Subgroups — C₅×#5708 #11756093

Order 960.

428 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#883	C₂	1	1	yes	maximal, characteristic
9	C₅×#883	C₂	1	1	yes	maximal, characteristic
10	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₅×#879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#552	—	3	1	no	maximal, Hall
17	C₂×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₅×#217	C₂²	1	1	yes	characteristic
31	C₅×#217	C₂²	1	1	yes	characteristic
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
38	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
39	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
49	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
50	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
51	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
52	#5708	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×#126	—	3	1	no	—
54	C₅×#126	D₃	1	1	yes	characteristic, complemented
55	C₅×#125	—	3	1	no	—
56	C₅×#125	—	3	1	no	—
57	C₅×#125	—	3	1	no	—
58	C₅×#123	—	3	1	no	—
59	C₅×#123	—	3	1	no	—
60	C₅×C₂²⋊Q₈	—	3	1	no	—
61	C₅×C₂²⋊Q₈	—	3	1	no	—
62	C₄×C₅×Q₈	—	3	1	no	—
63	C₄×C₅×D₄	—	3	1	no	—
64	C₅×#117	—	3	1	no	—
65	C₅×#117	—	3	1	no	—
66	C₅×#117	—	3	1	no	—
67	C₂×C₅×C₄⋊C₄	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₅×#67	—	2	2	no	—
77	C₂×C₅×Dic₃	—	2	2	no	—
78	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₄×C₅×D₃	—	2	2	no	—
86	C₄×C₅×D₃	—	2	2	no	—
87	C₄×C₅×D₃	—	2	2	no	—
88	C₅×Dic₆	—	2	2	no	—
89	C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
90	#896	C₂×C₅	1	1	yes	characteristic, complemented
91	#892	C₂×C₅	1	1	yes	characteristic, complemented
92	D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
93	#890	C₂×C₅	1	1	yes	characteristic, complemented
94	#889	C₂×C₅	1	1	yes	characteristic, complemented
95	#889	C₂×C₅	1	1	yes	characteristic, complemented
96	#883	C₂×C₅	1	1	yes	characteristic
97	#883	C₂×C₅	1	1	yes	characteristic
98	#67⋊C₄	C₂×C₅	1	1	yes	characteristic
99	#879	C₂×C₅	1	1	yes	characteristic, complemented
100	#878	C₂×C₅	1	1	yes	characteristic, complemented
101	#877	C₂×C₅	1	1	yes	characteristic, complemented
102	#872	C₂×C₅	1	1	yes	characteristic, complemented
103	C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×Q₈	—	3	1	no	—
105	C₂×C₅×D₄	—	3	1	no	—
106	C₂²×C₄×C₅	—	3	1	no	—
107	C₂²×C₄×C₅	—	3	1	no	—
108	C₂²×C₄×C₅	—	3	1	no	—
109	C₂²×C₄×C₅	—	3	1	no	—
110	C₅×C₄⋊C₄	—	3	1	no	—
111	C₅×C₄⋊C₄	—	3	1	no	—
112	C₅×C₄⋊C₄	—	3	1	no	—
113	C₅×C₄⋊C₄	—	3	1	no	—
114	C₅×C₄⋊C₄	—	3	1	no	—
115	C₅×C₄⋊C₄	—	3	1	no	—
116	C₅×C₄⋊C₄	—	3	1	no	—
117	C₅×C₄⋊C₄	—	3	1	no	—
118	C₅×C₄⋊C₄	—	3	1	no	—
119	C₅×C₄⋊C₄	—	3	1	no	—
120	C₅×C₄⋊C₄	—	3	1	no	—
121	C₅×C₄⋊C₄	—	3	1	no	—
122	C₅×C₄⋊C₄	—	3	1	no	—
123	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₅×C₂²⋊C₄	—	3	1	no	—
127	C₅×C₂²⋊C₄	—	3	1	no	—
128	C₅×C₂²⋊C₄	—	3	1	no	—
129	C₅×C₂²⋊C₄	—	3	1	no	—
130	C₅×C₂²⋊C₄	—	3	1	no	—
131	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₄²×C₅	—	3	1	no	—
135	C₄²×C₅	—	3	1	no	—
136	C₄²×C₅	—	3	1	no	—
137	C₄²×C₅	—	3	1	no	—
138	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
139	#552	—	3	1	no	Sylow
140	C₂²×C₃×C₅	—	2	1	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	2	1	no	—
143	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
144	C₂×C₅×D₃	—	2	1	no	—
145	C₂×C₅×D₃	—	2	1	no	—
146	C₂×C₅×D₃	#41	1	2	yes	—
147	C₃×C₄×C₅	—	2	1	no	—
148	C₃×C₄×C₅	—	2	1	no	—
149	C₃×C₄×C₅	—	2	1	no	—
150	C₃×C₄×C₅	—	2	1	no	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₅×Dic₃	—	2	1	no	—
