Subgroups — C₅×#23062 #11945782

Order 1280.

778 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#475	C₂	1	1	yes	maximal, characteristic
2	C₅×#2365	C₂	1	1	yes	maximal, characteristic
3	C₅×#2355	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic
5	C₅×#1948	C₂	1	1	yes	maximal, characteristic
6	C₅×#1933	C₂	1	2	yes	maximal
7	C₅×#1927	C₂	1	2	yes	maximal
8	C₅×#1919	C₂	1	2	yes	maximal
9	C₄×C₅×#106	C₂	1	2	yes	maximal
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	—	2	1	no	—
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×#475	C₄	1	8	yes	complemented
16	C₂×C₅×#106	C₂²	1	2	yes	—
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#103	C₂²	1	1	yes	characteristic
20	C₂×C₅×#103	C₂²	1	1	yes	characteristic
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₅×#391	—	2	1	no	—
25	C₅×#391	C₂²	1	2	yes	—
26	C₅×#389	C₂²	1	2	yes	—
27	C₅×#387	—	2	2	no	—
28	C₅×#387	—	2	2	no	—
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₅×#382	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	—	2	1	no	—
32	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	1	yes	characteristic
37	C₅×#340	C₂²	1	1	yes	characteristic
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#23062	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	—	2	1	no	—
44	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₅×C₄⋊Q₈	—	2	2	no	—
49	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
50	C₄×C₅×Q₈	—	2	2	no	—
51	C₄×C₅×Q₈	—	4	4	no	—
52	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	—	2	2	no	—
67	C₂×C₄²×C₅	—	2	1	no	—
68	C₂×C₄²×C₅	—	2	2	no	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#106	—	2	4	no	—
72	C₅×#106	C₂×C₄	1	8	yes	—
73	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
74	C₅×#103	—	2	2	no	—
75	C₅×#103	—	2	2	no	—
76	C₅×#103	C₂×C₄	1	8	yes	—
77	C₄×C₅×C₈	—	2	4	no	—
78	C₄×C₅×C₈	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	2	no	—
81	C₅×#95	—	2	1	no	—
82	C₅×#95	—	2	2	no	—
83	C₅×#95	—	2	2	no	—
84	C₅×#95	—	2	2	no	—
85	C₅×#95	D₄	1	2	yes	—
86	C₂×#475	C₂×C₅	1	1	yes	characteristic
87	#2365	C₂×C₅	1	1	yes	characteristic
88	#2355	C₂×C₅	1	1	yes	characteristic
89	#1990	C₂×C₅	1	1	yes	characteristic
90	#1948	C₂×C₅	1	1	yes	characteristic
91	#1933	C₂×C₅	1	2	yes	—
92	#1927	C₂×C₅	1	2	yes	—
93	#1919	C₂×C₅	1	2	yes	—
94	C₄×#106	C₂×C₅	1	2	yes	—
95	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
96	C₄×#103	C₂×C₅	1	1	yes	characteristic
97	C₂×C₅×Q₈	—	2	4	no	—
98	C₂×C₅×Q₈	—	2	1	no	—
99	C₂×C₅×Q₈	—	2	1	no	—
100	C₂×C₅×Q₈	—	2	1	no	—
101	C₂×C₅×Q₈	—	2	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×Q₈	—	4	2	no	—
104	C₂×C₅×Q₈	—	4	2	no	—
105	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	2	1	no	—
108	C₂²×C₄×C₅	—	2	2	no	—
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	2	1	no	—
111	C₂²×C₄×C₅	—	2	2	no	—
112	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
125	C₂×C₅×C₈	#41	1	2	yes	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	1	no	—
135	C₅×C₄⋊C₄	—	2	2	no	—
136	C₅×C₄⋊C₄	—	4	4	no	—
137	C₅×C₄⋊C₄	—	4	2	no	—
138	C₅×C₄⋊C₄	—	8	1	no	—
139	C₅×C₄⋊C₄	SD₁₆	1	4	yes	—
140	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
141	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
142	C₅×C₄⋊C₄	#41	1	2	yes	—
143	C₄²×C₅	—	2	4	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	4	4	no	—
147	C₄²×C₅	—	4	2	no	—
148	C₄²×C₅	—	8	2	no	—
149	C₄²×C₅	C₂²×C₄	1	2	yes	—
150	C₄²×C₅	#41	1	2	yes	—
151	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×Q₈	—	2	1	no	—
153	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
154	#475	C₄×C₅	1	8	yes	complemented
155	C₂×#106	C₂²×C₅	1	2	yes	—
156	C₂×#106	C₂²×C₅	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
158	C₂×#103	C₂²×C₅	1	1	yes	characteristic
159	C₂×#103	C₂²×C₅	1	1	yes	characteristic
160	C₂×#103	C₂²×C₅	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
162	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
163	#391	—	2	1	no	—
164	#391	C₂²×C₅	1	2	yes	—
165	#389	C₂²×C₅	1	2	yes	—
166	#387	—	2	2	no	—
167	#387	—	2	2	no	—
168	#384	C₂²×C₅	1	1	yes	characteristic
169	#382	—	2	1	no	—
170	C₄×C₄⋊C₄	—	2	1	no	—
171	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
173	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	#340	C₂²×C₅	1	1	yes	characteristic
176	#340	C₂²×C₅	1	2	yes	—
177	#340	C₂²×C₅	1	2	yes	—
178	#340	C₂²×C₅	1	2	yes	—
179	#340	C₂²×C₅	1	1	yes	characteristic
180	#336	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₅×Q₈	—	2	2	no	—
183	C₅×Q₈	—	2	2	no	—
184	C₅×Q₈	—	4	1	no	—
185	C₅×Q₈	—	4	1	no	—
186	C₅×Q₈	—	4	8	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	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	4	1	no	—
