Subgroups — C₅×#5636 #11756021

Order 960.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 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×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#554	—	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	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₅×Dic₃	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×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₆	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₂²⋊C₄	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×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
38	C₅×Dic₃⋊C₄	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	C₅×Dic₃⋊C₄	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	#5636	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×C₄⋊Q₈	—	3	1	no	—
54	C₅×#125	—	3	1	no	—
55	C₅×#125	—	3	1	no	—
56	C₅×C₂²⋊Q₈	—	3	1	no	—
57	C₅×C₂²⋊Q₈	—	3	1	no	—
58	C₅×C₂²⋊Q₈	—	3	1	no	—
59	C₅×C₂²⋊Q₈	—	3	1	no	—
60	C₅×C₂²⋊Q₈	—	3	1	no	—
61	C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
62	C₄×C₅×Q₈	—	3	1	no	—
63	C₄×C₅×D₄	—	3	1	no	—
64	C₄×C₅×D₄	—	3	1	no	—
65	C₄×C₅×D₄	—	3	1	no	—
66	C₂×C₅×C₄⋊C₄	—	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	C₃×C₅×Q₈	—	4	1	no	—
71	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₅×#67	Q₈	1	4	yes	complemented
79	C₂×C₅×Dic₃	—	2	2	no	—
80	C₂×C₅×Dic₃	—	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	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₄×C₅×D₃	—	2	2	no	—
89	C₄×C₅×D₃	—	4	1	no	—
90	C₄×C₅×D₃	—	4	1	no	—
91	C₅×Dic₆	—	2	2	no	—
92	C₅×Dic₆	—	4	1	no	—
93	C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
94	#946	C₂×C₅	1	1	yes	characteristic, complemented
95	#944	C₂×C₅	1	1	yes	characteristic, complemented
96	C₄×#67	C₂×C₅	1	1	yes	characteristic
97	C₂×Dic₃⋊C₄	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	D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
101	#889	C₂×C₅	1	1	yes	characteristic, complemented
102	#889	C₂×C₅	1	1	yes	characteristic, complemented
103	#887	C₂×C₅	1	1	yes	characteristic, complemented
104	#67⋊C₄	C₂×C₅	1	1	yes	characteristic
105	#67⋊C₄	C₂×C₅	1	1	yes	characteristic
106	#878	C₂×C₅	1	1	yes	characteristic, complemented
107	#878	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×C₅×Q₈	—	3	1	no	—
109	C₂×C₅×Q₈	—	3	1	no	—
110	C₂×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
111	C₂×C₅×D₄	—	3	1	no	—
112	C₂²×C₄×C₅	—	3	1	no	—
113	C₂²×C₄×C₅	—	3	1	no	—
114	C₂²×C₄×C₅	—	3	1	no	—
115	C₂²×C₄×C₅	—	3	1	no	—
116	C₂²×C₄×C₅	—	3	1	no	—
117	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
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	—	3	1	no	—
124	C₅×C₄⋊C₄	—	3	1	no	—
125	C₅×C₄⋊C₄	—	3	1	no	—
126	C₅×C₄⋊C₄	—	3	1	no	—
127	C₅×C₄⋊C₄	—	3	1	no	—
128	C₅×C₄⋊C₄	—	3	1	no	—
129	C₅×C₄⋊C₄	—	3	1	no	—
130	C₅×C₄⋊C₄	—	3	1	no	—
131	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₅×C₂²⋊C₄	—	3	1	no	—
135	C₅×C₂²⋊C₄	—	3	1	no	—
136	C₅×C₂²⋊C₄	—	3	1	no	—
137	C₅×C₂²⋊C₄	—	3	1	no	—
138	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
139	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
140	C₄²×C₅	—	3	1	no	—
141	C₄²×C₅	—	3	1	no	—
142	C₄²×C₅	—	3	1	no	—
143	#554	—	3	1	no	Sylow
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	C₂×Q₈	1	2	yes	—
147	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₅×D₃	—	2	1	no	—
