Subgroups — C₅×#5701 #11756086

Order 960.

384 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic
2	C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#879	C₂	1	1	yes	maximal, characteristic
9	C₅×#879	C₂	1	1	yes	maximal, characteristic
10	C₅×#879	C₂	1	1	yes	maximal, characteristic
11	C₅×#878	C₂	1	1	yes	maximal, characteristic
12	C₅×#878	C₂	1	1	yes	maximal, characteristic
13	C₅×#877	C₂	1	1	yes	maximal, characteristic
14	C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#541	—	3	1	no	maximal, Hall
17	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₅×#217	C₂²	1	1	yes	characteristic
28	C₅×#217	C₂²	1	1	yes	characteristic
29	C₅×#217	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
32	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₅×Dic₃⋊C₄	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	C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
48	C₄×C₅×Dic₃	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	#5701	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
53	C₅×C₄⋊Q₈	—	3	1	no	—
54	C₅×#126	—	3	1	no	—
55	C₅×#126	—	3	1	no	—
56	C₅×#126	—	3	1	no	—
57	C₅×#126	D₃	1	1	yes	characteristic
58	C₅×#125	—	3	1	no	—
59	C₅×#125	—	3	1	no	—
60	C₅×#125	—	3	1	no	—
61	C₅×#125	—	3	1	no	—
62	C₅×#125	—	3	1	no	—
63	C₅×C₂²⋊Q₈	—	3	1	no	—
64	C₅×C₂²⋊Q₈	—	3	1	no	—
65	C₄×C₅×Q₈	—	3	1	no	—
66	C₄×C₅×Q₈	—	3	1	no	—
67	C₅×#117	—	3	1	no	—
68	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
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×C₅×Dic₃	—	2	2	no	—
76	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₅×Dic₆	—	2	2	no	—
85	C₅×Dic₆	—	2	2	no	—
86	C₃×#126	C₂×C₅	1	1	yes	characteristic
87	#890	C₂×C₅	1	1	yes	characteristic, complemented
88	#889	C₂×C₅	1	1	yes	characteristic, complemented
89	#889	C₂×C₅	1	1	yes	characteristic, complemented
90	#889	C₂×C₅	1	1	yes	characteristic, complemented
91	#888	C₂×C₅	1	1	yes	characteristic, complemented
92	#887	C₂×C₅	1	1	yes	characteristic, complemented
93	#879	C₂×C₅	1	1	yes	characteristic
94	#879	C₂×C₅	1	1	yes	characteristic
95	#879	C₂×C₅	1	1	yes	characteristic
96	#878	C₂×C₅	1	1	yes	characteristic
97	#878	C₂×C₅	1	1	yes	characteristic
98	#877	C₂×C₅	1	1	yes	characteristic
99	#870	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×Q₈	—	3	1	no	—
102	C₂×C₅×Q₈	—	3	1	no	—
103	C₂²×C₄×C₅	—	3	1	no	—
104	C₅×C₄⋊C₄	—	3	1	no	—
105	C₅×C₄⋊C₄	—	3	1	no	—
106	C₅×C₄⋊C₄	—	3	1	no	—
107	C₅×C₄⋊C₄	—	3	1	no	—
108	C₅×C₄⋊C₄	—	3	1	no	—
109	C₅×C₄⋊C₄	—	3	1	no	—
110	C₅×C₄⋊C₄	—	3	1	no	—
111	C₅×C₄⋊C₄	—	3	1	no	—
112	C₅×C₄⋊C₄	—	3	1	no	—
113	C₅×C₄⋊C₄	—	3	1	no	—
114	C₅×C₄⋊C₄	—	3	1	no	—
115	C₅×C₄⋊C₄	—	3	1	no	—
116	C₅×C₄⋊C₄	—	3	1	no	—
117	C₅×C₄⋊C₄	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
122	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₅×C₂²⋊C₄	—	3	1	no	—
125	C₅×C₂²⋊C₄	—	3	1	no	—
126	C₅×C₂²⋊C₄	—	3	1	no	—
127	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₄²×C₅	—	3	1	no	—
131	C₄²×C₅	—	3	1	no	—
132	C₄²×C₅	—	3	1	no	—
133	C₄²×C₅	—	3	1	no	—
134	C₄²×C₅	—	3	1	no	—
135	C₄²×C₅	C₂×D₃	1	1	yes	characteristic
136	#541	—	3	1	no	Sylow
137	C₂²×C₃×C₅	—	2	1	no	—
138	C₂²×C₃×C₅	—	2	1	no	—
139	C₂²×C₃×C₅	—	2	1	no	—
140	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	—	2	1	no	—
145	C₃×C₄×C₅	—	2	1	no	—
146	C₃×C₄×C₅	—	2	1	no	—
147	C₅×Dic₃	—	2	1	no	—
148	C₅×Dic₃	—	2	1	no	—
149	C₅×Dic₃	—	2	1	no	—
150	C₅×Dic₃	—	2	1	no	—
151	C₅×Dic₃	—	2	1	no	—
152	C₅×Dic₃	—	2	1	no	—
153	C₅×Dic₃	—	2	1	no	—
154	C₅×Dic₃	#41	1	2	yes	—
155	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
156	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
157	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
159	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
162	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
165	#217	C₂²×C₅	1	1	yes	characteristic
166	#217	C₂²×C₅	1	1	yes	characteristic
167	#217	C₂²×C₅	1	1	yes	characteristic
168	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
169	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
170	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
171	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
172	C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
173	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
176	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
182	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
186	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
