Subgroups — C₅×#19424 #11942144

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3210	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3100	C₂	1	1	yes	maximal, characteristic
4	C₅×#2975	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	2	yes	maximal, complemented
6	C₅×#1699	C₂	1	2	yes	maximal, complemented
7	C₅×#1689	C₂	1	2	yes	maximal, complemented
8	C₅×#1685	C₂	1	2	yes	maximal, complemented
9	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1553	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#494	C₂²	1	1	yes	characteristic, complemented
16	C₅×#492	C₂²	1	1	yes	characteristic, complemented
17	C₅×#487	C₂²	1	1	yes	characteristic, complemented
18	C₅×#486	C₂²	1	1	yes	characteristic, complemented
19	C₅×#484	—	2	1	no	—
20	C₅×#480	—	2	1	no	—
21	C₅×#474	C₂²	1	2	yes	—
22	C₅×#474	C₂²	1	2	yes	—
23	C₅×#464	—	2	2	no	—
24	C₅×#461	C₂²	1	2	yes	—
25	C₅×#459	C₂²	1	2	yes	—
26	C₅×#452	—	2	2	no	—
27	C₅×#450	—	2	1	no	—
28	C₅×#447	—	2	1	no	—
29	C₅×#440	—	2	2	no	—
30	C₄×C₅×D₈	—	2	2	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#436	C₂²	1	2	yes	—
34	C₅×#432	C₂²	1	1	yes	characteristic
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×#407	—	2	2	no	—
39	C₅×#335	C₂²	1	2	yes	complemented
40	C₅×#334	C₂²	1	2	yes	complemented
41	C₅×#332	C₂²	1	2	yes	complemented
42	C₅×#332	C₂²	1	2	yes	complemented
43	C₅×#332	C₂²	1	2	yes	complemented
44	C₅×#331	C₂²	1	2	yes	complemented
45	#19424	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
56	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₅×#127	C₂³	1	1	yes	characteristic
59	C₅×#125	—	2	1	no	—
60	C₅×#124	—	2	1	no	—
61	C₅×C₂²⋊Q₈	—	2	1	no	—
62	C₅×C₂²⋊Q₈	—	2	1	no	—
63	C₅×#121	—	2	1	no	—
64	C₅×#121	—	2	1	no	—
65	C₄×C₅×Q₈	—	2	1	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	D₄	1	2	yes	—
72	C₄×C₅×D₄	C₂³	1	2	yes	—
73	C₅×#117	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	2	no	—
78	C₅×#107	—	2	2	no	—
79	C₅×C₄⋊C₈	D₄	1	2	yes	—
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₄⋊C₈	C₂³	1	2	yes	—
82	C₅×C₄⋊C₈	C₂³	1	2	yes	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×#102	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	1	no	—
90	C₅×C₂²⋊C₈	—	2	1	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	2	no	—
94	C₅×C₂²⋊C₈	D₄	1	2	yes	—
95	C₅×#97	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
100	#3210	C₂×C₅	1	1	yes	characteristic, complemented
101	#3110	C₂×C₅	1	1	yes	characteristic, complemented
102	#3100	C₂×C₅	1	1	yes	characteristic
103	#2975	C₂×C₅	1	1	yes	characteristic, complemented
104	#1701	C₂×C₅	1	2	yes	complemented
105	#1699	C₂×C₅	1	2	yes	complemented
106	#1689	C₂×C₅	1	2	yes	complemented
107	#1685	C₂×C₅	1	2	yes	complemented
108	#1572	C₂×C₅	1	1	yes	characteristic, complemented
109	#1553	C₂×C₅	1	1	yes	characteristic, complemented
110	#1544	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	1	no	—
112	C₅×#41	—	8	2	no	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×D₄	—	2	1	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	4	2	no	—
121	C₂×C₅×D₄	—	4	1	no	—
122	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	8	2	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×SD₁₆	—	4	4	no	—
133	C₅×SD₁₆	—	8	2	no	—
134	C₅×D₈	—	4	4	no	—
135	C₅×M₁₆	—	8	2	no	—