199	C₂×C₄×C₅	—	4	1	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	1	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	2	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
215	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
216	C₂×C₄×C₅	#135	1	2	yes	—
217	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
222	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
223	C₅×C₈	—	2	4	no	—
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	—	4	1	no	—
226	C₂²×Q₈	—	2	1	no	—
227	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₅	1	2	yes	—
230	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
233	C₄×Q₈	—	2	2	no	—
234	C₄×Q₈	—	4	4	no	—
235	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
244	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂³×C₅	1	2	yes	—
253	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
254	#106	—	2	4	no	—
255	#106	C₂×C₄×C₅	1	8	yes	—
256	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
257	#103	—	2	2	no	—
258	#103	—	2	2	no	—
259	#103	C₂×C₄×C₅	1	8	yes	—
260	C₄×C₈	—	2	4	no	—
261	C₄×C₈	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	1	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	C₅×D₄	1	2	yes	—
269	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₅	#547	1	1	yes	characteristic
271	C₂²×C₅	#548	1	1	yes	characteristic
272	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
273	C₂²×C₅	C₂×#135	1	1	yes	characteristic
274	C₂²×C₅	#577	1	1	yes	characteristic
275	C₂²×C₅	#578	1	1	yes	characteristic
276	C₄×C₅	—	2	4	no	—
277	C₄×C₅	—	2	2	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	8	1	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	C₄×SD₁₆	1	4	yes	—
286	C₄×C₅	C₄×#41	1	1	yes	characteristic
287	C₄×C₅	#519	1	1	yes	characteristic
288	C₄×C₅	#552	1	1	yes	characteristic
289	C₄×C₅	#556	1	1	yes	characteristic
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
318	C₂×C₈	C₅×#41	1	2	yes	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	8	1	no	—
332	C₄⋊C₄	C₅×SD₁₆	1	4	yes	—
333	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
334	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
335	C₄⋊C₄	C₅×#41	1	2	yes	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	4	no	—
340	C₄²	—	4	2	no	—
341	C₄²	—	8	2	no	—
342	C₄²	C₂²×C₄×C₅	1	2	yes	—
343	C₄²	C₅×#41	1	2	yes	—
344	C₂×C₅	#2362	1	1	yes	characteristic
345	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
346	C₂×C₅	#2947	1	1	yes	characteristic
347	C₂×C₅	#3335	1	1	yes	characteristic
348	C₂×C₅	#3342	1	1	yes	characteristic
349	C₂×C₅	#3359	1	1	yes	characteristic
350	C₂×C₅	#3365	1	1	yes	characteristic
351	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	—	2	2	no	—
354	Q₈	—	4	8	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	4	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
383	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
385	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
386	C₂×C₄	C₅×#135	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
388	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
390	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
391	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	2	2	no	—
395	C₈	—	4	1	no	—
396	C₅	#23062	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
398	C₂²	C₅×#547	1	1	yes	characteristic
399	C₂²	C₅×#548	1	1	yes	characteristic
400	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
401	C₂²	C₂×C₅×#135	1	1	yes	characteristic
402	C₂²	C₅×#577	1	1	yes	characteristic
403	C₂²	C₅×#578	1	1	yes	characteristic
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	C₄×C₅×SD₁₆	1	4	yes	—
414	C₄	C₄×C₅×#41	1	1	yes	characteristic
415	C₄	C₅×#519	1	1	yes	characteristic
416	C₄	C₅×#552	1	1	yes	characteristic
417	C₄	C₅×#556	1	1	yes	characteristic
418	C₂	C₅×#2362	1	1	yes	characteristic
419	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
420	C₂	C₅×#2947	1	1	yes	characteristic
421	C₂	C₅×#3335	1	1	yes	characteristic
422	C₂	C₅×#3342	1	1	yes	characteristic
423	C₂	C₅×#3359	1	1	yes	characteristic
424	C₂	C₅×#3365	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₅×#475	C₄	semidirect
42. #23062	C₅	direct (N × H)
154. #475	C₄×C₅	semidirect
396. C₅	#23062	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#475	2
C₅×#2365	2
C₅×#2355	2
C₅×#1990	2
C₅×#1948	2
C₅×#1933	2
C₅×#1927	2
C₅×#1919	2
C₄×C₅×#106	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#103	2
#23062	5

Subgroups — C5×#23062 #11945782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23062 #11945782