Subgroups — C₅×#5640 #11756025

Order 960.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#885	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#885	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#884	C₂	1	1	yes	maximal, characteristic
15	C₅×#879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#542	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#217	C₂²	1	1	yes	characteristic
32	C₅×#217	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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₅×C₄⋊Dic₃	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	#5640	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×C₄⋊Q₈	—	3	1	no	—
54	C₅×#126	—	3	1	no	—
55	C₅×#126	—	3	1	no	—
56	C₅×#124	—	3	1	no	—
57	C₅×#124	—	3	1	no	—
58	C₅×#124	—	3	1	no	—
59	C₅×#123	—	3	1	no	—
60	C₅×#123	—	3	1	no	—
61	C₅×C₂²⋊Q₈	—	3	1	no	—
62	C₅×C₂²⋊Q₈	—	3	1	no	—
63	C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
64	C₅×#121	—	3	1	no	—
65	C₄×C₅×Q₈	—	3	1	no	—
66	C₄×C₅×D₄	—	3	1	no	—
67	C₅×#117	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₃×C₅×Q₈	—	4	1	no	—
72	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₅×#67	—	2	2	no	—
80	C₅×#67	—	4	1	no	—
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	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₅×D₁₂	—	4	1	no	—
88	C₄×C₅×D₃	—	2	2	no	—
89	C₄×C₅×D₃	—	4	1	no	—
90	C₅×Dic₆	—	2	2	no	—
91	C₅×Dic₆	—	4	1	no	—
92	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
93	#947	C₂×C₅	1	1	yes	characteristic, complemented
94	#944	C₂×C₅	1	1	yes	characteristic, complemented
95	#929	C₂×C₅	1	1	yes	characteristic, complemented
96	C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
97	#898	C₂×C₅	1	1	yes	characteristic, complemented
98	#896	C₂×C₅	1	1	yes	characteristic, complemented
99	#896	C₂×C₅	1	1	yes	characteristic, complemented
100	#894	C₂×C₅	1	1	yes	characteristic, complemented
101	#892	C₂×C₅	1	1	yes	characteristic, complemented
102	#887	C₂×C₅	1	1	yes	characteristic, complemented
103	#885	C₂×C₅	1	1	yes	characteristic, complemented
104	#885	C₂×C₅	1	1	yes	characteristic, complemented
105	#884	C₂×C₅	1	1	yes	characteristic
106	#879	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×C₅×Q₈	—	3	1	no	—
108	C₂×C₅×Q₈	—	3	1	no	—
109	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
110	C₂×C₅×D₄	—	3	1	no	—
111	C₂×C₅×D₄	—	3	1	no	—
112	C₂×C₅×D₄	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	3	1	no	—
115	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
132	C₅×C₂²⋊C₄	—	3	1	no	—
133	C₅×C₂²⋊C₄	—	3	1	no	—
134	C₅×C₂²⋊C₄	—	3	1	no	—
135	C₅×C₂²⋊C₄	—	3	1	no	—
136	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
137	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
138	C₄²×C₅	—	3	1	no	—
139	C₄²×C₅	—	3	1	no	—
140	C₄²×C₅	—	3	1	no	—
141	C₄²×C₅	—	3	1	no	—
142	#542	—	3	1	no	Sylow
143	C₂²×C₃×C₅	—	2	1	no	—
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
147	C₂×C₅×D₃	—	2	1	no	—
148	C₂×C₅×D₃	—	2	1	no	—
149	C₂×C₅×D₃	—	2	1	no	—
150	C₂×C₅×D₃	—	2	1	no	—
151	C₂×C₅×D₃	—	2	1	no	—
152	C₂×C₅×D₃	—	2	1	no	—
153	C₃×C₄×C₅	—	2	1	no	—
154	C₃×C₄×C₅	—	2	1	no	—
155	C₃×C₄×C₅	—	2	1	no	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₅×Dic₃	—	2	1	no	—
160	C₅×Dic₃	—	2	1	no	—
161	C₅×Dic₃	—	2	1	no	—
162	C₅×Dic₃	—	2	1	no	—
163	C₅×Dic₃	—	2	1	no	—
164	C₅×Dic₃	#41	1	2	yes	—
165	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×#67	C₂²×C₅	1	1	yes	characteristic
168	C₂×#67	C₂²×C₅	1	1	yes	characteristic
169	C₂×D₁₂	C₂²×C₅	1	1	yes	characteristic
170	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
172	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
