Subgroups — C₅×#34189 #11956909

Order 1280.

2342 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	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#2357	C₂	1	4	yes	maximal, complemented
3	C₅×#2356	C₂	1	4	yes	maximal, complemented
4	C₅×#2353	C₂	1	8	yes	maximal, complemented
5	C₅×#2314	C₂	1	4	yes	maximal, complemented
6	C₅×#2311	C₂	1	2	yes	maximal
7	C₅×#2285	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2283	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2274	C₂	1	2	yes	maximal, complemented
11	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
12	C₄×C₅×#41	C₄	1	16	yes	complemented
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₂×C₅×#117	C₂²	1	2	yes	—
17	C₂×C₅×#117	C₂²	1	1	yes	characteristic
18	C₂×C₅×#117	C₂²	1	2	yes	—
19	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₅	C₂²	1	2	yes	—
22	C₅×#391	C₂²	1	4	yes	—
23	C₅×#390	C₂²	1	4	yes	—
24	C₅×#388	C₂²	1	16	yes	—
25	C₅×#387	C₂²	1	16	yes	—
26	C₅×#386	C₂²	1	8	yes	—
27	C₅×#384	C₂²	1	2	yes	—
28	C₅×#383	C₂²	1	8	yes	—
29	C₅×#382	C₂²	1	2	yes	—
30	C₅×#382	C₂²	1	2	yes	—
31	C₅×#382	C₂²	1	4	yes	—
32	C₅×#382	C₂²	1	2	yes	—
33	C₅×#381	C₂²	1	8	yes	—
34	C₅×#380	C₂²	1	8	yes	—
35	C₅×#380	C₂²	1	4	yes	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	8	yes	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	8	yes	—
38	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
39	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
40	C₄×C₅×C₂²⋊C₄	C₂²	1	8	yes	—
41	C₅×#376	C₂²	1	8	yes	—
42	C₂×C₅×#95	C₂²	1	4	yes	—
43	#34189	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	4	no	—
45	C₂×C₅×#41	—	2	4	no	—
46	C₂×C₅×#41	C₂×C₄	1	8	yes	—
47	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂³	1	2	yes	—
51	C₂³×C₄×C₅	C₂³	1	4	yes	—
52	C₂³×C₄×C₅	C₂³	1	2	yes	—
53	C₂³×C₄×C₅	C₂³	1	4	yes	—
54	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₄×C₅×Q₈	C₂×C₄	1	16	yes	complemented
56	C₄×C₅×D₄	C₂×C₄	1	32	yes	—
57	C₄×C₅×D₄	C₂×C₄	1	16	yes	complemented
58	C₅×#117	—	2	8	no	—
59	C₅×#117	C₂×C₄	1	8	yes	—
60	C₅×#117	C₂×C₄	1	16	yes	complemented
61	C₂×C₅×C₄⋊C₄	—	2	8	no	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
66	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
72	C₂×C₄²×C₅	C₂×C₄	1	8	yes	—
73	C₂×C₄²×C₅	C₂×C₄	1	16	yes	complemented
74	C₂×C₄²×C₅	C₂³	1	4	yes	—
75	C₂×C₄²×C₅	C₂³	1	16	yes	—
76	C₂×C₄²×C₅	C₂³	1	4	yes	—
77	C₂×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₄²×C₅	C₂³	1	2	yes	—
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₅×#95	C₂³	1	8	yes	—
82	C₅×#95	C₂³	1	8	yes	—
83	C₅×#95	C₂³	1	4	yes	—
84	C₅×#95	C₂³	1	16	yes	—
85	C₅×#95	C₂³	1	4	yes	—
86	C₅×#95	C₂³	1	16	yes	—
87	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic
88	#2357	C₂×C₅	1	4	yes	complemented
89	#2356	C₂×C₅	1	4	yes	complemented
90	#2353	C₂×C₅	1	8	yes	complemented
91	#2314	C₂×C₅	1	4	yes	complemented
92	#2311	C₂×C₅	1	2	yes	—
93	#2285	C₂×C₅	1	1	yes	characteristic, complemented
94	#2283	C₂×C₅	1	4	yes	complemented
95	C₂×#382	C₂×C₅	1	1	yes	characteristic, complemented
96	#2274	C₂×C₅	1	2	yes	complemented
97	C₂⁴×C₅	C₂⁴	1	2	yes	—
98	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
99	C₅×#41	—	2	32	no	—
