Subgroups — C₅×#71638 #14281563

Order 1920.

552 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#4925	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4535	C₂	1	2	yes	maximal, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
6	C₅×#1476	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic
8	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₃×C₄×C₅×D₄	—	2	1	no	—
11	C₃×C₄×C₅×D₄	—	2	1	no	—
12	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
19	C₅×#830	—	2	1	no	—
20	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
21	C₄×C₅×C₃⋊C₈	—	2	1	no	—
22	C₄×C₅×C₃⋊C₈	—	2	1	no	—
23	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
24	#71638	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	D₃	1	1	yes	characteristic
26	C₅×#431	—	3	1	no	—
27	C₂×C₄×C₅×C₈	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₃×C₅×#41	C₈	1	4	yes	complemented
32	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₄²×C₅	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	4	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	2	no	—
58	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
59	#4925	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
61	#4535	C₂×C₅	1	2	yes	complemented
62	D₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	complemented
63	C₂×C₅×#41	Dic₃	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	6	1	no	—
65	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic
70	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
71	C₅×#117	—	2	1	no	—
72	C₅×#117	Dic₃	1	1	yes	characteristic
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	3	2	no	—
76	C₅×C₂²⋊C₈	—	6	1	no	—
77	C₄×C₅×C₈	—	3	2	no	—
78	C₄×C₅×C₈	—	6	1	no	—
79	C₄×C₅×C₈	—	6	1	no	—
80	#1476	—	3	1	no	Sylow
81	C₂³×C₃×C₅	—	2	1	no	—
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₃×C₅×Q₈	—	2	1	no	—
84	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	2	1	no	—
87	C₃×C₅×D₄	C₂×C₈	1	2	yes	complemented
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
100	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₅×C₃⋊C₈	—	2	4	no	—
105	C₅×C₃⋊C₈	—	4	2	no	—
106	C₂×C₃×#41	C₄×C₅	1	1	yes	characteristic
107	C₃×C₄×Q₈	C₄×C₅	1	1	yes	characteristic
108	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
109	C₃×C₄×D₄	—	2	1	no	—
110	C₃×C₄×D₄	—	2	1	no	—
111	C₃×C₄×D₄	C₄×C₅	1	1	yes	characteristic
112	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
113	C₃×#117	—	2	1	no	—
114	C₃×#117	C₄×C₅	1	1	yes	characteristic
115	C₂×C₃×C₄²	—	2	1	no	—
116	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
117	C₂²×C₃⋊C₈	—	2	1	no	—
118	#830	—	2	1	no	—
119	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
120	C₄×C₃⋊C₈	—	2	1	no	—
121	C₄×C₃⋊C₈	—	2	1	no	—
122	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	C₃⋊C₈	1	4	yes	complemented
125	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
126	C₂×C₅×D₄	—	2	1	no	—
127	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	1	no	—
129	C₂²×C₄×C₅	—	2	1	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
132	C₂²×C₄×C₅	#67	1	1	yes	characteristic
133	C₂²×C₄×C₅	#67	1	1	yes	characteristic
134	C₂×C₅×C₈	—	6	4	no	—
135	C₂×C₅×C₈	—	6	2	no	—
136	C₂×C₅×C₈	—	6	2	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
140	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
141	C₅×C₂²⋊C₄	—	2	1	no	—
142	C₅×C₂²⋊C₄	—	2	1	no	—
143	C₅×C₂²⋊C₄	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	—	2	1	no	—
147	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
148	C₄²×C₅	#67	1	1	yes	characteristic
149	C₄²×C₅	#67	1	1	yes	characteristic
150	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₄×#41	C₅×D₃	1	1	yes	characteristic
152	#431	—	3	1	no	—
153	C₂×C₄×C₈	—	3	1	no	—
154	Q₈⋊C₈	—	3	2	no	—
155	D₄⋊C₈	—	3	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	4	1	no	—
160	C₂²×C₃×C₅	—	4	1	no	—
161	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
162	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₃×C₄×C₅	—	2	2	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
169	C₃×C₄×C₅	#104	1	2	yes	—
170	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
172	C₃×C₄×C₅	#135	1	2	yes	—
173	C₃×#41	—	2	2	no	—
174	C₃×#41	C₅×C₈	1	4	yes	complemented
175	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂×C₃×D₄	—	2	1	no	—
177	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	—	2	1	no	—
186	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₂²⋊C₄	—	2	1	no	—
191	C₃×C₄²	—	2	1	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	—	2	1	no	—
194	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
195	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
196	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
197	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
198	C₂×C₃⋊C₈	—	2	4	no	—
199	C₂×C₃⋊C₈	—	2	2	no	—
200	C₂×C₃⋊C₈	—	2	2	no	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	#217	1	1	yes	characteristic
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	C₂×C₃⋊C₈	1	2	yes	complemented
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	C₂×C₃⋊C₈	1	2	yes	complemented
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
217	C₂×C₄×C₅	#208	1	2	yes	—
218	C₂×C₄×C₅	#217	1	1	yes	characteristic
219	C₂×C₄×C₅	#217	1	1	yes	characteristic
220	C₂×C₄×C₅	#217	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
224	C₅×C₈	—	6	4	no	—
225	C₅×C₈	—	12	2	no	—
