Subgroups — C₅×#65926 #13106741

Order 1600.

798 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅²×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4086	C₂	1	2	yes	maximal, complemented
6	C₅×#4085	C₂	1	2	yes	maximal, complemented
7	C₅×#4083	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4031	C₂	1	2	yes	maximal, complemented
9	C₅×#4030	C₂	1	2	yes	maximal, complemented
10	C₅×#4028	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4023	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
13	C₂³×C₅×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅²×D₄	C₂²	1	2	yes	complemented
16	C₂×C₅×C₂²⋊D₅	—	2	4	no	—
17	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
25	C₅×#711	—	2	4	no	—
26	C₂×C₅×D₂₀	C₂²	1	2	yes	complemented
27	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
29	C₅²×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₅²×C₂²⋊C₄	C₂²	1	2	yes	complemented
31	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
32	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
33	C₅×#685	C₂²	1	2	yes	complemented
34	C₅×#685	C₂²	1	2	yes	complemented
35	C₅×#683	C₂²	1	2	yes	complemented
36	C₄×C₅×Dic₅	C₂²	1	2	yes	complemented
37	C₅×#535	—	5	1	no	maximal
38	#65926	C₅	1	1	yes	maximal, characteristic, direct product factor
39	C₂³×C₅²	—	2	2	no	—
40	C₂³×C₅²	—	4	2	no	—
41	C₂³×C₅²	C₂³	1	2	yes	—
42	C₂³×C₅²	C₂³	1	1	yes	characteristic
43	C₂³×C₅²	C₂³	1	1	yes	characteristic
44	C₂²×C₅×D₅	—	2	2	no	—
45	C₂²×C₅×D₅	—	4	2	no	—
46	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×D₅	C₂³	1	2	yes	—
48	C₅²×D₄	—	2	2	no	—
49	C₅²×D₄	—	4	2	no	—
50	C₂×C₄×C₅²	C₂³	1	2	yes	—
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₅×C₂²⋊D₅	—	2	2	no	—
53	C₅×C₂²⋊D₅	—	2	2	no	—
54	C₅×C₂²⋊D₅	—	2	4	no	—
55	C₅×C₂²⋊D₅	—	2	4	no	—
56	C₅×C₂²⋊D₅	—	4	2	no	—
57	C₅×C₂²⋊D₅	—	4	2	no	—
58	C₂×C₅×Dic₅	—	2	2	no	—
59	C₂×C₅×Dic₅	D₄	1	4	yes	complemented
60	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
61	C₂×C₅×Dic₅	C₂³	1	2	yes	—
62	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
63	C₂×C₅×Dic₅	C₂³	1	1	yes	characteristic
64	C₅×D₂₀	—	4	2	no	—
65	C₄×C₅×D₅	—	2	2	no	—
66	C₅×Dic₁₀	—	2	2	no	—
67	C₂×C₅×#41	—	5	1	no	—
68	C₂²×C₅×D₄	—	5	1	no	—
69	C₂²×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#711	C₂×C₅	1	1	yes	characteristic, complemented
71	C₅×#127	—	5	2	no	—
72	C₅×#124	—	5	2	no	—
73	C₅×#121	—	5	2	no	—
74	C₅×#121	—	5	2	no	—
75	C₅×#120	—	2	2	no	—
76	C₅×#120	—	5	1	no	—
77	C₅×#120	—	5	1	no	—
78	C₅×#120	—	5	1	no	—
79	C₅×#120	D₅	1	1	yes	characteristic, complemented
80	C₅×#120	C₂×C₅	1	1	yes	characteristic, complemented
81	C₅×#117	—	5	1	no	—
82	#4099	C₂×C₅	1	1	yes	characteristic, complemented
83	#4086	C₂×C₅	1	2	yes	complemented
84	#4085	C₂×C₅	1	2	yes	complemented
85	#4083	C₂×C₅	1	1	yes	characteristic, complemented
86	#4031	C₂×C₅	1	2	yes	complemented
87	#4030	C₂×C₅	1	2	yes	complemented
