Subgroups — C₅×#69424 #14280290

Order 1920.

1472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃⋊#95	C₂	1	4	yes	maximal
5	C₅×#1446	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
9	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
10	C₂²×C₅×Dic₆	—	2	2	no	—
11	C₂²×C₅×Dic₆	—	2	2	no	—
12	C₂²×C₅×Dic₆	—	2	8	no	—
13	C₂²×C₅×Dic₆	C₄	1	4	yes	complemented
14	C₃×C₅×#95	—	2	2	no	—
15	C₅×C₃⋊#95	—	2	2	no	—
16	C₅×C₃⋊#95	—	2	8	no	—
17	#69424	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂³×C₅×Q₈	—	3	1	no	—
19	C₂×C₅×#95	—	3	4	no	—
20	C₂×C₅×#95	—	3	1	no	—
21	C₂×C₅×#95	D₃	1	1	yes	characteristic
22	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
23	C₂²×C₃×C₄×C₅	—	2	4	no	—
24	C₂²×C₃×C₄×C₅	—	2	4	no	—
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	4	no	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
32	C₂²×C₅×Dic₃	—	2	2	no	—
33	C₂²×C₅×Dic₃	—	2	4	no	—
34	C₂²×C₅×Dic₃	—	2	2	no	—
35	C₂²×C₅×Dic₃	—	2	2	no	—
36	C₂²×C₅×Dic₃	—	2	4	no	—
37	C₂²×C₅×Dic₃	—	2	4	no	—
38	C₂²×C₅×Dic₃	—	2	2	no	—
39	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
40	C₂²×C₅×Dic₃	D₄	1	8	yes	—
41	C₂²×C₅×Dic₃	Q₈	1	4	yes	complemented
42	C₂×C₅×Dic₆	—	2	16	no	—
43	C₂×C₅×Dic₆	—	2	16	no	—
44	C₂×C₅×Dic₆	—	2	8	no	—
45	C₂×C₅×Dic₆	—	2	16	no	—
46	C₂³×Dic₆	C₂×C₅	1	1	yes	characteristic
47	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
48	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic
49	C₂×C₃⋊#95	C₂×C₅	1	4	yes	—
50	C₂²×C₅×Q₈	—	3	4	no	—
51	C₂²×C₅×Q₈	—	6	8	no	—
52	C₂²×C₅×Q₈	—	6	2	no	—
53	C₂²×C₅×Q₈	—	6	2	no	—
54	C₂³×C₄×C₅	—	3	2	no	—
55	C₂³×C₄×C₅	—	3	2	no	—
56	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
57	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
58	C₅×#95	—	2	2	no	—
59	C₅×#95	—	6	8	no	—
60	C₅×#95	—	6	2	no	—
61	#1446	—	3	1	no	Sylow
62	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
63	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
64	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
65	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
67	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
68	C₂³×C₃×C₅	#41	1	2	yes	—
69	C₂³×C₃×C₅	#41	1	2	yes	—
70	C₂×C₃×C₄×C₅	—	2	4	no	—
71	C₂×C₃×C₄×C₅	—	2	4	no	—
72	C₂×C₃×C₄×C₅	—	2	4	no	—
73	C₂×C₃×C₄×C₅	—	2	8	no	—
74	C₂×C₃×C₄×C₅	—	2	4	no	—
75	C₂×C₃×C₄×C₅	—	4	2	no	—
76	C₂×C₃×C₄×C₅	—	4	4	no	—
77	C₂×C₃×C₄×C₅	—	4	2	no	—
78	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
79	C₂×C₅×Dic₃	—	2	4	no	—
80	C₂×C₅×Dic₃	—	2	4	no	—
81	C₂×C₅×Dic₃	—	2	8	no	—
82	C₂×C₅×Dic₃	—	2	8	no	—
83	C₂×C₅×Dic₃	—	2	8	no	—
84	C₂×C₅×Dic₃	—	2	4	no	—
85	C₂×C₅×Dic₃	—	4	2	no	—
86	C₂×C₅×Dic₃	—	4	2	no	—
87	C₂×C₅×Dic₃	—	4	4	no	—
88	C₂×C₅×Dic₃	C₂²⋊C₄	1	8	yes	—
89	C₅×Dic₆	—	2	32	no	—
90	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
91	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
92	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
93	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
94	C₂²×Dic₆	—	2	2	no	—
95	C₂²×Dic₆	—	2	2	no	—
96	C₂²×Dic₆	—	2	8	no	—
97	C₂²×Dic₆	C₄×C₅	1	4	yes	complemented
98	C₃×#95	—	2	2	no	—
99	C₃⋊#95	—	2	2	no	—
100	C₃⋊#95	—	2	8	no	—
101	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