173	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	#217	C₂²×C₅	1	1	yes	characteristic
180	#217	C₂²×C₅	1	1	yes	characteristic
181	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
186	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
188	(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
190	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
191	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
192	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
193	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
194	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
195	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
197	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
198	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
199	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
200	C₂³×C₅	—	3	1	no	—
201	C₂³×C₅	—	3	1	no	—
202	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₅×Q₈	—	4	1	no	—
204	C₅×Q₈	—	6	2	no	—
205	C₅×Q₈	—	12	1	no	—
206	C₅×D₄	—	6	2	no	—
207	C₅×D₄	—	12	1	no	—
208	C₅×D₄	—	12	1	no	—
209	C₂×C₄×C₅	—	3	1	no	—
210	C₂×C₄×C₅	—	3	1	no	—
211	C₂×C₄×C₅	—	3	1	no	—
212	C₂×C₄×C₅	—	3	1	no	—
213	C₂×C₄×C₅	—	3	1	no	—
214	C₂×C₄×C₅	—	3	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	6	2	no	—
217	C₂×C₄×C₅	—	12	1	no	—
218	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₄⋊Q₈	—	3	1	no	—
225	#126	—	3	1	no	—
226	#126	—	3	1	no	—
227	#124	—	3	1	no	—
228	#124	—	3	1	no	—
229	#124	—	3	1	no	—
230	#123	—	3	1	no	—
231	#123	—	3	1	no	—
232	C₂²⋊Q₈	—	3	1	no	—
233	C₂²⋊Q₈	—	3	1	no	—
234	C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
235	#121	—	3	1	no	—
236	C₄×Q₈	—	3	1	no	—
237	C₄×D₄	—	3	1	no	—
238	#117	—	3	1	no	—
239	C₂×C₃×C₅	—	4	1	no	—
240	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
241	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
243	C₅×D₃	—	4	1	no	—
244	C₅×D₃	—	4	1	no	—
245	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
246	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
247	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
248	C₃×Q₈	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
256	#67	—	2	2	no	—
257	#67	—	4	1	no	—
258	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
259	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
260	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
261	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
262	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
263	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
264	D₁₂	—	4	1	no	—
265	C₄×D₃	—	2	2	no	—
266	C₄×D₃	—	4	1	no	—
267	Dic₆	—	2	2	no	—
268	Dic₆	—	4	1	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	6	1	no	—
273	C₂²×C₅	—	6	1	no	—
274	C₂²×C₅	—	6	1	no	—
275	C₂²×C₅	—	6	1	no	—
276	C₂²×C₅	—	6	1	no	—
277	C₂²×C₅	—	6	1	no	—
278	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	3	2	no	—
286	C₄×C₅	—	6	1	no	—
287	C₄×C₅	—	6	1	no	—
288	C₄×C₅	—	6	1	no	—
289	C₄×C₅	—	6	1	no	—
290	C₄×C₅	—	6	1	no	—
291	C₂×Q₈	—	3	1	no	—
292	C₂×Q₈	—	3	1	no	—
293	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
294	C₂×D₄	—	3	1	no	—
295	C₂×D₄	—	3	1	no	—
296	C₂×D₄	—	3	1	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	—	3	1	no	—
299	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
300	C₄⋊C₄	—	3	1	no	—
301	C₄⋊C₄	—	3	1	no	—
302	C₄⋊C₄	—	3	1	no	—
303	C₄⋊C₄	—	3	1	no	—
304	C₄⋊C₄	—	3	1	no	—
305	C₄⋊C₄	—	3	1	no	—
306	C₄⋊C₄	—	3	1	no	—
307	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
308	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
309	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
310	C₂²⋊C₄	—	3	1	no	—
311	C₂²⋊C₄	—	3	1	no	—