88	#4028	C₂×C₅	1	1	yes	characteristic, complemented
89	#4023	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂²×C₅²	—	2	2	no	—
91	C₂²×C₅²	—	2	1	no	—
92	C₂²×C₅²	—	2	2	no	—
93	C₂²×C₅²	—	2	2	no	—
94	C₂²×C₅²	—	2	2	no	—
95	C₂²×C₅²	—	2	2	no	—
96	C₂²×C₅²	—	4	4	no	—
97	C₂²×C₅²	C₂×D₄	1	2	yes	—
98	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
99	C₂×C₅×D₅	—	2	1	no	—
100	C₂×C₅×D₅	—	2	2	no	—
101	C₂×C₅×D₅	—	2	2	no	—
102	C₂×C₅×D₅	—	2	2	no	—
103	C₂×C₅×D₅	—	2	2	no	—
104	C₂×C₅×D₅	—	4	4	no	—
105	C₄×C₅²	—	2	1	no	—
106	C₄×C₅²	—	2	2	no	—
107	C₅×Dic₅	—	2	1	no	—
108	C₅×Dic₅	—	2	2	no	—
109	C₅×Dic₅	C₂×D₄	1	2	yes	—
110	C₅×Dic₅	C₂×D₄	1	2	yes	—
111	C₂⁴×C₅	—	2	2	no	—
112	C₂⁴×C₅	—	5	1	no	—
113	C₂⁴×C₅	C₂×D₅	1	1	yes	characteristic
114	C₂⁴×C₅	C₂²×C₅	1	1	yes	characteristic
115	C₂³×D₅	C₂²×C₅	1	1	yes	characteristic
116	C₅×#41	—	10	4	no	—
117	C₂×C₅×Q₈	—	5	1	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	4	no	—
120	C₂×C₅×D₄	—	5	1	no	—
121	C₂×C₅×D₄	—	5	2	no	—
122	C₂×C₅×D₄	—	5	2	no	—
123	C₂×C₅×D₄	—	5	1	no	—
124	C₂×C₅×D₄	—	5	2	no	—
125	C₂×C₅×D₄	—	5	2	no	—
126	C₂×C₅×D₄	—	5	2	no	—
127	C₂×C₅×D₄	—	10	4	no	—
128	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
129	C₂×C₅×D₄	C₂×D₅	1	2	yes	complemented
130	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂²×C₅	1	2	yes	complemented
132	C₂²×C₄×C₅	—	5	1	no	—
133	C₂²×C₄×C₅	—	5	1	no	—
134	C₂²×C₄×C₅	—	5	1	no	—
135	C₂×C₂²⋊D₅	—	2	4	no	—
136	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	—
138	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	—
139	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
141	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
142	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic
143	C₂²×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
144	#711	—	2	4	no	—
145	C₂×D₂₀	C₂²×C₅	1	2	yes	complemented
146	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
147	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₅×C₄⋊C₄	—	5	2	no	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	4	no	—
151	C₅×C₂²⋊C₄	—	5	1	no	—
152	C₅×C₂²⋊C₄	—	5	2	no	—
153	C₅×C₂²⋊C₄	—	5	2	no	—
154	C₅×C₂²⋊C₄	—	5	2	no	—
155	C₅×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
156	C₅×C₂²⋊C₄	C₂×D₅	1	2	yes	complemented
157	C₅×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
159	C₄²×C₅	—	5	2	no	—
160	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic
161	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
162	#685	C₂²×C₅	1	2	yes	complemented
163	#685	C₂²×C₅	1	2	yes	complemented
164	#683	C₂²×C₅	1	2	yes	complemented
165	C₄×Dic₅	C₂²×C₅	1	2	yes	complemented
166	#535	—	5	1	no	Sylow
167	C₂×C₅²	—	2	2	no	—
168	C₂×C₅²	—	4	2	no	—
169	C₂×C₅²	—	4	1	no	—
170	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₅²	H(5,𝔽₂)	1	2	yes	—
172	C₅×D₅	—	4	1	no	—
173	C₅×D₅	—	4	2	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	—	2	2	no	—
178	C₂³×C₅	—	2	2	no	—
179	C₂³×C₅	—	4	4	no	—
