Subgroups — C₅×#66163 #13106982

Order 1600.

832 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4085	C₂	1	2	yes	maximal, complemented
6	C₅×#4083	C₂	1	2	yes	maximal, complemented
7	C₅×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4076	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4075	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#685	C₂	1	2	yes	maximal, complemented
12	C₂³×C₅×D₅	C₂²	1	2	yes	—
13	C₅²×#41	—	2	4	no	—
14	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅²×D₄	C₂²	1	2	yes	complemented
17	C₂²×C₄×C₅²	C₂²	1	2	yes	complemented
18	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂²×C₅×Dic₅	C₂²	1	2	yes	complemented
23	C₅×D₄×D₅	—	2	4	no	—
24	C₂×C₅×D₂₀	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
26	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
27	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
28	C₅×#685	C₂²	1	1	yes	characteristic
29	C₅×#685	C₂²	1	2	yes	—
30	C₅×#685	C₂²	1	2	yes	complemented
31	C₅×#685	C₂²	1	2	yes	complemented
32	C₅×#685	C₂²	1	2	yes	complemented
33	C₅×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
34	C₅×#683	C₂²	1	1	yes	characteristic, complemented
35	C₅×#683	C₂²	1	2	yes	complemented
36	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₅×#546	—	5	1	no	maximal
38	#66163	C₅	1	1	yes	maximal, characteristic, direct product factor
39	C₂³×C₅²	C₂³	1	1	yes	characteristic
40	C₂³×C₅²	C₂³	1	2	yes	—
41	C₂²×C₅×D₅	—	2	4	no	—
42	C₂²×C₅×D₅	—	2	4	no	—
43	C₂²×C₅×D₅	—	4	2	no	—
44	C₂²×C₅×D₅	C₂³	1	2	yes	—
45	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
46	C₅²×Q₈	—	2	2	no	—
47	C₅²×D₄	—	2	4	no	—
48	C₅²×D₄	D₄	1	4	yes	complemented
49	C₂×C₄×C₅²	—	2	4	no	—
50	C₂×C₄×C₅²	—	2	2	no	—
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₂×C₄×C₅²	C₂³	1	2	yes	—
53	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
54	C₅×C₂²⋊D₅	—	2	4	no	—
55	C₅×C₂²⋊D₅	—	2	2	no	—
56	C₅×C₂²⋊D₅	—	4	2	no	—
57	C₂×C₅×Dic₅	—	4	2	no	—
58	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
59	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
60	C₂×C₅×Dic₅	C₂³	1	2	yes	—
61	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
62	C₅×D₂₀	—	2	2	no	—
63	C₄×C₅×D₅	—	2	2	no	—
64	C₂×C₅×#41	—	2	2	no	—
65	C₂×C₅×#41	D₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×D₄	—	5	1	no	—
68	C₂×D₄×D₅	C₂×C₅	1	1	yes	characteristic, complemented
69	C₅×#124	—	5	1	no	—
70	C₅×#123	—	5	2	no	—
71	C₅×C₂²⋊Q₈	—	5	1	no	—
72	C₅×#121	—	5	2	no	—
73	C₅×#121	—	5	1	no	—
74	C₅×#120	—	5	2	no	—
75	C₄×C₅×D₄	—	5	1	no	—
76	C₄×C₅×D₄	—	5	1	no	—
77	C₂×C₅×C₂²⋊C₄	—	5	2	no	—
78	#4093	C₂×C₅	1	1	yes	characteristic, complemented
79	#4092	C₂×C₅	1	1	yes	characteristic, complemented
80	#4085	C₂×C₅	1	2	yes	complemented
81	#4083	C₂×C₅	1	2	yes	complemented
82	D₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
