Subgroups — C₅×#19244 #11941964

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3246	C₂	1	1	yes	maximal, characteristic
2	C₅×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3141	C₂	1	1	yes	maximal, characteristic
4	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1704	C₂	1	2	yes	maximal, complemented
6	C₅×#1698	C₂	1	2	yes	maximal, complemented
7	C₅×#1684	C₂	1	2	yes	maximal, complemented
8	C₅×#1678	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#333	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1540	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×#500	—	2	1	no	—
16	C₅×#489	—	2	2	no	—
17	C₅×#487	—	2	1	no	—
18	C₅×#487	C₂²	1	2	yes	—
19	C₅×#486	C₂²	1	2	yes	—
20	C₅×#484	—	2	2	no	—
21	C₅×#477	C₂²	1	2	yes	—
22	C₅×#477	C₂²	1	2	yes	—
23	C₅×#476	—	2	1	no	—
24	C₅×#475	C₂²	1	2	yes	—
25	C₅×#465	—	2	2	no	—
26	C₅×#461	—	2	1	no	—
27	C₅×#460	C₂²	1	2	yes	—
28	C₅×#446	—	2	2	no	—
29	C₅×#446	C₂²	1	2	yes	—
30	C₅×C₈×Q₈	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#424	—	2	1	no	—
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₅×#417	—	2	1	no	—
36	C₅×#417	—	2	1	no	—
37	C₅×#405	—	2	1	no	—
38	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	C₅×#333	C₂²	1	2	yes	—
42	C₅×#333	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	1	yes	characteristic
44	C₅×#332	C₂²	1	1	yes	characteristic
45	C₅×#331	C₂²	1	1	yes	characteristic
46	C₅×#331	C₂²	1	1	yes	characteristic
47	#19244	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×SD₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
52	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×C₄⋊Q₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₅×#127	C₂³	1	1	yes	characteristic
63	C₅×#125	—	2	1	no	—
64	C₅×#124	—	2	1	no	—
65	C₅×C₂²⋊Q₈	—	2	1	no	—
66	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
67	C₅×#121	—	2	1	no	—
68	C₅×#121	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	C₂³	1	2	yes	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₅×#117	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊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×#106	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
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×#103	—	2	2	no	—
93	C₅×#103	—	2	2	no	—
94	C₅×#102	—	2	2	no	—
95	C₅×#102	—	2	2	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	1	no	—
98	C₅×#97	—	2	2	no	—
99	C₅×#97	D₄	1	2	yes	—
100	C₄×C₅×C₈	—	2	2	no	—
101	C₄×C₅×C₈	—	2	1	no	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3246	C₂×C₅	1	1	yes	characteristic
104	#3230	C₂×C₅	1	1	yes	characteristic, complemented
105	#3141	C₂×C₅	1	1	yes	characteristic
106	#2962	C₂×C₅	1	1	yes	characteristic, complemented
107	#1704	C₂×C₅	1	2	yes	complemented
108	#1698	C₂×C₅	1	2	yes	complemented
109	#1684	C₂×C₅	1	2	yes	complemented
110	#1678	C₂×C₅	1	2	yes	complemented
111	#1565	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#333	C₂×C₅	1	1	yes	characteristic, complemented
113	#1540	C₂×C₅	1	1	yes	characteristic
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	4	2	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	4	1	no	—
120	C₂×C₅×Q₈	—	8	2	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×SD₁₆	—	8	2	no	—
132	C₅×M₁₆	—	2	2	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	1	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	—	4	2	no	—
140	C₂×C₅×C₈	—	8	1	no	—
141	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
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	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	4	1	no	—
153	C₅×C₄⋊C₄	—	4	1	no	—
154	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₅×C₂²⋊C₄	—	2	2	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₅×C₂²⋊C₄	—	4	1	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₅	#41	1	1	yes	characteristic
162	C₄²×C₅	C₂⁴	1	1	yes	characteristic
163	#533	C₂²×C₅	1	1	yes	characteristic
164	#532	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	#500	—	2	1	no	—
167	#489	—	2	2	no	—
168	#487	—	2	1	no	—
169	#487	C₂²×C₅	1	2	yes	—
170	#486	C₂²×C₅	1	2	yes	—
171	#484	—	2	2	no	—
172	#477	C₂²×C₅	1	2	yes	—
173	#477	C₂²×C₅	1	2	yes	—
174	#476	—	2	1	no	—
175	#475	C₂²×C₅	1	2	yes	—
176	#465	—	2	2	no	—
177	#461	—	2	1	no	—
178	#460	C₂²×C₅	1	2	yes	—
179	#446	—	2	2	no	—
180	#446	C₂²×C₅	1	2	yes	—
181	C₈×Q₈	C₂²×C₅	1	2	yes	—
182	#431	C₂²×C₅	1	1	yes	characteristic
183	#424	—	2	1	no	—
184	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	#417	—	2	1	no	—
187	#417	—	2	1	no	—
188	#405	—	2	1	no	—
189	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
190	#335	C₂²×C₅	1	2	yes	—
191	#334	C₂²×C₅	1	2	yes	—
192	#333	C₂²×C₅	1	2	yes	—
193	#333	C₂²×C₅	1	2	yes	—
194	#332	C₂²×C₅	1	1	yes	characteristic
195	#332	C₂²×C₅	1	1	yes	characteristic
