Subgroups — C₅×#21169 #11943889

Order 1280.

1026 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#427	C₂	1	2	yes	maximal
2	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2285	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic
5	C₅×#1949	C₂	1	4	yes	maximal, complemented
6	C₅×#1948	C₂	1	2	yes	maximal, complemented
7	C₅×#1947	C₂	1	2	yes	maximal, complemented
8	C₅×#1735	C₂	1	2	yes	maximal
9	C₂³×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₅×#117	C₂²	1	2	yes	—
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#427	—	2	8	no	—
15	C₂×C₅×#107	C₂²	1	4	yes	—
16	C₂×C₅×#106	C₂²	1	4	yes	—
17	C₂×C₅×C₄⋊C₈	C₄	1	8	yes	complemented
18	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₅×#384	C₂²	1	2	yes	—
22	C₅×#382	C₂²	1	2	yes	—
23	C₅×#380	—	2	1	no	—
24	C₅×#380	—	2	1	no	—
25	C₄×C₅×C₄⋊C₄	—	2	1	no	—
26	C₄×C₅×C₄⋊C₄	—	2	1	no	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
30	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
31	C₅×#376	—	2	1	no	—
32	C₄³×C₅	—	2	1	no	—
33	C₅×#340	C₂²	1	4	yes	—
34	C₅×#340	C₂²	1	4	yes	—
35	#21169	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×C₈	—	2	4	no	—
40	C₂²×C₅×C₈	—	2	4	no	—
41	C₂²×C₅×C₈	C₂×C₄	1	8	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₅×#117	—	2	2	no	—
45	C₅×#117	—	2	2	no	—
46	C₅×#117	—	2	4	no	—
47	C₅×#117	—	2	4	no	—
48	C₅×#117	D₄	1	4	yes	—
49	C₅×#117	Q₈	1	4	yes	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
53	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₄²×C₅	—	2	1	no	—
59	C₂×C₄²×C₅	—	2	1	no	—
60	C₂×C₄²×C₅	—	2	2	no	—
61	C₂×C₄²×C₅	—	2	2	no	—
62	C₂×C₄²×C₅	—	2	2	no	—
63	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	Q₈	1	4	yes	—
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#107	—	2	8	no	—
70	C₅×#106	—	2	8	no	—
71	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
72	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
73	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	—
74	C₅×#95	—	2	2	no	—
75	C₅×#95	—	2	2	no	—
76	C₅×#95	—	2	2	no	—
77	C₅×#95	—	2	2	no	—
78	C₂×#427	C₂×C₅	1	2	yes	—
79	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
80	#2285	C₂×C₅	1	1	yes	characteristic
81	C₄×#117	C₂×C₅	1	1	yes	characteristic
82	#1949	C₂×C₅	1	4	yes	complemented
83	#1948	C₂×C₅	1	2	yes	complemented
84	#1947	C₂×C₅	1	2	yes	complemented
85	#1735	C₂×C₅	1	2	yes	—
86	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	4	no	—
91	C₂²×C₄×C₅	—	4	2	no	—
92	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₅	#41	1	2	yes	—
104	C₂²×C₄×C₅	#41	1	2	yes	—
105	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
106	C₂×C₅×C₈	—	2	16	no	—
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	C₂²×C₄	1	4	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
113	C₅×C₄⋊C₄	—	2	2	no	—
114	C₅×C₄⋊C₄	—	2	2	no	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	2	4	no	—
117	C₅×C₄⋊C₄	—	4	4	no	—
118	C₅×C₄⋊C₄	—	4	4	no	—
119	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
120	C₅×C₄⋊C₄	C₂×Q₈	1	4	yes	—
121	C₅×C₂²⋊C₄	—	2	4	no	—
122	C₅×C₂²⋊C₄	—	2	4	no	—
123	C₅×C₂²⋊C₄	—	4	4	no	—
124	C₄²×C₅	—	2	4	no	—
125	C₄²×C₅	—	2	4	no	—
126	C₄²×C₅	—	4	4	no	—
127	C₄²×C₅	—	4	4	no	—
128	C₄²×C₅	—	4	4	no	—
129	C₄²×C₅	C₄⋊C₄	1	4	yes	—
130	C₄²×C₅	C₄⋊C₄	1	4	yes	—
131	C₄²×C₅	C₂²×C₄	1	2	yes	—
132	C₄²×C₅	C₂²×C₄	1	2	yes	—
133	C₄²×C₅	C₂×Q₈	1	2	yes	—
134	C₄²×C₅	C₂×Q₈	1	2	yes	—
135	C₂³×C₈	C₂²×C₅	1	2	yes	—
136	C₂×#117	C₂²×C₅	1	2	yes	—
137	C₂×#117	C₂²×C₅	1	1	yes	characteristic