83	#4076	C₂×C₅	1	1	yes	characteristic, complemented
84	#4075	C₂×C₅	1	2	yes	complemented
85	C₄×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×#685	C₂×C₅	1	2	yes	complemented
87	C₂²×C₅²	—	2	2	no	—
88	C₂²×C₅²	—	2	2	no	—
89	C₂²×C₅²	—	2	1	no	—
90	C₂²×C₅²	—	2	1	no	—
91	C₂²×C₅²	—	2	1	no	—
92	C₂²×C₅²	C₂×D₄	1	4	yes	—
93	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
94	C₂×C₅×D₅	—	2	1	no	—
95	C₂×C₅×D₅	—	2	2	no	—
96	C₂×C₅×D₅	—	2	2	no	—
97	C₂×C₅×D₅	—	2	1	no	—
98	C₂×C₅×D₅	—	2	2	no	—
99	C₂×C₅×D₅	—	4	8	no	—
100	C₂×C₅×D₅	#41	1	2	yes	complemented
101	C₄×C₅²	—	2	1	no	—
102	C₄×C₅²	—	2	2	no	—
103	C₄×C₅²	C₂×D₄	1	2	yes	—
104	C₅×Dic₅	—	2	1	no	—
105	C₅×Dic₅	—	2	1	no	—
106	C₅×Dic₅	—	2	1	no	—
107	C₅×Dic₅	—	2	2	no	—
108	C₂⁴×C₅	—	5	2	no	—
109	C₂³×D₅	C₂²×C₅	1	2	yes	—
110	C₅×#41	—	2	16	no	—
111	C₅×#41	—	2	4	no	—
112	C₅×#41	—	2	4	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
115	C₂×C₅×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	4	no	—
118	C₂×C₅×D₄	—	5	1	no	—
119	C₂×C₅×D₄	—	5	2	no	—
120	C₂×C₅×D₄	—	5	2	no	—
121	C₂×C₅×D₄	—	5	1	no	—
122	C₂×C₅×D₄	—	10	4	no	—
123	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
124	C₂×C₅×D₄	C₂×D₅	1	2	yes	complemented
125	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₅×D₄	C₂²×C₅	1	2	yes	complemented
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	5	2	no	—
130	C₂²×C₄×C₅	—	5	1	no	—
131	C₂²×C₄×C₅	C₂×D₅	1	2	yes	complemented
132	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
133	C₂²×C₄×C₅	C₂²×C₅	1	2	yes	complemented
134	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	—
136	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
138	C₂²×Dic₅	C₂²×C₅	1	2	yes	complemented
139	D₄×D₅	—	2	4	no	—
140	C₂×D₂₀	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic
142	C₅×C₄⋊C₄	—	5	1	no	—
143	C₅×C₄⋊C₄	—	5	1	no	—
144	C₅×C₄⋊C₄	—	5	2	no	—
145	C₅×C₂²⋊C₄	—	5	2	no	—
146	C₅×C₂²⋊C₄	—	5	1	no	—
147	C₅×C₂²⋊C₄	—	5	1	no	—
148	C₅×C₂²⋊C₄	—	5	2	no	—
149	C₅×C₂²⋊C₄	—	5	2	no	—
150	C₅×C₂²⋊C₄	—	5	2	no	—
151	C₅×C₂²⋊C₄	—	5	2	no	—
152	C₄²×C₅	—	5	1	no	—
153	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
155	#685	C₂²×C₅	1	1	yes	characteristic
156	#685	C₂²×C₅	1	2	yes	—
157	#685	C₂²×C₅	1	2	yes	complemented
158	#685	C₂²×C₅	1	2	yes	complemented
159	#685	C₂²×C₅	1	2	yes	complemented
160	C₄⋊Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
161	#683	C₂²×C₅	1	1	yes	characteristic, complemented
162	#683	C₂²×C₅	1	2	yes	complemented
163	C₄×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
164	#546	—	5	1	no	Sylow
165	C₂×C₅²	—	2	4	no	—
166	C₂×C₅²	—	4	1	no	—
167	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₅²	C₂×#41	1	1	yes	characteristic
169	C₂×C₅²	H(5,𝔽₂)	1	1	yes	characteristic
170	C₅×D₅	—	2	2	no	—
171	C₅×D₅	—	4	2	no	—
172	C₂³×C₅	—	2	2	no	—
