Subgroups — C₅×#19570 #11942290

Order 1280.

584 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3254	C₂	1	1	yes	maximal, characteristic
2	C₅×#3227	C₂	1	1	yes	maximal, characteristic
3	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	2	yes	maximal, complemented
6	C₅×#1692	C₂	1	2	yes	maximal, complemented
7	C₅×#1682	C₂	1	2	yes	maximal, complemented
8	C₅×#1672	C₂	1	2	yes	maximal, complemented
9	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1543	C₂	1	1	yes	maximal, characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₅×#498	C₂²	1	2	yes	—
16	C₅×#494	—	2	1	no	—
17	C₅×#487	—	2	1	no	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#481	—	2	2	no	—
20	C₅×#477	C₂²	1	2	yes	—
21	C₅×#476	—	2	1	no	—
22	C₅×#476	—	2	1	no	—
23	C₅×#474	—	2	1	no	—
24	C₅×#468	—	2	2	no	—
25	C₅×#462	C₂²	1	2	yes	—
26	C₅×#462	C₂²	1	2	yes	—
27	C₅×#461	—	2	1	no	—
28	C₅×#460	C₂²	1	2	yes	—
29	C₅×#451	—	2	2	no	—
30	C₅×#446	—	2	1	no	—
31	C₅×#446	C₂²	1	2	yes	—
32	C₅×C₈×Q₈	—	2	1	no	—
33	C₅×C₈×Q₈	C₂²	1	2	yes	—
34	C₅×#433	—	2	2	no	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#423	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	1	yes	characteristic
42	C₅×#333	C₂²	1	1	yes	characteristic
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#331	C₂²	1	1	yes	characteristic
46	C₅×#331	C₂²	1	1	yes	characteristic
47	#19570	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂²×C₅×Q₈	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₅×C₄⋊Q₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
58	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₅×#127	C₂³	1	1	yes	characteristic
62	C₅×#125	—	2	1	no	—
63	C₅×#124	—	2	1	no	—
64	C₅×C₂²⋊Q₈	—	2	1	no	—
65	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
66	C₅×#121	—	2	1	no	—
67	C₅×#121	—	2	1	no	—
68	C₄×C₅×Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	C₂³	1	2	yes	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₅×#117	—	2	1	no	—
73	C₂×C₅×C₄⋊C₄	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#107	—	2	2	no	—
77	C₅×#106	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	1	no	—
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×#103	—	2	2	no	—
90	C₅×#103	—	2	2	no	—
91	C₅×#103	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#102	—	2	2	no	—
94	C₅×#102	—	2	2	no	—
95	C₅×C₂²⋊C₈	—	2	1	no	—
96	C₅×C₂²⋊C₈	—	2	1	no	—
97	C₅×C₂²⋊C₈	D₄	1	2	yes	—
98	C₅×#97	—	2	2	no	—
99	C₄×C₅×C₈	—	2	2	no	—
100	C₄×C₅×C₈	—	2	1	no	—
101	C₄×C₅×C₈	—	2	1	no	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3254	C₂×C₅	1	1	yes	characteristic
104	#3227	C₂×C₅	1	1	yes	characteristic
105	#3209	C₂×C₅	1	1	yes	characteristic, complemented
106	#2986	C₂×C₅	1	1	yes	characteristic, complemented
107	#1702	C₂×C₅	1	2	yes	complemented
108	#1692	C₂×C₅	1	2	yes	complemented
109	#1682	C₂×C₅	1	2	yes	complemented
110	#1672	C₂×C₅	1	2	yes	complemented
111	#1574	C₂×C₅	1	1	yes	characteristic, complemented
112	#1546	C₂×C₅	1	1	yes	characteristic, complemented
113	#1543	C₂×C₅	1	1	yes	characteristic
114	C₅×#41	—	8	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	4	1	no	—
119	C₂×C₅×Q₈	—	8	1	no	—
120	C₂×C₅×Q₈	—	8	1	no	—
121	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	#41	1	1	yes	characteristic
131	C₅×Q₁₆	—	8	2	no	—
132	C₅×Q₁₆	—	8	2	no	—
133	C₅×SD₁₆	—	8	2	no	—
134	C₅×M₁₆	—	8	1	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	1	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
142	C₅×C₄⋊C₄	—	2	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	4	1	no	—
152	C₅×C₄⋊C₄	—	4	1	no	—
153	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	2	no	—
155	C₅×C₂²⋊C₄	—	4	1	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₄²×C₅	—	2	2	no	—
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	#41	1	1	yes	characteristic
161	C₄²×C₅	C₂⁴	1	1	yes	characteristic
162	#533	C₂²×C₅	1	1	yes	characteristic
163	#532	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
165	#498	C₂²×C₅	1	2	yes	—
166	#494	—	2	1	no	—
167	#487	—	2	1	no	—
168	#486	C₂²×C₅	1	2	yes	—
169	#481	—	2	2	no	—
170	#477	C₂²×C₅	1	2	yes	—
171	#476	—	2	1	no	—
172	#476	—	2	1	no	—
173	#474	—	2	1	no	—
174	#468	—	2	2	no	—
175	#462	C₂²×C₅	1	2	yes	—
176	#462	C₂²×C₅	1	2	yes	—
177	#461	—	2	1	no	—
178	#460	C₂²×C₅	1	2	yes	—
179	#451	—	2	2	no	—
180	#446	—	2	1	no	—
181	#446	C₂²×C₅	1	2	yes	—
182	C₈×Q₈	—	2	1	no	—
183	C₈×Q₈	C₂²×C₅	1	2	yes	—
184	#433	—	2	2	no	—
185	#431	C₂²×C₅	1	1	yes	characteristic
186	#431	C₂²×C₅	1	1	yes	characteristic
187	#431	C₂²×C₅	1	1	yes	characteristic
188	#423	C₂²×C₅	1	1	yes	characteristic
189	#335	C₂²×C₅	1	2	yes	—
190	#334	C₂²×C₅	1	2	yes	—
191	#333	C₂²×C₅	1	1	yes	characteristic
192	#333	C₂²×C₅	1	1	yes	characteristic
193	#332	C₂²×C₅	1	2	yes	—
194	#332	C₂²×C₅	1	2	yes	—
