Subgroups — C₅×#35001 #11957721

Order 1280.

4298 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#534	C₂	1	4	yes	maximal, complemented
2	C₂²×C₅×#121	C₂	1	2	yes	maximal, complemented
3	C₅×#2856	C₂	1	4	yes	maximal, complemented
4	C₅×#2656	C₂	1	4	yes	maximal, complemented
5	C₅×#2539	C₂	1	8	yes	maximal, complemented
6	C₅×#2501	C₂	1	4	yes	maximal, complemented
7	C₅×#2433	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×D₄	C₂²	1	4	yes	—
10	C₂³×C₅×D₄	C₂²	1	2	yes	complemented
11	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₅×#534	—	2	32	no	—
13	C₂×C₅×#127	C₂²	1	4	yes	complemented
14	C₂×C₅×#123	C₂²	1	16	yes	complemented
15	C₂×C₅×#121	—	2	16	no	—
16	C₂×C₅×#121	C₂²	1	4	yes	—
17	C₂×C₅×#121	C₂²	1	4	yes	—
18	C₂×C₅×#121	C₂²	1	4	yes	complemented
19	C₂×C₅×#121	C₂²	1	4	yes	complemented
20	C₂×C₅×#121	C₂²	1	16	yes	complemented
21	C₂×C₅×#120	C₂²	1	16	yes	complemented
22	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
26	C₅×#399	C₂²	1	16	yes	complemented
27	C₅×#392	C₂²	1	16	yes	complemented
28	C₅×#390	C₂²	1	8	yes	complemented
29	C₅×#390	C₂²	1	16	yes	complemented
30	C₅×#384	C₂²	1	4	yes	complemented
31	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
32	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
33	C₂×C₅×#95	C₂²	1	2	yes	complemented
34	#35001	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂⁵×C₅	C₂³	1	4	yes	—
36	C₂⁵×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×D₄	—	2	16	no	—
38	C₂²×C₅×D₄	—	2	32	no	—
39	C₂²×C₅×D₄	—	2	8	no	—
40	C₂²×C₅×D₄	—	4	8	no	—
41	C₂²×C₅×D₄	C₂³	1	4	yes	—
42	C₂²×C₅×D₄	C₂³	1	8	yes	—
43	C₂²×C₅×D₄	C₂³	1	8	yes	—
44	C₂²×C₅×D₄	C₂³	1	16	yes	—
45	C₂²×C₅×D₄	C₂³	1	4	yes	—
46	C₂³×C₄×C₅	—	4	4	no	—
47	C₂³×C₄×C₅	D₄	1	8	yes	complemented
48	C₂³×C₄×C₅	C₂³	1	4	yes	—
49	C₂³×C₄×C₅	C₂³	1	2	yes	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₅	C₂³	1	2	yes	—
53	C₂³×C₄×C₅	C₂³	1	4	yes	—
54	C₅×#127	—	4	8	no	—
55	C₅×#123	—	2	64	no	—
56	C₅×#121	—	2	16	no	—
57	C₅×#121	—	2	16	no	—
58	C₅×#121	—	2	16	no	—
59	C₅×#121	—	2	16	no	—
60	C₅×#121	—	2	64	no	—
61	C₅×#120	—	2	64	no	—
62	C₂×C₅×C₄⋊C₄	—	2	8	no	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
66	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
67	C₂×C₅×C₂²⋊C₄	D₄	1	16	yes	complemented
68	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂³	1	32	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₄²×C₅	—	4	4	no	—
73	C₂×C₄²×C₅	C₂³	1	4	yes	—
74	C₂×C₄²×C₅	C₂³	1	4	yes	—
75	C₅×#95	C₂³	1	8	yes	—
76	C₂×#534	C₂×C₅	1	4	yes	complemented
77	C₂²×#121	C₂×C₅	1	2	yes	complemented
78	#2856	C₂×C₅	1	4	yes	complemented
79	#2656	C₂×C₅	1	4	yes	complemented
80	#2539	C₂×C₅	1	8	yes	complemented
81	#2501	C₂×C₅	1	4	yes	complemented
82	#2433	C₂×C₅	1	4	yes	complemented
83	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
