Subgroups — C₅×#70755 #14281629

Order 1920.

528 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	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4459	C₂	1	2	yes	maximal, complemented
5	C₅×#4456	C₂	1	2	yes	maximal, complemented
6	C₅×#1477	—	3	1	no	maximal, Hall
7	C₂×C₅×#235	C₄	1	1	yes	characteristic
8	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₄×C₅×#67	—	2	1	no	—
10	C₄×C₅×#67	—	2	1	no	—
11	C₅×#926	C₄	1	1	yes	characteristic
12	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
13	C₄×C₅×D₁₂	C₄	1	1	yes	characteristic
14	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₅×#872	—	2	1	no	—
16	C₄²×C₅×D₃	—	2	1	no	—
17	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic
18	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	—	2	1	no	—
20	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₅×C₄⋊(C₃⋊C₈)	—	2	1	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
24	#70755	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	—	3	1	no	—
26	C₅×#431	D₃	1	1	yes	characteristic, complemented
27	C₂×C₅×C₄⋊C₈	—	3	1	no	—
28	C₅×Q₈⋊C₈	—	3	2	no	—
29	C₅×D₄⋊C₈	—	3	2	no	—
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂×C₅×#67	—	2	1	no	—
34	C₅×#235	—	2	2	no	—
35	C₅×#235	C₈	1	4	yes	complemented
36	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×C₅×D₃	—	2	1	no	—
38	C₂×C₄×C₅×D₃	—	2	1	no	—
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₅×#217	—	2	1	no	—
47	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
48	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
49	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×Dic₃⋊C₄	—	2	1	no	—
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₄×C₅×Dic₃	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₅×C₃⋊C₈	—	4	2	no	—
58	C₄×#235	C₂×C₅	1	1	yes	characteristic
59	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
61	#4459	C₂×C₅	1	2	yes	complemented
62	#4456	C₂×C₅	1	2	yes	complemented
63	C₂×C₅×#41	—	3	1	no	—
64	C₂²×C₅×C₈	—	6	1	no	—
65	C₄×C₅×Q₈	—	3	1	no	—
66	C₄×C₅×Q₈	—	3	1	no	—
67	C₄×C₅×D₄	—	3	1	no	—
68	C₄×C₅×D₄	—	3	1	no	—
69	C₄×C₅×D₄	—	6	1	no	—
70	C₄×C₅×D₄	—	6	1	no	—
71	C₅×#117	—	3	1	no	—
72	C₅×#117	—	6	1	no	—
73	C₂×C₄²×C₅	—	6	1	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
75	C₅×C₄⋊C₈	—	2	1	no	—
76	C₅×C₄⋊C₈	—	3	2	no	—
77	C₅×C₄⋊C₈	—	6	1	no	—
78	C₅×C₂²⋊C₈	—	2	1	no	—
79	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
80	#1477	—	3	1	no	Sylow
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₅×D₃	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	4	1	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
90	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₅×#67	—	2	4	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₂×C₅×Dic₃	—	2	1	no	—
98	C₅×D₁₂	—	2	1	no	—
99	C₅×D₁₂	C₂×C₈	1	2	yes	complemented
100	C₄×C₅×D₃	—	2	4	no	—
101	C₄×C₅×D₃	—	4	2	no	—
102	C₄×C₅×D₃	—	4	1	no	—
103	C₄×C₅×D₃	—	4	1	no	—
104	C₅×Dic₆	—	2	1	no	—
105	C₅×Dic₆	C₂×C₈	1	2	yes	complemented
106	C₃×C₅×C₈	—	4	2	no	—
107	C₅×C₃⋊C₈	—	4	2	no	—
108	C₂×#235	C₄×C₅	1	1	yes	characteristic
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₄×#67	—	2	1	no	—
111	C₄×#67	—	2	1	no	—
112	#926	C₄×C₅	1	1	yes	characteristic
113	C₂²×C₃⋊C₈	—	2	1	no	—
114	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
115	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
116	#872	—	2	1	no	—
117	C₄²×D₃	—	2	1	no	—
118	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
119	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
120	C₃×C₄⋊C₈	—	2	1	no	—
121	C₃×C₂²⋊C₈	—	2	1	no	—
122	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
123	C₄⋊(C₃⋊C₈)	—	2	1	no	—
124	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
125	C₅×#41	—	3	4	no	—
126	C₅×#41	—	6	2	no	—
127	C₂×C₅×Q₈	—	3	1	no	—
128	C₂×C₅×D₄	—	3	1	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂²×C₄×C₅	—	6	1	no	—
131	C₂²×C₄×C₅	—	6	1	no	—
132	C₂²×C₄×C₅	—	6	1	no	—
133	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
134	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
135	C₂²×C₄×C₅	#67	1	1	yes	characteristic
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	6	2	no	—
138	C₂×C₅×C₈	—	12	2	no	—
139	C₅×C₄⋊C₄	—	3	1	no	—