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	5	1	no	—
175	C₂³×C₅	—	5	2	no	—
176	C₂³×C₅	—	10	4	no	—
177	C₂³×C₅	—	10	4	no	—
178	C₂³×C₅	—	20	2	no	—
179	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
180	C₂³×C₅	C₂²×D₅	1	2	yes	—
181	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
182	C₂³×C₅	C₂³×C₅	1	2	yes	—
183	C₂²×D₅	—	2	4	no	—
184	C₂²×D₅	—	2	4	no	—
185	C₂²×D₅	—	4	2	no	—
186	C₂²×D₅	C₂³×C₅	1	2	yes	—
187	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
188	C₅×Q₈	—	2	8	no	—
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	2	2	no	—
191	C₅×D₄	—	2	16	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	8	no	—
195	C₅×D₄	—	10	2	no	—
196	C₅×D₄	—	10	4	no	—
197	C₅×D₄	—	10	2	no	—
198	C₅×D₄	—	20	2	no	—
199	C₅×D₄	C₂²⋊D₅	1	4	yes	complemented
200	C₅×D₄	C₅×D₄	1	4	yes	complemented
201	C₂×C₄×C₅	—	2	16	no	—
202	C₂×C₄×C₅	—	2	8	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	5	1	no	—
211	C₂×C₄×C₅	—	5	1	no	—
212	C₂×C₄×C₅	—	5	2	no	—
213	C₂×C₄×C₅	—	5	1	no	—
214	C₂×C₄×C₅	—	10	2	no	—
215	C₂×C₄×C₅	—	20	2	no	—
216	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
218	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
221	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
222	C₂²⋊D₅	—	2	4	no	—
223	C₂²⋊D₅	—	2	2	no	—
224	C₂²⋊D₅	—	4	2	no	—
225	C₂×Dic₅	—	4	2	no	—
226	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
227	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
228	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
229	C₂×Dic₅	C₂³×C₅	1	2	yes	—
230	D₂₀	—	2	2	no	—
231	C₄×D₅	—	2	2	no	—
232	C₂×#41	C₅×D₅	1	1	yes	characteristic, complemented
233	C₂²×D₄	—	5	1	no	—
234	#124	—	5	1	no	—
235	#123	—	5	2	no	—
236	C₂²⋊Q₈	—	5	1	no	—
237	#121	—	5	2	no	—
238	#121	—	5	1	no	—
239	#120	—	5	2	no	—
240	C₄×D₄	—	5	1	no	—
241	C₄×D₄	—	5	1	no	—
242	C₂×C₂²⋊C₄	—	5	2	no	—
243	C₅²	#546	1	1	yes	characteristic, complemented, Sylow
244	C₂²×C₅	—	2	2	no	—
245	C₂²×C₅	—	2	2	no	—
246	C₂²×C₅	—	2	2	no	—
247	C₂²×C₅	—	2	2	no	—
248	C₂²×C₅	—	2	4	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	1	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	8	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	4	4	no	—
259	C₂²×C₅	—	4	2	no	—
260	C₂²×C₅	—	4	2	no	—
261	C₂²×C₅	—	5	2	no	—
262	C₂²×C₅	—	10	1	no	—
263	C₂²×C₅	—	10	1	no	—
264	C₂²×C₅	—	10	2	no	—
265	C₂²×C₅	—	10	2	no	—
266	C₂²×C₅	—	10	2	no	—
267	C₂²×C₅	—	20	8	no	—
268	C₂²×C₅	C₂×C₂²⋊D₅	1	4	yes	—
269	C₂²×C₅	C₂×C₅×D₄	1	4	yes	—
270	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
271	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
272	C₂×D₅	—	2	1	no	—
273	C₂×D₅	—	2	1	no	—
274	C₂×D₅	—	2	2	no	—
275	C₂×D₅	—	2	2	no	—
276	C₂×D₅	—	2	2	no	—
277	C₂×D₅	—	4	8	no	—
278	C₂×D₅	C₅×#41	1	2	yes	complemented
279	C₄×C₅	—	2	4	no	—
280	C₄×C₅	—	2	8	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	4	no	—
