Subgroups — C₅×#69980 #14283159

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#924	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic
4	C₅×#4467	C₂	1	4	yes	maximal, complemented
5	C₅×#1508	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₅×#217	—	2	1	no	—
10	C₂×C₅×#217	—	2	1	no	—
11	C₂×C₅×C₄⋊Dic₃	C₄	1	1	yes	characteristic, complemented
12	C₅×#924	—	2	1	no	—
13	C₅×#924	—	2	1	no	—
14	C₅×#924	C₄	1	2	yes	complemented
15	C₅×#924	C₂²	1	2	yes	—
16	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
17	C₂×C₄×C₅×Dic₃	—	2	1	no	—
18	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
19	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₅×C₃⋊#95	C₂²	1	2	yes	—
21	#69980	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
23	C₅×#407	D₃	1	1	yes	characteristic
24	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
25	C₅×#328	—	3	4	no	—
26	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	—	4	2	no	—
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	D₄	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₅×Dic₃	—	2	1	no	—
35	C₂²×C₅×Dic₃	—	2	1	no	—
36	C₂²×C₅×Dic₃	—	2	2	no	—
37	C₂×C₅×Dic₆	—	2	1	no	—
38	C₂×C₅×Dic₆	—	4	2	no	—
39	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
40	C₃×C₅×M₁₆	—	4	2	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₅×#217	—	2	4	no	—
43	C₅×#217	—	2	2	no	—
44	C₅×#217	—	2	2	no	—
45	C₅×C₄⋊Dic₃	—	2	1	no	—
46	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
47	C₅×Dic₃⋊C₄	—	2	2	no	—
48	C₅×Dic₃⋊C₄	—	2	2	no	—
49	C₄×C₅×Dic₃	—	4	2	no	—
50	C₂×#924	C₂×C₅	1	1	yes	characteristic
51	C₃×#407	C₂×C₅	1	1	yes	characteristic
52	C₄×#217	C₂×C₅	1	1	yes	characteristic
53	#4467	C₂×C₅	1	4	yes	complemented
54	C₂²×C₅×Q₈	—	3	1	no	—
55	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₅×C₂²⋊Q₈	—	3	2	no	—
58	C₅×C₂²⋊Q₈	—	3	2	no	—
59	C₅×C₂²⋊Q₈	—	6	1	no	—
60	C₅×C₂²⋊Q₈	—	6	1	no	—
61	C₂×C₅×C₄⋊C₄	—	3	1	no	—
62	C₂×C₅×C₄⋊C₄	—	6	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
64	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
65	C₂×C₄²×C₅	—	6	1	no	—
66	C₅×C₂²⋊C₈	—	2	1	no	—
67	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
68	C₅×#95	—	3	2	no	—
69	#1508	—	3	1	no	Sylow
70	C₂³×C₃×C₅	—	2	2	no	—
71	C₂³×C₃×C₅	—	2	2	no	—
72	C₂³×C₃×C₅	—	4	1	no	—
73	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
74	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	4	1	no	—
80	C₂×C₃×C₄×C₅	—	4	1	no	—
81	C₂×C₃×C₄×C₅	—	4	1	no	—
82	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₅×Dic₃	—	2	4	no	—
87	C₂×C₅×Dic₃	—	2	2	no	—
88	C₂×C₅×Dic₃	—	2	2	no	—
89	C₂×C₅×Dic₃	—	4	2	no	—
90	C₂×C₅×Dic₃	—	4	2	no	—
91	C₂×C₅×Dic₃	—	4	2	no	—
92	C₂×C₅×Dic₃	—	4	2	no	—
93	C₅×Dic₆	—	4	2	no	—
94	C₅×Dic₆	—	4	2	no	—
95	C₃×C₅×C₈	—	4	2	no	—
96	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
97	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
98	C₂×C₃×M₁₆	—	2	1	no	—
99	C₂×#217	—	2	1	no	—
100	C₂×#217	—	2	1	no	—
101	C₂×C₄⋊Dic₃	C₄×C₅	1	1	yes	characteristic, complemented
102	#924	—	2	1	no	—
103	#924	—	2	1	no	—
104	#924	C₄×C₅	1	2	yes	complemented
105	#924	C₂²×C₅	1	2	yes	—
106	C₂×Dic₃⋊C₄	—	2	1	no	—
107	C₂×C₄×Dic₃	—	2	1	no	—
108	C₃×C₂²⋊C₈	—	2	1	no	—
109	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
110	C₃⋊#95	C₂²×C₅	1	2	yes	—
111	C₂⁴×C₅	D₁₂	1	1	yes	characteristic
112	C₂×C₅×Q₈	—	3	2	no	—
113	C₂×C₅×Q₈	—	6	1	no	—
114	C₂×C₅×Q₈	—	12	2	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	6	1	no	—
117	C₂²×C₄×C₅	—	6	1	no	—
118	C₂²×C₄×C₅	—	6	2	no	—
119	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