136	C₅×M₁₆	—	8	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	2	2	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	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₅×C₂²⋊C₄	—	2	2	no	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	—	4	1	no	—
155	C₅×C₂²⋊C₄	—	4	1	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₄²×C₅	—	4	1	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×D₄	C₂²×C₅	1	1	yes	characteristic
165	#494	C₂²×C₅	1	1	yes	characteristic, complemented
166	#492	C₂²×C₅	1	1	yes	characteristic, complemented
167	#487	C₂²×C₅	1	1	yes	characteristic, complemented
168	#486	C₂²×C₅	1	1	yes	characteristic, complemented
169	#484	—	2	1	no	—
170	#480	—	2	1	no	—
171	#474	C₂²×C₅	1	2	yes	—
172	#474	C₂²×C₅	1	2	yes	—
173	#464	—	2	2	no	—
174	#461	C₂²×C₅	1	2	yes	—
175	#459	C₂²×C₅	1	2	yes	—
176	#452	—	2	2	no	—
177	#450	—	2	1	no	—
178	#447	—	2	1	no	—
179	#440	—	2	2	no	—
180	C₄×D₈	—	2	2	no	—
181	#436	—	2	2	no	—
182	#436	C₂²×C₅	1	2	yes	—
183	#436	C₂²×C₅	1	2	yes	—
184	#432	C₂²×C₅	1	1	yes	characteristic
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	#407	—	2	2	no	—
189	#335	C₂²×C₅	1	2	yes	complemented
190	#334	C₂²×C₅	1	2	yes	complemented
191	#332	C₂²×C₅	1	2	yes	complemented
192	#332	C₂²×C₅	1	2	yes	complemented
193	#332	C₂²×C₅	1	2	yes	complemented
194	#331	C₂²×C₅	1	2	yes	complemented
195	C₂³×C₅	—	2	2	no	—
196	C₂³×C₅	—	4	2	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	—	8	1	no	—
199	C₂³×C₅	—	8	1	no	—
200	C₂³×C₅	#121	1	1	yes	characteristic
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×D₄	—	2	2	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	8	1	no	—
210	C₅×D₄	—	8	2	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	8	2	no	—
221	C₂×C₄×C₅	—	8	2	no	—
222	C₂×C₄×C₅	—	8	1	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	2	no	—
233	C₅×C₈	—	4	2	no	—
234	C₂×#41	—	2	1	no	—
235	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
236	C₂³×C₄	—	2	1	no	—
237	C₂×Q₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
246	#127	C₂³×C₅	1	1	yes	characteristic
247	#125	—	2	1	no	—
248	#124	—	2	1	no	—
249	C₂²⋊Q₈	—	2	1	no	—
250	C₂²⋊Q₈	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	—	2	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	C₅×D₄	1	2	yes	—
260	C₄×D₄	C₂³×C₅	1	2	yes	—
261	#117	—	2	1	no	—
262	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
265	#107	—	2	2	no	—
266	#107	—	2	2	no	—
267	C₄⋊C₈	C₅×D₄	1	2	yes	—
268	C₄⋊C₈	C₂³×C₅	1	2	yes	—
269	C₄⋊C₈	C₂³×C₅	1	2	yes	—
270	C₄⋊C₈	C₂³×C₅	1	2	yes	—
271	#103	—	2	2	no	—
272	#103	—	2	2	no	—
273	#102	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	2	no	—
276	#102	—	2	2	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	2	1	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	C₅×D₄	1	2	yes	—
283	#97	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	8	4	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	—	8	1	no	—
297	C₂²×C₅	—	8	1	no	—
298	C₂²×C₅	C₂×#121	1	1	yes	characteristic
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	2	1	no	—
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	8	1	no	—
305	C₄×C₅	—	8	1	no	—
306	C₄×C₅	—	8	1	no	—
307	C₄×C₅	#575	1	2	yes	—
308	C₄×C₅	#576	1	2	yes	—
309	C₂⁴	—	2	1	no	—
