Subgroups — C₅×#74050 #14319908

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#877	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5211	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4955	C₂	1	2	yes	maximal
6	C₅×#4667	C₂	1	4	yes	maximal, complemented
7	C₅×#4666	C₂	1	4	yes	maximal, complemented
8	C₅×#2280	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	8	no	—
13	C₂²×C₄×C₅×D₃	C₄	1	8	yes	complemented
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₅×#217	C₂²	1	2	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
20	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
21	C₅×#877	—	2	8	no	—
22	C₃×C₅×#95	C₂²	1	4	yes	complemented
23	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
24	#74050	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂⁴×C₄×C₅	—	3	1	no	—
26	C₂×C₅×#117	—	3	2	no	—
27	C₅×#381	—	3	1	no	—
28	C₅×#381	D₃	1	1	yes	characteristic, complemented
29	C₅×#380	—	3	4	no	—
30	C₅×#379	—	3	2	no	—
31	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂³×C₅×D₃	—	2	4	no	—
34	C₂³×C₅×D₃	—	2	8	no	—
35	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
36	C₂³×C₅×D₃	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
42	C₂²×C₅×Dic₃	D₄	1	8	yes	—
43	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	—	2	32	no	—
47	C₂×C₄×C₅×D₃	—	2	8	no	—
48	C₂×C₄×C₅×D₃	—	2	8	no	—
49	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
50	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₅×#217	—	2	4	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	16	no	—
54	C₅×Dic₃⋊C₄	—	2	8	no	—
55	C₄×C₅×Dic₃	—	2	8	no	—
56	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
57	C₂×#877	C₂×C₅	1	2	yes	complemented
58	C₃×#381	C₂×C₅	1	1	yes	characteristic, complemented
59	#5211	C₂×C₅	1	1	yes	characteristic, complemented
60	#4955	C₂×C₅	1	2	yes	—
61	#4667	C₂×C₅	1	4	yes	complemented
62	#4666	C₂×C₅	1	4	yes	complemented
63	C₂⁵×C₅	—	3	1	no	—
64	C₂³×C₄×C₅	—	3	1	no	—
65	C₂³×C₄×C₅	—	3	8	no	—
66	C₂³×C₄×C₅	—	3	2	no	—
67	C₂³×C₄×C₅	—	3	2	no	—
68	C₂³×C₄×C₅	—	6	8	no	—
69	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
70	C₅×#117	—	6	8	no	—
71	C₂×C₅×C₄⋊C₄	—	3	4	no	—
72	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
74	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
75	C₂×C₄²×C₅	—	3	4	no	—
76	C₅×#95	—	3	4	no	—
77	C₅×#95	C₂×D₃	1	4	yes	complemented
78	#2280	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
83	C₂²×C₅×D₃	—	2	32	no	—
84	C₂²×C₅×D₃	—	2	8	no	—
85	C₂²×C₅×D₃	—	2	4	no	—
86	C₂²×C₅×D₃	—	2	4	no	—
87	C₂²×C₅×D₃	—	2	16	no	—
88	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₅×D₃	#41	1	8	yes	—
90	C₂×C₃×C₄×C₅	—	2	8	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	8	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	C₂²⋊C₄	1	16	yes	complemented
98	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
99	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
100	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
101	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
102	C₄×C₅×D₃	—	2	16	no	—
103	C₄×C₅×D₃	—	2	16	no	—
104	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₄×D₃	—	2	8	no	—
108	C₂²×C₄×D₃	C₄×C₅	1	8	yes	complemented
109	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
110	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
111	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
112	C₂×#217	C₂²×C₅	1	2	yes	—
113	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
114	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
115	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
116	#877	—	2	8	no	—
117	C₃×#95	C₂²×C₅	1	4	yes	complemented
118	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
119	C₂⁴×C₅	—	3	2	no	—
120	C₂⁴×C₅	—	3	4	no	—
121	C₂⁴×C₅	—	6	8	no	—
122	C₂⁴×C₅	—	6	4	no	—
123	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	3	4	no	—
126	C₂²×C₄×C₅	—	3	8	no	—
127	C₂²×C₄×C₅	—	3	1	no	—
128	C₂²×C₄×C₅	—	3	1	no	—
129	C₂²×C₄×C₅	—	3	8	no	—
130	C₂²×C₄×C₅	—	3	8	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	32	no	—
133	C₂²×C₄×C₅	—	6	8	no	—
134	C₂²×C₄×C₅	—	6	8	no	—
135	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
136	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
137	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
