Subgroups — C₅×#69734 #14281566

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	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4925	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×#1476	—	3	1	no	maximal, Hall
7	C₂×C₅×#235	C₄	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	—	2	1	no	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₄×C₅×#67	—	2	1	no	—
11	C₄×C₅×#67	—	2	1	no	—
12	C₅×#926	C₄	1	1	yes	characteristic
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×C₄×C₅×C₈	—	2	1	no	—
20	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#830	—	2	1	no	—
22	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
23	C₄×C₅×C₃⋊C₈	—	2	1	no	—
24	#69734	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₄×C₅×#41	—	3	1	no	—
26	C₅×#431	—	3	1	no	—
27	C₂×C₄×C₅×C₈	D₃	1	1	yes	characteristic, complemented
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	4	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
47	C₅×#217	—	2	1	no	—
48	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
50	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₅×Dic₃⋊C₄	—	2	1	no	—
53	C₅×Dic₃⋊C₄	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₂×C₅×C₃⋊C₈	—	2	2	no	—
58	C₄×#235	C₂×C₅	1	1	yes	characteristic
59	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
60	#4925	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	—	2	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	—	3	2	no	—
76	C₅×C₂²⋊C₈	—	6	1	no	—
77	C₄×C₅×C₈	—	2	1	no	—
78	C₄×C₅×C₈	—	6	1	no	—
79	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
80	#1476	—	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	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×C₈	1	2	yes	—
89	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₅×#67	—	2	4	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₂×C₅×Dic₃	—	2	1	no	—
96	C₂×C₅×Dic₃	—	2	1	no	—
97	C₅×D₁₂	—	2	1	no	—
98	C₅×D₁₂	C₂×C₈	1	2	yes	complemented
99	C₄×C₅×D₃	—	2	4	no	—
100	C₄×C₅×D₃	—	4	2	no	—
101	C₄×C₅×D₃	—	4	2	no	—
102	C₅×Dic₆	—	2	1	no	—
103	C₅×Dic₆	C₂×C₈	1	2	yes	complemented
104	C₃×C₅×C₈	—	2	4	no	—
105	C₅×C₃⋊C₈	—	4	2	no	—
106	C₂×#235	C₄×C₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	—	2	1	no	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₄×#67	—	2	1	no	—
110	C₄×#67	—	2	1	no	—
111	#926	C₄×C₅	1	1	yes	characteristic
112	C₄×D₁₂	C₄×C₅	1	1	yes	characteristic
113	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
114	#872	—	2	1	no	—
115	C₄²×D₃	—	2	1	no	—
116	C₄×Dic₆	C₄×C₅	1	1	yes	characteristic
117	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄×C₈	—	2	1	no	—
119	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
120	#830	—	2	1	no	—
121	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
122	C₄×C₃⋊C₈	—	2	1	no	—
123	C₅×#41	—	3	4	no	—
124	C₅×#41	—	6	2	no	—
125	C₂×C₅×Q₈	—	3	1	no	—
126	C₂×C₅×D₄	—	3	1	no	—
127	C₂×C₅×D₄	—	6	1	no	—
128	C₂²×C₄×C₅	—	6	1	no	—
129	C₂²×C₄×C₅	—	6	1	no	—
130	C₂²×C₄×C₅	—	6	1	no	—
131	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
132	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
133	C₂²×C₄×C₅	#67	1	1	yes	characteristic
134	C₂×C₅×C₈	—	2	4	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	6	2	no	—
137	C₅×C₄⋊C₄	—	3	1	no	—
138	C₅×C₄⋊C₄	—	3	1	no	—
139	C₅×C₄⋊C₄	—	6	1	no	—
140	C₅×C₄⋊C₄	—	6	1	no	—
141	C₅×C₂²⋊C₄	—	6	1	no	—
142	C₅×C₂²⋊C₄	—	6	1	no	—
143	C₅×C₂²⋊C₄	—	6	1	no	—
144	C₄²×C₅	—	6	1	no	—
145	C₄²×C₅	—	6	1	no	—
146	C₄²×C₅	—	6	1	no	—
147	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
148	C₄²×C₅	D₁₂	1	1	yes	characteristic
149	C₄²×C₅	#67	1	1	yes	characteristic
150	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₄×#41	—	3	1	no	—
152	#431	—	3	1	no	—
153	C₂×C₄×C₈	C₅×D₃	1	1	yes	characteristic, complemented
