Subgroups — #12068627

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2965	C₂	1	1	yes	maximal, characteristic
2	#10614254	C₂	1	1	yes	maximal, characteristic
3	#10614253	C₂	1	1	yes	maximal, characteristic
4	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601546	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601544	C₂	1	2	yes	maximal, complemented
7	#10601543	C₂	1	2	yes	maximal, complemented
8	#10600644	C₂	1	2	yes	maximal, complemented
9	#10600643	C₂	1	2	yes	maximal, complemented
10	#10600524	C₂	1	1	yes	maximal, characteristic, complemented
11	#10600522	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₅×#446	C₄	1	1	yes	characteristic
14	C₅×#446	C₄	1	1	yes	characteristic
15	C₅×#436	C₄	1	1	yes	characteristic
16	C₅×#436	C₄	1	1	yes	characteristic
17	C₅×#435	C₄	1	2	yes	—
18	C₅×#435	C₄	1	2	yes	—
19	C₅×#431	C₂²	1	2	yes	—
20	C₅×#431	C₂²	1	1	yes	characteristic
21	C₄×C₅×M₁₆	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	#65313	—	2	1	no	—
24	Q₈×#168	—	2	1	no	—
25	#65301	—	2	1	no	—
26	#65301	—	2	2	no	—
27	#65300	—	2	2	no	—
28	D₄×#168	—	2	1	no	—
29	#65215	C₂²	1	2	yes	—
30	#65214	C₂²	1	2	yes	—
31	#65214	C₂²	1	1	yes	characteristic
32	#65214	C₂²	1	1	yes	characteristic
33	#65213	C₂²	1	2	yes	—
34	#65213	C₂²	1	1	yes	characteristic
35	#65213	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#168	C₂²	1	2	yes	—
37	#64678	C₂²	1	1	yes	characteristic
38	#64678	C₂²	1	2	yes	—
39	#64678	C₂²	1	2	yes	—
40	#64678	C₂²	1	2	yes	—
41	#64678	C₂²	1	1	yes	characteristic
42	#64678	C₂²	1	2	yes	—
43	#64677	C₂²	1	2	yes	—
44	#64677	C₂²	1	2	yes	—
45	#64677	C₂²	1	1	yes	characteristic
46	#64677	C₂²	1	1	yes	characteristic
47	#17839	—	5	1	no	maximal, Sylow
48	C₂×C₅×#41	Q₈	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
50	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
54	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
55	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
56	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×D₄	D₄	1	1	yes	characteristic
58	C₄×C₅×D₄	D₄	1	2	yes	—
59	C₅×#117	Q₈	1	1	yes	characteristic
60	C₅×#117	Q₈	1	2	yes	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×#681	—	2	1	no	—
64	C₂×#681	—	2	2	no	—
65	C₂×#681	—	2	1	no	—
66	C₂²×#168	—	2	2	no	—
67	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
68	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
74	C₅×#97	C₂×C₄	1	2	yes	—
75	C₅×#97	C₂×C₄	1	2	yes	—
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₄×C₅×C₈	C₂³	1	2	yes	—
81	C₂²⋊#168	—	2	2	no	—
82	C₂²⋊#168	—	2	1	no	—
83	C₂²⋊#168	—	2	2	no	—
84	C₂²⋊#168	—	2	1	no	—
85	C₄⋊#168	—	2	1	no	—
86	C₄⋊#168	—	2	2	no	—
87	C₄⋊#168	—	2	1	no	—
88	C₄⋊#168	—	2	2	no	—
89	C₄⋊#168	C₂³	1	1	yes	characteristic
90	C₄⋊#168	C₂³	1	1	yes	characteristic
91	C₄⋊#168	C₂³	1	1	yes	characteristic
92	C₄⋊#168	C₂³	1	2	yes	—
93	C₄⋊#168	C₂³	1	2	yes	—
94	C₄⋊#168	C₂³	1	1	yes	characteristic
95	#3935	—	2	2	no	—
96	C₄×#168	—	2	1	no	—
97	C₄×#168	—	2	1	no	—
98	C₄×#168	—	2	2	no	—
99	#2991	—	5	1	no	—
100	#2990	—	5	1	no	—
101	#2965	D₅	1	1	yes	characteristic
102	#1574	—	5	1	no	—
103	#1574	—	5	1	no	—
104	#1572	—	5	2	no	—
105	#1571	—	5	2	no	—
106	#1569	—	5	2	no	—
107	#1567	—	5	1	no	—
108	#1565	—	5	2	no	—
109	#1564	—	5	1	no	—
110	C₅×#41	—	4	2	no	—
111	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
120	C₅×M₁₆	—	2	4	no	—
121	C₅×M₁₆	—	4	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	4	1	no	—
124	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
130	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
131	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
132	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