286	C₄×C₅	—	10	1	no	—
287	C₄×C₅	—	10	1	no	—
288	C₄×C₅	—	10	2	no	—
289	C₄×C₅	—	10	1	no	—
290	C₄×C₅	C₂×C₂²⋊D₅	1	2	yes	—
291	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
292	Dic₅	—	2	1	no	—
293	Dic₅	—	2	1	no	—
294	Dic₅	—	2	1	no	—
295	Dic₅	—	2	2	no	—
296	C₂⁴	—	5	2	no	—
297	#41	—	2	4	no	—
298	C₂×Q₈	C₂×C₅×D₅	1	1	yes	characteristic, complemented
299	C₂×D₄	—	5	1	no	—
300	C₂×D₄	—	5	2	no	—
301	C₂×D₄	—	5	2	no	—
302	C₂×D₄	—	5	1	no	—
303	C₂×D₄	—	10	4	no	—
304	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
305	C₂×D₄	C₂×C₅×D₅	1	2	yes	complemented
306	C₂²×C₄	—	5	2	no	—
307	C₂²×C₄	—	5	1	no	—
308	C₂²×C₄	C₂×C₅×D₅	1	2	yes	complemented
309	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
310	C₄⋊C₄	—	5	1	no	—
311	C₄⋊C₄	—	5	1	no	—
312	C₄⋊C₄	—	5	2	no	—
313	C₂²⋊C₄	—	5	2	no	—
314	C₂²⋊C₄	—	5	1	no	—
315	C₂²⋊C₄	—	5	1	no	—
316	C₂²⋊C₄	—	5	2	no	—
317	C₂²⋊C₄	—	5	2	no	—
318	C₂²⋊C₄	—	5	2	no	—
319	C₂²⋊C₄	—	5	2	no	—
320	C₄²	—	5	1	no	—
321	C₂×C₅	—	2	4	no	—
322	C₂×C₅	—	2	4	no	—
323	C₂×C₅	—	2	2	no	—
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	2	2	no	—
326	C₂×C₅	—	4	8	no	—
327	C₂×C₅	—	4	4	no	—
328	C₂×C₅	—	4	1	no	—
329	C₂×C₅	—	4	1	no	—
330	C₂×C₅	—	10	2	no	—
331	C₂×C₅	—	20	2	no	—
332	C₂×C₅	D₅×#41	1	1	yes	characteristic
333	C₂×C₅	#4149	1	1	yes	characteristic
334	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
335	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
336	C₂×C₅	C₂×C₅×#41	1	1	yes	characteristic
337	C₂×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic
338	D₅	—	2	2	no	—
339	D₅	—	4	2	no	—
340	C₂³	—	5	1	no	—
341	C₂³	—	5	2	no	—
342	C₂³	—	10	4	no	—
343	C₂³	—	10	4	no	—
344	C₂³	—	20	2	no	—
345	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
346	C₂³	C₂²×C₅×D₅	1	2	yes	—
347	Q₈	—	2	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	10	2	no	—
350	D₄	—	10	4	no	—
351	D₄	—	10	2	no	—
352	D₄	—	20	2	no	—
353	D₄	C₅×C₂²⋊D₅	1	4	yes	complemented
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	5	1	no	—
357	C₂×C₄	—	5	1	no	—
358	C₂×C₄	—	5	2	no	—
359	C₂×C₄	—	5	1	no	—
360	C₂×C₄	—	10	2	no	—
361	C₂×C₄	—	20	2	no	—
362	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
364	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
365	C₅	—	2	2	no	—
366	C₅	#66163	1	1	yes	characteristic, direct product factor
367	C₅	C₅×#546	1	1	yes	characteristic, complemented
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	5	2	no	—
374	C₂²	—	10	1	no	—
375	C₂²	—	10	1	no	—
376	C₂²	—	10	2	no	—
377	C₂²	—	10	2	no	—
378	C₂²	—	10	2	no	—
379	C₂²	—	20	8	no	—
380	C₂²	C₂×C₅×C₂²⋊D₅	1	4	yes	—
381	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	2	no	—
384	C₄	—	10	1	no	—
385	C₄	—	10	1	no	—
386	C₄	—	10	2	no	—
387	C₄	—	10	1	no	—
388	C₄	C₂×C₅×C₂²⋊D₅	1	2	yes	—
389	C₂	—	2	4	no	—
390	C₂	—	4	1	no	—
391	C₂	—	10	2	no	—