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	C₂²⋊C₈	1	2	yes	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₅×D₃	—	2	2	no	—
161	C₂×C₅×D₃	—	4	1	no	—
162	C₂×C₅×D₃	—	4	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	C₂²⋊C₈	1	2	yes	—
166	C₃×C₄×C₅	#104	1	2	yes	—
167	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
168	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	#135	1	2	yes	—
170	C₅×Dic₃	—	2	2	no	—
171	C₅×Dic₃	—	4	1	no	—
172	C₅×Dic₃	—	4	1	no	—
173	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
176	C₂×#67	—	2	1	no	—
177	#235	—	2	2	no	—
178	#235	C₅×C₈	1	4	yes	complemented
179	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂×C₄×D₃	—	2	1	no	—
181	C₂×C₄×D₃	—	2	1	no	—
182	C₂×C₄×D₃	—	2	1	no	—
183	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂×C₃×C₈	—	2	4	no	—
185	C₂×C₃×C₈	—	2	2	no	—
186	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
187	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
188	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
189	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
190	#217	—	2	1	no	—
191	(C₂×D₃)⋊C₄	—	2	1	no	—
192	(C₂×D₃)⋊C₄	—	2	1	no	—
193	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
194	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
195	Dic₃⋊C₄	—	2	1	no	—
196	Dic₃⋊C₄	—	2	1	no	—
197	C₄×Dic₃	—	2	1	no	—
198	C₄×Dic₃	—	2	1	no	—
199	C₄×Dic₃	—	2	1	no	—
200	C₂×C₃⋊C₈	—	2	2	no	—
201	C₂³×C₅	—	6	1	no	—
202	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
203	C₅×Q₈	—	3	2	no	—
204	C₅×Q₈	—	6	1	no	—
205	C₅×D₄	—	3	2	no	—
206	C₅×D₄	—	6	4	no	—
207	C₅×D₄	—	6	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	6	1	no	—
211	C₂×C₄×C₅	—	6	4	no	—
212	C₂×C₄×C₅	—	6	1	no	—
213	C₂×C₄×C₅	—	6	1	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	—	12	2	no	—
216	C₂×C₄×C₅	D₃×C₈	1	2	yes	—
217	C₂×C₄×C₅	ΓL(1,𝔽₂₅)	1	2	yes	—
218	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
224	C₅×C₈	—	2	4	no	—
225	C₅×C₈	—	12	2	no	—
226	C₂×#41	—	3	1	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₄×Q₈	—	3	1	no	—
229	C₄×Q₈	—	3	1	no	—
230	C₄×D₄	—	3	1	no	—
231	C₄×D₄	—	3	1	no	—
232	C₄×D₄	—	6	1	no	—
233	C₄×D₄	—	6	1	no	—
234	#117	—	3	1	no	—
235	#117	—	6	1	no	—
236	C₂×C₄²	—	6	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	—	2	1	no	—
241	C₄×C₈	—	6	1	no	—
242	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
245	C₂×C₃×C₅	#416	1	1	yes	characteristic
246	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
247	C₅×D₃	—	4	2	no	—
248	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²×D₃	—	2	1	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
256	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	#67	—	2	4	no	—
261	C₂×Dic₃	—	2	1	no	—
262	C₂×Dic₃	—	2	1	no	—
263	C₂×Dic₃	—	2	1	no	—
264	D₁₂	—	2	1	no	—
265	D₁₂	C₂×C₅×C₈	1	2	yes	complemented
266	C₄×D₃	—	2	4	no	—
267	C₄×D₃	—	4	2	no	—
268	C₄×D₃	—	4	2	no	—
269	Dic₆	—	2	1	no	—
270	Dic₆	C₂×C₅×C₈	1	2	yes	complemented
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	—	6	2	no	—
276	C₂²×C₅	—	12	1	no	—
277	C₂²×C₅	—	12	1	no	—
278	C₂²×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
279	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	6	2	no	—
283	C₄×C₅	—	12	1	no	—
284	C₄×C₅	—	12	1	no	—
285	C₄×C₅	#805	1	2	yes	—
286	C₄×C₅	(C₂×D₃)⋊C₈	1	2	yes	—
287	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
288	C₄×C₅	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
289	C₄×C₅	#904	1	2	yes	—
290	#41	—	3	4	no	—
291	#41	—	6	2	no	—
292	C₂×Q₈	—	3	1	no	—
293	C₂×D₄	—	3	1	no	—
294	C₂×D₄	—	6	1	no	—
295	C₂²×C₄	—	6	1	no	—
296	C₂²×C₄	—	6	1	no	—
297	C₂²×C₄	—	6	1	no	—
298	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