84	C₂⁴×C₅	—	2	8	no	—
85	C₂⁴×C₅	—	2	16	no	—
86	C₂⁴×C₅	—	4	2	no	—
87	C₂⁴×C₅	—	4	2	no	—
88	C₂⁴×C₅	—	4	8	no	—
89	C₂⁴×C₅	—	4	8	no	—
90	C₂⁴×C₅	C₂×D₄	1	8	yes	—
91	C₂⁴×C₅	C₂×D₄	1	4	yes	—
92	C₂⁴×C₅	C₂⁴	1	8	yes	—
93	C₂⁴×C₅	C₂⁴	1	2	yes	—
94	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
95	C₂×C₅×D₄	—	2	32	no	—
96	C₂×C₅×D₄	—	2	16	no	—
97	C₂×C₅×D₄	—	2	16	no	—
98	C₂×C₅×D₄	—	2	32	no	—
99	C₂×C₅×D₄	—	2	8	no	—
100	C₂×C₅×D₄	—	2	8	no	—
101	C₂×C₅×D₄	—	2	32	no	—
102	C₂×C₅×D₄	—	2	16	no	—
103	C₂×C₅×D₄	—	4	8	no	—
104	C₂×C₅×D₄	—	4	32	no	—
105	C₂×C₅×D₄	—	4	16	no	—
106	C₂×C₅×D₄	—	4	16	no	—
107	C₂×C₅×D₄	—	4	64	no	—
108	C₂²×C₄×C₅	—	2	4	no	—
109	C₂²×C₄×C₅	—	2	8	no	—
110	C₂²×C₄×C₅	—	2	8	no	—
111	C₂²×C₄×C₅	—	2	16	no	—
112	C₂²×C₄×C₅	—	4	16	no	—
113	C₂²×C₄×C₅	—	4	4	no	—
114	C₂²×C₄×C₅	—	4	4	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	4	4	no	—
117	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
118	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	16	yes	complemented
122	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
126	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
127	C₅×C₄⋊C₄	—	2	8	no	—
128	C₅×C₄⋊C₄	—	2	8	no	—
129	C₅×C₄⋊C₄	—	2	32	no	—
130	C₅×C₂²⋊C₄	—	2	16	no	—
131	C₅×C₂²⋊C₄	—	2	16	no	—
132	C₅×C₂²⋊C₄	—	2	64	no	—
133	C₅×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
134	C₄²×C₅	—	2	8	no	—
135	C₄²×C₅	—	4	4	no	—
136	C₂³×D₄	C₂²×C₅	1	4	yes	—
137	C₂³×D₄	C₂²×C₅	1	2	yes	complemented
138	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic
139	#534	—	2	32	no	—
140	C₂×#127	C₂²×C₅	1	4	yes	complemented
141	C₂×#123	C₂²×C₅	1	16	yes	complemented
142	C₂×#121	—	2	16	no	—
143	C₂×#121	C₂²×C₅	1	4	yes	—
144	C₂×#121	C₂²×C₅	1	4	yes	—
145	C₂×#121	C₂²×C₅	1	4	yes	complemented
146	C₂×#121	C₂²×C₅	1	16	yes	complemented
147	C₂×#121	C₂²×C₅	1	4	yes	complemented
148	C₂×#120	C₂²×C₅	1	16	yes	complemented
149	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
150	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
151	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
152	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
153	#399	C₂²×C₅	1	16	yes	complemented
154	#392	C₂²×C₅	1	16	yes	complemented
155	#390	C₂²×C₅	1	8	yes	complemented
156	#390	C₂²×C₅	1	16	yes	complemented
157	#384	C₂²×C₅	1	4	yes	complemented
158	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
159	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
160	C₂×#95	C₂²×C₅	1	2	yes	complemented
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	2	4	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	4	no	—
165	C₂³×C₅	—	2	8	no	—
166	C₂³×C₅	—	2	16	no	—
167	C₂³×C₅	—	2	16	no	—
168	C₂³×C₅	—	2	16	no	—
169	C₂³×C₅	—	4	4	no	—
170	C₂³×C₅	—	4	4	no	—
171	C₂³×C₅	—	4	16	no	—
172	C₂³×C₅	—	4	16	no	—
173	C₂³×C₅	—	4	16	no	—