312	C₂²⋊C₄	—	3	1	no	—
313	C₂²⋊C₄	—	3	1	no	—
314	C₂²⋊C₄	—	3	1	no	—
315	C₂²⋊C₄	—	3	1	no	—
316	C₂²⋊C₄	—	3	1	no	—
317	C₂²⋊C₄	—	3	1	no	—
318	C₂²⋊C₄	—	3	1	no	—
319	C₂²⋊C₄	—	3	1	no	—
320	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
322	C₄²	—	3	1	no	—
323	C₄²	—	3	1	no	—
324	C₄²	—	3	1	no	—
325	C₄²	—	3	1	no	—
326	C₃×C₅	#542	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
331	C₂×D₃	—	2	1	no	—
332	C₂×D₃	—	2	1	no	—
333	C₂×D₃	—	2	1	no	—
334	C₂×D₃	—	2	1	no	—
335	C₂×D₃	—	2	1	no	—
336	C₂×D₃	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	2	1	no	—
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	2	1	no	—
343	Dic₃	—	2	1	no	—
344	Dic₃	—	2	1	no	—
345	Dic₃	—	2	1	no	—
346	Dic₃	—	2	1	no	—
347	Dic₃	—	2	1	no	—
348	Dic₃	C₅×#41	1	2	yes	—
349	C₂×C₅	—	4	1	no	—
350	C₂×C₅	—	12	1	no	—
351	C₂×C₅	—	12	1	no	—
352	C₂×C₅	#1004	1	1	yes	characteristic
353	C₂×C₅	#1007	1	1	yes	characteristic
354	C₂×C₅	D₃×#41	1	1	yes	characteristic
355	C₂³	—	3	1	no	—
356	C₂³	—	3	1	no	—
357	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
358	Q₈	—	4	1	no	—
359	Q₈	—	6	2	no	—
360	Q₈	—	12	1	no	—
361	D₄	—	6	2	no	—
362	D₄	—	12	1	no	—
363	D₄	—	12	1	no	—
364	C₂×C₄	—	3	1	no	—
365	C₂×C₄	—	3	1	no	—
366	C₂×C₄	—	3	1	no	—
367	C₂×C₄	—	3	1	no	—
368	C₂×C₄	—	3	1	no	—
369	C₂×C₄	—	3	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	6	2	no	—
372	C₂×C₄	—	12	1	no	—
373	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₂×C₃	—	4	1	no	—
380	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
381	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
383	D₃	—	4	1	no	—
384	D₃	—	4	1	no	—
385	C₅	#5640	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	6	1	no	—
390	C₂²	—	6	1	no	—
391	C₂²	—	6	1	no	—
392	C₂²	—	6	1	no	—
393	C₂²	—	6	1	no	—
394	C₂²	—	6	1	no	—
395	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	3	2	no	—
403	C₄	—	6	1	no	—
404	C₄	—	6	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	6	1	no	—
407	C₄	—	6	1	no	—
408	C₃	C₅×#542	1	1	yes	characteristic, complemented, Sylow
409	C₂	—	4	1	no	—
410	C₂	—	12	1	no	—
411	C₂	—	12	1	no	—
412	C₂	C₅×#1004	1	1	yes	characteristic
413	C₂	C₅×#1007	1	1	yes	characteristic
414	C₂	C₅×D₃×#41	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×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₅×#884	C₂
hypercenter	C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#542
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₅×#947	C₂	semidirect
3. C₅×#944	C₂	semidirect
4. C₅×#929	C₂	semidirect
5. C₄×C₅×#67	C₂	semidirect
6. C₅×#898	C₂	semidirect
7. C₅×#896	C₂	semidirect
8. C₅×#896	C₂	semidirect
9. C₅×#894	C₂	semidirect
10. C₅×#892	C₂	semidirect
11. C₅×#887	C₂	semidirect
12. C₅×#885	C₂	semidirect
13. C₅×#885	C₂	semidirect
15. C₅×#879	C₂	semidirect
52. #5640	C₅	direct (N × H)
63. C₅×C₂²⋊Q₈	D₃	semidirect
92. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
93. #947	C₂×C₅	semidirect
94. #944	C₂×C₅	semidirect
95. #929	C₂×C₅	semidirect
96. C₄×#67	C₂×C₅	semidirect
97. #898	C₂×C₅	semidirect
98. #896	C₂×C₅	semidirect
99. #896	C₂×C₅	semidirect
100. #894	C₂×C₅	semidirect
101. #892	C₂×C₅	semidirect
102. #887	C₂×C₅	semidirect
103. #885	C₂×C₅	semidirect
104. #885	C₂×C₅	semidirect
106. #879	C₂×C₅	semidirect
234. C₂²⋊Q₈	C₅×D₃	semidirect
326. C₃×C₅	#542	semidirect
385. C₅	#5640	direct (N × H)
408. C₃	C₅×#542	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₂²⋊Q₈	2
C₅×#947	2
C₅×#944	2
C₅×#929	2
C₄×C₅×#67	2
C₅×#898	2
C₅×#896	2
C₅×#894	2
C₅×#892	2
C₅×#887	2
C₅×#885	2
C₅×#884	2
C₅×#879	2
C₅×#542	3
#5640	5

Subgroups — C5×#5640 #11756025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5640 #11756025