299	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
300	C₂²×C₄	C₅×#67	1	1	yes	characteristic
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	6	2	no	—
304	C₄⋊C₄	—	3	1	no	—
305	C₄⋊C₄	—	3	1	no	—
306	C₄⋊C₄	—	6	1	no	—
307	C₄⋊C₄	—	6	1	no	—
308	C₂²⋊C₄	—	6	1	no	—
309	C₂²⋊C₄	—	6	1	no	—
310	C₂²⋊C₄	—	6	1	no	—
311	C₄²	—	6	1	no	—
312	C₄²	—	6	1	no	—
313	C₄²	—	6	1	no	—
314	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
315	C₄²	C₅×D₁₂	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	C₅×C₂²⋊C₈	1	2	yes	—
322	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×D₃	—	2	2	no	—
324	C₂×D₃	—	4	1	no	—
325	C₂×D₃	—	4	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	C₅×C₂²⋊C₈	1	2	yes	—
329	C₃×C₄	C₅×#104	1	2	yes	—
330	C₃×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
331	C₃×C₄	C₂×C₅×M₁₆	1	1	yes	characteristic
332	C₃×C₄	C₅×#135	1	2	yes	—
333	Dic₃	—	2	2	no	—
334	Dic₃	—	4	1	no	—
335	Dic₃	—	4	1	no	—
336	C₂×C₅	—	2	2	no	—
337	C₂×C₅	—	12	2	no	—
338	C₂×C₅	C₂×#805	1	1	yes	characteristic
339	C₂×C₅	C₂×(C₂×D₃)⋊C₈	1	1	yes	characteristic
340	C₂×C₅	#5113	1	1	yes	characteristic
341	C₂³	—	6	1	no	—
342	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	Q₈	—	3	2	no	—
344	Q₈	—	6	1	no	—
345	D₄	—	3	2	no	—
346	D₄	—	6	4	no	—
347	D₄	—	6	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	6	1	no	—
351	C₂×C₄	—	6	4	no	—
352	C₂×C₄	—	6	1	no	—
353	C₂×C₄	—	6	1	no	—
354	C₂×C₄	—	12	2	no	—
355	C₂×C₄	—	12	2	no	—
356	C₂×C₄	C₅×D₃×C₈	1	2	yes	—
357	C₂×C₄	C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
358	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
362	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
363	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
364	C₈	—	2	4	no	—
365	C₈	—	12	2	no	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	C₂×C₅×C₂²⋊C₈	1	1	yes	characteristic
368	C₂×C₃	C₅×#416	1	1	yes	characteristic
369	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
370	D₃	—	4	2	no	—
371	C₅	#69734	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	6	2	no	—
375	C₂²	—	12	1	no	—
376	C₂²	—	12	1	no	—
377	C₂²	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
378	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	6	2	no	—
382	C₄	—	12	1	no	—
383	C₄	—	12	1	no	—
384	C₄	C₅×#805	1	2	yes	—
385	C₄	C₅×(C₂×D₃)⋊C₈	1	2	yes	—
386	C₄	C₂×C₅×D₃×C₈	1	1	yes	characteristic
387	C₄	C₂×C₅×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
388	C₄	C₅×#904	1	2	yes	—
389	C₃	C₅×#1476	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	2	2	no	—
391	C₂	—	12	2	no	—
392	C₂	C₂×C₅×#805	1	1	yes	characteristic
393	C₂	C₂×C₅×(C₂×D₃)⋊C₈	1	1	yes	characteristic
394	C₂	C₅×#5113	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	D₁₂
commutator	C₃×C₄	C₂²×C₅×C₈
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#235	C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₂×C₄×C₅×C₈	D₃
hypocenter	C₃	C₅×#1476
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
3. C₅×#4925	C₂	semidirect
4. C₅×#4459	C₂	semidirect
5. C₅×#4456	C₂	semidirect
24. #69734	C₅	direct (N × H)
27. C₂×C₄×C₅×C₈	D₃	semidirect
35. C₅×#235	C₈	semidirect
59. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
60. #4925	C₂×C₅	semidirect
61. #4459	C₂×C₅	semidirect
62. #4456	C₂×C₅	semidirect
98. C₅×D₁₂	C₂×C₈	semidirect
103. C₅×Dic₆	C₂×C₈	semidirect
153. C₂×C₄×C₈	C₅×D₃	semidirect
178. #235	C₅×C₈	semidirect
265. D₁₂	C₂×C₅×C₈	semidirect
270. Dic₆	C₂×C₅×C₈	semidirect
318. C₃×C₅	#1476	semidirect
371. C₅	#69734	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
C₄×C₅×#235	2
C₂×C₃×C₄×C₅×C₈	2
C₅×#4925	2
C₅×#4459	2
C₅×#4456	2
C₅×#1476	3
#69734	5

Subgroups — C5×#69734 #14281566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69734 #14281566