196	#331	C₂²×C₅	1	1	yes	characteristic
197	#331	C₂²×C₅	1	1	yes	characteristic
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	#121	1	1	yes	characteristic
200	C₅×Q₈	—	2	2	no	—
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	—	4	1	no	—
204	C₅×Q₈	—	8	1	no	—
205	C₅×Q₈	—	8	2	no	—
206	C₅×Q₈	—	8	2	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	4	1	no	—
210	C₅×D₄	—	4	1	no	—
211	C₅×D₄	—	8	1	no	—
212	C₅×D₄	—	8	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	8	2	no	—
221	C₂×C₄×C₅	—	8	2	no	—
222	C₂×C₄×C₅	#121	1	1	yes	characteristic
223	C₂×C₄×C₅	#121	1	1	yes	characteristic
224	C₂×C₄×C₅	#121	1	1	yes	characteristic
225	C₂×C₄×C₅	#135	1	2	yes	—
226	C₂×C₄×C₅	#137	1	2	yes	—
227	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₅×C₈	—	2	2	no	—
231	C₅×C₈	—	2	2	no	—
232	C₅×C₈	—	4	1	no	—
233	C₅×C₈	—	4	1	no	—
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	1	no	—
237	C₂×#41	—	2	1	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
241	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
248	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
249	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
250	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
251	#127	C₂³×C₅	1	1	yes	characteristic
252	#125	—	2	1	no	—
253	#124	—	2	1	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
256	#121	—	2	1	no	—
257	#121	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	C₂³×C₅	1	2	yes	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	2	1	no	—
262	#117	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#106	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	—	2	1	no	—
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	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₅	1	2	yes	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	C₂²⋊C₈	—	2	1	no	—
287	#97	—	2	2	no	—
288	#97	C₅×D₄	1	2	yes	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	C₂³×C₅	1	2	yes	—
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	#464	1	2	yes	—
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	—	4	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	8	1	no	—
305	C₄×C₅	—	8	2	no	—
306	C₄×C₅	#464	1	2	yes	—
307	C₄×C₅	C₂×#135	1	1	yes	characteristic
308	C₄×C₅	C₂×#137	1	1	yes	characteristic
309	C₄×C₅	#577	1	1	yes	characteristic
310	C₄×C₅	#578	1	1	yes	characteristic
311	#41	—	4	2	no	—
312	#41	—	4	2	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	4	1	no	—
317	C₂×Q₈	—	8	2	no	—
318	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₄	C₅×#41	1	1	yes	characteristic
328	SD₁₆	—	8	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	2	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	—	4	2	no	—
337	C₂×C₈	—	8	1	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	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₄²	—	2	2	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	—	2	2	no	—
361	C₂×C₅	—	16	1	no	—
362	C₂×C₅	C₂×#464	1	1	yes	characteristic
363	C₂×C₅	#3063	1	1	yes	characteristic
364	C₂×C₅	#3068	1	1	yes	characteristic
365	C₂³	—	4	1	no	—
366	C₂³	C₅×#121	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	8	1	no	—
372	Q₈	—	8	2	no	—
373	Q₈	—	8	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	1	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	1	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	C₅×#135	1	2	yes	—
393	C₂×C₄	C₅×#137	1	2	yes	—
394	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₅	#19244	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	C₅×#464	1	2	yes	—
411	C₂²	C₂×C₅×#121	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	2	no	—
419	C₄	C₅×#464	1	2	yes	—
420	C₄	C₂×C₅×#135	1	1	yes	characteristic
421	C₄	C₂×C₅×#137	1	1	yes	characteristic
422	C₄	C₅×#577	1	1	yes	characteristic
423	C₄	C₅×#578	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₂×C₅×#464	1	1	yes	characteristic
427	C₂	C₅×#3063	1	1	yes	characteristic
428	C₂	C₅×#3068	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
2. C₅×#3230	C₂	semidirect
4. C₅×#2962	C₂	semidirect
5. C₅×#1704	C₂	semidirect
6. C₅×#1698	C₂	semidirect
7. C₅×#1684	C₂	semidirect
8. C₅×#1678	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₂×C₅×#333	C₂	semidirect
47. #19244	C₅	direct (N × H)
104. #3230	C₂×C₅	semidirect
106. #2962	C₂×C₅	semidirect
107. #1704	C₂×C₅	semidirect
108. #1698	C₂×C₅	semidirect
109. #1684	C₂×C₅	semidirect
110. #1678	C₂×C₅	semidirect
111. #1565	C₂×C₅	semidirect
112. C₂×#333	C₂×C₅	semidirect
404. C₅	#19244	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×#3246	2
C₅×#3230	2
C₅×#3141	2
C₅×#2962	2
C₅×#1704	2
C₅×#1698	2
C₅×#1684	2
C₅×#1678	2
C₅×#1565	2
C₂×C₅×#333	2
C₅×#1540	2
#19244	5

Subgroups — C5×#19244 #11941964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19244 #11941964