138	C₅×C₄⋊C₄	—	6	8	no	—
139	C₅×C₂²⋊C₄	—	2	4	no	—
140	C₅×C₂²⋊C₄	—	6	16	no	—
141	C₅×C₂²⋊C₄	—	6	4	no	—
142	C₄²×C₅	—	6	8	no	—
143	C₂⁴×C₄	—	3	1	no	—
144	C₂×#117	—	3	2	no	—
145	#381	—	3	1	no	—
146	#381	C₅×D₃	1	1	yes	characteristic, complemented
147	#380	—	3	4	no	—
148	#379	—	3	2	no	—
149	C₄×C₂²⋊C₄	—	3	4	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
156	C₂×C₅×D₃	—	2	32	no	—
157	C₂×C₅×D₃	—	2	4	no	—
158	C₂×C₅×D₃	—	2	4	no	—
159	C₂×C₅×D₃	—	2	16	no	—
160	C₂×C₅×D₃	#117	1	8	yes	complemented
161	C₃×C₄×C₅	—	2	4	no	—
162	C₃×C₄×C₅	—	4	4	no	—
163	C₅×Dic₃	—	4	4	no	—
164	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
165	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
167	C₂³×D₃	—	2	4	no	—
168	C₂³×D₃	—	2	8	no	—
169	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
170	C₂³×D₃	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
174	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
175	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
176	C₂²×Dic₃	C₅×D₄	1	8	yes	—
177	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
178	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
179	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
180	C₂×C₄×D₃	—	2	32	no	—
181	C₂×C₄×D₃	—	2	8	no	—
182	C₂×C₄×D₃	—	2	8	no	—
183	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
184	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
185	C₃×C₂²⋊C₄	—	2	4	no	—
186	#217	—	2	4	no	—
187	(C₂×D₃)⋊C₄	—	2	16	no	—
188	Dic₃⋊C₄	—	2	8	no	—
189	C₄×Dic₃	—	2	8	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	—	3	4	no	—
192	C₂³×C₅	—	3	8	no	—
193	C₂³×C₅	—	6	16	no	—
194	C₂³×C₅	—	6	32	no	—
195	C₂³×C₅	—	6	8	no	—
196	C₂³×C₅	—	6	4	no	—
197	C₂³×C₅	—	6	4	no	—
198	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
199	C₂³×C₅	D₃×D₄	1	4	yes	—
200	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
201	C₂×C₄×C₅	—	2	8	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	—	3	16	no	—
206	C₂×C₄×C₅	—	3	2	no	—
207	C₂×C₄×C₅	—	3	2	no	—
208	C₂×C₄×C₅	—	3	4	no	—
209	C₂×C₄×C₅	—	3	4	no	—
210	C₂×C₄×C₅	—	6	16	no	—
211	C₂×C₄×C₅	—	6	16	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	—	6	8	no	—
214	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
215	C₂⁵	—	3	1	no	—
216	C₂³×C₄	—	3	1	no	—
217	C₂³×C₄	—	3	8	no	—
218	C₂³×C₄	—	3	2	no	—
219	C₂³×C₄	—	3	2	no	—
220	C₂³×C₄	—	6	8	no	—
221	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
222	#117	—	6	8	no	—
223	C₂×C₄⋊C₄	—	3	4	no	—
224	C₂×C₂²⋊C₄	—	3	2	no	—
225	C₂×C₂²⋊C₄	—	3	8	no	—
226	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
227	C₂×C₄²	—	3	4	no	—
228	#95	—	3	4	no	—
229	#95	C₂×C₅×D₃	1	4	yes	complemented
230	C₂×C₃×C₅	—	2	4	no	—
231	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×#117	1	2	yes	—
233	C₂×C₃×C₅	#525	1	4	yes	—
234	C₅×D₃	—	2	8	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
237	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
238	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
239	C₂²×D₃	—	2	32	no	—
240	C₂²×D₃	—	2	8	no	—
241	C₂²×D₃	—	2	4	no	—
242	C₂²×D₃	—	2	4	no	—
243	C₂²×D₃	—	2	16	no	—
244	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
245	C₂²×D₃	C₅×#41	1	8	yes	—
246	C₂×C₃×C₄	—	2	8	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	8	no	—
250	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
251	C₂×Dic₃	—	2	4	no	—
252	C₂×Dic₃	—	2	8	no	—
253	C₂×Dic₃	C₅×C₂²⋊C₄	1	16	yes	complemented
254	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
255	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
256	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
257	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
258	C₄×D₃	—	2	16	no	—
259	C₄×D₃	—	2	16	no	—
260	C₂²×C₅	—	2	8	no	—
261	C₂²×C₅	—	2	4	no	—
262	C₂²×C₅	—	3	8	no	—
263	C₂²×C₅	—	6	32	no	—
264	C₂²×C₅	—	6	16	no	—
265	C₂²×C₅	—	6	4	no	—
266	C₂²×C₅	—	6	4	no	—
267	C₂²×C₅	D₃×C₂²⋊C₄	1	4	yes	—
268	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
269	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
270	C₂²×C₅	D₃×#41	1	4	yes	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	3	4	no	—
273	C₄×C₅	—	3	4	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	—	12	4	no	—
276	C₂⁴	—	3	2	no	—
277	C₂⁴	—	3	4	no	—
278	C₂⁴	—	6	8	no	—
279	C₂⁴	—	6	4	no	—