133	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
134	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
135	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
136	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
137	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₅	C₂²×C₄	1	2	yes	—
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₅	C₂×D₄	1	2	yes	—
141	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
142	C₄²×C₅	C₂×Q₈	1	2	yes	—
143	C₄²×C₅	C₂⁴	1	1	yes	characteristic
144	#681	—	8	1	no	—
145	#681	—	8	2	no	—
146	#681	—	8	1	no	—
147	C₂×#168	—	2	1	no	—
148	C₂×#168	—	2	1	no	—
149	C₂×#168	—	2	1	no	—
150	C₂×#168	—	2	1	no	—
151	C₂×#168	—	2	2	no	—
152	C₂×#168	—	2	2	no	—
153	C₂×#168	—	8	2	no	—
154	C₄×#41	C₂×D₅	1	1	yes	characteristic
155	#446	—	10	1	no	—
156	#446	Dic₅	1	1	yes	characteristic
157	#446	Dic₅	1	1	yes	characteristic
158	C₈×Q₈	—	10	1	no	—
159	#436	—	10	1	no	—
160	#436	—	10	2	no	—
161	#436	Dic₅	1	1	yes	characteristic
162	#436	Dic₅	1	1	yes	characteristic
163	#435	—	10	2	no	—
164	#435	Dic₅	1	2	yes	—
165	#435	Dic₅	1	2	yes	—
166	C₈×D₄	—	10	1	no	—
167	#432	—	5	2	no	—
168	#431	—	5	1	no	—
169	#431	—	5	1	no	—
170	#431	—	5	2	no	—
171	#431	C₂×D₅	1	2	yes	—
172	#431	C₂×D₅	1	1	yes	characteristic
173	#423	—	5	1	no	—
174	#423	—	5	1	no	—
175	#423	—	5	2	no	—
176	C₂×C₄⋊C₈	—	5	2	no	—
177	C₄×M₁₆	C₂×D₅	1	2	yes	—
178	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
179	#335	—	5	1	no	—
180	#335	—	5	1	no	—
181	#335	—	5	2	no	—
182	#335	—	5	2	no	—
183	#335	—	5	2	no	—
184	#335	—	5	2	no	—
185	#334	—	5	1	no	—
186	#334	—	5	1	no	—
187	#334	—	5	2	no	—
188	#334	—	5	2	no	—
189	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
191	C₅×Q₈	—	2	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	#131	1	2	yes	—
219	#168	—	4	1	no	—
220	#168	—	4	2	no	—
221	#168	—	4	1	no	—
222	#168	—	4	2	no	—
223	#168	—	4	1	no	—
224	#168	—	4	1	no	—
225	C₂×#41	Dic₁₀	1	1	yes	characteristic
226	C₂×M₁₆	—	10	1	no	—
227	C₂×M₁₆	—	10	2	no	—
228	C₂×M₁₆	—	10	1	no	—
229	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
230	C₂×M₁₆	C₂×Dic₅	1	2	yes	—
231	C₂²×C₈	—	10	2	no	—
232	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
233	C₂²×C₈	C₂×Dic₅	1	1	yes	characteristic
234	C₄×Q₈	D₂₀	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₅	1	1	yes	characteristic
236	C₄×D₄	D₂₀	1	1	yes	characteristic
237	C₄×D₄	D₂₀	1	2	yes	—
238	C₄×D₄	C₂×Dic₅	1	2	yes	—
239	C₄×D₄	C₂×Dic₅	1	1	yes	characteristic
240	#117	Dic₁₀	1	1	yes	characteristic
241	#117	Dic₁₀	1	2	yes	—
242	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₅	1	2	yes	—
244	C₄⋊C₈	—	5	1	no	—
245	C₄⋊C₈	—	5	1	no	—
246	C₄⋊C₈	—	5	1	no	—
247	C₄⋊C₈	—	5	2	no	—
248	C₄⋊C₈	—	5	1	no	—
249	C₄⋊C₈	—	5	2	no	—
250	C₄⋊C₈	—	10	2	no	—
251	C₄⋊C₈	—	10	1	no	—
252	C₄⋊C₈	—	10	1	no	—
253	C₄⋊C₈	—	10	2	no	—
254	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
255	C₄⋊C₈	C₂×Dic₅	1	2	yes	—
256	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
257	C₄⋊C₈	C₂×Dic₅	1	1	yes	characteristic
258	C₂²⋊C₈	—	10	1	no	—
259	C₂²⋊C₈	—	10	2	no	—
260	C₂²⋊C₈	—	10	1	no	—
261	C₂²⋊C₈	—	10	2	no	—
262	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
263	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
264	C₂²⋊C₈	C₂×Dic₅	1	2	yes	—
265	#97	—	10	2	no	—
266	#97	C₂×Dic₅	1	2	yes	—
267	#97	C₂×Dic₅	1	2	yes	—
268	C₄×C₈	—	10	1	no	—
269	C₄×C₈	—	10	1	no	—
270	C₄×C₈	—	10	2	no	—
271	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
272	C₄×C₈	C₂×Dic₅	1	1	yes	characteristic
273	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
274	C₄×C₈	C₂²×D₅	1	2	yes	—
275	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	#430	1	2	yes	—