187	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
188	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
189	C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
190	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
191	C₅×Q₈	—	6	2	no	—
192	C₅×Q₈	—	6	2	no	—
193	C₂×C₄×C₅	—	3	1	no	—
194	C₂×C₄×C₅	—	3	1	no	—
195	C₂×C₄×C₅	—	3	1	no	—
196	C₂×C₄×C₅	—	3	1	no	—
197	C₂×C₄×C₅	—	3	1	no	—
198	C₂×C₄×C₅	—	3	1	no	—
199	C₂×C₄×C₅	—	3	1	no	—
200	C₂×C₄×C₅	—	3	1	no	—
201	C₂×C₄×C₅	—	6	2	no	—
202	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₄⋊Q₈	—	3	1	no	—
209	#126	—	3	1	no	—
210	#126	—	3	1	no	—
211	#126	—	3	1	no	—
212	#126	C₅×D₃	1	1	yes	characteristic
213	#125	—	3	1	no	—
214	#125	—	3	1	no	—
215	#125	—	3	1	no	—
216	#125	—	3	1	no	—
217	#125	—	3	1	no	—
218	C₂²⋊Q₈	—	3	1	no	—
219	C₂²⋊Q₈	—	3	1	no	—
220	C₄×Q₈	—	3	1	no	—
221	C₄×Q₈	—	3	1	no	—
222	#117	—	3	1	no	—
223	C₂×C₃×C₅	—	4	1	no	—
224	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
226	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
227	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₂×Dic₃	—	2	2	no	—
235	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
236	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
237	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
238	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
239	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
240	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
241	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
242	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
243	Dic₆	—	2	2	no	—
244	Dic₆	—	2	2	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	2	1	no	—
251	C₄×C₅	—	2	1	no	—
252	C₄×C₅	—	2	1	no	—
253	C₄×C₅	—	2	1	no	—
254	C₄×C₅	—	2	1	no	—
255	C₄×C₅	—	3	2	no	—
256	C₄×C₅	—	6	1	no	—
257	C₄×C₅	—	6	1	no	—
258	C₄×C₅	—	6	1	no	—
259	C₄×C₅	—	6	1	no	—
260	C₄×C₅	—	6	1	no	—
261	C₄×C₅	—	6	1	no	—
262	C₄×C₅	—	6	1	no	—
263	C₂×Q₈	—	3	1	no	—
264	C₂×Q₈	—	3	1	no	—
265	C₂²×C₄	—	3	1	no	—
266	C₄⋊C₄	—	3	1	no	—
267	C₄⋊C₄	—	3	1	no	—
268	C₄⋊C₄	—	3	1	no	—
269	C₄⋊C₄	—	3	1	no	—
270	C₄⋊C₄	—	3	1	no	—
271	C₄⋊C₄	—	3	1	no	—
272	C₄⋊C₄	—	3	1	no	—
273	C₄⋊C₄	—	3	1	no	—
274	C₄⋊C₄	—	3	1	no	—
275	C₄⋊C₄	—	3	1	no	—
276	C₄⋊C₄	—	3	1	no	—
277	C₄⋊C₄	—	3	1	no	—
278	C₄⋊C₄	—	3	1	no	—
279	C₄⋊C₄	—	3	1	no	—
280	C₄⋊C₄	—	3	1	no	—
281	C₄⋊C₄	—	3	1	no	—
282	C₄⋊C₄	—	3	1	no	—
283	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
284	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
285	C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
286	C₂²⋊C₄	—	3	1	no	—
287	C₂²⋊C₄	—	3	1	no	—
288	C₂²⋊C₄	—	3	1	no	—
289	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
290	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
291	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
292	C₄²	—	3	1	no	—
293	C₄²	—	3	1	no	—
294	C₄²	—	3	1	no	—
295	C₄²	—	3	1	no	—
296	C₄²	—	3	1	no	—
297	C₄²	C₂×C₅×D₃	1	1	yes	characteristic
298	C₃×C₅	#541	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	Dic₃	—	2	1	no	—
310	Dic₃	—	2	1	no	—
311	Dic₃	—	2	1	no	—
312	Dic₃	—	2	1	no	—
313	Dic₃	—	2	1	no	—
314	Dic₃	—	2	1	no	—
315	Dic₃	—	2	1	no	—
316	Dic₃	C₅×#41	1	2	yes	—
317	C₂×C₅	—	4	1	no	—
318	C₂×C₅	D₃×#41	1	1	yes	characteristic
319	C₂×C₅	#1010	1	1	yes	characteristic
320	C₂×C₅	#1010	1	1	yes	characteristic
321	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
322	Q₈	—	6	2	no	—
323	Q₈	—	6	2	no	—
324	C₂×C₄	—	3	1	no	—
325	C₂×C₄	—	3	1	no	—
326	C₂×C₄	—	3	1	no	—
327	C₂×C₄	—	3	1	no	—
328	C₂×C₄	—	3	1	no	—
329	C₂×C₄	—	3	1	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	3	1	no	—
332	C₂×C₄	—	6	2	no	—
333	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
339	C₂×C₃	—	4	1	no	—
340	C₂×C₃	C₂×C₅×#41	1	1	yes	characteristic
341	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
342	C₂×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
343	C₅	#5701	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	3	2	no	—
355	C₄	—	6	1	no	—
356	C₄	—	6	1	no	—
357	C₄	—	6	1	no	—
358	C₄	—	6	1	no	—
359	C₄	—	6	1	no	—
360	C₄	—	6	1	no	—
361	C₄	—	6	1	no	—
362	C₃	C₅×#541	1	1	yes	characteristic, complemented, Sylow
363	C₂	—	4	1	no	—
364	C₂	C₅×D₃×#41	1	1	yes	characteristic
365	C₂	C₅×#1010	1	1	yes	characteristic
366	C₂	C₅×#1010	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×#126	C₂
socle	C₂²×C₃×C₅	C₂⁴
prime radical	C₂³×C₃×C₅	C₂³
hypercenter	C₅×#126	D₃
hypocenter	C₃	C₅×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#126