102	C₂×C₅×Q₈	—	6	16	no	—
103	C₂×C₅×Q₈	—	6	16	no	—
104	C₂×C₅×Q₈	—	6	16	no	—
105	C₂×C₅×Q₈	—	6	8	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	2	4	no	—
109	C₂²×C₄×C₅	—	2	4	no	—
110	C₂²×C₄×C₅	—	2	2	no	—
111	C₂²×C₄×C₅	—	3	4	no	—
112	C₂²×C₄×C₅	—	3	8	no	—
113	C₂²×C₄×C₅	—	3	4	no	—
114	C₂²×C₄×C₅	—	6	2	no	—
115	C₂²×C₄×C₅	—	6	4	no	—
116	C₂²×C₄×C₅	—	6	2	no	—
117	C₂²×C₄×C₅	—	6	2	no	—
118	C₂²×C₄×C₅	—	6	4	no	—
119	C₂²×C₄×C₅	—	6	4	no	—
120	C₂²×C₄×C₅	—	6	2	no	—
121	C₂²×C₄×C₅	Dic₆	1	4	yes	complemented
122	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
123	C₂²×C₄×C₅	D₁₂	1	2	yes	—
124	C₂²×C₄×C₅	#67	1	2	yes	—
125	C₂³×Q₈	—	3	1	no	—
126	C₂×#95	—	3	4	no	—
127	C₂×#95	—	3	1	no	—
128	C₂×#95	C₅×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
132	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
133	C₂²×C₃×C₅	#120	1	2	yes	—
134	C₂²×C₃×C₅	#120	1	2	yes	—
135	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
136	C₂²×C₃×C₅	C₂²⋊Q₈	1	4	yes	—
137	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
138	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
139	C₂²×C₃×C₅	#124	1	1	yes	characteristic
140	C₂²×C₃×C₅	#124	1	4	yes	—
141	C₂²×C₃×C₅	#124	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	—
144	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
145	C₃×C₄×C₅	—	2	4	no	—
146	C₃×C₄×C₅	—	4	4	no	—
147	C₅×Dic₃	—	2	8	no	—
148	C₅×Dic₃	—	4	4	no	—
149	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
150	C₂²×C₃×C₄	—	2	4	no	—
151	C₂²×C₃×C₄	—	2	4	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	2	4	no	—
155	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
156	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
157	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
158	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
159	C₂²×Dic₃	—	2	2	no	—
160	C₂²×Dic₃	—	2	4	no	—
161	C₂²×Dic₃	—	2	2	no	—
162	C₂²×Dic₃	—	2	2	no	—
163	C₂²×Dic₃	—	2	4	no	—
164	C₂²×Dic₃	—	2	4	no	—
165	C₂²×Dic₃	—	2	2	no	—
166	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
167	C₂²×Dic₃	C₅×D₄	1	8	yes	—
168	C₂²×Dic₃	C₅×Q₈	1	4	yes	complemented
169	C₂×Dic₆	—	2	16	no	—
170	C₂×Dic₆	—	2	16	no	—
171	C₂×Dic₆	—	2	8	no	—
172	C₂×Dic₆	—	2	16	no	—
173	C₂³×C₅	C₂×Dic₆	1	2	yes	—
174	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
175	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
176	C₂³×C₅	#235	1	2	yes	—
177	C₂³×C₅	D₃×D₄	1	4	yes	—
178	C₂³×C₅	#237	1	2	yes	—
179	C₂³×C₅	D₃×Q₈	1	2	yes	—
180	C₂³×C₅	C₂×#67	1	1	yes	characteristic
181	C₅×Q₈	—	6	32	no	—
182	C₂×C₄×C₅	—	2	4	no	—
183	C₂×C₄×C₅	—	2	4	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	8	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	3	8	no	—
188	C₂×C₄×C₅	—	4	4	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	6	4	no	—
192	C₂×C₄×C₅	—	6	8	no	—
193	C₂×C₄×C₅	—	6	4	no	—
194	C₂×C₄×C₅	—	6	8	no	—
195	C₂×C₄×C₅	—	6	8	no	—
196	C₂×C₄×C₅	—	6	4	no	—
197	C₂×C₄×C₅	—	12	2	no	—
198	C₂×C₄×C₅	—	12	2	no	—
199	C₂×C₄×C₅	—	12	4	no	—
200	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
201	C₂²×Q₈	—	3	4	no	—
202	C₂²×Q₈	—	6	8	no	—
203	C₂²×Q₈	—	6	2	no	—
204	C₂²×Q₈	—	6	2	no	—
205	C₂³×C₄	—	3	2	no	—
206	C₂³×C₄	—	3	2	no	—