280	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	3	4	no	—
283	C₂²×C₄	—	3	8	no	—
284	C₂²×C₄	—	3	1	no	—
285	C₂²×C₄	—	3	1	no	—
286	C₂²×C₄	—	3	8	no	—
287	C₂²×C₄	—	3	8	no	—
288	C₂²×C₄	—	3	4	no	—
289	C₂²×C₄	—	6	32	no	—
290	C₂²×C₄	—	6	8	no	—
291	C₂²×C₄	—	6	8	no	—
292	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
293	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
294	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
295	C₄⋊C₄	—	6	8	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	6	16	no	—
298	C₂²⋊C₄	—	6	4	no	—
299	C₄²	—	6	8	no	—
300	C₃×C₅	#2280	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	2	8	no	—
303	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
304	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
305	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
306	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
307	C₂×D₃	—	2	32	no	—
308	C₂×D₃	—	2	4	no	—
309	C₂×D₃	—	2	4	no	—
310	C₂×D₃	—	2	16	no	—
311	C₂×D₃	C₅×#117	1	8	yes	complemented
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	4	4	no	—
314	Dic₃	—	4	4	no	—
315	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
316	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
317	C₂×C₅	—	2	4	no	—
318	C₂×C₅	—	6	8	no	—
319	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₅	D₃×#117	1	2	yes	—
321	C₂×C₅	#5656	1	4	yes	—
322	C₂³	—	2	4	no	—
323	C₂³	—	3	4	no	—
324	C₂³	—	3	8	no	—
325	C₂³	—	6	16	no	—
326	C₂³	—	6	32	no	—
327	C₂³	—	6	8	no	—
328	C₂³	—	6	4	no	—
329	C₂³	—	6	4	no	—
330	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
331	C₂³	C₅×D₃×D₄	1	4	yes	—
332	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	3	16	no	—
338	C₂×C₄	—	3	2	no	—
339	C₂×C₄	—	3	2	no	—
340	C₂×C₄	—	3	4	no	—
341	C₂×C₄	—	3	4	no	—
342	C₂×C₄	—	6	16	no	—
343	C₂×C₄	—	6	16	no	—
344	C₂×C₄	—	6	4	no	—
345	C₂×C₄	—	6	8	no	—
346	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
347	C₂×C₃	—	2	4	no	—
348	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₂×C₃	C₂×C₅×#117	1	2	yes	—
350	C₂×C₃	C₅×#525	1	4	yes	—
351	D₃	—	2	8	no	—
352	C₅	#74050	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	2	8	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	3	8	no	—
356	C₂²	—	6	32	no	—
357	C₂²	—	6	16	no	—
358	C₂²	—	6	4	no	—
359	C₂²	—	6	4	no	—
360	C₂²	C₅×D₃×C₂²⋊C₄	1	4	yes	—
361	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
362	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
363	C₂²	C₅×D₃×#41	1	4	yes	—
364	C₄	—	2	4	no	—
365	C₄	—	3	4	no	—
366	C₄	—	3	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	12	4	no	—
369	C₃	C₅×#2280	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	4	no	—
371	C₂	—	6	8	no	—
372	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
373	C₂	C₅×D₃×#117	1	2	yes	—
374	C₂	C₅×#5656	1	4	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#381	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#381	D₃
hypocenter	C₃	C₅×#2280
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#381

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#877	C₂	semidirect
3. C₃×C₅×#381	C₂	semidirect
4. C₅×#5211	C₂	semidirect
6. C₅×#4667	C₂	semidirect
7. C₅×#4666	C₂	semidirect
13. C₂²×C₄×C₅×D₃	C₄	semidirect
19. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
20. C₂×C₄×C₅×Dic₃	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₅×C₃⋊#95	C₂²	semidirect
24. #74050	C₅	direct (N × H)
28. C₅×#381	D₃	semidirect
57. C₂×#877	C₂×C₅	semidirect
58. C₃×#381	C₂×C₅	semidirect
59. #5211	C₂×C₅	semidirect
61. #4667	C₂×C₅	semidirect
62. #4666	C₂×C₅	semidirect
77. C₅×#95	C₂×D₃	semidirect
97. C₂×C₅×Dic₃	C₂²⋊C₄	semidirect
108. C₂²×C₄×D₃	C₄×C₅	semidirect
114. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
115. C₂×C₄×Dic₃	C₂²×C₅	semidirect
117. C₃×#95	C₂²×C₅	semidirect
118. C₃⋊#95	C₂²×C₅	semidirect
146. #381	C₅×D₃	semidirect
160. C₂×C₅×D₃	#117	semidirect
229. #95	C₂×C₅×D₃	semidirect
253. C₂×Dic₃	C₅×C₂²⋊C₄	semidirect
300. C₃×C₅	#2280	semidirect
311. C₂×D₃	C₅×#117	semidirect
352. C₅	#74050	direct (N × H)
369. C₃	C₅×#2280	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂×C₅×#877	2
C₃×C₅×#381	2
C₅×#5211	2
C₅×#4955	2
C₅×#4667	2
C₅×#4666	2
C₅×#2280	3
#74050	5

Subgroups — C5×#74050 #14319908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74050 #14319908