174	C₂³×C₅	—	4	16	no	—
175	C₂³×C₅	—	8	32	no	—
176	C₂³×C₅	#127	1	16	yes	complemented
177	C₂³×C₅	C₂²×D₄	1	8	yes	—
178	C₂³×C₅	C₂²×D₄	1	4	yes	—
179	C₂³×C₅	C₂²×D₄	1	2	yes	—
180	C₂³×C₅	C₂²×D₄	1	4	yes	—
181	C₂³×C₅	C₂⁵	1	1	yes	characteristic
182	C₅×D₄	—	4	16	no	—
183	C₅×D₄	—	4	32	no	—
184	C₅×D₄	—	4	32	no	—
185	C₅×D₄	—	4	16	no	—
186	C₅×D₄	—	8	32	no	—
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	8	no	—
191	C₂×C₄×C₅	—	2	8	no	—
192	C₂×C₄×C₅	—	2	16	no	—
193	C₂×C₄×C₅	—	2	8	no	—
194	C₂×C₄×C₅	—	2	16	no	—
195	C₂×C₄×C₅	—	4	8	no	—
196	C₂×C₄×C₅	—	4	4	no	—
197	C₂×C₄×C₅	—	4	16	no	—
198	C₂×C₄×C₅	—	4	16	no	—
199	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₅	C₂²×D₄	1	16	yes	—
201	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
204	C₂⁵	C₂³×C₅	1	4	yes	—
205	C₂⁵	C₂³×C₅	1	1	yes	characteristic
206	C₂²×D₄	—	2	16	no	—
207	C₂²×D₄	—	2	32	no	—
208	C₂²×D₄	—	2	8	no	—
209	C₂²×D₄	—	4	8	no	—
210	C₂²×D₄	C₂³×C₅	1	8	yes	—
211	C₂²×D₄	C₂³×C₅	1	4	yes	—
212	C₂²×D₄	C₂³×C₅	1	8	yes	—
213	C₂²×D₄	C₂³×C₅	1	16	yes	—
214	C₂²×D₄	C₂³×C₅	1	4	yes	—
215	C₂³×C₄	—	4	4	no	—
216	C₂³×C₄	C₅×D₄	1	8	yes	complemented
217	C₂³×C₄	C₂³×C₅	1	4	yes	—
218	C₂³×C₄	C₂³×C₅	1	2	yes	—
219	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₅	1	2	yes	—
221	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₅	1	4	yes	—
223	#127	—	4	8	no	—
224	#123	—	2	64	no	—
225	#121	—	2	16	no	—
226	#121	—	2	16	no	—
227	#121	—	2	16	no	—
228	#121	—	2	16	no	—
229	#121	—	2	64	no	—
230	#120	—	2	64	no	—
231	C₂×C₄⋊C₄	—	2	8	no	—
232	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
233	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
234	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
235	C₂×C₂²⋊C₄	—	2	16	no	—
236	C₂×C₂²⋊C₄	C₅×D₄	1	16	yes	complemented
237	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₅	1	32	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
241	C₂×C₄²	—	4	4	no	—
242	C₂×C₄²	C₂³×C₅	1	4	yes	—
243	C₂×C₄²	C₂³×C₅	1	4	yes	—
244	#95	C₂³×C₅	1	8	yes	—
245	C₂²×C₅	—	2	4	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	—	2	4	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	8	no	—
250	C₂²×C₅	—	2	16	no	—
251	C₂²×C₅	—	4	16	no	—
252	C₂²×C₅	—	4	8	no	—
253	C₂²×C₅	—	4	8	no	—
254	C₂²×C₅	—	4	8	no	—
255	C₂²×C₅	—	4	32	no	—
256	C₂²×C₅	—	8	32	no	—
257	C₂²×C₅	C₂×#127	1	8	yes	—
258	C₂²×C₅	C₂×#127	1	4	yes	—
259	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
260	C₂²×C₅	C₂³×D₄	1	2	yes	—
261	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₅	#585	1	2	yes	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	4	no	—
265	C₄×C₅	—	2	16	no	—
266	C₄×C₅	—	4	8	no	—
267	C₄×C₅	#534	1	4	yes	complemented
268	C₂⁴	—	2	8	no	—
269	C₂⁴	—	2	16	no	—
270	C₂⁴	—	4	2	no	—
271	C₂⁴	—	4	2	no	—
272	C₂⁴	—	4	8	no	—
273	C₂⁴	—	4	8	no	—
274	C₂⁴	C₂×C₅×D₄	1	8	yes	—
