Subgroups — C₅×#7952 #11930672

Order 1280.

610 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
3	C₅×#2285	C₂	1	1	yes	maximal, characteristic
4	C₅×#1285	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#117	C₄	1	2	yes	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₅×#432	—	2	1	no	—
8	C₅×#432	—	2	1	no	—
9	C₅×#432	—	2	1	no	—
10	C₅×#432	—	2	1	no	—
11	C₅×#432	C₄	1	2	yes	complemented
12	C₅×#432	C₄	1	2	yes	complemented
13	C₅×#432	C₂²	1	2	yes	—
14	C₅×#432	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	—	2	1	no	—
16	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	complemented
17	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
18	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
19	C₂×C₅×#97	—	2	1	no	—
20	C₂×C₅×#97	C₄	1	2	yes	complemented
21	C₅×#384	—	2	1	no	—
22	C₅×#382	—	2	1	no	—
23	C₅×#380	—	2	1	no	—
24	C₅×#380	—	2	1	no	—
25	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
26	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	#7952	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
31	C₂²×C₅×C₈	—	2	2	no	—
32	C₂²×C₅×C₈	—	2	2	no	—
33	C₅×#117	—	4	4	no	—
34	C₂×C₅×C₄⋊C₄	—	2	2	no	—
35	C₂×C₅×C₄⋊C₄	—	2	2	no	—
36	C₂×C₅×C₄⋊C₄	—	2	2	no	—
37	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
38	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₅×C₄⋊C₈	—	2	2	no	—
52	C₅×C₄⋊C₈	—	2	2	no	—
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
55	C₅×C₂²⋊C₈	—	2	2	no	—
56	C₅×C₂²⋊C₈	—	2	2	no	—
57	C₅×C₂²⋊C₈	—	2	2	no	—
58	C₅×C₂²⋊C₈	—	2	2	no	—
59	C₅×#97	—	2	2	no	—
60	C₅×#97	—	2	2	no	—
61	C₅×#97	—	2	2	no	—
62	C₅×#97	C₂×C₄	1	4	yes	—
63	C₅×#95	—	2	2	no	—
64	C₅×#95	—	2	2	no	—
65	C₂×#432	C₂×C₅	1	1	yes	characteristic
66	C₂×#432	C₂×C₅	1	1	yes	characteristic
67	#2285	C₂×C₅	1	1	yes	characteristic
68	#1285	C₂×C₅	1	4	yes	complemented
69	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅	—	2	2	no	—
71	C₂²×C₄×C₅	—	2	2	no	—
72	C₂²×C₄×C₅	—	2	4	no	—
73	C₂²×C₄×C₅	—	4	2	no	—
74	C₂²×C₄×C₅	—	4	2	no	—
75	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×C₈	—	2	4	no	—
94	C₂×C₅×C₈	—	2	4	no	—
95	C₂×C₅×C₈	—	4	4	no	—
96	C₂×C₅×C₈	—	4	4	no	—
97	C₅×C₄⋊C₄	—	4	4	no	—
98	C₅×C₄⋊C₄	—	4	4	no	—
99	C₅×C₄⋊C₄	—	4	4	no	—
100	C₅×C₂²⋊C₄	—	4	4	no	—
101	C₄²×C₅	—	4	4	no	—
102	C₄²×C₅	C₄²	1	1	yes	characteristic
103	C₄²×C₅	C₄²	1	1	yes	characteristic
104	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
118	C₂×#117	C₄×C₅	1	2	yes	—
119	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
120	#432	—	2	1	no	—
121	#432	—	2	1	no	—
122	#432	—	2	1	no	—
123	#432	—	2	1	no	—
124	#432	C₄×C₅	1	2	yes	complemented
125	#432	C₄×C₅	1	2	yes	complemented
126	#432	C₂²×C₅	1	2	yes	—
127	#432	C₂²×C₅	1	2	yes	—
128	C₂×C₄⋊C₈	—	2	1	no	—
129	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	complemented
130	C₂×C₂²⋊C₈	—	2	1	no	—
131	C₂×C₂²⋊C₈	—	2	1	no	—
132	C₂×#97	—	2	1	no	—
133	C₂×#97	C₄×C₅	1	2	yes	complemented
134	#384	—	2	1	no	—
135	#382	—	2	1	no	—
136	#380	—	2	1	no	—
137	#380	—	2	1	no	—
138	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
139	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂³×C₅	—	4	1	no	—
141	C₂³×C₅	—	4	1	no	—
142	C₂³×C₅	#95	1	1	yes	characteristic
143	C₂³×C₅	#95	1	1	yes	characteristic
144	C₂³×C₅	#100	1	2	yes	—
145	C₂³×C₅	#101	1	2	yes	—
146	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₅	—	2	2	no	—
148	C₂×C₄×C₅	—	2	2	no	—
149	C₂×C₄×C₅	—	2	2	no	—
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	1	no	—
152	C₂×C₄×C₅	—	2	1	no	—
153	C₂×C₄×C₅	—	2	1	no	—
154	C₂×C₄×C₅	—	2	1	no	—
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	4	1	no	—
162	C₂×C₄×C₅	—	4	1	no	—
163	C₂×C₄×C₅	—	4	1	no	—
164	C₂×C₄×C₅	—	4	1	no	—
165	C₂×C₄×C₅	—	4	1	no	—
166	C₂×C₄×C₅	—	4	1	no	—
167	C₂×C₄×C₅	—	4	4	no	—
168	C₂×C₄×C₅	—	4	4	no	—
169	C₂×C₄×C₅	—	4	4	no	—
170	C₂×C₄×C₅	#95	1	1	yes	characteristic
171	C₂×C₄×C₅	#95	1	1	yes	characteristic
172	C₂×C₄×C₅	#95	1	1	yes	characteristic
173	C₂×C₄×C₅	#95	1	1	yes	characteristic
174	C₂×C₄×C₅	#95	1	1	yes	characteristic
175	C₂×C₄×C₅	#95	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₅×C₈	—	4	4	no	—
183	C₅×C₈	—	4	4	no	—
184	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	2	no	—
189	#117	—	4	4	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₂²⋊C₄	—	2	2	no	—
194	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
195	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
