Subgroups — C₅×#69888 #14296008

Order 1920.

584 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	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#825	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5002	C₂	1	1	yes	maximal, characteristic
6	C₅×#4558	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1765	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₅×#901	—	2	2	no	—
17	C₅×#901	C₄	1	4	yes	complemented
18	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
19	C₂×C₅×D₃×C₈	—	2	1	no	—
20	C₃×C₅×#97	—	2	1	no	—
21	C₃×C₄×C₅×C₈	—	2	1	no	—
22	C₅×#825	C₄	1	4	yes	complemented
23	C₅×#815	—	2	2	no	—
24	C₅×#810	C₄	1	2	yes	complemented
25	C₅×#809	C₄	1	2	yes	complemented
26	#69888	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#131	—	3	1	no	—
28	C₂×C₅×#104	—	3	1	no	—
29	C₅×#416	—	3	1	no	—
30	C₅×#405	D₃	1	1	yes	characteristic, complemented
31	C₂×C₅×#97	—	3	1	no	—
32	C₅×#341	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	1	no	—
36	C₂²×C₅×Dic₃	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	C₂×C₄	1	2	yes	—
40	C₅×#235	C₂×C₄	1	2	yes	—
41	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₄×C₅×Dic₃	—	2	1	no	—
55	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
56	C₅×#208	—	2	1	no	—
57	C₅×#208	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
62	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
63	C₅×D₃×C₈	—	2	4	no	—
64	C₂×#901	C₂×C₅	1	1	yes	characteristic
65	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×#825	C₂×C₅	1	1	yes	characteristic
67	C₂×#815	C₂×C₅	1	1	yes	characteristic, complemented
68	#5002	C₂×C₅	1	1	yes	characteristic
69	#4558	C₂×C₅	1	1	yes	characteristic, complemented
70	#4532	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₅×#41	—	3	1	no	—
72	C₅×#131	—	3	4	no	—
73	C₅×#131	—	6	2	no	—
74	C₂×C₅×M₁₆	—	3	1	no	—
75	C₂×C₅×M₁₆	—	6	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	—	3	1	no	—
78	C₂²×C₅×C₈	—	6	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#117	C₂×D₃	1	1	yes	characteristic
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₅×#104	—	3	4	no	—
83	C₅×#103	—	3	2	no	—
84	C₅×#102	—	3	2	no	—
85	C₅×#97	—	2	1	no	—
86	C₅×#97	—	6	2	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	#1765	—	3	1	no	Sylow
89	C₂³×C₃×C₅	#41	1	1	yes	characteristic
90	C₂²×C₅×D₃	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₅×#67	—	2	2	no	—
99	C₅×#67	—	2	2	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₂×C₅×Dic₃	—	2	2	no	—
102	C₂×C₅×Dic₃	—	4	2	no	—
103	C₅×D₁₂	—	2	1	no	—
104	C₅×D₁₂	C₄²	1	2	yes	—
105	C₄×C₅×D₃	—	2	2	no	—
106	C₄×C₅×D₃	—	2	2	no	—
107	C₅×Dic₆	—	2	1	no	—
108	C₅×Dic₆	C₄²	1	2	yes	—
109	C₃×C₅×C₈	—	2	2	no	—
110	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
111	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
112	C₅×C₃⋊C₈	—	2	2	no	—
113	C₅×C₃⋊C₈	—	2	2	no	—
114	C₂×#235	C₂²×C₅	1	1	yes	characteristic
115	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
116	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
117	C₃×#117	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂×#208	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
121	#901	—	2	2	no	—
122	#901	C₄×C₅	1	4	yes	complemented
123	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
124	C₂×D₃×C₈	—	2	1	no	—
125	C₃×#97	—	2	1	no	—
126	C₃×C₄×C₈	—	2	1	no	—
127	#825	C₄×C₅	1	4	yes	complemented
128	#815	—	2	2	no	—
129	#810	C₄×C₅	1	2	yes	complemented
130	#809	C₄×C₅	1	2	yes	complemented
131	C₅×#41	—	3	2	no	—
132	C₅×#41	—	3	2	no	—
133	C₅×#41	—	6	1	no	—
134	C₅×#41	—	6	1	no	—
135	C₂×C₅×Q₈	—	3	1	no	—
136	C₂×C₅×D₄	—	3	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂²×C₄×C₅	—	6	1	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
141	C₅×M₁₆	—	2	1	no	—
142	C₅×M₁₆	—	3	2	no	—
143	C₅×M₁₆	—	6	1	no	—
144	C₅×M₁₆	—	6	4	no	—
145	C₅×M₁₆	C₄×D₃	1	2	yes	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	6	1	no	—
149	C₂×C₅×C₈	—	6	1	no	—
150	C₂×C₅×C₈	—	6	1	no	—
151	C₂×C₅×C₈	—	6	4	no	—
