Subgroups — C₅×#21925 #11944645

Order 1280.

648 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2298	C₂	1	1	yes	maximal, characteristic
2	C₅×#1924	C₂	1	2	yes	maximal
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1917	C₂	1	2	yes	maximal, complemented
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1843	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1798	C₂	1	1	yes	maximal, characteristic
9	C₅×#1798	C₂	1	1	yes	maximal, characteristic
10	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₅×#388	C₄	1	2	yes	—
24	C₅×#388	C₄	1	2	yes	—
25	C₅×#387	C₄	1	2	yes	—
26	C₅×#387	C₄	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	#21925	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₅×#117	—	2	2	no	—
46	C₅×#117	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊C₈	—	2	2	no	—
64	C₅×C₄⋊C₈	—	2	2	no	—
65	C₅×C₄⋊C₈	—	2	2	no	—
66	C₅×C₄⋊C₈	—	2	2	no	—
67	C₅×C₄⋊C₈	—	4	2	no	—
68	C₅×C₄⋊C₈	—	4	2	no	—
69	C₅×C₂²⋊C₈	—	4	2	no	—
70	C₅×C₂²⋊C₈	—	4	2	no	—
71	C₅×#97	—	4	2	no	—
72	C₄×C₅×C₈	—	4	2	no	—
73	C₅×#95	C₂×C₄	1	2	yes	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	C₅×#95	C₂×C₄	1	2	yes	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₅×#95	C₂×C₄	1	2	yes	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	#2298	C₂×C₅	1	1	yes	characteristic
80	#1924	C₂×C₅	1	2	yes	—
81	#1923	C₂×C₅	1	2	yes	—
82	#1917	C₂×C₅	1	2	yes	complemented
83	#1916	C₂×C₅	1	2	yes	complemented
84	#1843	C₂×C₅	1	1	yes	characteristic, complemented
85	#1832	C₂×C₅	1	1	yes	characteristic, complemented
86	#1798	C₂×C₅	1	1	yes	characteristic
87	#1798	C₂×C₅	1	1	yes	characteristic
88	#1767	C₂×C₅	1	1	yes	characteristic, complemented
89	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	—	2	1	no	—
92	C₂²×C₄×C₅	—	2	1	no	—
93	C₂²×C₄×C₅	—	2	1	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	1	no	—
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	4	2	no	—
123	C₅×C₂²⋊C₄	—	2	2	no	—
124	C₅×C₂²⋊C₄	—	2	2	no	—
125	C₅×C₂²⋊C₄	—	2	4	no	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₄²×C₅	—	2	4	no	—
128	C₄²×C₅	—	2	1	no	—
129	C₄²×C₅	—	2	1	no	—
130	C₄²×C₅	—	2	1	no	—
131	C₄²×C₅	—	2	1	no	—
132	C₄²×C₅	—	2	1	no	—
133	C₄²×C₅	—	2	1	no	—
134	C₄²×C₅	—	2	1	no	—
135	C₄²×C₅	—	2	1	no	—
136	C₄²×C₅	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	—	4	2	no	—
139	C₄²×C₅	#41	1	2	yes	—
140	C₄²×C₅	#41	1	2	yes	—
141	C₂×#117	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
147	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
149	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
150	C₂×#97	C₂²×C₅	1	2	yes	—
151	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
152	#388	C₄×C₅	1	2	yes	—
153	#388	C₄×C₅	1	2	yes	—
154	#387	C₄×C₅	1	2	yes	—
155	#387	C₄×C₅	1	2	yes	—
156	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
159	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	#376	C₂²×C₅	1	1	yes	characteristic
161	C₄³	C₂²×C₅	1	1	yes	characteristic
162	#336	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	2	yes	—
164	#336	C₂²×C₅	1	2	yes	—
165	#336	C₂²×C₅	1	2	yes	—
166	#336	C₂²×C₅	1	2	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	C₂³×C₅	—	2	1	no	—
169	C₂³×C₅	—	2	1	no	—
170	C₂³×C₅	—	2	1	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	1	no	—
197	C₂×C₄×C₅	—	4	1	no	—
198	C₂×C₄×C₅	#117	1	2	yes	—
199	C₂×C₄×C₅	#117	1	2	yes	—
200	C₂×C₄×C₅	#131	1	4	yes	—
201	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
207	C₅×C₈	—	4	2	no	—
208	C₅×C₈	—	4	2	no	—
209	C₅×C₈	—	4	2	no	—
210	C₅×C₈	—	4	2	no	—
211	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₅	1	2	yes	—
213	C₂²×C₈	C₂³×C₅	1	2	yes	—