149	C₂×C₅×D₃	—	2	1	no	—
150	C₂×C₅×D₃	C₂×Q₈	1	2	yes	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	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	C₅×Dic₃	—	2	1	no	—
158	C₅×Dic₃	—	2	1	no	—
159	C₅×Dic₃	—	2	1	no	—
160	C₅×Dic₃	—	2	1	no	—
161	C₅×Dic₃	—	2	1	no	—
162	C₅×Dic₃	C₂×Q₈	1	2	yes	—
163	C₅×Dic₃	#41	1	2	yes	—
164	C₂×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×#67	C₂²×C₅	1	1	yes	characteristic
167	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
168	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄×D₃	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	(C₂×D₃)⋊C₄	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	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
184	C₄⋊Dic₃	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	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	C₂³×C₅	—	3	1	no	—
200	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₅×Q₈	—	4	1	no	—
202	C₅×Q₈	—	6	2	no	—
203	C₅×Q₈	—	12	1	no	—
204	C₅×D₄	—	3	4	no	—
205	C₂×C₄×C₅	—	3	1	no	—
206	C₂×C₄×C₅	—	3	1	no	—
207	C₂×C₄×C₅	—	3	1	no	—
208	C₂×C₄×C₅	—	3	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	—	4	1	no	—
213	C₂×C₄×C₅	—	6	2	no	—
214	C₂×C₄×C₅	—	6	2	no	—
215	C₂×C₄×C₅	—	12	1	no	—
216	C₂×C₄×C₅	—	12	1	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	#125	—	3	1	no	—
226	#125	—	3	1	no	—
227	C₂²⋊Q₈	—	3	1	no	—
228	C₂²⋊Q₈	—	3	1	no	—
229	C₂²⋊Q₈	—	3	1	no	—
230	C₂²⋊Q₈	—	3	1	no	—
231	C₂²⋊Q₈	—	3	1	no	—
232	C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
233	C₄×Q₈	—	3	1	no	—
234	C₄×D₄	—	3	1	no	—
235	C₄×D₄	—	3	1	no	—
236	C₄×D₄	—	3	1	no	—
237	C₂×C₄⋊C₄	—	3	1	no	—
238	C₂×C₄⋊C₄	—	3	1	no	—
239	C₂×C₃×C₅	—	2	2	no	—
240	C₂×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
242	C₂×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
243	C₅×D₃	—	2	2	no	—
244	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
245	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
246	C₃×Q₈	—	4	1	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
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	#67	C₅×Q₈	1	4	yes	complemented
255	C₂×Dic₃	—	2	2	no	—
256	C₂×Dic₃	—	4	1	no	—
257	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
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	C₄×D₃	—	2	2	no	—
265	C₄×D₃	—	4	1	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	—	3	2	no	—
272	C₂²×C₅	—	6	1	no	—
273	C₂²×C₅	—	6	1	no	—
274	C₂²×C₅	D₃×Q₈	1	2	yes	—
275	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	3	2	no	—
283	C₄×C₅	—	3	2	no	—
284	C₄×C₅	—	6	1	no	—
285	C₄×C₅	—	6	1	no	—
286	C₄×C₅	—	6	1	no	—
287	C₄×C₅	—	6	1	no	—
288	C₄×C₅	—	6	1	no	—
289	C₂×Q₈	—	3	1	no	—
290	C₂×Q₈	—	3	1	no	—
291	C₂×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
292	C₂×D₄	—	3	1	no	—
293	C₂²×C₄	—	3	1	no	—
294	C₂²×C₄	—	3	1	no	—
295	C₂²×C₄	—	3	1	no	—
296	C₂²×C₄	—	3	1	no	—
297	C₂²×C₄	—	3	1	no	—
298	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
299	C₄⋊C₄	—	3	1	no	—
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	—	3	1	no	—
308	C₄⋊C₄	—	3	1	no	—
309	C₄⋊C₄	—	3	1	no	—
310	C₄⋊C₄	—	3	1	no	—
311	C₄⋊C₄	—	3	1	no	—
312	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
313	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
314	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₅×D₃	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
