no	—
111	C₅×C₄⋊C₄	—	2	2	no	—
112	C₅×C₄⋊C₄	—	2	2	no	—
113	C₅×C₂²⋊C₄	—	2	4	no	—
114	C₅×C₂²⋊C₄	—	2	4	no	—
115	C₅×C₂²⋊C₄	—	2	4	no	—
116	C₄²×C₅	—	2	2	no	—
117	C₄²×C₅	—	2	2	no	—
118	C₄²×C₅	—	2	2	no	—
119	C₄²×C₅	—	2	2	no	—
120	C₄²×C₅	—	2	4	no	—
121	C₄²×C₅	—	4	2	no	—
122	C₄²×C₅	—	4	2	no	—
123	C₄²×C₅	—	4	1	no	—
124	C₄²×C₅	M₁₆	1	4	yes	—
125	C₄²×C₅	#41	1	2	yes	—
126	C₄²×C₅	#41	1	2	yes	—
127	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
128	C₂×C₄×D₄	C₄×C₅	1	1	yes	characteristic
129	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄²	C₂²×C₅	1	2	yes	—
131	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
133	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
134	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
135	C₂×#97	C₂²×C₅	1	4	yes	—
136	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
137	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
138	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
139	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
140	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
141	C₄×C₂²⋊C₄	C₄×C₅	1	2	yes	—
142	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
143	C₄³	C₂²×C₅	1	1	yes	characteristic
144	#336	C₂²×C₅	1	1	yes	characteristic
145	#336	C₂²×C₅	1	2	yes	—
146	#336	C₂²×C₅	1	4	yes	—
147	#336	C₂²×C₅	1	2	yes	—
148	#336	C₂²×C₅	1	1	yes	characteristic
149	C₂³×C₅	—	2	2	no	—
150	C₂³×C₅	—	2	2	no	—
151	C₂³×C₅	—	2	2	no	—
152	C₂³×C₅	—	2	2	no	—
153	C₂³×C₅	—	2	2	no	—
154	C₂³×C₅	—	2	2	no	—
155	C₂³×C₅	C₂×M₁₆	1	4	yes	—
156	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
157	C₅×D₄	—	2	8	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	1	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	4	8	no	—
179	C₂×C₄×C₅	—	4	8	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	4	4	no	—
182	C₂×C₄×C₅	#117	1	2	yes	—
183	C₂×C₄×C₅	#117	1	2	yes	—
184	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
185	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
186	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
188	C₂×C₄×C₅	#131	1	2	yes	—
189	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×#41	1	2	yes	—
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
193	C₅×C₈	—	2	4	no	—
194	C₅×C₈	—	4	2	no	—
195	C₅×C₈	—	4	4	no	—
196	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
198	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
199	C₂³×C₄	C₂³×C₅	1	2	yes	—
200	C₂²×C₈	C₂³×C₅	1	2	yes	—
201	C₂²×C₈	C₂³×C₅	1	4	yes	—
202	C₂²×C₈	C₂³×C₅	1	2	yes	—
203	C₄×D₄	—	2	4	no	—
204	C₄×D₄	—	2	4	no	—
205	C₄×D₄	—	2	2	no	—
206	C₄×D₄	—	2	2	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
213	C₂×C₄²	—	4	4	no	—
214	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₅	1	2	yes	—
223	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
224	C₄⋊C₈	—	2	4	no	—
225	C₄⋊C₈	—	2	4	no	—
226	C₂²⋊C₈	—	2	8	no	—
227	C₂²⋊C₈	—	4	4	no	—
228	#97	—	4	4	no	—
229	C₄×C₈	—	2	4	no	—
230	#95	C₂×C₄×C₅	1	2	yes	—
231	#95	C₂×C₄×C₅	1	2	yes	—
232	#95	C₂×C₄×C₅	1	2	yes	—
233	C₂²×C₅	—	2	4	no	—
234	C₂²×C₅	—	2	4	no	—
235	C₂²×C₅	—	2	4	no	—
236	C₂²×C₅	—	4	2	no	—
237	C₂²×C₅	—	4	2	no	—
238	C₂²×C₅	—	4	2	no	—
239	C₂²×C₅	—	4	2	no	—
240	C₂²×C₅	C₂×#117	1	1	yes	characteristic
241	C₂²×C₅	C₄×#41	1	1	yes	characteristic
242	C₂²×C₅	#518	1	1	yes	characteristic
243	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
