Subgroups — C₅×#21304 #11944024

Order 1280.

1162 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×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#1985	C₂	1	4	yes	maximal, complemented
5	C₅×#1984	C₂	1	4	yes	maximal, complemented
6	C₅×#1729	C₂	1	1	yes	maximal, characteristic
7	C₅×#1729	C₂	1	1	yes	maximal, characteristic
8	C₅×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#533	—	2	4	no	—
15	C₅×#533	—	2	4	no	—
16	C₂×C₅×C₄⋊Q₈	C₄	1	2	yes	—
17	C₂×C₅×#125	C₄	1	2	yes	—
18	C₂×C₅×C₂²⋊Q₈	C₄	1	4	yes	—
19	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
20	C₂×C₅×#117	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#424	—	2	4	no	—
24	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
25	C₅×#405	—	2	4	no	—
26	C₂×C₅×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
28	C₅×#336	C₂²	1	2	yes	—
29	C₅×#336	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	4	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	#21304	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₅×Q₈	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×M₁₆	—	2	2	no	—
39	C₂×C₅×M₁₆	—	2	2	no	—
40	C₂×C₅×M₁₆	—	2	2	no	—
41	C₂×C₅×M₁₆	—	2	2	no	—
42	C₂×C₅×M₁₆	—	2	2	no	—
43	C₂×C₅×M₁₆	Q₈	1	4	yes	complemented
44	C₂²×C₅×C₈	—	2	2	no	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	—	2	2	no	—
49	C₂²×C₅×C₈	Q₈	1	4	yes	complemented
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	—	2	8	no	—
56	C₅×#125	—	2	8	no	—
57	C₅×C₂²⋊Q₈	—	2	16	no	—
58	C₄×C₅×Q₈	—	2	8	no	—
59	C₄×C₅×Q₈	—	2	8	no	—
60	C₅×#117	—	2	2	no	—
61	C₅×#117	—	2	2	no	—
62	C₅×#117	D₄	1	4	yes	—
63	C₅×#117	D₄	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
66	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₅	—	2	2	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	2	yes	—
75	C₂×C₄²×C₅	C₂³	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	2	yes	—
77	C₅×C₄⋊C₈	—	2	8	no	—
78	C₅×#97	—	2	4	no	—
79	C₄×C₅×C₈	—	2	4	no	—
80	C₂×#533	C₂×C₅	1	1	yes	characteristic
81	C₂×#424	C₂×C₅	1	1	yes	characteristic
82	C₂×#405	C₂×C₅	1	1	yes	characteristic
83	#1985	C₂×C₅	1	4	yes	complemented
84	#1984	C₂×C₅	1	4	yes	complemented
85	#1729	C₂×C₅	1	1	yes	characteristic
86	#1729	C₂×C₅	1	1	yes	characteristic
87	#1728	C₂×C₅	1	1	yes	characteristic
88	C₂×#336	C₂×C₅	1	1	yes	characteristic
89	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₅×Q₈	—	2	8	no	—
91	C₂×C₅×Q₈	—	2	8	no	—
92	C₂×C₅×Q₈	—	4	4	no	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	—	2	4	no	—
95	C₂²×C₄×C₅	—	4	2	no	—
96	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
105	C₂²×C₄×C₅	#41	1	2	yes	—
106	C₂²×C₄×C₅	#41	1	2	yes	—
107	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
108	C₅×M₁₆	—	2	8	no	—
109	C₅×M₁₆	—	4	4	no	—
110	C₂×C₅×C₈	—	2	8	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	4	4	no	—
124	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
125	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
126	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	16	no	—
129	C₅×C₄⋊C₄	—	2	8	no	—
130	C₅×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₅×C₂²⋊C₄	C₂²⋊C₄	1	8	yes	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	C₂×D₄	1	4	yes	—
140	C₄²×C₅	C₂×D₄	1	4	yes	—
141	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
142	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
143	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
145	#533	—	2	4	no	—
146	#533	—	2	4	no	—
147	C₂×C₄⋊Q₈	C₄×C₅	1	2	yes	—
148	C₂×#125	C₄×C₅	1	2	yes	—
149	C₂×C₂²⋊Q₈	C₄×C₅	1	4	yes	—
150	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
151	C₂×#117	C₂²×C₅	1	1	yes	characteristic
152	C₂×#117	C₂²×C₅	1	1	yes	characteristic
153	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
154	#424	—	2	4	no	—
155	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
156	#405	—	2	4	no	—
157	C₂×#97	C₂²×C₅	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
159	#336	C₂²×C₅	1	2	yes	—
160	#336	C₂²×C₅	1	2	yes	—
161	#336	C₂²×C₅	1	4	yes	—
162	#336	C₂²×C₅	1	2	yes	—
163	#336	C₂²×C₅	1	4	yes	—
164	#336	C₂²×C₅	1	2	yes	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂³×C₅	C₄×Q₈	1	2	yes	—
169	C₂³×C₅	C₄×Q₈	1	2	yes	—
170	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₅×Q₈	—	4	16	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	4	8	no	—
183	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	—
184	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
186	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
187	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
188	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
189	C₂×C₄×C₅	#124	1	4	yes	—
190	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
191	C₂×C₄×C₅	#131	1	4	yes	—
192	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
198	C₅×C₈	—	2	2	no	—
199	C₅×C₈	—	2	2	no	—
200	C₅×C₈	—	2	4	no	—
201	C₅×C₈	—	4	2	no	—
202	C₅×C₈	—	4	2	no	—
203	C₂²×Q₈	C₂×C₄×C₅	1	4	yes	—
204	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
