Subgroups — C₅×#60619 #11983339

Order 1280.

2206 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#535	C₂	1	1	yes	maximal, characteristic
3	C₅×#3140	C₂	1	4	yes	maximal, complemented
4	C₅×#3138	C₂	1	4	yes	maximal, complemented
5	C₅×#3136	C₂	1	16	yes	maximal, complemented
6	C₅×#2896	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#418	C₂	1	2	yes	maximal, complemented
8	C₅×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
12	C₅×#544	—	2	2	no	—
13	C₅×#544	C₂²	1	8	yes	complemented
14	C₅×#543	—	2	2	no	—
15	C₅×#535	—	2	4	no	—
16	C₅×#535	C₂²	1	8	yes	—
17	C₅×#533	—	2	4	no	—
18	C₅×#533	C₂²	1	4	yes	complemented
19	C₂×C₅×#127	C₂²	1	2	yes	—
20	C₂×C₅×#124	C₂²	1	2	yes	—
21	C₂×C₅×#121	—	2	2	no	—
22	C₂×C₅×#120	—	2	2	no	—
23	C₂×C₅×#117	C₂²	1	2	yes	—
24	C₂×C₅×#117	C₂²	1	1	yes	characteristic
25	C₅×#490	C₂²	1	16	yes	complemented
26	C₅×#489	C₂²	1	16	yes	complemented
27	C₅×#488	C₂²	1	16	yes	complemented
28	C₅×#486	C₂²	1	16	yes	complemented
29	C₅×#419	C₂²	1	4	yes	complemented
30	C₅×#418	C₂²	1	8	yes	—
31	C₅×#418	C₂²	1	8	yes	complemented
32	C₅×#418	C₂²	1	4	yes	complemented
33	C₅×#417	C₂²	1	8	yes	complemented
34	C₅×#416	C₂²	1	8	yes	complemented
35	C₂×C₅×#102	C₂²	1	8	yes	complemented
36	C₅×#405	C₂²	1	8	yes	complemented
37	C₄×C₅×M₁₆	C₂²	1	4	yes	complemented
38	#60619	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁵×C₅	—	2	1	no	—
40	C₂×C₅×#41	—	2	2	no	—
41	C₂×C₅×#41	—	2	8	no	—
42	C₂×C₅×#41	C₂³	1	4	yes	—
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	2	no	—
47	C₂²×C₅×D₄	—	2	4	no	—
48	C₂²×C₅×D₄	—	2	8	no	—
49	C₂²×C₅×D₄	C₂³	1	4	yes	—
50	C₂²×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂×C₅×M₁₆	—	2	8	no	—
55	C₂×C₅×M₁₆	C₂³	1	4	yes	—
56	C₂×C₅×M₁₆	C₂³	1	4	yes	—
57	C₂²×C₅×C₈	C₂³	1	4	yes	—
58	C₅×C₄⋊Q₈	—	2	8	no	—
59	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
60	C₅×#127	—	2	4	no	—
61	C₅×#127	C₂³	1	8	yes	—
62	C₅×#125	—	2	8	no	—
63	C₅×#125	C₂³	1	8	yes	complemented
64	C₅×#124	—	2	4	no	—
65	C₅×#124	C₂³	1	8	yes	—
66	C₅×C₂²⋊Q₈	—	2	8	no	—
67	C₅×C₂²⋊Q₈	—	2	16	no	—
68	C₅×#121	—	2	16	no	—
69	C₅×#120	—	2	16	no	—
70	C₄×C₅×Q₈	—	2	8	no	—
71	C₅×#117	—	2	2	no	—
72	C₅×#117	—	2	2	no	—
73	C₅×#117	D₄	1	4	yes	—
74	C₅×#117	C₂³	1	4	yes	—
75	C₅×#117	C₂³	1	4	yes	—
76	C₅×#117	C₂³	1	4	yes	—
77	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
81	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
82	C₂×C₄²×C₅	—	2	2	no	—
83	C₂×C₄²×C₅	C₂³	1	2	yes	—
84	C₅×#103	C₂³	1	16	yes	complemented
85	C₅×#102	C₂³	1	32	yes	—
86	C₅×#102	C₂³	1	16	yes	complemented
87	C₅×#97	C₂³	1	8	yes	complemented
88	C₄×C₅×C₈	C₂³	1	8	yes	complemented
89	#3458	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#535	C₂×C₅	1	1	yes	characteristic
91	#3140	C₂×C₅	1	4	yes	complemented
92	#3138	C₂×C₅	1	4	yes	complemented
93	#3136	C₂×C₅	1	16	yes	complemented
94	#2896	C₂×C₅	1	2	yes	complemented
95	C₂×#418	C₂×C₅	1	2	yes	complemented
96	#2873	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂⁴×C₅	—	2	2	no	—
98	C₂⁴×C₅	—	2	1	no	—
99	C₂⁴×C₅	—	2	4	no	—
100	C₂⁴×C₅	—	4	4	no	—
101	C₂⁴×C₅	—	8	4	no	—
102	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
103	C₅×#41	—	2	8	no	—
104	C₅×#41	—	2	8	no	—