152	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
153	C₂×C₅×C₈	D₁₂	1	2	yes	—
154	C₂×C₅×C₈	#67	1	1	yes	characteristic
155	C₂×C₅×C₈	#67	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	3	2	no	—
160	C₄²×C₅	—	6	1	no	—
161	C₂×#131	—	3	1	no	—
162	C₂×#104	—	3	1	no	—
163	#416	—	3	1	no	—
164	#405	C₅×D₃	1	1	yes	characteristic, complemented
165	C₂×#97	—	3	1	no	—
166	#341	—	3	1	no	—
167	#339	—	3	1	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	#117	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	2	no	—
173	C₂×C₅×D₃	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
176	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
178	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	—	4	2	no	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂×#67	—	2	1	no	—
183	C₂²×Dic₃	—	2	1	no	—
184	#235	—	2	1	no	—
185	#235	—	2	1	no	—
186	#235	C₂×C₄×C₅	1	2	yes	—
187	#235	C₂×C₄×C₅	1	2	yes	—
188	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂×C₄×D₃	—	2	1	no	—
190	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
191	C₃×M₁₆	—	2	1	no	—
192	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
195	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
196	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
197	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
199	C₃×C₂²⋊C₄	—	2	1	no	—
200	C₃×C₄²	—	2	1	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	—
203	#208	—	2	1	no	—
204	#208	C₂×C₄×C₅	1	2	yes	—
205	C₂×C₃⋊C₈	—	2	1	no	—
206	C₂×C₃⋊C₈	—	2	1	no	—
207	C₂×C₃⋊C₈	—	2	1	no	—
208	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
209	ΓL(1,𝔽₂₅)	—	2	4	no	—
210	D₃×C₈	—	2	4	no	—
211	C₂³×C₅	—	6	1	no	—
212	C₂³×C₅	#235	1	1	yes	characteristic
213	C₅×Q₈	—	3	2	no	—
214	C₅×Q₈	—	6	1	no	—
215	C₅×D₄	—	3	2	no	—
216	C₅×D₄	—	6	2	no	—
217	C₅×D₄	—	6	2	no	—
218	C₅×D₄	—	6	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	6	2	no	—
222	C₂×C₄×C₅	—	6	2	no	—
223	C₂×C₄×C₅	—	6	2	no	—
224	C₂×C₄×C₅	—	12	2	no	—
225	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
229	C₂×C₄×C₅	#235	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	6	2	no	—
233	C₅×C₈	—	6	2	no	—
234	C₅×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
235	C₅×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
236	C₂×#41	—	3	1	no	—
237	#131	—	3	4	no	—
238	#131	—	6	2	no	—
239	C₂×M₁₆	—	3	1	no	—
240	C₂×M₁₆	—	6	1	no	—
241	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
242	C₂²×C₈	—	3	1	no	—
243	C₂²×C₈	—	6	1	no	—
244	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
245	#117	C₂×C₅×D₃	1	1	yes	characteristic
246	C₂×C₄²	—	3	1	no	—
247	#104	—	3	4	no	—
248	#103	—	3	2	no	—
249	#102	—	3	2	no	—
250	#97	—	2	1	no	—
251	#97	—	6	2	no	—
252	C₄×C₈	—	2	1	no	—
253	C₂×C₃×C₅	—	2	1	no	—
254	C₂×C₃×C₅	—	2	1	no	—
255	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₃×C₅	#444	1	2	yes	—
257	C₅×D₃	—	4	2	no	—
258	C₂³×C₃	C₅×#41	1	1	yes	characteristic
259	C₂²×D₃	—	2	1	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
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	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
267	#67	—	2	2	no	—
268	#67	—	2	2	no	—
269	C₂×Dic₃	—	2	1	no	—
270	C₂×Dic₃	—	2	2	no	—
271	C₂×Dic₃	—	4	2	no	—
272	D₁₂	—	2	1	no	—
273	D₁₂	C₄²×C₅	1	2	yes	—
274	C₄×D₃	—	2	2	no	—
275	C₄×D₃	—	2	2	no	—
276	Dic₆	—	2	1	no	—
277	Dic₆	C₄²×C₅	1	2	yes	—
278	C₃×C₈	—	2	2	no	—
279	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
280	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
281	C₃⋊C₈	—	2	2	no	—
282	C₃⋊C₈	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	6	2	no	—
285	C₂²×C₅	—	12	2	no	—
286	C₂²×C₅	#872	1	1	yes	characteristic
287	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
288	C₂²×C₅	C₄×#67	1	1	yes	characteristic
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	6	2	no	—
291	C₄×C₅	—	12	2	no	—
292	C₄×C₅	C₄²×D₃	1	1	yes	characteristic
293	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
294	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