207	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
208	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
209	#95	—	2	2	no	—
210	#95	—	6	8	no	—
211	#95	—	6	2	no	—
212	C₂×C₃×C₅	#379	1	1	yes	characteristic
213	C₂×C₃×C₅	#391	1	4	yes	—
214	C₂×C₃×C₅	#391	1	1	yes	characteristic
215	C₂×C₃×C₅	#391	1	1	yes	characteristic
216	C₂×C₃×C₅	#393	1	2	yes	—
217	C₂×C₃×C₅	#393	1	2	yes	—
218	C₂×C₃×C₅	#395	1	2	yes	—
219	C₂×C₃×C₅	#395	1	2	yes	—
220	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
221	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
222	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
223	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
225	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
226	C₂³×C₃	C₅×#41	1	2	yes	—
227	C₂³×C₃	C₅×#41	1	2	yes	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	8	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	—	4	4	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
237	C₂×Dic₃	—	2	4	no	—
238	C₂×Dic₃	—	2	4	no	—
239	C₂×Dic₃	—	2	8	no	—
240	C₂×Dic₃	—	2	8	no	—
241	C₂×Dic₃	—	2	8	no	—
242	C₂×Dic₃	—	2	4	no	—
243	C₂×Dic₃	—	4	2	no	—
244	C₂×Dic₃	—	4	2	no	—
245	C₂×Dic₃	—	4	4	no	—
246	C₂×Dic₃	C₅×C₂²⋊C₄	1	8	yes	—
247	Dic₆	—	2	32	no	—
248	C₂²×C₅	C₄×Dic₆	1	2	yes	—
249	C₂²×C₅	#869	1	1	yes	characteristic
250	C₂²×C₅	#875	1	1	yes	characteristic
251	C₂²×C₅	#878	1	4	yes	—
252	C₂²×C₅	D₃×C₂²⋊C₄	1	2	yes	—
253	C₂²×C₅	#882	1	2	yes	—
254	C₂²×C₅	#885	1	4	yes	—
255	C₂²×C₅	#887	1	2	yes	—
256	C₂²×C₅	#888	1	4	yes	—
257	C₂²×C₅	#896	1	4	yes	—
258	C₂²×C₅	#897	1	2	yes	—
259	C₂²×C₅	#924	1	2	yes	—
260	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
261	C₂²×C₅	#936	1	1	yes	characteristic
262	C₂²×C₅	#937	1	2	yes	—
263	C₂²×C₅	#944	1	1	yes	characteristic
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	4	4	no	—
266	C₄×C₅	—	6	8	no	—
267	C₄×C₅	—	12	4	no	—
268	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
269	C₂×Q₈	—	6	16	no	—
270	C₂×Q₈	—	6	16	no	—
271	C₂×Q₈	—	6	16	no	—
272	C₂×Q₈	—	6	8	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	3	4	no	—
279	C₂²×C₄	—	3	8	no	—
280	C₂²×C₄	—	3	4	no	—
281	C₂²×C₄	—	6	2	no	—
282	C₂²×C₄	—	6	4	no	—
283	C₂²×C₄	—	6	2	no	—
284	C₂²×C₄	—	6	2	no	—
285	C₂²×C₄	—	6	4	no	—
286	C₂²×C₄	—	6	4	no	—
287	C₂²×C₄	—	6	2	no	—
288	C₂²×C₄	C₅×Dic₆	1	4	yes	complemented
289	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
290	C₂²×C₄	C₅×D₁₂	1	2	yes	—
291	C₂²×C₄	C₅×#67	1	2	yes	—
292	C₃×C₅	#1446	1	1	yes	characteristic, complemented, Hall
293	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	2	yes	—
294	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
295	C₂²×C₃	C₄×C₅×Q₈	1	2	yes	—
296	C₂²×C₃	C₄×C₅×Q₈	1	2	yes	—
297	C₂²×C₃	C₅×#120	1	2	yes	—
298	C₂²×C₃	C₅×#120	1	2	yes	—
299	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
300	C₂²×C₃	C₅×C₂²⋊Q₈	1	4	yes	—
301	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
302	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
303	C₂²×C₃	C₅×#124	1	1	yes	characteristic
304	C₂²×C₃	C₅×#124	1	4	yes	—
305	C₂²×C₃	C₅×#124	1	1	yes	characteristic
306	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
307	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	—