154	C₅×Dic₃	—	2	1	no	—
155	C₅×Dic₃	—	2	1	no	—
156	C₅×Dic₃	—	2	1	no	—
157	C₅×Dic₃	—	2	1	no	—
158	C₅×Dic₃	—	2	1	no	—
159	C₅×Dic₃	#41	1	2	yes	—
160	C₂×#67	C₂²×C₅	1	1	yes	characteristic
161	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
165	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
166	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
173	#217	C₂²×C₅	1	1	yes	characteristic
174	#217	C₂²×C₅	1	1	yes	characteristic
175	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
179	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
180	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
181	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
182	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
190	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
192	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
193	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
194	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
195	C₂³×C₅	—	3	1	no	—
196	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₅×Q₈	—	6	2	no	—
198	C₅×D₄	—	6	2	no	—
199	C₂×C₄×C₅	—	3	1	no	—
200	C₂×C₄×C₅	—	3	1	no	—
201	C₂×C₄×C₅	—	3	1	no	—
202	C₂×C₄×C₅	—	3	1	no	—
203	C₂×C₄×C₅	—	3	1	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂×C₄×C₅	—	6	2	no	—
207	C₂×C₄×C₅	—	6	2	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	—	6	2	no	—
210	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
216	#126	—	3	1	no	—
217	#126	C₅×D₃	1	1	yes	characteristic, complemented
218	#125	—	3	1	no	—
219	#125	—	3	1	no	—
220	#125	—	3	1	no	—
221	#123	—	3	1	no	—
222	#123	—	3	1	no	—
223	C₂²⋊Q₈	—	3	1	no	—
224	C₂²⋊Q₈	—	3	1	no	—
225	C₄×Q₈	—	3	1	no	—
226	C₄×D₄	—	3	1	no	—
227	#117	—	3	1	no	—
228	#117	—	3	1	no	—
229	#117	—	3	1	no	—
230	C₂×C₄⋊C₄	—	3	1	no	—
231	C₂×C₃×C₅	—	4	1	no	—
232	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
235	C₅×D₃	—	2	2	no	—
236	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
237	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	#67	—	2	2	no	—
245	C₂×Dic₃	—	2	2	no	—
246	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
247	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
248	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
249	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
250	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
251	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
252	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
253	C₄×D₃	—	2	2	no	—
254	C₄×D₃	—	2	2	no	—
255	C₄×D₃	—	2	2	no	—
256	Dic₆	—	2	2	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	3	2	no	—
261	C₂²×C₅	—	6	1	no	—
262	C₂²×C₅	—	6	1	no	—
263	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
264	C₄×C₅	—	2	1	no	—
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	3	2	no	—
271	C₄×C₅	—	6	1	no	—
272	C₄×C₅	—	6	1	no	—
273	C₄×C₅	—	6	1	no	—
274	C₄×C₅	—	6	1	no	—
275	C₄×C₅	—	6	1	no	—
276	C₄×C₅	—	6	1	no	—
277	C₂×Q₈	—	3	1	no	—
278	C₂×D₄	—	3	1	no	—
279	C₂²×C₄	—	3	1	no	—
280	C₂²×C₄	—	3	1	no	—
281	C₂²×C₄	—	3	1	no	—
282	C₂²×C₄	—	3	1	no	—
283	C₄⋊C₄	—	3	1	no	—
284	C₄⋊C₄	—	3	1	no	—
285	C₄⋊C₄	—	3	1	no	—
286	C₄⋊C₄	—	3	1	no	—
287	C₄⋊C₄	—	3	1	no	—
288	C₄⋊C₄	—	3	1	no	—
289	C₄⋊C₄	—	3	1	no	—
290	C₄⋊C₄	—	3	1	no	—
291	C₄⋊C₄	—	3	1	no	—
292	C₄⋊C₄	—	3	1	no	—
293	C₄⋊C₄	—	3	1	no	—
294	C₄⋊C₄	—	3	1	no	—
295	C₄⋊C₄	—	3	1	no	—
296	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
297	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