105	C₅×#41	—	4	8	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	8	no	—
108	C₂×C₅×Q₈	—	2	4	no	—
109	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
110	C₂×C₅×D₄	—	2	4	no	—
111	C₂×C₅×D₄	—	2	4	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	16	no	—
115	C₂×C₅×D₄	—	2	8	no	—
116	C₂×C₅×D₄	—	2	8	no	—
117	C₂×C₅×D₄	—	2	8	no	—
118	C₂×C₅×D₄	—	2	4	no	—
119	C₂×C₅×D₄	—	4	4	no	—
120	C₂×C₅×D₄	—	4	4	no	—
121	C₂×C₅×D₄	—	4	8	no	—
122	C₂×C₅×D₄	—	8	8	no	—
123	C₂×C₅×D₄	C₂⁴	1	4	yes	—
124	C₂×C₅×D₄	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	4	4	no	—
129	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	#41	1	8	yes	—
133	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
135	C₅×M₁₆	—	2	8	no	—
136	C₅×M₁₆	—	2	8	no	—
137	C₂×C₅×C₈	—	2	8	no	—
138	C₂×C₅×C₈	C₂⁴	1	8	yes	—
139	C₅×C₄⋊C₄	—	2	4	no	—
140	C₅×C₄⋊C₄	—	2	8	no	—
141	C₅×C₄⋊C₄	—	2	16	no	—
142	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
143	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
144	C₅×C₂²⋊C₄	—	2	4	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₅×C₂²⋊C₄	—	2	16	no	—
147	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
148	C₄²×C₅	—	2	4	no	—
149	C₄²×C₅	—	2	4	no	—
150	C₄²×C₅	C₂×D₄	1	4	yes	—
151	C₄²×C₅	C₂⁴	1	4	yes	—
152	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
153	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
154	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
155	#544	—	2	2	no	—
156	#544	C₂²×C₅	1	8	yes	complemented
157	#543	—	2	2	no	—
158	#535	—	2	4	no	—
159	#535	C₂²×C₅	1	8	yes	—
160	#533	—	2	4	no	—
161	#533	C₂²×C₅	1	4	yes	complemented
162	C₂×#127	C₂²×C₅	1	2	yes	—
163	C₂×#124	C₂²×C₅	1	2	yes	—
164	C₂×#121	—	2	2	no	—
165	C₂×#120	—	2	2	no	—
166	C₂×#117	C₂²×C₅	1	2	yes	—
167	C₂×#117	C₂²×C₅	1	1	yes	characteristic
168	#490	C₂²×C₅	1	16	yes	complemented
169	#489	C₂²×C₅	1	16	yes	complemented
170	#488	C₂²×C₅	1	16	yes	complemented
171	#486	C₂²×C₅	1	16	yes	complemented
172	#419	C₂²×C₅	1	4	yes	complemented
173	#418	C₂²×C₅	1	8	yes	—
174	#418	C₂²×C₅	1	8	yes	complemented
175	#418	C₂²×C₅	1	4	yes	complemented
176	#417	C₂²×C₅	1	8	yes	complemented
177	#416	C₂²×C₅	1	8	yes	complemented
178	C₂×#102	C₂²×C₅	1	8	yes	complemented
179	#405	C₂²×C₅	1	8	yes	complemented
180	C₄×M₁₆	C₂²×C₅	1	4	yes	complemented
181	C₂³×C₅	—	2	4	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	4	no	—
185	C₂³×C₅	—	4	8	no	—
186	C₂³×C₅	—	4	2	no	—
187	C₂³×C₅	—	4	4	no	—
188	C₂³×C₅	—	4	8	no	—
189	C₂³×C₅	—	8	8	no	—
190	C₂³×C₅	—	8	16	no	—
191	C₂³×C₅	#124	1	4	yes	—
192	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂³×C₅	C₂²×D₄	1	2	yes	—
194	C₅×Q₈	—	2	4	no	—
195	C₅×Q₈	—	4	2	no	—
196	C₅×Q₈	—	8	8	no	—
197	C₅×D₄	—	2	8	no	—
198	C₅×D₄	—	2	4	no	—
199	C₅×D₄	—	4	8	no	—
200	C₅×D₄	—	4	8	no	—
201	C₅×D₄	—	4	4	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	8	16	no	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	4	4	no	—
207	C₂×C₄×C₅	—	4	2	no	—
208	C₂×C₄×C₅	—	4	8	no	—
209	C₂×C₄×C₅	—	8	4	no	—
210	C₂×C₄×C₅	#124	1	4	yes	—
211	C₂×C₄×C₅	#124	1	8	yes	—
212	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₅	C₂×#41	1	4	yes	—
216	C₂×C₄×C₅	C₂×#41	1	4	yes	—
217	C₂×C₄×C₅	C₂×#41	1	4	yes	—