122	C₂²×C₄×C₅	#67	1	1	yes	characteristic
123	C₂²×C₄×C₅	#67	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₅×M₁₆	—	4	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₅×C₄⋊C₄	—	3	2	no	—
128	C₅×C₄⋊C₄	—	6	1	no	—
129	C₅×C₄⋊C₄	—	6	2	no	—
130	C₅×C₄⋊C₄	—	6	2	no	—
131	C₅×C₂²⋊C₄	—	6	4	no	—
132	C₅×C₂²⋊C₄	—	6	2	no	—
133	C₅×C₂²⋊C₄	—	6	2	no	—
134	C₄²×C₅	—	12	2	no	—
135	C₂×C₂²⋊Q₈	—	3	1	no	—
136	#407	C₅×D₃	1	1	yes	characteristic
137	C₄×C₂²⋊C₄	—	3	1	no	—
138	#328	—	3	4	no	—
139	C₂²×C₃×C₅	—	2	1	no	—
140	C₂²×C₃×C₅	—	2	1	no	—
141	C₂²×C₃×C₅	—	2	1	no	—
142	C₂²×C₃×C₅	—	2	1	no	—
143	C₂²×C₃×C₅	—	2	1	no	—
144	C₂²×C₃×C₅	—	2	1	no	—
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	—	4	4	no	—
147	C₂²×C₃×C₅	#104	1	2	yes	—
148	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₃×C₅	#137	1	2	yes	—
150	C₃×C₄×C₅	—	2	1	no	—
151	C₃×C₄×C₅	—	2	1	no	—
152	C₃×C₄×C₅	—	2	1	no	—
153	C₃×C₄×C₅	#99	1	2	yes	—
154	C₅×Dic₃	—	4	4	no	—
155	C₅×Dic₃	—	4	2	no	—
156	C₅×Dic₃	—	4	2	no	—
157	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	—	4	2	no	—
159	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
162	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
165	C₂²×Dic₃	—	2	1	no	—
166	C₂²×Dic₃	—	2	1	no	—
167	C₂²×Dic₃	—	2	2	no	—
168	C₂×Dic₆	—	2	1	no	—
169	C₂×Dic₆	—	4	2	no	—
170	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
171	C₃×M₁₆	—	4	2	no	—
172	C₂×C₃×C₈	—	2	2	no	—
173	#217	—	2	4	no	—
174	#217	—	2	2	no	—
175	#217	—	2	2	no	—
176	C₄⋊Dic₃	—	2	1	no	—
177	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
178	Dic₃⋊C₄	—	2	2	no	—
179	Dic₃⋊C₄	—	2	2	no	—
180	C₄×Dic₃	—	4	2	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	4	1	no	—
184	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
185	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
186	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
187	C₅×Q₈	—	12	2	no	—
188	C₅×Q₈	—	12	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	6	4	no	—
196	C₂×C₄×C₅	—	6	2	no	—
197	C₂×C₄×C₅	—	6	2	no	—
198	C₂×C₄×C₅	—	12	2	no	—
199	C₂×C₄×C₅	—	12	2	no	—
200	C₂×C₄×C₅	—	12	2	no	—
201	C₂×C₄×C₅	—	12	2	no	—
202	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
206	C₅×C₈	—	4	2	no	—
207	C₂²×Q₈	—	3	1	no	—
208	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
209	C₂×M₁₆	—	2	1	no	—
210	C₂²⋊Q₈	—	3	2	no	—
211	C₂²⋊Q₈	—	3	2	no	—
212	C₂²⋊Q₈	—	6	1	no	—
213	C₂²⋊Q₈	—	6	1	no	—
214	C₂×C₄⋊C₄	—	3	1	no	—
215	C₂×C₄⋊C₄	—	6	1	no	—
216	C₂×C₂²⋊C₄	—	6	1	no	—
217	C₂×C₂²⋊C₄	—	6	1	no	—
218	C₂×C₄²	—	6	1	no	—
219	C₂²⋊C₈	—	2	1	no	—
220	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
221	#95	—	3	2	no	—
222	C₂×C₃×C₅	—	2	2	no	—
223	C₂×C₃×C₅	—	2	2	no	—
224	C₂×C₃×C₅	—	4	1	no	—
225	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
226	C₂×C₃×C₅	#419	1	1	yes	characteristic
227	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	2	2	no	—
230	C₂³×C₃	—	4	1	no	—
231	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
232	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
233	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	4	1	no	—
238	C₂×C₃×C₄	—	4	1	no	—
239	C₂×C₃×C₄	—	4	1	no	—
240	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂×Dic₃	—	2	4	no	—
245	C₂×Dic₃	—	2	2	no	—
246	C₂×Dic₃	—	2	2	no	—
247	C₂×Dic₃	—	4	2	no	—
248	C₂×Dic₃	—	4	2	no	—
249	C₂×Dic₃	—	4	2	no	—
250	C₂×Dic₃	—	4	2	no	—
251	Dic₆	—	4	2	no	—
252	Dic₆	—	4	2	no	—
253	C₃×C₈	—	4	2	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	1	no	—
257	C₂²×C₅	—	2	1	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	4	no	—
262	C₂²×C₅	#825	1	2	yes	—
263	C₂²×C₅	#909	1	2	yes	—
