Subgroups — C₅×#22838 #11945558

Order 1280.

732 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2293	C₂	1	1	yes	maximal, characteristic
2	C₅×#1955	C₂	1	2	yes	maximal
3	C₅×#1924	C₂	1	2	yes	maximal, complemented
4	C₅×#1923	C₂	1	2	yes	maximal, complemented
5	C₅×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1818	C₂	1	2	yes	maximal, complemented
7	C₅×#1771	C₂	1	2	yes	maximal, complemented
8	C₅×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1750	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	2	yes	—
12	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×#97	C₂²	1	2	yes	—
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#390	C₄	1	1	yes	characteristic
22	C₅×#390	C₄	1	1	yes	characteristic
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#389	C₄	1	1	yes	characteristic
25	C₅×#388	C₄	1	2	yes	—
26	C₅×#388	C₄	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₅	C₂²	1	1	yes	characteristic
30	C₅×#336	C₂²	1	1	yes	characteristic
31	C₅×#336	C₂²	1	1	yes	characteristic
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	1	yes	characteristic
36	C₅×#336	C₂²	1	1	yes	characteristic
37	#22838	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
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	C₄×C₅×D₄	—	2	2	no	—
45	C₄×C₅×D₄	—	2	2	no	—
46	C₅×#117	—	4	2	no	—
47	C₅×#117	—	4	2	no	—
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	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂³	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₅×C₄⋊C₈	—	2	4	no	—
67	C₅×C₄⋊C₈	—	2	4	no	—
68	C₅×C₂²⋊C₈	—	2	4	no	—
69	C₅×C₂²⋊C₈	—	2	4	no	—
70	C₅×C₂²⋊C₈	—	4	2	no	—
71	C₅×C₂²⋊C₈	—	4	2	no	—
72	C₅×#97	—	2	4	no	—
73	C₅×#97	—	4	2	no	—
74	C₄×C₅×C₈	—	4	2	no	—
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	#2293	C₂×C₅	1	1	yes	characteristic
79	#1955	C₂×C₅	1	2	yes	—
80	#1924	C₂×C₅	1	2	yes	complemented
81	#1923	C₂×C₅	1	2	yes	complemented
82	#1831	C₂×C₅	1	1	yes	characteristic, complemented
83	#1818	C₂×C₅	1	2	yes	complemented
84	#1771	C₂×C₅	1	2	yes	complemented
85	#1767	C₂×C₅	1	1	yes	characteristic, complemented
86	#1750	C₂×C₅	1	2	yes	complemented
87	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₅×D₄	—	2	2	no	—
89	C₂×C₅×D₄	—	4	1	no	—
90	C₂×C₅×D₄	—	4	1	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
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	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
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	#41	1	4	yes	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	4	1	no	—
121	C₅×C₄⋊C₄	—	4	1	no	—
122	C₅×C₄⋊C₄	—	4	2	no	—
123	C₅×C₄⋊C₄	—	4	2	no	—
124	C₅×C₂²⋊C₄	—	2	4	no	—
125	C₅×C₂²⋊C₄	—	2	4	no	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₅×C₂²⋊C₄	—	4	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	4	1	no	—
135	C₄²×C₅	—	4	1	no	—
136	C₄²×C₅	—	4	1	no	—
137	C₄²×C₅	#41	1	2	yes	—
138	C₄²×C₅	#41	1	2	yes	—
139	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂×#117	C₂²×C₅	1	2	yes	—
141	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
142	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
143	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
144	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
145	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
146	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
147	C₂×#97	C₂²×C₅	1	2	yes	—
148	C₂×#97	C₂²×C₅	1	2	yes	—
149	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
150	#390	C₄×C₅	1	1	yes	characteristic
151	#390	C₄×C₅	1	1	yes	characteristic
152	#389	C₄×C₅	1	1	yes	characteristic
153	#389	C₄×C₅	1	1	yes	characteristic
154	#388	C₄×C₅	1	2	yes	—
155	#388	C₄×C₅	1	2	yes	—
156	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
158	C₄³	C₂²×C₅	1	1	yes	characteristic
159	#336	C₂²×C₅	1	1	yes	characteristic
160	#336	C₂²×C₅	1	2	yes	—
161	#336	C₂²×C₅	1	2	yes	—
162	#336	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	1	yes	characteristic
164	#336	C₂²×C₅	1	1	yes	characteristic
165	#336	C₂²×C₅	1	1	yes	characteristic
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	2	2	no	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	2	2	no	—
170	C₂³×C₅	—	2	2	no	—
171	C₂³×C₅	—	2	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₅×D₄	—	4	4	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	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	1	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	1	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	#117	1	2	yes	—