205	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	2	no	—
208	C₂×M₁₆	—	2	2	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	C₅×Q₈	1	4	yes	complemented
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	2	2	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	C₅×Q₈	1	4	yes	complemented
218	C₂²×C₈	C₂³×C₅	1	2	yes	—
219	C₂²×C₈	C₂³×C₅	1	2	yes	—
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₄⋊Q₈	—	2	8	no	—
224	#125	—	2	8	no	—
225	C₂²⋊Q₈	—	2	16	no	—
226	C₄×Q₈	—	2	8	no	—
227	C₄×Q₈	—	2	8	no	—
228	#117	—	2	2	no	—
229	#117	—	2	2	no	—
230	#117	C₅×D₄	1	4	yes	—
231	#117	C₅×D₄	1	4	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
234	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
235	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₅	1	2	yes	—
243	C₂×C₄²	C₂³×C₅	1	2	yes	—
244	C₂×C₄²	C₂³×C₅	1	2	yes	—
245	C₄⋊C₈	—	2	8	no	—
246	#97	—	2	4	no	—
247	C₄×C₈	—	2	4	no	—
248	C₂²×C₅	—	2	4	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	2	no	—
251	C₂²×C₅	—	2	4	no	—
252	C₂²×C₅	#391	1	4	yes	—
253	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
255	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
256	C₂²×C₅	C₂×#131	1	2	yes	—
257	C₂²×C₅	#568	1	2	yes	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	2	8	no	—
260	C₄×C₅	—	4	2	no	—
261	C₄×C₅	—	4	4	no	—
262	C₄×C₅	#391	1	4	yes	—
263	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₄×C₅	C₂×#124	1	1	yes	characteristic
266	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
267	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	—	2	8	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
276	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
280	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
281	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
282	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
283	C₂²×C₄	C₅×#41	1	2	yes	—
284	C₂²×C₄	C₅×#41	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
286	M₁₆	—	2	8	no	—
287	M₁₆	—	4	4	no	—
288	C₂×C₈	—	2	8	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	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	—	4	4	no	—
302	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
303	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
304	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	16	no	—
307	C₄⋊C₄	—	2	8	no	—
308	C₄⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₂²⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	C₂×C₅×D₄	1	4	yes	—
318	C₄²	C₂×C₅×D₄	1	4	yes	—
319	C₂×C₅	—	2	4	no	—
320	C₂×C₅	C₂×#391	1	1	yes	characteristic
321	C₂×C₅	#2880	1	2	yes	—
322	C₂×C₅	#2960	1	1	yes	characteristic
323	C₂×C₅	#2961	1	1	yes	characteristic
324	C₂×C₅	#2962	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
328	C₂³	C₄×C₅×Q₈	1	2	yes	—
329	C₂³	C₄×C₅×Q₈	1	2	yes	—
330	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
331	Q₈	—	4	16	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	8	no	—
343	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	8	yes	—
344	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
345	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
346	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
347	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
348	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
349	C₂×C₄	C₅×#124	1	4	yes	—
350	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
351	C₂×C₄	C₅×#131	1	4	yes	—
352	C₂×C₄	C₂²×C₅×D₄	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	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	4	no	—
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₅	#21304	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	C₅×#391	1	4	yes	—
369	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
371	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
372	C₂²	C₂×C₅×#131	1	2	yes	—
373	C₂²	C₅×#568	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	8	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	C₅×#391	1	4	yes	—
379	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
380	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
381	C₄	C₂×C₅×#124	1	1	yes	characteristic
382	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×C₅×#391	1	1	yes	characteristic
385	C₂	C₅×#2880	1	2	yes	—
386	C₂	C₅×#2960	1	1	yes	characteristic
387	C₂	C₅×#2961	1	1	yes	characteristic
388	C₂	C₅×#2962	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×#1985	C₂	semidirect
5. C₅×#1984	C₂	semidirect
34. #21304	C₅	direct (N × H)
43. C₂×C₅×M₁₆	Q₈	semidirect
49. C₂²×C₅×C₈	Q₈	semidirect
83. #1985	C₂×C₅	semidirect
84. #1984	C₂×C₅	semidirect
211. C₂×M₁₆	C₅×Q₈	semidirect
217. C₂²×C₈	C₅×Q₈	semidirect
363. C₅	#21304	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×#533	2
C₂×C₅×#424	2
C₂×C₅×#405	2
C₅×#1985	2
C₅×#1984	2
C₅×#1729	2
C₅×#1728	2
C₂×C₅×#336	2
#21304	5

Subgroups — C5×#21304 #11944024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21304 #11944024