295	C₄×C₅	C₄×#67	1	1	yes	characteristic
296	#41	—	3	2	no	—
297	#41	—	3	2	no	—
298	#41	—	6	1	no	—
299	#41	—	6	1	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	C₂²×C₅×D₃	1	1	yes	characteristic
306	M₁₆	—	2	1	no	—
307	M₁₆	—	3	2	no	—
308	M₁₆	—	6	1	no	—
309	M₁₆	—	6	4	no	—
310	M₁₆	C₄×C₅×D₃	1	2	yes	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	3	2	no	—
313	C₂×C₈	—	6	1	no	—
314	C₂×C₈	—	6	1	no	—
315	C₂×C₈	—	6	1	no	—
316	C₂×C₈	—	6	4	no	—
317	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
318	C₂×C₈	C₅×D₁₂	1	2	yes	—
319	C₂×C₈	C₅×#67	1	1	yes	characteristic
320	C₂×C₈	C₅×#67	1	1	yes	characteristic
321	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	3	2	no	—
325	C₄²	—	6	1	no	—
326	C₃×C₅	#1765	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	C₅×#117	1	1	yes	characteristic
329	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
330	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
331	C₂×D₃	—	2	2	no	—
332	C₂×D₃	—	4	2	no	—
333	C₃×C₄	—	4	2	no	—
334	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
335	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
336	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
337	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
338	Dic₃	—	2	2	no	—
339	Dic₃	—	4	2	no	—
340	C₂×C₅	—	2	1	no	—
341	C₂×C₅	—	2	1	no	—
342	C₂×C₅	—	12	2	no	—
343	C₂×C₅	C₄×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₅	#5145	1	2	yes	—
345	C₂³	—	6	1	no	—
346	C₂³	C₅×#235	1	1	yes	characteristic
347	Q₈	—	3	2	no	—
348	Q₈	—	6	1	no	—
349	D₄	—	3	2	no	—
350	D₄	—	6	2	no	—
351	D₄	—	6	2	no	—
352	D₄	—	6	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	6	1	no	—
355	C₂×C₄	—	6	2	no	—
356	C₂×C₄	—	6	2	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	12	2	no	—
359	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×C₅×D₃	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	C₅×#235	1	1	yes	characteristic
364	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	6	2	no	—
367	C₈	—	6	2	no	—
368	C₈	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
369	C₈	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
373	C₂×C₃	C₅×#444	1	2	yes	—
374	D₃	—	4	2	no	—
375	C₅	#69888	1	1	yes	characteristic, direct product factor, Sylow
376	C₂²	—	2	2	no	—
377	C₂²	—	6	2	no	—
378	C₂²	—	12	2	no	—
379	C₂²	C₅×#872	1	1	yes	characteristic
380	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
381	C₂²	C₄×C₅×#67	1	1	yes	characteristic
382	C₄	—	4	2	no	—
383	C₄	—	6	2	no	—
384	C₄	—	12	2	no	—
385	C₄	C₄²×C₅×D₃	1	1	yes	characteristic
386	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
387	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
388	C₄	C₄×C₅×#67	1	1	yes	characteristic
389	C₃	C₅×#1765	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	12	2	no	—
393	C₂	C₄×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
394	C₂	C₅×#5145	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#405	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#405	D₃
hypocenter	C₃	C₅×#1765
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₅×#405

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#405	C₂	semidirect
4. C₂×C₅×#815	C₂	semidirect
6. C₅×#4558	C₂	semidirect
7. C₅×#4532	C₂	semidirect
17. C₅×#901	C₄	semidirect
22. C₅×#825	C₄	semidirect
24. C₅×#810	C₄	semidirect
25. C₅×#809	C₄	semidirect
26. #69888	C₅	direct (N × H)
30. C₅×#405	D₃	semidirect
65. C₃×#405	C₂×C₅	semidirect
67. C₂×#815	C₂×C₅	semidirect
69. #4558	C₂×C₅	semidirect
70. #4532	C₂×C₅	semidirect
122. #901	C₄×C₅	semidirect
127. #825	C₄×C₅	semidirect
129. #810	C₄×C₅	semidirect
130. #809	C₄×C₅	semidirect
164. #405	C₅×D₃	semidirect
326. C₃×C₅	#1765	semidirect
375. C₅	#69888	direct (N × H)
389. C₃	C₅×#1765	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
C₃×C₅×#405	2
C₂×C₅×#825	2
C₂×C₅×#815	2
C₅×#5002	2
C₅×#4558	2
C₅×#4532	2
C₅×#1765	3
#69888	5

Subgroups — C5×#69888 #14296008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69888 #14296008