392	C₂	—	20	2	no	—
393	C₂	C₅×D₅×#41	1	1	yes	characteristic
394	C₂	C₅×#4149	1	1	yes	characteristic
395	C₂	C₂²×C₅×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₂×C₅²×#41	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂×C₅×#41	D₅
hypocenter	C₅	C₅×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₅²×#41	C₂	semidirect
2. C₂×C₅×D₄×D₅	C₂	semidirect
3. C₅×#4093	C₂	semidirect
4. C₅×#4092	C₂	semidirect
5. C₅×#4085	C₂	semidirect
6. C₅×#4083	C₂	semidirect
7. C₅×D₄×Dic₅	C₂	semidirect
8. C₅×#4076	C₂	semidirect
9. C₅×#4075	C₂	semidirect
10. C₄×C₅×C₂²⋊D₅	C₂	semidirect
11. C₂×C₅×#685	C₂	semidirect
14. C₂×C₅²×Q₈	C₂²	semidirect
16. C₂×C₅²×D₄	C₂²	semidirect
17. C₂²×C₄×C₅²	C₂²	semidirect
18. C₂²×C₄×C₅²	C₂²	semidirect
21. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
22. C₂²×C₅×Dic₅	C₂²	semidirect
26. C₅×C₂²⋊Dic₅	C₂²	semidirect
27. C₅×C₂²⋊Dic₅	C₂²	semidirect
30. C₅×#685	C₂²	semidirect
31. C₅×#685	C₂²	semidirect
32. C₅×#685	C₂²	semidirect
33. C₅×C₄⋊Dic₅	C₂²	semidirect
34. C₅×#683	C₂²	semidirect
35. C₅×#683	C₂²	semidirect
36. C₄×C₅×Dic₅	C₂²	semidirect
38. #66163	C₅	direct (N × H)
48. C₅²×D₄	D₄	semidirect
65. C₂×C₅×#41	D₅	semidirect
66. C₂×C₅×#41	C₂×C₅	semidirect
68. C₂×D₄×D₅	C₂×C₅	semidirect
78. #4093	C₂×C₅	semidirect
79. #4092	C₂×C₅	semidirect
80. #4085	C₂×C₅	semidirect
81. #4083	C₂×C₅	semidirect
82. D₄×Dic₅	C₂×C₅	semidirect
83. #4076	C₂×C₅	semidirect
84. #4075	C₂×C₅	semidirect
85. C₄×C₂²⋊D₅	C₂×C₅	semidirect
86. C₂×#685	C₂×C₅	semidirect
100. C₂×C₅×D₅	#41	semidirect
114. C₂×C₅×Q₈	C₂×D₅	semidirect
115. C₂×C₅×Q₈	C₂²×C₅	semidirect
124. C₂×C₅×D₄	C₂×D₅	semidirect
126. C₂×C₅×D₄	C₂²×C₅	semidirect
131. C₂²×C₄×C₅	C₂×D₅	semidirect
132. C₂²×C₄×C₅	C₂×D₅	semidirect
133. C₂²×C₄×C₅	C₂²×C₅	semidirect
134. C₂²×C₄×C₅	C₂²×C₅	semidirect
137. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
138. C₂²×Dic₅	C₂²×C₅	semidirect
153. C₂²⋊Dic₅	C₂²×C₅	semidirect
154. C₂²⋊Dic₅	C₂²×C₅	semidirect
157. #685	C₂²×C₅	semidirect
158. #685	C₂²×C₅	semidirect
159. #685	C₂²×C₅	semidirect
160. C₄⋊Dic₅	C₂²×C₅	semidirect
161. #683	C₂²×C₅	semidirect
162. #683	C₂²×C₅	semidirect
163. C₄×Dic₅	C₂²×C₅	semidirect
199. C₅×D₄	C₂²⋊D₅	semidirect
200. C₅×D₄	C₅×D₄	semidirect
232. C₂×#41	C₅×D₅	semidirect
243. C₅²	#546	semidirect
278. C₂×D₅	C₅×#41	semidirect
298. C₂×Q₈	C₂×C₅×D₅	semidirect
305. C₂×D₄	C₂×C₅×D₅	semidirect
308. C₂²×C₄	C₂×C₅×D₅	semidirect
309. C₂²×C₄	C₂×C₅×D₅	semidirect
353. D₄	C₅×C₂²⋊D₅	semidirect
366. C₅	#66163	direct (N × H)
367. C₅	C₅×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅²×#41	2
C₂×C₅×D₄×D₅	2
C₅×#4093	2
C₅×#4092	2
C₅×#4085	2
C₅×#4083	2
C₅×D₄×Dic₅	2
C₅×#4076	2
C₅×#4075	2
C₄×C₅×C₂²⋊D₅	2
C₂×C₅×#685	2
C₅×#546	5
#66163	5

Subgroups — C5×#66163 #13106982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66163 #13106982