275	C₂⁴	C₂×C₅×D₄	1	4	yes	—
276	C₂⁴	C₂⁴×C₅	1	8	yes	—
277	C₂⁴	C₂⁴×C₅	1	2	yes	—
278	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
279	C₂×D₄	—	2	32	no	—
280	C₂×D₄	—	2	16	no	—
281	C₂×D₄	—	2	16	no	—
282	C₂×D₄	—	2	32	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	32	no	—
286	C₂×D₄	—	2	16	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	—	4	32	no	—
289	C₂×D₄	—	4	16	no	—
290	C₂×D₄	—	4	16	no	—
291	C₂×D₄	—	4	64	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	16	no	—
296	C₂²×C₄	—	4	16	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
302	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
303	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
304	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
305	C₂²×C₄	C₂×C₅×D₄	1	16	yes	complemented
306	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
307	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	32	no	—
314	C₂²⋊C₄	—	2	16	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₂²⋊C₄	—	2	64	no	—
317	C₂²⋊C₄	C₂×C₅×D₄	1	32	yes	complemented
318	C₄²	—	2	8	no	—
319	C₄²	—	4	4	no	—
320	C₂×C₅	—	2	8	no	—
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	—	8	8	no	—
323	C₂×C₅	C₂²×#127	1	1	yes	characteristic
324	C₂×C₅	C₂×#534	1	1	yes	characteristic
325	C₂×C₅	#3449	1	1	yes	characteristic
326	C₂×C₅	#3496	1	4	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	4	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	16	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	16	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	16	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	4	16	no	—
341	C₂³	—	8	32	no	—
342	C₂³	C₅×#127	1	16	yes	complemented
343	C₂³	C₂²×C₅×D₄	1	8	yes	—
344	C₂³	C₂²×C₅×D₄	1	4	yes	—
345	C₂³	C₂²×C₅×D₄	1	2	yes	—
346	C₂³	C₂²×C₅×D₄	1	4	yes	—
347	C₂³	C₂⁵×C₅	1	1	yes	characteristic
348	D₄	—	4	16	no	—
349	D₄	—	4	32	no	—
350	D₄	—	4	32	no	—
351	D₄	—	4	16	no	—
352	D₄	—	8	32	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	16	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	2	16	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	4	16	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
366	C₂×C₄	C₂²×C₅×D₄	1	16	yes	—
367	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
368	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
369	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
370	C₅	#35001	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	16	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	4	8	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	32	no	—
382	C₂²	—	8	32	no	—
383	C₂²	C₂×C₅×#127	1	8	yes	—
384	C₂²	C₂×C₅×#127	1	4	yes	—
385	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
386	C₂²	C₂³×C₅×D₄	1	2	yes	—
387	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