244	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
245	C₂²×C₅	C₂×#131	1	1	yes	characteristic
246	C₂²×C₅	#568	1	1	yes	characteristic
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	—	4	1	no	—
253	C₄×C₅	—	4	2	no	—
254	C₄×C₅	—	4	2	no	—
255	C₄×C₅	#432	1	4	yes	—
256	C₄×C₅	#553	1	2	yes	—
257	C₄×C₅	#559	1	2	yes	—
258	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	C₅×M₁₆	1	4	yes	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₅×#41	1	4	yes	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	2	4	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	4	2	no	—
303	C₄²	—	4	2	no	—
304	C₄²	—	4	1	no	—
305	C₄²	C₅×M₁₆	1	4	yes	—
306	C₄²	C₅×#41	1	2	yes	—
307	C₄²	C₅×#41	1	2	yes	—
308	C₂×C₅	—	4	4	no	—
309	C₂×C₅	#2357	1	1	yes	characteristic
310	C₂×C₅	C₂×#432	1	1	yes	characteristic
311	C₂×C₅	#2925	1	1	yes	characteristic
312	C₂×C₅	#2965	1	1	yes	characteristic
313	C₂×C₅	#2970	1	1	yes	characteristic
314	C₂×C₅	#2974	1	1	yes	characteristic
315	C₂×C₅	#2975	1	1	yes	characteristic
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	C₂×C₅×M₁₆	1	4	yes	—
323	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
324	D₄	—	2	8	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₅×#117	1	2	yes	—
350	C₂×C₄	C₅×#117	1	2	yes	—
351	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
352	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
353	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
354	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
355	C₂×C₄	C₅×#131	1	2	yes	—
356	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×#41	1	2	yes	—
358	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
359	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
360	C₈	—	2	4	no	—
361	C₈	—	4	2	no	—
362	C₈	—	4	4	no	—
363	C₅	#22839	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	C₂×C₅×#117	1	1	yes	characteristic
372	C₂²	C₄×C₅×#41	1	1	yes	characteristic
373	C₂²	C₅×#518	1	1	yes	characteristic
374	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
375	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
376	C₂²	C₂×C₅×#131	1	1	yes	characteristic
377	C₂²	C₅×#568	1	1	yes	characteristic
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₅×#432	1	4	yes	—
387	C₄	C₅×#553	1	2	yes	—
388	C₄	C₅×#559	1	2	yes	—
389	C₂	—	4	4	no	—
390	C₂	C₅×#2357	1	1	yes	characteristic
391	C₂	C₂×C₅×#432	1	1	yes	characteristic
392	C₂	C₅×#2925	1	1	yes	characteristic
393	C₂	C₅×#2965	1	1	yes	characteristic
394	C₂	C₅×#2970	1	1	yes	characteristic
395	C₂	C₅×#2974	1	1	yes	characteristic
396	C₂	C₅×#2975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×C₄
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
3. C₅×#1924	C₂	semidirect
4. C₅×#1831	C₂	semidirect
5. C₅×#1817	C₂	semidirect
6. C₅×#1770	C₂	semidirect
7. C₄×C₅×C₄⋊C₈	C₂	semidirect
8. C₅×#1749	C₂	semidirect
31. #22839	C₅	direct (N × H)
71. #1924	C₂×C₅	semidirect
72. #1831	C₂×C₅	semidirect
73. #1817	C₂×C₅	semidirect
74. #1770	C₂×C₅	semidirect
75. C₄×C₄⋊C₈	C₂×C₅	semidirect
76. #1749	C₂×C₅	semidirect
363. C₅	#22839	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₅×D₄	2
C₅×#1954	2
C₅×#1924	2
C₅×#1831	2
C₅×#1817	2
C₅×#1770	2
C₄×C₅×C₄⋊C₈	2
C₅×#1749	2
#22839	5

Subgroups — C5×#22839 #11945559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22839 #11945559