140	C₅×C₄⋊C₄	—	3	1	no	—
141	C₅×C₄⋊C₄	—	6	1	no	—
142	C₅×C₄⋊C₄	—	6	1	no	—
143	C₅×C₂²⋊C₄	—	6	1	no	—
144	C₅×C₂²⋊C₄	—	6	1	no	—
145	C₅×C₂²⋊C₄	—	6	1	no	—
146	C₄²×C₅	—	6	1	no	—
147	C₄²×C₅	—	6	1	no	—
148	C₄²×C₅	—	6	1	no	—
149	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
150	C₄²×C₅	D₁₂	1	1	yes	characteristic
151	C₄²×C₅	#67	1	1	yes	characteristic
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₄×#41	—	3	1	no	—
154	#431	C₅×D₃	1	1	yes	characteristic, complemented
155	C₂×C₄⋊C₈	—	3	1	no	—
156	Q₈⋊C₈	—	3	2	no	—
157	D₄⋊C₈	—	3	2	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	—	2	1	no	—
160	C₂²×C₃×C₅	C₂²⋊C₈	1	2	yes	—
161	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₅×D₃	—	2	2	no	—
163	C₂×C₅×D₃	—	4	1	no	—
164	C₂×C₅×D₃	—	4	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	2	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
169	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
170	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
171	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₃×C₄×C₅	#137	1	1	yes	characteristic
173	C₅×Dic₃	—	2	2	no	—
174	C₅×Dic₃	—	4	1	no	—
175	C₅×Dic₃	—	4	1	no	—
176	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
179	C₂×#67	—	2	1	no	—
180	#235	—	2	2	no	—
181	#235	C₅×C₈	1	4	yes	complemented
182	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
183	C₂×C₄×D₃	—	2	1	no	—
184	C₂×C₄×D₃	—	2	1	no	—
185	C₂×C₄×D₃	—	2	1	no	—
186	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
187	C₂×C₃×C₈	—	2	2	no	—
188	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
189	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
190	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
191	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
192	#217	—	2	1	no	—
193	(C₂×D₃)⋊C₄	—	2	1	no	—
194	(C₂×D₃)⋊C₄	—	2	1	no	—
195	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
196	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
197	Dic₃⋊C₄	—	2	1	no	—
198	Dic₃⋊C₄	—	2	1	no	—
199	C₄×Dic₃	—	2	1	no	—
200	C₄×Dic₃	—	2	1	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂×C₃⋊C₈	—	4	2	no	—
204	C₂³×C₅	—	6	1	no	—
205	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
206	C₅×Q₈	—	3	2	no	—
207	C₅×Q₈	—	6	1	no	—
208	C₅×D₄	—	3	2	no	—
209	C₅×D₄	—	6	4	no	—
210	C₅×D₄	—	6	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	6	1	no	—
215	C₂×C₄×C₅	—	6	4	no	—
216	C₂×C₄×C₅	—	6	1	no	—
217	C₂×C₄×C₅	—	6	1	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	—	12	1	no	—
220	C₂×C₄×C₅	—	12	1	no	—
221	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
222	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
223	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×C₈	—	4	2	no	—
230	C₅×C₈	—	12	2	no	—
231	C₂×#41	—	3	1	no	—
232	C₂²×C₈	—	6	1	no	—
233	C₄×Q₈	—	3	1	no	—
234	C₄×Q₈	—	3	1	no	—
235	C₄×D₄	—	3	1	no	—
236	C₄×D₄	—	3	1	no	—
237	C₄×D₄	—	6	1	no	—
238	C₄×D₄	—	6	1	no	—
239	#117	—	3	1	no	—
240	#117	—	6	1	no	—
241	C₂×C₄²	—	6	1	no	—
242	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	3	2	no	—
245	C₄⋊C₈	—	6	1	no	—
246	C₂²⋊C₈	—	2	1	no	—
247	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
250	C₂×C₃×C₅	#417	1	1	yes	characteristic
251	C₂×C₃×C₅	#421	1	1	yes	characteristic
252	C₅×D₃	—	4	2	no	—
253	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂²×D₃	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
262	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
263	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	#67	—	2	4	no	—
267	C₂×Dic₃	—	2	1	no	—
268	C₂×Dic₃	—	2	1	no	—
269	C₂×Dic₃	—	2	1	no	—
270	D₁₂	—	2	1	no	—
271	D₁₂	C₂×C₅×C₈	1	2	yes	complemented
272	C₄×D₃	—	2	4	no	—
273	C₄×D₃	—	4	2	no	—
274	C₄×D₃	—	4	1	no	—
275	C₄×D₃	—	4	1	no	—
276	Dic₆	—	2	1	no	—
277	Dic₆	C₂×C₅×C₈	1	2	yes	complemented
278	C₃×C₈	—	4	2	no	—
279	C₃⋊C₈	—	4	2	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	1	no	—
282	C₂²×C₅	—	6	2	no	—
283	C₂²×C₅	—	12	1	no	—
284	C₂²×C₅	—	12	1	no	—
285	C₂²×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
286	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	6	2	no	—
291	C₄×C₅	—	12	1	no	—
292	C₄×C₅	—	12	1	no	—
293	C₄×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