308	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	4	4	no	—
311	Dic₃	—	2	8	no	—
312	Dic₃	—	4	4	no	—
313	C₂×C₅	#4646	1	4	yes	—
314	C₂×C₅	#4656	1	2	yes	—
315	C₂×C₅	#4673	1	2	yes	—
316	C₂×C₅	#4929	1	1	yes	characteristic
317	C₂×C₅	#4947	1	2	yes	—
318	C₂×C₅	#4955	1	1	yes	characteristic
319	C₂×C₅	#4973	1	1	yes	characteristic
320	C₂×C₅	#4979	1	2	yes	—
321	C₂³	C₂×C₅×Dic₆	1	2	yes	—
322	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
323	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
324	C₂³	C₅×#235	1	2	yes	—
325	C₂³	C₅×D₃×D₄	1	4	yes	—
326	C₂³	C₅×#237	1	2	yes	—
327	C₂³	C₅×D₃×Q₈	1	2	yes	—
328	C₂³	C₂×C₅×#67	1	1	yes	characteristic
329	Q₈	—	6	32	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	3	8	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	6	4	no	—
340	C₂×C₄	—	6	8	no	—
341	C₂×C₄	—	6	4	no	—
342	C₂×C₄	—	6	8	no	—
343	C₂×C₄	—	6	8	no	—
344	C₂×C₄	—	6	4	no	—
345	C₂×C₄	—	12	2	no	—
346	C₂×C₄	—	12	2	no	—
347	C₂×C₄	—	12	4	no	—
348	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
349	C₂×C₃	C₅×#379	1	1	yes	characteristic
350	C₂×C₃	C₅×#391	1	4	yes	—
351	C₂×C₃	C₅×#391	1	1	yes	characteristic
352	C₂×C₃	C₅×#391	1	1	yes	characteristic
353	C₂×C₃	C₅×#393	1	2	yes	—
354	C₂×C₃	C₅×#393	1	2	yes	—
355	C₂×C₃	C₅×#395	1	2	yes	—
356	C₂×C₃	C₅×#395	1	2	yes	—
357	C₅	#69424	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	C₄×C₅×Dic₆	1	2	yes	—
359	C₂²	C₅×#869	1	1	yes	characteristic
360	C₂²	C₅×#875	1	1	yes	characteristic
361	C₂²	C₅×#878	1	4	yes	—
362	C₂²	C₅×D₃×C₂²⋊C₄	1	2	yes	—
363	C₂²	C₅×#882	1	2	yes	—
364	C₂²	C₅×#885	1	4	yes	—
365	C₂²	C₅×#887	1	2	yes	—
366	C₂²	C₅×#888	1	4	yes	—
367	C₂²	C₅×#896	1	4	yes	—
368	C₂²	C₅×#897	1	2	yes	—
369	C₂²	C₅×#924	1	2	yes	—
370	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
371	C₂²	C₅×#936	1	1	yes	characteristic
372	C₂²	C₅×#937	1	2	yes	—
373	C₂²	C₅×#944	1	1	yes	characteristic
374	C₄	—	2	4	no	—
375	C₄	—	4	4	no	—
376	C₄	—	6	8	no	—
377	C₄	—	12	4	no	—
378	C₃	C₅×#1446	1	1	yes	characteristic, complemented, Sylow
379	C₂	C₅×#4646	1	4	yes	—
380	C₂	C₅×#4656	1	2	yes	—
381	C₂	C₅×#4673	1	2	yes	—
382	C₂	C₅×#4929	1	1	yes	characteristic
383	C₂	C₅×#4947	1	2	yes	—
384	C₂	C₅×#4955	1	1	yes	characteristic
385	C₂	C₅×#4973	1	1	yes	characteristic
386	C₂	C₅×#4979	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#95	C₂
socle, prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₅×#95	D₃
hypocenter	C₃	C₅×#1446
LCS	G ▷ C₂³×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂×C₅×#95

Complements

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

N	H ≅ G/N	type
13. C₂²×C₅×Dic₆	C₄	semidirect
17. #69424	C₅	direct (N × H)
31. C₂²×C₃×C₄×C₅	Q₈	semidirect
41. C₂²×C₅×Dic₃	Q₈	semidirect
97. C₂²×Dic₆	C₄×C₅	semidirect
121. C₂²×C₄×C₅	Dic₆	semidirect
158. C₂²×C₃×C₄	C₅×Q₈	semidirect
168. C₂²×Dic₃	C₅×Q₈	semidirect
288. C₂²×C₄	C₅×Dic₆	semidirect
292. C₃×C₅	#1446	semidirect
357. C₅	#69424	direct (N × H)
378. C₃	C₅×#1446	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₆	2
C₂×C₃×C₅×#95	2
C₂×C₅×C₃⋊#95	2
C₅×#1446	3
#69424	5

Subgroups — C5×#69424 #14280290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69424 #14280290