298	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
299	C₂²⋊C₄	—	3	1	no	—
300	C₂²⋊C₄	—	3	1	no	—
301	C₂²⋊C₄	—	3	1	no	—
302	C₂²⋊C₄	—	3	1	no	—
303	C₂²⋊C₄	—	3	1	no	—
304	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
305	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
307	C₄²	—	3	1	no	—
308	C₄²	—	3	1	no	—
309	C₄²	—	3	1	no	—
310	C₄²	—	3	1	no	—
311	C₄²	C₂×C₅×D₃	1	1	yes	characteristic
312	C₃×C₅	#552	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	—	2	1	no	—
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
317	C₂×D₃	—	2	1	no	—
318	C₂×D₃	—	2	1	no	—
319	C₂×D₃	C₅×#41	1	2	yes	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	Dic₃	—	2	1	no	—
327	Dic₃	—	2	1	no	—
328	Dic₃	—	2	1	no	—
329	Dic₃	—	2	1	no	—
330	Dic₃	—	2	1	no	—
331	Dic₃	—	2	1	no	—
332	Dic₃	C₅×#41	1	2	yes	—
333	C₂×C₅	—	4	1	no	—
334	C₂×C₅	—	6	2	no	—
335	C₂×C₅	D₃×#41	1	1	yes	characteristic
336	C₂×C₅	D₃×#41	1	1	yes	characteristic
337	C₂×C₅	#1010	1	1	yes	characteristic
338	C₂³	—	3	1	no	—
339	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
340	Q₈	—	6	2	no	—
341	D₄	—	6	2	no	—
342	C₂×C₄	—	3	1	no	—
343	C₂×C₄	—	3	1	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	3	1	no	—
346	C₂×C₄	—	3	1	no	—
347	C₂×C₄	—	3	1	no	—
348	C₂×C₄	—	3	1	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	6	2	no	—
352	C₂×C₄	—	6	2	no	—
353	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
359	C₂×C₃	—	4	1	no	—
360	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
361	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
362	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
363	D₃	—	2	2	no	—
364	C₅	#5708	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	3	2	no	—
369	C₂²	—	6	1	no	—
370	C₂²	—	6	1	no	—
371	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	3	2	no	—
379	C₄	—	6	1	no	—
380	C₄	—	6	1	no	—
381	C₄	—	6	1	no	—
382	C₄	—	6	1	no	—
383	C₄	—	6	1	no	—
384	C₄	—	6	1	no	—
385	C₃	C₅×#552	1	1	yes	characteristic, complemented, Sylow
386	C₂	—	4	1	no	—
387	C₂	—	6	2	no	—
388	C₂	C₅×D₃×#41	1	1	yes	characteristic
389	C₂	C₅×D₃×#41	1	1	yes	characteristic
390	C₂	C₅×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#126	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#67	C₂²
hypercenter	C₅×#126	D₃
hypocenter	C₃	C₅×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#126

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#126	C₂	semidirect
2. C₅×#896	C₂	semidirect
3. C₅×#892	C₂	semidirect
4. C₅×D₃×C₄⋊C₄	C₂	semidirect
5. C₅×#890	C₂	semidirect
6. C₅×#889	C₂	semidirect
7. C₅×#889	C₂	semidirect
11. C₅×#879	C₂	semidirect
12. C₅×#878	C₂	semidirect
13. C₅×#877	C₂	semidirect
14. C₅×#872	C₂	semidirect
15. C₄×C₅×Dic₆	C₂	semidirect
52. #5708	C₅	direct (N × H)
54. C₅×#126	D₃	semidirect
89. C₃×#126	C₂×C₅	semidirect
90. #896	C₂×C₅	semidirect
91. #892	C₂×C₅	semidirect
92. D₃×C₄⋊C₄	C₂×C₅	semidirect
93. #890	C₂×C₅	semidirect
94. #889	C₂×C₅	semidirect
95. #889	C₂×C₅	semidirect
99. #879	C₂×C₅	semidirect
100. #878	C₂×C₅	semidirect
101. #877	C₂×C₅	semidirect
102. #872	C₂×C₅	semidirect
103. C₄×Dic₆	C₂×C₅	semidirect
217. #126	C₅×D₃	semidirect
312. C₃×C₅	#552	semidirect
364. C₅	#5708	direct (N × H)
385. C₃	C₅×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#126	2
C₅×#896	2
C₅×#892	2
C₅×D₃×C₄⋊C₄	2
C₅×#890	2
C₅×#889	2
C₅×#883	2
C₅×#67⋊C₄	2
C₅×#879	2
C₅×#878	2
C₅×#877	2
C₅×#872	2
C₄×C₅×Dic₆	2
C₅×#552	3
#5708	5

Subgroups — C5×#5708 #11756093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5708 #11756093