100	C₂×C₅×Q₈	—	2	2	no	—
101	C₂×C₅×Q₈	—	2	2	no	—
102	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
103	C₂×C₅×D₄	—	2	4	no	—
104	C₂×C₅×D₄	—	2	4	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	—	2	2	no	—
107	C₂×C₅×D₄	C₂²×C₄	1	8	yes	—
108	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₅	—	2	4	no	—
110	C₂²×C₄×C₅	—	2	4	no	—
111	C₂²×C₄×C₅	—	2	8	no	—
112	C₂²×C₄×C₅	—	4	8	no	—
113	C₂²×C₄×C₅	—	4	4	no	—
114	C₂²×C₄×C₅	—	4	8	no	—
115	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
116	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
117	C₂²×C₄×C₅	C₂²×C₄	1	16	yes	—
118	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₅	#41	1	4	yes	—
120	C₂²×C₄×C₅	#41	1	4	yes	—
121	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
122	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×C₄⋊C₄	—	2	8	no	—
130	C₅×C₄⋊C₄	—	2	8	no	—
131	C₅×C₄⋊C₄	—	2	8	no	—
132	C₅×C₄⋊C₄	—	4	8	no	—
133	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
134	C₅×C₄⋊C₄	C₂²×C₄	1	16	yes	—
135	C₅×C₂²⋊C₄	—	2	8	no	—
136	C₅×C₂²⋊C₄	—	4	16	no	—
137	C₅×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
138	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
139	C₄²×C₅	—	2	8	no	—
140	C₄²×C₅	—	4	16	no	—
141	C₄²×C₅	C₂²×C₄	1	4	yes	—
142	C₄²×C₅	C₂²×C₄	1	4	yes	—
143	C₄²×C₅	C₂²×C₄	1	8	yes	—
144	C₄²×C₅	C₂²×C₄	1	8	yes	—
145	C₄²×C₅	C₂²×C₄	1	16	yes	—
146	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
147	C₄×#41	C₄×C₅	1	16	yes	complemented
148	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
149	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
150	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
151	C₂×#117	C₂²×C₅	1	2	yes	—
152	C₂×#117	C₂²×C₅	1	1	yes	characteristic
153	C₂×#117	C₂²×C₅	1	2	yes	—
154	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₄²	C₂²×C₅	1	2	yes	—
157	#391	C₂²×C₅	1	4	yes	—
158	#390	C₂²×C₅	1	4	yes	—
159	#388	C₂²×C₅	1	16	yes	—
160	#387	C₂²×C₅	1	16	yes	—
161	#386	C₂²×C₅	1	8	yes	—
162	#384	C₂²×C₅	1	2	yes	—
163	#383	C₂²×C₅	1	8	yes	—
164	#382	C₂²×C₅	1	2	yes	—
165	#382	C₂²×C₅	1	4	yes	—
166	#382	C₂²×C₅	1	2	yes	—
167	#382	C₂²×C₅	1	2	yes	—
168	#381	C₂²×C₅	1	8	yes	—
169	#380	C₂²×C₅	1	8	yes	—
170	#380	C₂²×C₅	1	4	yes	—
171	C₄×C₄⋊C₄	C₂²×C₅	1	8	yes	—
172	C₄×C₄⋊C₄	C₂²×C₅	1	8	yes	—
173	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
174	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
175	C₄×C₂²⋊C₄	C₂²×C₅	1	8	yes	—
176	#376	C₂²×C₅	1	8	yes	—
177	C₂×#95	C₂²×C₅	1	4	yes	—
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	8	no	—
182	C₂³×C₅	C₂³×C₄	1	4	yes	—
183	C₂³×C₅	C₂³×C₄	1	2	yes	—
184	C₂³×C₅	C₂×#41	1	2	yes	—
185	C₂³×C₅	C₂×#41	1	2	yes	—
186	C₂³×C₅	C₂⁵	1	1	yes	characteristic
187	C₅×Q₈	—	2	8	no	—
188	C₅×D₄	—	2	16	no	—
189	C₅×D₄	—	2	8	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	8	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	16	no	—
196	C₂×C₄×C₅	—	2	8	no	—
197	C₂×C₄×C₅	—	2	8	no	—
198	C₂×C₄×C₅	—	2	8	no	—
199	C₂×C₄×C₅	—	2	16	no	—
200	C₂×C₄×C₅	—	2	8	no	—
201	C₂×C₄×C₅	—	4	8	no	—
202	C₂×C₄×C₅	—	4	16	no	—
203	C₂×C₄×C₅	—	8	8	no	—
204	C₂×C₄×C₅	#117	1	16	yes	—
205	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