290	C₄×C₅	C₂×#131	1	1	yes	characteristic
291	C₄×C₅	#568	1	1	yes	characteristic
292	C₄×C₅	#576	1	1	yes	characteristic
293	C₄×C₅	#578	1	1	yes	characteristic
294	#41	—	4	2	no	—
295	C₂×Q₈	C₄⋊Dic₅	1	1	yes	characteristic
296	C₂×D₄	C₄⋊Dic₅	1	1	yes	characteristic
297	C₂×D₄	C₄⋊Dic₅	1	2	yes	—
298	C₂²×C₄	C₂×Dic₁₀	1	1	yes	characteristic
299	C₂²×C₄	C₂×Dic₁₀	1	2	yes	—
300	C₂²×C₄	C₂×D₂₀	1	2	yes	—
301	C₂²×C₄	C₂×D₂₀	1	1	yes	characteristic
302	C₂²×C₄	C₂²×Dic₅	1	1	yes	characteristic
303	C₂²×C₄	C₂²×Dic₅	1	2	yes	—
304	M₁₆	—	2	4	no	—
305	M₁₆	—	4	2	no	—
306	M₁₆	—	40	1	no	—
307	M₁₆	—	40	2	no	—
308	M₁₆	—	40	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	10	1	no	—
312	C₂×C₈	—	10	1	no	—
313	C₂×C₈	—	10	1	no	—
314	C₂×C₈	—	10	1	no	—
315	C₂×C₈	—	10	2	no	—
316	C₂×C₈	—	10	2	no	—
317	C₂×C₈	—	40	2	no	—
318	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
319	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
320	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
321	C₂×C₈	C₂²×Dic₅	1	2	yes	—
322	C₂×C₈	C₂²×Dic₅	1	2	yes	—
323	C₂×C₈	C₂²×Dic₅	1	1	yes	characteristic
324	C₄⋊C₄	C₄⋊Dic₅	1	2	yes	—
325	C₄⋊C₄	C₄⋊Dic₅	1	1	yes	characteristic
326	C₄⋊C₄	C₄⋊Dic₅	1	2	yes	—
327	C₄⋊C₄	C₄⋊Dic₅	1	1	yes	characteristic
328	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
329	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
330	C₂²⋊C₄	C₄⋊Dic₅	1	2	yes	—
331	C₄²	C₂×Dic₁₀	1	1	yes	characteristic
332	C₄²	C₂×Dic₁₀	1	2	yes	—
333	C₄²	C₂×D₂₀	1	1	yes	characteristic
334	C₄²	C₂×D₂₀	1	2	yes	—
335	C₄²	C₂²×Dic₅	1	1	yes	characteristic
336	C₄²	C₂²×Dic₅	1	2	yes	—
337	C₄²	C₂³×D₅	1	1	yes	characteristic
338	C₂×C₅	—	4	1	no	—
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	#2906	1	1	yes	characteristic
341	C₂×C₅	#2913	1	1	yes	characteristic
342	C₂×C₅	C₂×#430	1	1	yes	characteristic
343	C₂³	C₂×C₄⋊Dic₅	1	1	yes	characteristic
344	C₂³	C₂×C₄⋊Dic₅	1	2	yes	—
345	Q₈	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
360	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
362	C₂×C₄	C₂×C₄⋊Dic₅	1	2	yes	—
363	C₂×C₄	C₂×C₄⋊Dic₅	1	1	yes	characteristic
364	C₂×C₄	C₂²×Dic₁₀	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₂₀	1	1	yes	characteristic
366	C₂×C₄	C₂³×Dic₅	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	2	no	—
372	C₈	—	20	1	no	—
373	C₈	—	20	2	no	—
374	C₈	—	20	1	no	—
375	C₈	—	20	2	no	—
376	C₈	—	20	1	no	—
377	C₈	—	20	1	no	—
378	C₈	#4094	1	2	yes	—
379	C₅	#17839	1	1	yes	characteristic, complemented, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₄⋊Dic₅	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	#65414	1	2	yes	—
394	C₄	#66086	1	1	yes	characteristic
395	C₄	#66087	1	1	yes	characteristic
396	C₄	C₂×#4094	1	1	yes	characteristic
397	C₄	#66153	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	#10614243	1	1	yes	characteristic
401	C₂	C₂×#65414	1	1	yes	characteristic
402	C₂	#10615516	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₀
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#2965	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×C₅×#41	Q₈
cosocle	C₄²×C₅	C₂⁴
hypercenter	#2965	D₅
hypocenter	C₅	#17839
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
4. #10601546	C₂	semidirect
5. #10601546	C₂	semidirect
6. #10601544	C₂	semidirect
7. #10601543	C₂	semidirect
8. #10600644	C₂	semidirect
9. #10600643	C₂	semidirect
10. #10600524	C₂	semidirect
11. #10600522	C₂	semidirect
379. C₅	#17839	semidirect

Maximal subgroups

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

subgroup	index
C₅×#2965	2
#10614254	2
#10614253	2
#10601546	2
#10601544	2
#10601543	2
#10600644	2
#10600643	2
#10600524	2
#10600522	2
#17839	5