214	C₂²×C₈	C₂³×C₅	1	2	yes	—
215	C₂²×C₈	C₂³×C₅	1	2	yes	—
216	#117	—	2	2	no	—
217	#117	—	2	2	no	—
218	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
224	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
225	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
228	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
234	C₄⋊C₈	—	2	2	no	—
235	C₄⋊C₈	—	2	2	no	—
236	C₄⋊C₈	—	2	2	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	4	2	no	—
239	C₄⋊C₈	—	4	2	no	—
240	C₂²⋊C₈	—	4	2	no	—
241	C₂²⋊C₈	—	4	2	no	—
242	#97	—	4	2	no	—
243	C₄×C₈	—	4	2	no	—
244	#95	C₂×C₄×C₅	1	2	yes	—
245	#95	C₂×C₄×C₅	1	2	yes	—
246	#95	C₂×C₄×C₅	1	2	yes	—
247	#95	C₂×C₄×C₅	1	2	yes	—
248	#95	C₂×C₄×C₅	1	2	yes	—
249	#95	C₂×C₄×C₅	1	2	yes	—
250	C₂²×C₅	—	4	1	no	—
251	C₂²×C₅	—	4	1	no	—
252	C₂²×C₅	—	4	1	no	—
253	C₂²×C₅	—	4	2	no	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	C₂×#117	1	1	yes	characteristic
256	C₂²×C₅	#520	1	1	yes	characteristic
257	C₂²×C₅	#520	1	1	yes	characteristic
258	C₂²×C₅	C₂×#131	1	2	yes	—
259	C₂²×C₅	#568	1	2	yes	—
260	C₄×C₅	—	2	2	no	—
261	C₄×C₅	—	2	2	no	—
262	C₄×C₅	—	2	4	no	—
263	C₄×C₅	—	4	1	no	—
264	C₄×C₅	—	4	1	no	—
265	C₄×C₅	—	4	1	no	—
266	C₄×C₅	—	4	2	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	#540	1	1	yes	characteristic
270	C₄×C₅	#541	1	1	yes	characteristic
271	C₄×C₅	#542	1	1	yes	characteristic
272	C₄×C₅	#542	1	1	yes	characteristic
273	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
286	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	4	2	no	—
322	C₄²	C₅×#41	1	2	yes	—
323	C₄²	C₅×#41	1	2	yes	—
324	C₂×C₅	—	8	1	no	—
325	C₂×C₅	#2314	1	1	yes	characteristic
326	C₂×C₅	#2922	1	1	yes	characteristic
327	C₂×C₅	#2923	1	1	yes	characteristic
328	C₂×C₅	#2992	1	2	yes	—
329	C₂×C₅	#2993	1	2	yes	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	C₅×#117	1	2	yes	—
361	C₂×C₄	C₅×#117	1	2	yes	—
362	C₂×C₄	C₅×#131	1	4	yes	—
363	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
364	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
365	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
368	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
369	C₈	—	4	2	no	—
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₅	#21925	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂×C₅×#117	1	1	yes	characteristic
380	C₂²	C₅×#520	1	1	yes	characteristic
381	C₂²	C₅×#520	1	1	yes	characteristic
382	C₂²	C₂×C₅×#131	1	2	yes	—
383	C₂²	C₅×#568	1	2	yes	—
384	C₄	—	2	4	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	C₅×#540	1	1	yes	characteristic
394	C₄	C₅×#541	1	1	yes	characteristic
395	C₄	C₅×#542	1	1	yes	characteristic
396	C₄	C₅×#542	1	1	yes	characteristic
397	C₂	—	8	1	no	—
398	C₂	C₅×#2314	1	1	yes	characteristic
399	C₂	C₅×#2922	1	1	yes	characteristic
400	C₂	C₅×#2923	1	1	yes	characteristic
401	C₂	C₅×#2992	1	2	yes	—
402	C₂	C₅×#2993	1	2	yes	—

	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	C₂⁴×C₅	C₂²×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
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
6. C₅×#1843	C₂	semidirect
7. C₅×#1832	C₂	semidirect
10. C₅×#1767	C₂	semidirect
11. C₄×C₅×C₄⋊C₈	C₂	semidirect
39. #21925	C₅	direct (N × H)
82. #1917	C₂×C₅	semidirect
83. #1916	C₂×C₅	semidirect
84. #1843	C₂×C₅	semidirect
85. #1832	C₂×C₅	semidirect
88. #1767	C₂×C₅	semidirect
89. C₄×C₄⋊C₈	C₂×C₅	semidirect
373. C₅	#21925	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×#2298	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1843	2
C₅×#1832	2
C₅×#1798	2
C₅×#1767	2
C₄×C₅×C₄⋊C₈	2
#21925	5

Subgroups — C5×#21925 #11944645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21925 #11944645