321	C₄²	—	3	1	no	—
322	C₄²	—	3	1	no	—
323	C₄²	—	3	1	no	—
324	C₃×C₅	#554	1	1	yes	characteristic, complemented, Hall
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	C₂×C₅×Q₈	1	2	yes	—
328	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
329	C₂×D₃	—	2	1	no	—
330	C₂×D₃	—	2	1	no	—
331	C₂×D₃	C₂×C₅×Q₈	1	2	yes	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	Dic₃	—	2	1	no	—
339	Dic₃	—	2	1	no	—
340	Dic₃	—	2	1	no	—
341	Dic₃	—	2	1	no	—
342	Dic₃	—	2	1	no	—
343	Dic₃	C₂×C₅×Q₈	1	2	yes	—
344	Dic₃	C₅×#41	1	2	yes	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	6	2	no	—
347	C₂×C₅	#1004	1	1	yes	characteristic
348	C₂×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
349	C₂×C₅	D₃×#41	1	1	yes	characteristic
350	C₂³	—	3	1	no	—
351	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	6	2	no	—
354	Q₈	—	12	1	no	—
355	D₄	—	3	4	no	—
356	C₂×C₄	—	3	1	no	—
357	C₂×C₄	—	3	1	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	3	1	no	—
360	C₂×C₄	—	3	1	no	—
361	C₂×C₄	—	3	1	no	—
362	C₂×C₄	—	3	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	6	2	no	—
365	C₂×C₄	—	6	2	no	—
366	C₂×C₄	—	12	1	no	—
367	C₂×C₄	—	12	1	no	—
368	C₂×C₄	—	12	1	no	—
369	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
377	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
378	C₂×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
379	D₃	—	2	2	no	—
380	C₅	#5636	1	1	yes	characteristic, direct product factor, Sylow
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	3	2	no	—
384	C₂²	—	6	1	no	—
385	C₂²	—	6	1	no	—
386	C₂²	C₅×D₃×Q₈	1	2	yes	—
387	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	3	2	no	—
395	C₄	—	3	2	no	—
396	C₄	—	6	1	no	—
397	C₄	—	6	1	no	—
398	C₄	—	6	1	no	—
399	C₄	—	6	1	no	—
400	C₄	—	6	1	no	—
401	C₃	C₅×#554	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	6	2	no	—
404	C₂	C₅×#1004	1	1	yes	characteristic
405	C₂	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
406	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	C₂×C₅×#67	C₂²
hypercenter	C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#554
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×#946	C₂	semidirect
3. C₅×#944	C₂	semidirect
5. C₂×C₅×Dic₃⋊C₄	C₂	semidirect
6. C₅×#896	C₂	semidirect
7. C₅×#896	C₂	semidirect
8. C₅×D₃×C₄⋊C₄	C₂	semidirect
9. C₅×#889	C₂	semidirect
10. C₅×#889	C₂	semidirect
11. C₅×#887	C₂	semidirect
14. C₅×#878	C₂	semidirect
15. C₅×#878	C₂	semidirect
52. #5636	C₅	direct (N × H)
61. C₅×C₂²⋊Q₈	D₃	semidirect
78. C₅×#67	Q₈	semidirect
93. C₃×C₂²⋊Q₈	C₂×C₅	semidirect
94. #946	C₂×C₅	semidirect
95. #944	C₂×C₅	semidirect
97. C₂×Dic₃⋊C₄	C₂×C₅	semidirect
98. #896	C₂×C₅	semidirect
99. #896	C₂×C₅	semidirect
100. D₃×C₄⋊C₄	C₂×C₅	semidirect
101. #889	C₂×C₅	semidirect
102. #889	C₂×C₅	semidirect
103. #887	C₂×C₅	semidirect
106. #878	C₂×C₅	semidirect
107. #878	C₂×C₅	semidirect
232. C₂²⋊Q₈	C₅×D₃	semidirect
254. #67	C₅×Q₈	semidirect
324. C₃×C₅	#554	semidirect
380. C₅	#5636	direct (N × H)
401. C₃	C₅×#554	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×#946	2
C₅×#944	2
C₄×C₅×#67	2
C₂×C₅×Dic₃⋊C₄	2
C₅×#896	2
C₅×D₃×C₄⋊C₄	2
C₅×#889	2
C₅×#887	2
C₅×#67⋊C₄	2
C₅×#878	2
C₅×#554	3
#5636	5

Subgroups — C5×#5636 #11756021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5636 #11756021