218	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
219	C₅×C₈	—	2	8	no	—
220	C₂⁵	—	2	1	no	—
221	C₂×#41	—	2	2	no	—
222	C₂×#41	—	2	8	no	—
223	C₂×#41	C₂³×C₅	1	4	yes	—
224	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	4	no	—
229	C₂²×D₄	—	2	8	no	—
230	C₂²×D₄	C₂³×C₅	1	2	yes	—
231	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
232	C₂²×D₄	C₂³×C₅	1	4	yes	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
235	C₂×M₁₆	—	2	8	no	—
236	C₂×M₁₆	C₂³×C₅	1	4	yes	—
237	C₂×M₁₆	C₂³×C₅	1	4	yes	—
238	C₂²×C₈	C₂³×C₅	1	4	yes	—
239	C₄⋊Q₈	—	2	8	no	—
240	C₄⋊Q₈	C₂³×C₅	1	8	yes	complemented
241	#127	—	2	4	no	—
242	#127	C₂³×C₅	1	8	yes	—
243	#125	—	2	8	no	—
244	#125	C₂³×C₅	1	8	yes	complemented
245	#124	—	2	4	no	—
246	#124	C₂³×C₅	1	8	yes	—
247	C₂²⋊Q₈	—	2	8	no	—
248	C₂²⋊Q₈	—	2	16	no	—
249	#121	—	2	16	no	—
250	#120	—	2	16	no	—
251	C₄×Q₈	—	2	8	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	C₅×D₄	1	4	yes	—
255	#117	C₂³×C₅	1	4	yes	—
256	#117	C₂³×C₅	1	4	yes	—
257	#117	C₂³×C₅	1	4	yes	—
258	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂³×C₅	1	2	yes	—
265	#103	C₂³×C₅	1	16	yes	complemented
266	#102	C₂³×C₅	1	32	yes	—
267	#102	C₂³×C₅	1	16	yes	complemented
268	#97	C₂³×C₅	1	8	yes	complemented
269	C₄×C₈	C₂³×C₅	1	8	yes	complemented
270	C₂²×C₅	—	2	2	no	—
271	C₂²×C₅	—	2	4	no	—
272	C₂²×C₅	—	4	4	no	—
273	C₂²×C₅	—	4	4	no	—
274	C₂²×C₅	—	4	8	no	—
275	C₂²×C₅	—	4	2	no	—
276	C₂²×C₅	—	4	4	no	—
277	C₂²×C₅	—	8	4	no	—
278	C₂²×C₅	—	8	8	no	—
279	C₂²×C₅	—	8	16	no	—
280	C₂²×C₅	C₂×#124	1	2	yes	—
281	C₂²×C₅	C₂×#124	1	4	yes	—
282	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	8	no	—
284	C₄×C₅	—	4	8	no	—
285	C₄×C₅	—	4	2	no	—
286	C₄×C₅	C₂×#124	1	4	yes	—
287	C₄×C₅	C₂×#124	1	2	yes	—
288	C₄×C₅	C₂²×#41	1	2	yes	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	1	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	4	4	no	—
293	C₂⁴	—	8	4	no	—
294	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
295	#41	—	2	8	no	—
296	#41	—	2	8	no	—
297	#41	—	4	8	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	8	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	16	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	8	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	8	8	no	—
315	C₂×D₄	C₂⁴×C₅	1	4	yes	—
316	C₂×D₄	C₂⁴×C₅	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
322	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
323	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₅×#41	1	8	yes	—
325	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
327	M₁₆	—	2	8	no	—
328	M₁₆	—	2	8	no	—
329	C₂×C₈	—	2	8	no	—
330	C₂×C₈	C₂⁴×C₅	1	8	yes	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	16	no	—
334	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
335	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
336	C₂²⋊C₄	—	2	4	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	C₂×C₅×D₄	1	4	yes	—
343	C₄²	C₂⁴×C₅	1	4	yes	—
344	C₂×C₅	—	2	2	no	—
345	C₂×C₅	—	2	4	no	—
346	C₂×C₅	—	8	2	no	—
347	C₂×C₅	—	8	4	no	—
348	C₂×C₅	C₂²×#124	1	1	yes	characteristic
349	C₂×C₅	#3585	1	2	yes	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	4	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	8	8	no	—