180	C₂³×C₅	—	4	2	no	—
181	C₂³×C₅	—	4	2	no	—
182	C₂³×C₅	—	4	8	no	—
183	C₂³×C₅	—	5	2	no	—
184	C₂³×C₅	—	5	1	no	—
185	C₂³×C₅	—	10	2	no	—
186	C₂³×C₅	—	20	2	no	—
187	C₂³×C₅	C₂²×D₅	1	2	yes	—
188	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
189	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
190	C₂³×C₅	C₂³×C₅	1	2	yes	—
191	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
192	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
193	C₂²×D₅	—	2	2	no	—
194	C₂²×D₅	—	4	2	no	—
195	C₂²×D₅	C₂³×C₅	1	2	yes	—
196	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
197	C₅×Q₈	—	10	2	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	2	no	—
200	C₅×D₄	—	4	4	no	—
201	C₅×D₄	—	4	2	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	8	no	—
204	C₅×D₄	—	10	4	no	—
205	C₅×D₄	—	10	4	no	—
206	C₅×D₄	—	10	2	no	—
207	C₅×D₄	—	10	2	no	—
208	C₅×D₄	—	20	2	no	—
209	C₅×D₄	—	20	2	no	—
210	C₅×D₄	—	20	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	5	4	no	—
214	C₂×C₄×C₅	—	5	1	no	—
215	C₂×C₄×C₅	—	5	1	no	—
216	C₂×C₄×C₅	—	5	2	no	—
217	C₂×C₄×C₅	—	5	1	no	—
218	C₂×C₄×C₅	—	10	2	no	—
219	C₂×C₄×C₅	—	10	2	no	—
220	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
221	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂³×C₅	1	2	yes	—
223	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
224	C₂²⋊D₅	—	2	2	no	—
225	C₂²⋊D₅	—	2	2	no	—
226	C₂²⋊D₅	—	2	4	no	—
227	C₂²⋊D₅	—	2	4	no	—
228	C₂²⋊D₅	—	4	2	no	—
229	C₂²⋊D₅	—	4	2	no	—
230	C₂×Dic₅	—	2	2	no	—
231	C₂×Dic₅	C₅×D₄	1	4	yes	complemented
232	C₂×Dic₅	C₂³×C₅	1	2	yes	—
233	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
234	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
235	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
236	D₂₀	—	4	2	no	—
237	C₄×D₅	—	2	2	no	—
238	Dic₁₀	—	2	2	no	—
239	C₂×#41	—	5	1	no	—
240	C₂²×D₄	—	5	1	no	—
241	#127	—	5	2	no	—
242	#124	—	5	2	no	—
243	#121	—	5	2	no	—
244	#121	—	5	2	no	—
245	#120	—	5	1	no	—
246	#120	—	5	1	no	—
247	#120	—	5	1	no	—
248	#120	C₅×D₅	1	1	yes	characteristic, complemented
249	#117	—	5	1	no	—
250	C₅²	#535	1	1	yes	characteristic, complemented, Sylow
251	C₂²×C₅	—	2	2	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	2	8	no	—
254	C₂²×C₅	—	2	1	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	—	4	4	no	—
269	C₂²×C₅	—	4	2	no	—
270	C₂²×C₅	—	4	4	no	—
271	C₂²×C₅	—	4	4	no	—
272	C₂²×C₅	—	4	4	no	—
273	C₂²×C₅	—	4	16	no	—
274	C₂²×C₅	—	10	1	no	—
275	C₂²×C₅	—	10	2	no	—
276	C₂²×C₅	—	10	2	no	—
277	C₂²×C₅	—	10	2	no	—
278	C₂²×C₅	—	10	2	no	—
279	C₂²×C₅	—	20	4	no	—
280	C₂²×C₅	D₄×D₅	1	2	yes	—
281	C₂²×C₅	C₂×C₅×D₄	1	2	yes	—
282	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
283	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
284	C₂×D₅	—	2	1	no	—
285	C₂×D₅	—	2	2	no	—
286	C₂×D₅	—	2	2	no	—
287	C₂×D₅	—	2	2	no	—
288	C₂×D₅	—	2	2	no	—
289	C₂×D₅	—	4	4	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	4	no	—