388	C₂²	C₅×#585	1	2	yes	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	16	no	—
392	C₄	—	4	8	no	—
393	C₄	C₅×#534	1	4	yes	complemented
394	C₂	—	2	8	no	—
395	C₂	—	2	4	no	—
396	C₂	—	8	8	no	—
397	C₂	C₂²×C₅×#127	1	1	yes	characteristic
398	C₂	C₂×C₅×#534	1	1	yes	characteristic
399	C₂	C₅×#3449	1	1	yes	characteristic
400	C₂	C₅×#3496	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#534	C₂	semidirect
2. C₂²×C₅×#121	C₂	semidirect
3. C₅×#2856	C₂	semidirect
4. C₅×#2656	C₂	semidirect
5. C₅×#2539	C₂	semidirect
6. C₅×#2501	C₂	semidirect
7. C₅×#2433	C₂	semidirect
8. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
10. C₂³×C₅×D₄	C₂²	semidirect
13. C₂×C₅×#127	C₂²	semidirect
14. C₂×C₅×#123	C₂²	semidirect
18. C₂×C₅×#121	C₂²	semidirect
19. C₂×C₅×#121	C₂²	semidirect
20. C₂×C₅×#121	C₂²	semidirect
21. C₂×C₅×#120	C₂²	semidirect
22. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₄²×C₅	C₂²	semidirect
26. C₅×#399	C₂²	semidirect
27. C₅×#392	C₂²	semidirect
28. C₅×#390	C₂²	semidirect
29. C₅×#390	C₂²	semidirect
30. C₅×#384	C₂²	semidirect
31. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
32. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₂×C₅×#95	C₂²	semidirect
34. #35001	C₅	direct (N × H)
47. C₂³×C₄×C₅	D₄	semidirect
67. C₂×C₅×C₂²⋊C₄	D₄	semidirect
76. C₂×#534	C₂×C₅	semidirect
77. C₂²×#121	C₂×C₅	semidirect
78. #2856	C₂×C₅	semidirect
79. #2656	C₂×C₅	semidirect
80. #2539	C₂×C₅	semidirect
81. #2501	C₂×C₅	semidirect
82. #2433	C₂×C₅	semidirect
83. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
121. C₂²×C₄×C₅	C₂×D₄	semidirect
133. C₅×C₂²⋊C₄	C₂×D₄	semidirect
137. C₂³×D₄	C₂²×C₅	semidirect
140. C₂×#127	C₂²×C₅	semidirect
141. C₂×#123	C₂²×C₅	semidirect
145. C₂×#121	C₂²×C₅	semidirect
146. C₂×#121	C₂²×C₅	semidirect
147. C₂×#121	C₂²×C₅	semidirect
148. C₂×#120	C₂²×C₅	semidirect
149. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
151. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
152. C₂²×C₄²	C₂²×C₅	semidirect
153. #399	C₂²×C₅	semidirect
154. #392	C₂²×C₅	semidirect
155. #390	C₂²×C₅	semidirect
156. #390	C₂²×C₅	semidirect
157. #384	C₂²×C₅	semidirect
158. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
159. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
160. C₂×#95	C₂²×C₅	semidirect
176. C₂³×C₅	#127	semidirect
216. C₂³×C₄	C₅×D₄	semidirect
236. C₂×C₂²⋊C₄	C₅×D₄	semidirect
267. C₄×C₅	#534	semidirect
305. C₂²×C₄	C₂×C₅×D₄	semidirect
317. C₂²⋊C₄	C₂×C₅×D₄	semidirect
342. C₂³	C₅×#127	semidirect
370. C₅	#35001	direct (N × H)
393. C₄	C₅×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#534	2
C₂²×C₅×#121	2
C₅×#2856	2
C₅×#2656	2
C₅×#2539	2
C₅×#2501	2
C₅×#2433	2
C₂×C₄×C₅×C₂²⋊C₄	2
#35001	5

Subgroups — C5×#35001 #11957721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35001 #11957721