359	C₂³	—	8	16	no	—
360	C₂³	C₅×#124	1	4	yes	—
361	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
362	C₂³	C₂²×C₅×D₄	1	2	yes	—
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	8	no	—
366	D₄	—	2	8	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	8	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	16	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	C₅×#124	1	4	yes	—
380	C₂×C₄	C₅×#124	1	8	yes	—
381	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
382	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₂×C₅×#41	1	4	yes	—
385	C₂×C₄	C₂×C₅×#41	1	4	yes	—
386	C₂×C₄	C₂×C₅×#41	1	4	yes	—
387	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
388	C₈	—	2	8	no	—
389	C₅	#60619	1	1	yes	characteristic, direct product factor, Sylow
390	C₂²	—	2	2	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	8	no	—
397	C₂²	—	8	8	no	—
398	C₂²	—	8	4	no	—
399	C₂²	—	8	16	no	—
400	C₂²	C₂×C₅×#124	1	2	yes	—
401	C₂²	C₂×C₅×#124	1	4	yes	—
402	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
403	C₄	—	2	8	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	8	no	—
406	C₄	C₂×C₅×#124	1	4	yes	—
407	C₄	C₂×C₅×#124	1	2	yes	—
408	C₄	C₂²×C₅×#41	1	2	yes	—
409	C₂	—	2	2	no	—
410	C₂	—	2	4	no	—
411	C₂	—	8	4	no	—
412	C₂	—	8	2	no	—
413	C₂	C₂²×C₅×#124	1	1	yes	characteristic
414	C₂	C₅×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3458	C₂	semidirect
3. C₅×#3140	C₂	semidirect
4. C₅×#3138	C₂	semidirect
5. C₅×#3136	C₂	semidirect
6. C₅×#2896	C₂	semidirect
7. C₂×C₅×#418	C₂	semidirect
8. C₅×#2873	C₂	semidirect
13. C₅×#544	C₂²	semidirect
18. C₅×#533	C₂²	semidirect
25. C₅×#490	C₂²	semidirect
26. C₅×#489	C₂²	semidirect
27. C₅×#488	C₂²	semidirect
28. C₅×#486	C₂²	semidirect
29. C₅×#419	C₂²	semidirect
31. C₅×#418	C₂²	semidirect
32. C₅×#418	C₂²	semidirect
33. C₅×#417	C₂²	semidirect
34. C₅×#416	C₂²	semidirect
35. C₂×C₅×#102	C₂²	semidirect
36. C₅×#405	C₂²	semidirect
37. C₄×C₅×M₁₆	C₂²	semidirect
38. #60619	C₅	direct (N × H)
59. C₅×C₄⋊Q₈	C₂³	semidirect
63. C₅×#125	C₂³	semidirect
84. C₅×#103	C₂³	semidirect
86. C₅×#102	C₂³	semidirect
87. C₅×#97	C₂³	semidirect
88. C₄×C₅×C₈	C₂³	semidirect
89. #3458	C₂×C₅	semidirect
91. #3140	C₂×C₅	semidirect
92. #3138	C₂×C₅	semidirect
93. #3136	C₂×C₅	semidirect
94. #2896	C₂×C₅	semidirect
95. C₂×#418	C₂×C₅	semidirect
96. #2873	C₂×C₅	semidirect
156. #544	C₂²×C₅	semidirect
161. #533	C₂²×C₅	semidirect
168. #490	C₂²×C₅	semidirect
169. #489	C₂²×C₅	semidirect
170. #488	C₂²×C₅	semidirect
171. #486	C₂²×C₅	semidirect
172. #419	C₂²×C₅	semidirect
174. #418	C₂²×C₅	semidirect
175. #418	C₂²×C₅	semidirect
176. #417	C₂²×C₅	semidirect
177. #416	C₂²×C₅	semidirect
178. C₂×#102	C₂²×C₅	semidirect
179. #405	C₂²×C₅	semidirect
180. C₄×M₁₆	C₂²×C₅	semidirect
240. C₄⋊Q₈	C₂³×C₅	semidirect
244. #125	C₂³×C₅	semidirect
265. #103	C₂³×C₅	semidirect
267. #102	C₂³×C₅	semidirect
268. #97	C₂³×C₅	semidirect
269. C₄×C₈	C₂³×C₅	semidirect
389. C₅	#60619	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3458	2
C₂×C₅×#535	2
C₅×#3140	2
C₅×#3138	2
C₅×#3136	2
C₅×#2896	2
C₂×C₅×#418	2
C₅×#2873	2
#60619	5

Subgroups — C5×#60619 #11983339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60619 #11983339