310	#41	—	8	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	8	2	no	—
326	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₅×#41	1	1	yes	characteristic
329	Q₁₆	—	8	2	no	—
330	SD₁₆	—	4	4	no	—
331	SD₁₆	—	8	2	no	—
332	D₈	—	4	4	no	—
333	M₁₆	—	8	2	no	—
334	M₁₆	—	8	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
339	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	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	—	2	2	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
357	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
358	C₄²	C₅×#41	1	1	yes	characteristic
359	C₄²	C₂⁴×C₅	1	1	yes	characteristic
360	C₂×C₅	—	4	1	no	—
361	C₂×C₅	—	8	2	no	—
362	C₂×C₅	—	16	1	no	—
363	C₂×C₅	#3041	1	1	yes	characteristic
364	C₂×C₅	#3054	1	1	yes	characteristic
365	C₂×C₅	#3069	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	8	1	no	—
370	C₂³	—	8	1	no	—
371	C₂³	C₅×#121	1	1	yes	characteristic
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	1	no	—
381	D₄	—	8	2	no	—
382	C₂×C₄	—	2	2	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	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	8	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	C₅×#121	1	1	yes	characteristic
395	C₂×C₄	C₅×#121	1	1	yes	characteristic
396	C₂×C₄	C₅×#121	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₅	#19424	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	8	4	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	C₂×C₅×#121	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	1	no	—
425	C₄	C₅×#575	1	2	yes	—
426	C₄	C₅×#576	1	2	yes	—
427	C₂	—	4	1	no	—
428	C₂	—	8	2	no	—
429	C₂	—	16	1	no	—
430	C₂	C₅×#3041	1	1	yes	characteristic
431	C₂	C₅×#3054	1	1	yes	characteristic
432	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3100	C₂
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
1. C₅×#3210	C₂	semidirect
2. C₅×#3110	C₂	semidirect
4. C₅×#2975	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1689	C₂	semidirect
8. C₅×#1685	C₂	semidirect
9. C₅×#1572	C₂	semidirect
10. C₅×#1553	C₂	semidirect
11. C₅×#1544	C₂	semidirect
15. C₅×#494	C₂²	semidirect
16. C₅×#492	C₂²	semidirect
17. C₅×#487	C₂²	semidirect
18. C₅×#486	C₂²	semidirect
39. C₅×#335	C₂²	semidirect
40. C₅×#334	C₂²	semidirect
41. C₅×#332	C₂²	semidirect
42. C₅×#332	C₂²	semidirect
43. C₅×#332	C₂²	semidirect
44. C₅×#331	C₂²	semidirect
45. #19424	C₅	direct (N × H)
100. #3210	C₂×C₅	semidirect
101. #3110	C₂×C₅	semidirect
103. #2975	C₂×C₅	semidirect
104. #1701	C₂×C₅	semidirect
105. #1699	C₂×C₅	semidirect
106. #1689	C₂×C₅	semidirect
107. #1685	C₂×C₅	semidirect
108. #1572	C₂×C₅	semidirect
109. #1553	C₂×C₅	semidirect
110. #1544	C₂×C₅	semidirect
165. #494	C₂²×C₅	semidirect
166. #492	C₂²×C₅	semidirect
167. #487	C₂²×C₅	semidirect
168. #486	C₂²×C₅	semidirect
189. #335	C₂²×C₅	semidirect
190. #334	C₂²×C₅	semidirect
191. #332	C₂²×C₅	semidirect
192. #332	C₂²×C₅	semidirect
193. #332	C₂²×C₅	semidirect
194. #331	C₂²×C₅	semidirect
405. C₅	#19424	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×#3210	2
C₅×#3110	2
C₅×#3100	2
C₅×#2975	2
C₅×#1701	2
C₅×#1699	2
C₅×#1689	2
C₅×#1685	2
C₅×#1572	2
C₅×#1553	2
C₅×#1544	2
#19424	5

Subgroups — C5×#19424 #11942144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19424 #11942144