195	#331	C₂²×C₅	1	1	yes	characteristic
196	#331	C₂²×C₅	1	1	yes	characteristic
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	#121	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	2	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	8	1	no	—
205	C₅×Q₈	—	8	2	no	—
206	C₅×D₄	—	4	1	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	4	1	no	—
210	C₅×D₄	—	8	1	no	—
211	C₅×D₄	—	8	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	8	2	no	—
222	C₂×C₄×C₅	—	8	2	no	—
223	C₂×C₄×C₅	#121	1	1	yes	characteristic
224	C₂×C₄×C₅	#121	1	1	yes	characteristic
225	C₂×C₄×C₅	#121	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
229	C₅×C₈	—	2	2	no	—
230	C₅×C₈	—	2	2	no	—
231	C₅×C₈	—	4	2	no	—
232	C₅×C₈	—	4	1	no	—
233	C₅×C₈	—	4	1	no	—
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	—	4	1	no	—
236	C₂×#41	—	2	1	no	—
237	C₂²×Q₈	—	2	1	no	—
238	C₂×Q₁₆	—	2	2	no	—
239	C₂×Q₁₆	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₄⋊Q₈	—	2	1	no	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
246	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
247	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
248	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
249	#127	C₂³×C₅	1	1	yes	characteristic
250	#125	—	2	1	no	—
251	#124	—	2	1	no	—
252	C₂²⋊Q₈	—	2	1	no	—
253	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
254	#121	—	2	1	no	—
255	#121	—	2	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	C₂³×C₅	1	2	yes	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	#117	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
264	#107	—	2	2	no	—
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
271	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
275	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
276	C₄⋊C₈	C₂³×C₅	1	2	yes	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	C₅×D₄	1	2	yes	—
286	#97	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	C₂³×C₅	1	2	yes	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	8	1	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	—	8	1	no	—
297	C₂²×C₅	C₂×#121	1	1	yes	characteristic
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	4	2	no	—
303	C₄×C₅	—	8	2	no	—
304	C₄×C₅	—	8	1	no	—
305	C₄×C₅	#471	1	2	yes	—
306	C₄×C₅	#576	1	1	yes	characteristic
307	C₄×C₅	#577	1	1	yes	characteristic
308	C₄×C₅	#578	1	1	yes	characteristic
309	C₄×C₅	#578	1	1	yes	characteristic
310	#41	—	8	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×Q₈	—	8	1	no	—
316	C₂×Q₈	—	8	1	no	—
317	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₅×#41	1	1	yes	characteristic
327	Q₁₆	—	8	2	no	—
328	Q₁₆	—	8	2	no	—
329	SD₁₆	—	8	2	no	—
330	M₁₆	—	8	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
337	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
355	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
356	C₄²	C₅×#41	1	1	yes	characteristic
357	C₄²	C₂⁴×C₅	1	1	yes	characteristic
358	C₂×C₅	—	4	1	no	—
359	C₂×C₅	—	16	1	no	—
360	C₂×C₅	#3044	1	1	yes	characteristic
361	C₂×C₅	#3062	1	1	yes	characteristic
362	C₂×C₅	C₂×#471	1	1	yes	characteristic
363	C₂³	—	4	1	no	—
364	C₂³	C₅×#121	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	8	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	8	1	no	—
377	D₄	—	8	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	C₅×#121	1	1	yes	characteristic
390	C₂×C₄	C₅×#121	1	1	yes	characteristic
391	C₂×C₄	C₅×#121	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	1	no	—
402	C₅	#19570	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×C₅×#121	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	C₅×#471	1	2	yes	—
418	C₄	C₅×#576	1	1	yes	characteristic
419	C₄	C₅×#577	1	1	yes	characteristic
420	C₄	C₅×#578	1	1	yes	characteristic
421	C₄	C₅×#578	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	16	1	no	—
424	C₂	C₅×#3044	1	1	yes	characteristic
425	C₂	C₅×#3062	1	1	yes	characteristic
426	C₂	C₂×C₅×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#3209	C₂	semidirect
4. C₅×#2986	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1692	C₂	semidirect
7. C₅×#1682	C₂	semidirect
8. C₅×#1672	C₂	semidirect
9. C₅×#1574	C₂	semidirect
10. C₅×#1546	C₂	semidirect
47. #19570	C₅	direct (N × H)
105. #3209	C₂×C₅	semidirect
106. #2986	C₂×C₅	semidirect
107. #1702	C₂×C₅	semidirect
108. #1692	C₂×C₅	semidirect
109. #1682	C₂×C₅	semidirect
110. #1672	C₂×C₅	semidirect
111. #1574	C₂×C₅	semidirect
112. #1546	C₂×C₅	semidirect
402. C₅	#19570	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×#3254	2
C₅×#3227	2
C₅×#3209	2
C₅×#2986	2
C₅×#1702	2
C₅×#1692	2
C₅×#1682	2
C₅×#1672	2
C₅×#1574	2
C₅×#1546	2
C₅×#1543	2
#19570	5

Subgroups — C5×#19570 #11942290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19570 #11942290