206	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
207	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
208	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
209	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
210	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
211	C₂×C₄×C₅	C₂×#41	1	2	yes	—
212	C₂×C₄×C₅	C₂×#41	1	2	yes	—
213	C₂×C₄×C₅	C₂×#41	1	2	yes	—
214	C₂×C₄×C₅	C₂×#41	1	2	yes	—
215	C₂×#41	—	2	4	no	—
216	C₂×#41	—	2	4	no	—
217	C₂×#41	C₂×C₄×C₅	1	8	yes	—
218	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
219	C₂²×D₄	C₂³×C₅	1	2	yes	—
220	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₅	1	2	yes	—
222	C₂³×C₄	C₂³×C₅	1	4	yes	—
223	C₂³×C₄	C₂³×C₅	1	2	yes	—
224	C₂³×C₄	C₂³×C₅	1	4	yes	—
225	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₄×Q₈	C₂×C₄×C₅	1	16	yes	complemented
227	C₄×D₄	C₂×C₄×C₅	1	32	yes	—
228	C₄×D₄	C₂×C₄×C₅	1	16	yes	complemented
229	#117	—	2	8	no	—
230	#117	C₂×C₄×C₅	1	8	yes	—
231	#117	C₂×C₄×C₅	1	16	yes	complemented
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
234	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
235	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
236	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
237	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
243	C₂×C₄²	C₂×C₄×C₅	1	8	yes	—
244	C₂×C₄²	C₂×C₄×C₅	1	16	yes	complemented
245	C₂×C₄²	C₂³×C₅	1	4	yes	—
246	C₂×C₄²	C₂³×C₅	1	16	yes	—
247	C₂×C₄²	C₂³×C₅	1	2	yes	—
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₅	1	4	yes	—
250	C₂×C₄²	C₂³×C₅	1	2	yes	—
251	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
252	#95	C₂³×C₅	1	8	yes	—
253	#95	C₂³×C₅	1	8	yes	—
254	#95	C₂³×C₅	1	4	yes	—
255	#95	C₂³×C₅	1	16	yes	—
256	#95	C₂³×C₅	1	4	yes	—
257	#95	C₂³×C₅	1	16	yes	—
258	C₂²×C₅	—	2	4	no	—
259	C₂²×C₅	—	2	4	no	—
260	C₂²×C₅	—	2	4	no	—
261	C₂²×C₅	—	2	4	no	—
262	C₂²×C₅	—	2	8	no	—
263	C₂²×C₅	—	4	4	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	C₂×#117	1	4	yes	—
266	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
267	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
268	C₂²×C₅	C₂²×#41	1	1	yes	characteristic
269	C₂²×C₅	#585	1	4	yes	—
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	2	8	no	—
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	4	8	no	—
275	C₄×C₅	—	4	8	no	—
276	C₄×C₅	C₂×#117	1	4	yes	—
277	C₄×C₅	C₂×#117	1	4	yes	—
278	C₂⁴	C₂⁴×C₅	1	2	yes	—
279	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
280	#41	—	2	32	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	C₂²×C₄×C₅	1	8	yes	—
289	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	4	8	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	4	8	no	—
296	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
297	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
298	C₂²×C₄	C₂²×C₄×C₅	1	16	yes	—
299	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
300	C₂²×C₄	C₅×#41	1	4	yes	—
301	C₂²×C₄	C₅×#41	1	4	yes	—
302	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
303	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
304	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
307	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	4	8	no	—