264	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	12	4	no	—
269	C₄×C₅	—	12	2	no	—
270	C₄×C₅	—	12	2	no	—
271	C₄×C₅	#806	1	2	yes	—
272	C₂⁴	C₅×D₁₂	1	1	yes	characteristic
273	C₂×Q₈	—	3	2	no	—
274	C₂×Q₈	—	6	1	no	—
275	C₂×Q₈	—	12	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	6	1	no	—
278	C₂²×C₄	—	6	1	no	—
279	C₂²×C₄	—	6	2	no	—
280	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
281	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
282	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
283	C₂²×C₄	C₅×#67	1	1	yes	characteristic
284	C₂²×C₄	C₅×#67	1	1	yes	characteristic
285	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
286	M₁₆	—	4	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₄⋊C₄	—	3	2	no	—
289	C₄⋊C₄	—	6	1	no	—
290	C₄⋊C₄	—	6	2	no	—
291	C₄⋊C₄	—	6	2	no	—
292	C₂²⋊C₄	—	6	4	no	—
293	C₂²⋊C₄	—	6	2	no	—
294	C₂²⋊C₄	—	6	2	no	—
295	C₄²	—	12	2	no	—
296	C₃×C₅	#1508	1	1	yes	characteristic, complemented, Hall
297	C₂²×C₃	—	2	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	4	4	no	—
305	C₂²×C₃	C₅×#104	1	2	yes	—
306	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
307	C₂²×C₃	C₅×#137	1	2	yes	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	C₅×#99	1	2	yes	—
312	Dic₃	—	4	4	no	—
313	Dic₃	—	4	2	no	—
314	Dic₃	—	4	2	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	4	1	no	—
318	C₂×C₅	C₂×#806	1	1	yes	characteristic
319	C₂×C₅	#5120	1	1	yes	characteristic
320	C₂×C₅	C₂×#825	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	1	no	—
324	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
325	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
326	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
327	Q₈	—	12	2	no	—
328	Q₈	—	12	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	6	4	no	—
336	C₂×C₄	—	6	2	no	—
337	C₂×C₄	—	6	2	no	—
338	C₂×C₄	—	12	2	no	—
339	C₂×C₄	—	12	2	no	—
340	C₂×C₄	—	12	2	no	—
341	C₂×C₄	—	12	2	no	—
342	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
346	C₈	—	4	2	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	—	4	1	no	—
350	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
351	C₂×C₃	C₅×#419	1	1	yes	characteristic
352	C₂×C₃	C₂×C₅×#104	1	1	yes	characteristic
353	C₅	#69980	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	4	4	no	—
362	C₂²	C₅×#825	1	2	yes	—
363	C₂²	C₅×#909	1	2	yes	—
364	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	12	4	no	—
369	C₄	—	12	2	no	—
370	C₄	—	12	2	no	—
371	C₄	C₅×#806	1	2	yes	—
372	C₃	C₅×#1508	1	1	yes	characteristic, complemented, Sylow
373	C₂	—	2	2	no	—
374	C₂	—	2	2	no	—
375	C₂	—	4	1	no	—
376	C₂	C₂×C₅×#806	1	1	yes	characteristic
377	C₂	C₅×#5120	1	1	yes	characteristic
378	C₂	C₂×C₅×#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#407	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#407	D₃
hypocenter	C₃	C₅×#1508
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₅×#407

Complements

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

N	H ≅ G/N	type
4. C₅×#4467	C₂	semidirect
7. C₂²×C₅×Dic₆	C₄	semidirect
11. C₂×C₅×C₄⋊Dic₃	C₄	semidirect
14. C₅×#924	C₄	semidirect
21. #69980	C₅	direct (N × H)
53. #4467	C₂×C₅	semidirect
97. C₂²×Dic₆	C₄×C₅	semidirect
101. C₂×C₄⋊Dic₃	C₄×C₅	semidirect
104. #924	C₄×C₅	semidirect
296. C₃×C₅	#1508	semidirect
353. C₅	#69980	direct (N × H)
372. C₃	C₅×#1508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#924	2
C₃×C₅×#407	2
C₄×C₅×#217	2
C₅×#4467	2
C₅×#1508	3
#69980	5

Subgroups — C5×#69980 #14283159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69980 #14283159