Complements

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

N	H ≅ G/N	type
2. C₅×#890	C₂	semidirect
3. C₅×#889	C₂	semidirect
4. C₅×#889	C₂	semidirect
5. C₅×#889	C₂	semidirect
6. C₅×#888	C₂	semidirect
7. C₅×#887	C₂	semidirect
14. C₅×#870	C₂	semidirect
15. C₄×C₅×Dic₆	C₂	semidirect
52. #5701	C₅	direct (N × H)
87. #890	C₂×C₅	semidirect
88. #889	C₂×C₅	semidirect
89. #889	C₂×C₅	semidirect
90. #889	C₂×C₅	semidirect
91. #888	C₂×C₅	semidirect
92. #887	C₂×C₅	semidirect
99. #870	C₂×C₅	semidirect
100. C₄×Dic₆	C₂×C₅	semidirect
298. C₃×C₅	#541	semidirect
343. C₅	#5701	direct (N × H)
362. C₃	C₅×#541	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#126	2
C₅×#890	2
C₅×#889	2
C₅×#888	2
C₅×#887	2
C₅×#879	2
C₅×#878	2
C₅×#877	2
C₅×#870	2
C₄×C₅×Dic₆	2
C₅×#541	3
#5701	5

Subgroups — C5×#5701 #11756086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5701 #11756086