314	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
315	C₄⋊C₄	C₂²×C₄×C₅	1	16	yes	—
316	C₂²⋊C₄	—	2	8	no	—
317	C₂²⋊C₄	—	4	16	no	—
318	C₂²⋊C₄	C₂²×C₄×C₅	1	8	yes	—
319	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	—
320	C₄²	—	2	8	no	—
321	C₄²	—	4	16	no	—
322	C₄²	C₂²×C₄×C₅	1	4	yes	—
323	C₄²	C₂²×C₄×C₅	1	4	yes	—
324	C₄²	C₂²×C₄×C₅	1	8	yes	—
325	C₄²	C₂²×C₄×C₅	1	8	yes	—
326	C₄²	C₂²×C₄×C₅	1	16	yes	—
327	C₂×C₅	—	2	4	no	—
328	C₂×C₅	—	4	4	no	—
329	C₂×C₅	C₂²×#117	1	1	yes	characteristic
330	C₂×C₅	#3428	1	2	yes	—
331	C₂×C₅	#3510	1	2	yes	—
332	C₂×C₅	#3512	1	2	yes	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	8	no	—
337	C₂³	C₂³×C₄×C₅	1	4	yes	—
338	C₂³	C₂³×C₄×C₅	1	2	yes	—
339	C₂³	C₂×C₅×#41	1	2	yes	—
340	C₂³	C₂×C₅×#41	1	2	yes	—
341	C₂³	C₂⁵×C₅	1	1	yes	characteristic
342	Q₈	—	2	8	no	—
343	D₄	—	2	16	no	—
344	D₄	—	2	8	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	16	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	16	no	—
358	C₂×C₄	—	8	8	no	—
359	C₂×C₄	C₅×#117	1	16	yes	—
360	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
361	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
362	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
363	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
364	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
365	C₂×C₄	C₂³×C₄×C₅	1	2	yes	—
366	C₂×C₄	C₂×C₅×#41	1	2	yes	—
367	C₂×C₄	C₂×C₅×#41	1	2	yes	—
368	C₂×C₄	C₂×C₅×#41	1	2	yes	—
369	C₂×C₄	C₂×C₅×#41	1	2	yes	—
370	C₅	#34189	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₂×C₅×#117	1	4	yes	—
379	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
380	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
381	C₂²	C₂²×C₅×#41	1	1	yes	characteristic
382	C₂²	C₅×#585	1	4	yes	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	8	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	4	8	no	—
389	C₄	C₂×C₅×#117	1	4	yes	—
390	C₄	C₂×C₅×#117	1	4	yes	—
391	C₂	—	2	4	no	—
392	C₂	—	4	4	no	—
393	C₂	C₂²×C₅×#117	1	1	yes	characteristic
394	C₂	C₅×#3428	1	2	yes	—
395	C₂	C₅×#3510	1	2	yes	—
396	C₂	C₅×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2357	C₂	semidirect
3. C₅×#2356	C₂	semidirect
4. C₅×#2353	C₂	semidirect
5. C₅×#2314	C₂	semidirect
7. C₅×#2285	C₂	semidirect
8. C₅×#2283	C₂	semidirect
9. C₂×C₅×#382	C₂	semidirect
10. C₅×#2274	C₂	semidirect
12. C₄×C₅×#41	C₄	semidirect
43. #34189	C₅	direct (N × H)
55. C₄×C₅×Q₈	C₂×C₄	semidirect
57. C₄×C₅×D₄	C₂×C₄	semidirect
60. C₅×#117	C₂×C₄	semidirect
73. C₂×C₄²×C₅	C₂×C₄	semidirect
88. #2357	C₂×C₅	semidirect
89. #2356	C₂×C₅	semidirect
90. #2353	C₂×C₅	semidirect
91. #2314	C₂×C₅	semidirect
93. #2285	C₂×C₅	semidirect
94. #2283	C₂×C₅	semidirect
95. C₂×#382	C₂×C₅	semidirect
96. #2274	C₂×C₅	semidirect
147. C₄×#41	C₄×C₅	semidirect
226. C₄×Q₈	C₂×C₄×C₅	semidirect
228. C₄×D₄	C₂×C₄×C₅	semidirect
231. #117	C₂×C₄×C₅	semidirect
244. C₂×C₄²	C₂×C₄×C₅	semidirect
370. C₅	#34189	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×C₄×C₅×#41	2
C₅×#2357	2
C₅×#2356	2
C₅×#2353	2
C₅×#2314	2
C₅×#2311	2
C₅×#2285	2
C₅×#2283	2
C₂×C₅×#382	2
C₅×#2274	2
#34189	5

Subgroups — C5×#34189 #11956909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#34189 #11956909