204	C₂×C₄×C₅	#117	1	2	yes	—
205	C₂×C₄×C₅	#131	1	2	yes	—
206	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×#41	1	2	yes	—
208	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
210	C₅×C₈	—	2	4	no	—
211	C₅×C₈	—	4	2	no	—
212	C₅×C₈	—	4	2	no	—
213	C₅×C₈	—	4	2	no	—
214	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂³×C₄	C₂³×C₅	1	2	yes	—
216	C₂²×C₈	C₂³×C₅	1	2	yes	—
217	C₂²×C₈	C₂³×C₅	1	2	yes	—
218	C₂²×C₈	C₂³×C₅	1	2	yes	—
219	C₂²×C₈	C₂³×C₅	1	2	yes	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	#117	—	4	2	no	—
223	#117	—	4	2	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
226	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
229	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
230	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
231	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
232	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
233	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
234	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₅	1	2	yes	—
240	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₄⋊C₈	—	2	4	no	—
243	C₄⋊C₈	—	2	4	no	—
244	C₂²⋊C₈	—	2	4	no	—
245	C₂²⋊C₈	—	2	4	no	—
246	C₂²⋊C₈	—	4	2	no	—
247	C₂²⋊C₈	—	4	2	no	—
248	#97	—	2	4	no	—
249	#97	—	4	2	no	—
250	C₄×C₈	—	4	2	no	—
251	#95	C₂×C₄×C₅	1	2	yes	—
252	#95	C₂×C₄×C₅	1	2	yes	—
253	#95	C₂×C₄×C₅	1	2	yes	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	2	no	—
257	C₂²×C₅	—	4	2	no	—
258	C₂²×C₅	—	4	2	no	—
259	C₂²×C₅	—	4	2	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	C₂×#117	1	1	yes	characteristic
262	C₂²×C₅	C₄×#41	1	1	yes	characteristic
263	C₂²×C₅	#518	1	1	yes	characteristic
264	C₂²×C₅	C₂×#131	1	1	yes	characteristic
265	C₂²×C₅	#568	1	1	yes	characteristic
266	C₂²×C₅	#568	1	1	yes	characteristic
267	C₂²×C₅	#568	1	1	yes	characteristic
268	C₄×C₅	—	2	2	no	—
269	C₄×C₅	—	2	2	no	—
270	C₄×C₅	—	2	2	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	—	4	2	no	—
277	C₄×C₅	#553	1	2	yes	—
278	C₄×C₅	#559	1	2	yes	—
279	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
291	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
292	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
293	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	C₅×#41	1	4	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	C₅×#41	1	2	yes	—
330	C₄²	C₅×#41	1	2	yes	—
331	C₂×C₅	—	8	2	no	—
332	C₂×C₅	#2357	1	1	yes	characteristic
333	C₂×C₅	#2921	1	1	yes	characteristic
334	C₂×C₅	#2925	1	1	yes	characteristic
335	C₂×C₅	#2967	1	1	yes	characteristic
336	C₂×C₅	#2968	1	1	yes	characteristic
337	C₂×C₅	#2980	1	1	yes	characteristic
338	C₂×C₅	#2981	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	C₅×#117	1	2	yes	—
377	C₂×C₄	C₅×#117	1	2	yes	—
378	C₂×C₄	C₅×#131	1	2	yes	—
379	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×#41	1	2	yes	—
381	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
382	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
383	C₈	—	2	4	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₅	#22838	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×C₅×#117	1	1	yes	characteristic
396	C₂²	C₄×C₅×#41	1	1	yes	characteristic
397	C₂²	C₅×#518	1	1	yes	characteristic
398	C₂²	C₂×C₅×#131	1	1	yes	characteristic
399	C₂²	C₅×#568	1	1	yes	characteristic
400	C₂²	C₅×#568	1	1	yes	characteristic
401	C₂²	C₅×#568	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	2	no	—
411	C₄	C₅×#553	1	2	yes	—
412	C₄	C₅×#559	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	C₅×#2357	1	1	yes	characteristic
415	C₂	C₅×#2921	1	1	yes	characteristic
416	C₂	C₅×#2925	1	1	yes	characteristic
417	C₂	C₅×#2967	1	1	yes	characteristic
418	C₂	C₅×#2968	1	1	yes	characteristic
419	C₂	C₅×#2980	1	1	yes	characteristic
420	C₂	C₅×#2981	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×#1923	C₂	semidirect
5. C₅×#1831	C₂	semidirect
6. C₅×#1818	C₂	semidirect
7. C₅×#1771	C₂	semidirect
8. C₅×#1767	C₂	semidirect
9. C₅×#1750	C₂	semidirect
37. #22838	C₅	direct (N × H)
80. #1924	C₂×C₅	semidirect
81. #1923	C₂×C₅	semidirect
82. #1831	C₂×C₅	semidirect
83. #1818	C₂×C₅	semidirect
84. #1771	C₂×C₅	semidirect
85. #1767	C₂×C₅	semidirect
86. #1750	C₂×C₅	semidirect
387. C₅	#22838	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×#2293	2
C₅×#1955	2
C₅×#1924	2
C₅×#1923	2
C₅×#1831	2
C₅×#1818	2
C₅×#1771	2
C₅×#1767	2
C₅×#1750	2
#22838	5

Subgroups — C5×#22838 #11945558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22838 #11945558