294	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
295	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
296	C₄×C₅	#908	1	1	yes	characteristic
297	C₄×C₅	#909	1	1	yes	characteristic
298	#41	—	3	4	no	—
299	#41	—	6	2	no	—
300	C₂×Q₈	—	3	1	no	—
301	C₂×D₄	—	3	1	no	—
302	C₂×D₄	—	6	1	no	—
303	C₂²×C₄	—	6	1	no	—
304	C₂²×C₄	—	6	1	no	—
305	C₂²×C₄	—	6	1	no	—
306	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
307	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
308	C₂²×C₄	C₅×#67	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	6	2	no	—
311	C₂×C₈	—	12	2	no	—
312	C₄⋊C₄	—	3	1	no	—
313	C₄⋊C₄	—	3	1	no	—
314	C₄⋊C₄	—	6	1	no	—
315	C₄⋊C₄	—	6	1	no	—
316	C₂²⋊C₄	—	6	1	no	—
317	C₂²⋊C₄	—	6	1	no	—
318	C₂²⋊C₄	—	6	1	no	—
319	C₄²	—	6	1	no	—
320	C₄²	—	6	1	no	—
321	C₄²	—	6	1	no	—
322	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
323	C₄²	C₅×D₁₂	1	1	yes	characteristic
324	C₄²	C₅×#67	1	1	yes	characteristic
325	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
326	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	C₅×C₂²⋊C₈	1	2	yes	—
330	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×D₃	—	2	2	no	—
332	C₂×D₃	—	4	1	no	—
333	C₂×D₃	—	4	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	C₅×C₂²⋊C₈	1	2	yes	—
338	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
339	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
340	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₃×C₄	C₅×#137	1	1	yes	characteristic
342	Dic₃	—	2	2	no	—
343	Dic₃	—	4	1	no	—
344	Dic₃	—	4	1	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	—	12	2	no	—
347	C₂×C₅	#5005	1	1	yes	characteristic
348	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
349	C₂×C₅	#5133	1	1	yes	characteristic
350	C₂³	—	6	1	no	—
351	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
352	Q₈	—	3	2	no	—
353	Q₈	—	6	1	no	—
354	D₄	—	3	2	no	—
355	D₄	—	6	4	no	—
356	D₄	—	6	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	6	1	no	—
361	C₂×C₄	—	6	4	no	—
362	C₂×C₄	—	6	1	no	—
363	C₂×C₄	—	6	1	no	—
364	C₂×C₄	—	12	2	no	—
365	C₂×C₄	—	12	1	no	—
366	C₂×C₄	—	12	1	no	—
367	C₂×C₄	C₅×D₃×C₈	1	2	yes	—
368	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
369	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
373	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
374	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	12	2	no	—
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
379	C₂×C₃	C₅×#417	1	1	yes	characteristic
380	C₂×C₃	C₅×#421	1	1	yes	characteristic
381	D₃	—	4	2	no	—
382	C₅	#70755	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	6	2	no	—
386	C₂²	—	12	1	no	—
387	C₂²	—	12	1	no	—
388	C₂²	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
389	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	6	2	no	—
394	C₄	—	12	1	no	—
395	C₄	—	12	1	no	—
396	C₄	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
397	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
398	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
399	C₄	C₅×#908	1	1	yes	characteristic
400	C₄	C₅×#909	1	1	yes	characteristic
401	C₃	C₅×#1477	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	12	2	no	—
404	C₂	C₅×#5005	1	1	yes	characteristic
405	C₂	C₂×C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
406	C₂	C₅×#5133	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×#1477
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₅×#4459	C₂	semidirect
5. C₅×#4456	C₂	semidirect
24. #70755	C₅	direct (N × H)
26. C₅×#431	D₃	semidirect
35. C₅×#235	C₈	semidirect
59. C₃×#431	C₂×C₅	semidirect
60. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
61. #4459	C₂×C₅	semidirect
62. #4456	C₂×C₅	semidirect
99. C₅×D₁₂	C₂×C₈	semidirect
105. C₅×Dic₆	C₂×C₈	semidirect
154. #431	C₅×D₃	semidirect
181. #235	C₅×C₈	semidirect
271. D₁₂	C₂×C₅×C₈	semidirect
277. Dic₆	C₂×C₅×C₈	semidirect
326. C₃×C₅	#1477	semidirect
382. C₅	#70755	direct (N × H)
401. C₃	C₅×#1477	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#235	2
C₃×C₅×#431	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4459	2
C₅×#4456	2
C₅×#1477	3
#70755	5

Subgroups — C5×#70755 #14281629

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70755 #14281629