138	C₂×#117	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
140	#427	—	2	8	no	—
141	C₂×#107	C₂²×C₅	1	4	yes	—
142	C₂×#106	C₂²×C₅	1	4	yes	—
143	C₂×C₄⋊C₈	C₄×C₅	1	8	yes	complemented
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	#384	C₂²×C₅	1	2	yes	—
148	#382	C₂²×C₅	1	2	yes	—
149	#380	—	2	1	no	—
150	#380	—	2	1	no	—
151	C₄×C₄⋊C₄	—	2	1	no	—
152	C₄×C₄⋊C₄	—	2	1	no	—
153	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₄×C₂²⋊C₄	—	2	1	no	—
156	C₄×C₂²⋊C₄	—	2	1	no	—
157	#376	—	2	1	no	—
158	C₄³	—	2	1	no	—
159	#340	C₂²×C₅	1	4	yes	—
160	#340	C₂²×C₅	1	4	yes	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	2	2	no	—
163	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
164	C₂³×C₅	#121	1	2	yes	—
165	C₂³×C₅	C₂²⋊Q₈	1	2	yes	—
166	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	2	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	8	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	4	4	no	—
174	C₂×C₄×C₅	—	4	2	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	—	4	2	no	—
177	C₂×C₄×C₅	—	4	2	no	—
178	C₂×C₄×C₅	—	4	4	no	—
179	C₂×C₄×C₅	—	4	4	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
182	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
184	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
185	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
186	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₅	C₄×Q₈	1	4	yes	—
188	C₂×C₄×C₅	#121	1	2	yes	—
189	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄×C₅	#125	1	4	yes	—
191	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
192	C₂×C₄×C₅	#135	1	4	yes	—
193	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
199	C₅×C₈	—	2	4	no	—
200	C₅×C₈	—	2	4	no	—
201	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	—	2	4	no	—
206	C₂²×C₈	C₂×C₄×C₅	1	8	yes	—
207	C₂²×C₈	C₂³×C₅	1	2	yes	—
208	C₂²×C₈	C₂³×C₅	1	2	yes	—
209	#117	—	2	2	no	—
210	#117	—	2	2	no	—
211	#117	—	2	4	no	—
212	#117	—	2	4	no	—
213	#117	C₅×D₄	1	4	yes	—
214	#117	C₅×Q₈	1	4	yes	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
218	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
219	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₂²⋊C₄	—	2	1	no	—
222	C₂×C₂²⋊C₄	—	2	2	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	—	2	1	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
229	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
230	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
231	C₂×C₄²	C₅×Q₈	1	4	yes	—
232	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
234	#107	—	2	8	no	—
235	#106	—	2	8	no	—
236	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
237	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
238	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	C₂²×C₅	—	2	4	no	—
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	4	no	—
247	C₂²×C₅	#389	1	4	yes	—
248	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₅	C₂×#121	1	1	yes	characteristic
250	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
251	C₂²×C₅	C₂×#135	1	2	yes	—
252	C₂²×C₅	#575	1	2	yes	—
253	C₄×C₅	—	2	2	no	—
254	C₄×C₅	—	2	2	no	—
255	C₄×C₅	—	2	2	no	—
256	C₄×C₅	—	4	4	no	—
257	C₄×C₅	—	4	4	no	—
258	C₄×C₅	—	8	4	no	—
259	C₄×C₅	#389	1	4	yes	—
260	C₄×C₅	#427	1	4	yes	complemented
261	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
262	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
263	C₄×C₅	C₂×#125	1	1	yes	characteristic
264	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