226	C₂×#41	C₅×Dic₃	1	1	yes	characteristic
227	C₂²×C₈	—	6	1	no	—
228	C₄×Q₈	C₅×Dic₃	1	1	yes	characteristic
229	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	C₅×Dic₃	1	1	yes	characteristic
233	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
234	#117	—	2	1	no	—
235	#117	C₅×Dic₃	1	1	yes	characteristic
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
238	C₄⋊C₈	—	3	2	no	—
239	C₂²⋊C₈	—	6	1	no	—
240	C₄×C₈	—	3	2	no	—
241	C₄×C₈	—	6	1	no	—
242	C₄×C₈	—	6	1	no	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	—	4	2	no	—
245	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
246	C₂×C₃×C₅	#416	1	1	yes	characteristic
247	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
248	C₂³×C₃	—	2	1	no	—
249	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
250	C₃×Q₈	—	2	1	no	—
251	C₃×Q₈	C₂×C₅×C₈	1	2	yes	complemented
252	C₃×D₄	—	2	4	no	—
253	C₃×D₄	—	2	1	no	—
254	C₃×D₄	C₂×C₅×C₈	1	2	yes	complemented
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
267	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
268	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₃⋊C₈	—	2	4	no	—
272	C₃⋊C₈	—	4	2	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	2	no	—
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	1	no	—
278	C₂²×C₅	#830	1	2	yes	—
279	C₂²×C₅	C₂×#217	1	1	yes	characteristic
280	C₄×C₅	—	2	2	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	#830	1	2	yes	—
286	C₄×C₅	#837	1	2	yes	—
287	C₄×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
288	C₄×C₅	C₂×#208	1	1	yes	characteristic
289	C₄×C₅	#950	1	2	yes	—
290	#41	—	2	2	no	—
291	#41	C₅×C₃⋊C₈	1	4	yes	complemented
292	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
299	C₂²×C₄	C₅×#67	1	1	yes	characteristic
300	C₂²×C₄	C₅×#67	1	1	yes	characteristic
301	C₂×C₈	—	6	4	no	—
302	C₂×C₈	—	6	2	no	—
303	C₂×C₈	—	6	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
307	C₄⋊C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₂²⋊C₄	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	C₂×C₅×Dic₃	1	1	yes	characteristic
315	C₄²	C₅×#67	1	1	yes	characteristic
316	C₄²	C₅×#67	1	1	yes	characteristic
317	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
318	C₃×C₅	#1476	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	2	2	no	—
322	C₂²×C₃	—	4	1	no	—
323	C₂²×C₃	—	4	1	no	—
324	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
325	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	C₅×C₂²⋊C₈	1	2	yes	—
332	C₃×C₄	C₅×#104	1	2	yes	—
333	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
334	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
335	C₃×C₄	C₅×#135	1	2	yes	—
336	C₂×C₅	—	2	2	no	—
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	C₂×#830	1	1	yes	characteristic
339	C₂×C₅	#5233	1	1	yes	characteristic
340	C₂×C₅	C₂×#837	1	1	yes	characteristic
341	C₂³	—	2	1	no	—
342	C₂³	C₅×#217	1	1	yes	characteristic
343	Q₈	—	2	1	no	—
344	Q₈	C₂×C₅×C₃⋊C₈	1	2	yes	complemented
345	D₄	—	2	4	no	—
346	D₄	—	2	1	no	—
347	D₄	C₂×C₅×C₃⋊C₈	1	2	yes	complemented
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
357	C₂×C₄	C₅×#208	1	2	yes	—
358	C₂×C₄	C₅×#217	1	1	yes	characteristic
359	C₂×C₄	C₅×#217	1	1	yes	characteristic
360	C₂×C₄	C₅×#217	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
363	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
364	C₈	—	6	4	no	—
365	C₈	—	12	2	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	4	2	no	—
368	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
369	C₂×C₃	C₅×#416	1	1	yes	characteristic
370	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
371	C₅	#71638	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	C₅×#830	1	2	yes	—
378	C₂²	C₂×C₅×#217	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	C₅×#830	1	2	yes	—
385	C₄	C₅×#837	1	2	yes	—
386	C₄	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
387	C₄	C₂×C₅×#208	1	1	yes	characteristic
388	C₄	C₅×#950	1	2	yes	—
389	C₃	C₅×#1476	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	2	2	no	—
391	C₂	—	4	2	no	—
392	C₂	C₂×C₅×#830	1	1	yes	characteristic
393	C₂	C₅×#5233	1	1	yes	characteristic
394	C₂	C₂×C₅×#837	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	#67
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×C₅×#41	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#1476
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₅×#4925	C₂	semidirect
3. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×#4535	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
24. #71638	C₅	direct (N × H)
31. C₃×C₅×#41	C₈	semidirect
59. #4925	C₂×C₅	semidirect
60. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
61. #4535	C₂×C₅	semidirect
62. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
84. C₃×C₅×Q₈	C₂×C₈	semidirect
87. C₃×C₅×D₄	C₂×C₈	semidirect
124. C₅×#41	C₃⋊C₈	semidirect
174. C₃×#41	C₅×C₈	semidirect
204. C₅×Q₈	C₂×C₃⋊C₈	semidirect
207. C₅×D₄	C₂×C₃⋊C₈	semidirect
251. C₃×Q₈	C₂×C₅×C₈	semidirect
254. C₃×D₄	C₂×C₅×C₈	semidirect
291. #41	C₅×C₃⋊C₈	semidirect
318. C₃×C₅	#1476	semidirect
344. Q₈	C₂×C₅×C₃⋊C₈	semidirect
347. D₄	C₂×C₅×C₃⋊C₈	semidirect
371. C₅	#71638	direct (N × H)
389. C₃	C₅×#1476	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#4925	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1476	3
#71638	5

Subgroups — C5×#71638 #14281563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71638 #14281563