201	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
202	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
203	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
204	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
205	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	—	2	2	no	—
209	C₄⋊C₈	—	2	2	no	—
210	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
211	C₂²⋊C₈	—	2	2	no	—
212	C₂²⋊C₈	—	2	2	no	—
213	C₂²⋊C₈	—	2	2	no	—
214	C₂²⋊C₈	—	2	2	no	—
215	#97	—	2	2	no	—
216	#97	—	2	2	no	—
217	#97	—	2	2	no	—
218	#97	C₂×C₄×C₅	1	4	yes	—
219	#95	—	2	2	no	—
220	#95	—	2	2	no	—
221	C₂²×C₅	—	2	1	no	—
222	C₂²×C₅	—	2	1	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	1	no	—
225	C₂²×C₅	—	2	1	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	4	2	no	—
228	C₂²×C₅	—	4	2	no	—
229	C₂²×C₅	#343	1	2	yes	—
230	C₂²×C₅	#343	1	2	yes	—
231	C₂²×C₅	C₂×#95	1	1	yes	characteristic
232	C₂²×C₅	C₂×#100	1	1	yes	characteristic
233	C₂²×C₅	C₂×#101	1	1	yes	characteristic
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	1	no	—
237	C₄×C₅	—	2	1	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	8	4	no	—
245	C₄×C₅	H(3,ℤ/4)	1	2	yes	—
246	C₄×C₅	#421	1	2	yes	—
247	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
254	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
255	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	4	4	no	—
274	C₂×C₈	—	4	4	no	—
275	C₄⋊C₄	—	4	4	no	—
276	C₄⋊C₄	—	4	4	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₂²⋊C₄	—	4	4	no	—
279	C₄²	—	4	4	no	—
280	C₄²	C₄²×C₅	1	1	yes	characteristic
281	C₄²	C₄²×C₅	1	1	yes	characteristic
282	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
283	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
284	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
285	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
286	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
287	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
288	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
289	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
290	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
291	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
292	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
293	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
294	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
295	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
296	C₂×C₅	—	2	1	no	—
297	C₂×C₅	—	2	2	no	—
298	C₂×C₅	—	2	2	no	—
299	C₂×C₅	—	2	1	no	—
300	C₂×C₅	C₂×H(3,ℤ/4)	1	1	yes	characteristic
301	C₂×C₅	#1733	1	1	yes	characteristic
302	C₂×C₅	C₂×#343	1	1	yes	characteristic
303	C₂³	—	4	1	no	—
304	C₂³	—	4	1	no	—
305	C₂³	C₅×#95	1	1	yes	characteristic
306	C₂³	C₅×#95	1	1	yes	characteristic
307	C₂³	C₅×#100	1	2	yes	—
308	C₂³	C₅×#101	1	2	yes	—
309	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	C₅×#95	1	1	yes	characteristic
334	C₂×C₄	C₅×#95	1	1	yes	characteristic
335	C₂×C₄	C₅×#95	1	1	yes	characteristic
336	C₂×C₄	C₅×#95	1	1	yes	characteristic
337	C₂×C₄	C₅×#95	1	1	yes	characteristic
338	C₂×C₄	C₅×#95	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
340	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
345	C₈	—	4	4	no	—
346	C₈	—	4	4	no	—
347	C₅	#7952	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	C₅×#343	1	2	yes	—
357	C₂²	C₅×#343	1	2	yes	—
358	C₂²	C₂×C₅×#95	1	1	yes	characteristic
359	C₂²	C₂×C₅×#100	1	1	yes	characteristic
360	C₂²	C₂×C₅×#101	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	8	4	no	—
372	C₄	C₅×H(3,ℤ/4)	1	2	yes	—
373	C₄	C₅×#421	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	2	2	no	—
377	C₂	—	2	2	no	—
378	C₂	C₂×C₅×H(3,ℤ/4)	1	1	yes	characteristic
379	C₂	C₅×#1733	1	1	yes	characteristic
380	C₂	C₂×C₅×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1285	C₂	semidirect
11. C₅×#432	C₄	semidirect
12. C₅×#432	C₄	semidirect
16. C₂×C₅×C₄⋊C₈	C₄	semidirect
20. C₂×C₅×#97	C₄	semidirect
27. #7952	C₅	direct (N × H)
68. #1285	C₂×C₅	semidirect
124. #432	C₄×C₅	semidirect
125. #432	C₄×C₅	semidirect
129. C₂×C₄⋊C₈	C₄×C₅	semidirect
133. C₂×#97	C₄×C₅	semidirect
347. C₅	#7952	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#432	2
C₅×#2285	2
C₅×#1285	2
#7952	5

Subgroups — C5×#7952 #11930672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#7952 #11930672