265	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
272	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
274	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
280	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
281	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
282	C₂²×C₄	C₅×#41	1	2	yes	—
283	C₂²×C₄	C₅×#41	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
285	C₂×C₈	—	2	16	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
291	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	4	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
299	C₄⋊C₄	C₂×C₅×Q₈	1	4	yes	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	—	2	4	no	—
305	C₄²	—	4	4	no	—
306	C₄²	—	4	4	no	—
307	C₄²	—	4	4	no	—
308	C₄²	C₅×C₄⋊C₄	1	4	yes	—
309	C₄²	C₅×C₄⋊C₄	1	4	yes	—
310	C₄²	C₂²×C₄×C₅	1	2	yes	—
311	C₄²	C₂²×C₄×C₅	1	2	yes	—
312	C₄²	C₂×C₅×Q₈	1	2	yes	—
313	C₄²	C₂×C₅×Q₈	1	2	yes	—
314	C₂×C₅	—	2	4	no	—
315	C₂×C₅	C₂×#389	1	1	yes	characteristic
316	C₂×C₅	C₂×#427	1	1	yes	characteristic
317	C₂×C₅	#2911	1	1	yes	characteristic
318	C₂×C₅	#3035	1	2	yes	—
319	C₂×C₅	#3076	1	2	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
323	C₂³	C₅×#121	1	2	yes	—
324	C₂³	C₅×C₂²⋊Q₈	1	2	yes	—
325	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
341	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
342	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
343	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
344	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
345	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
346	C₂×C₄	C₄×C₅×Q₈	1	4	yes	—
347	C₂×C₄	C₅×#121	1	2	yes	—
348	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
349	C₂×C₄	C₅×#125	1	4	yes	—
350	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
351	C₂×C₄	C₅×#135	1	4	yes	—
352	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
357	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
358	C₈	—	2	4	no	—
359	C₈	—	2	4	no	—
360	C₅	#21169	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	4	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	C₅×#389	1	4	yes	—
366	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
367	C₂²	C₂×C₅×#121	1	1	yes	characteristic
368	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
369	C₂²	C₂×C₅×#135	1	2	yes	—
370	C₂²	C₅×#575	1	2	yes	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	4	no	—
376	C₄	—	8	4	no	—
377	C₄	C₅×#389	1	4	yes	—
378	C₄	C₅×#427	1	4	yes	complemented
379	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
380	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
381	C₄	C₂×C₅×#125	1	1	yes	characteristic
382	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×C₅×#389	1	1	yes	characteristic
385	C₂	C₂×C₅×#427	1	1	yes	characteristic
386	C₂	C₅×#2911	1	1	yes	characteristic
387	C₂	C₅×#3035	1	2	yes	—
388	C₂	C₅×#3076	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1949	C₂	semidirect
6. C₅×#1948	C₂	semidirect
7. C₅×#1947	C₂	semidirect
17. C₂×C₅×C₄⋊C₈	C₄	semidirect
35. #21169	C₅	direct (N × H)
82. #1949	C₂×C₅	semidirect
83. #1948	C₂×C₅	semidirect
84. #1947	C₂×C₅	semidirect
143. C₂×C₄⋊C₈	C₄×C₅	semidirect
260. C₄×C₅	#427	semidirect
360. C₅	#21169	direct (N × H)
378. C₄	C₅×#427	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#427	2
C₂²×C₅×C₄⋊C₈	2
C₅×#2285	2
C₄×C₅×#117	2
C₅×#1949	2
C₅×#1948	2
C₅×#1947	2
C₅×#1735	2
#21169	5

Subgroups — C5×#21169 #11943889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21169 #11943889