296	C₄×C₅	—	5	2	no	—
297	C₄×C₅	—	5	2	no	—
298	C₄×C₅	—	10	1	no	—
299	C₄×C₅	—	10	2	no	—
300	Dic₅	—	2	1	no	—
301	Dic₅	—	2	2	no	—
302	Dic₅	C₂×C₅×D₄	1	2	yes	—
303	Dic₅	C₂×C₅×D₄	1	2	yes	—
304	C₂⁴	—	5	1	no	—
305	C₂⁴	C₂×C₅×D₅	1	1	yes	characteristic
306	#41	—	10	4	no	—
307	C₂×Q₈	—	5	1	no	—
308	C₂×D₄	—	5	1	no	—
309	C₂×D₄	—	5	2	no	—
310	C₂×D₄	—	5	2	no	—
311	C₂×D₄	—	5	1	no	—
312	C₂×D₄	—	5	2	no	—
313	C₂×D₄	—	5	2	no	—
314	C₂×D₄	—	5	2	no	—
315	C₂×D₄	—	10	4	no	—
316	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
317	C₂×D₄	C₂×C₅×D₅	1	2	yes	complemented
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₄⋊C₄	—	5	2	no	—
322	C₂²⋊C₄	—	5	1	no	—
323	C₂²⋊C₄	—	5	2	no	—
324	C₂²⋊C₄	—	5	2	no	—
325	C₂²⋊C₄	—	5	2	no	—
326	C₂²⋊C₄	C₂×C₅×D₅	1	1	yes	characteristic
327	C₂²⋊C₄	C₂×C₅×D₅	1	2	yes	complemented
328	C₄²	—	5	2	no	—
329	C₂×C₅	—	2	2	no	—
330	C₂×C₅	—	2	2	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	2	4	no	—
333	C₂×C₅	—	4	4	no	—
334	C₂×C₅	—	4	8	no	—
335	C₂×C₅	—	4	1	no	—
336	C₂×C₅	—	4	2	no	—
337	C₂×C₅	—	4	1	no	—
338	C₂×C₅	—	4	2	no	—
339	C₂×C₅	—	8	2	no	—
340	C₂×C₅	—	20	2	no	—
341	C₂×C₅	—	20	1	no	—
342	C₂×C₅	C₂×D₄×D₅	1	1	yes	characteristic
343	C₂×C₅	#4144	1	2	yes	—
344	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
345	C₂×C₅	C₅×H(5,𝔽₂)	1	2	yes	—
346	D₅	—	4	2	no	—
347	D₅	—	4	1	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	5	2	no	—
351	C₂³	—	5	1	no	—
352	C₂³	—	10	2	no	—
353	C₂³	—	20	2	no	—
354	C₂³	C₂²×C₅×D₅	1	2	yes	—
355	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
356	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
357	Q₈	—	10	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	10	4	no	—
361	D₄	—	10	4	no	—
362	D₄	—	10	2	no	—
363	D₄	—	10	2	no	—
364	D₄	—	20	2	no	—
365	D₄	—	20	2	no	—
366	D₄	—	20	2	no	—
367	C₂×C₄	—	5	4	no	—
368	C₂×C₄	—	5	1	no	—
369	C₂×C₄	—	5	1	no	—
370	C₂×C₄	—	5	2	no	—
371	C₂×C₄	—	5	1	no	—
372	C₂×C₄	—	10	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	C₂²×C₅×D₅	1	2	yes	—
375	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
376	C₅	—	2	2	no	—
377	C₅	#65926	1	1	yes	characteristic, direct product factor
378	C₅	C₅×#535	1	1	yes	characteristic, complemented
379	C₂²	—	2	2	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	10	1	no	—
387	C₂²	—	10	2	no	—
388	C₂²	—	10	2	no	—
389	C₂²	—	10	2	no	—
390	C₂²	—	10	2	no	—
391	C₂²	—	20	4	no	—
392	C₂²	C₅×D₄×D₅	1	2	yes	—
393	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	5	2	no	—
397	C₄	—	5	2	no	—
398	C₄	—	10	1	no	—
399	C₄	—	10	2	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	4	1	no	—
403	C₂	—	20	2	no	—
404	C₂	—	20	1	no	—
405	C₂	C₂×C₅×D₄×D₅	1	1	yes	characteristic
406	C₂	C₅×#4144	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₅
Fitting	C₅²×#120	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₅×#120	D₅
hypocenter	C₅	C₅×#535
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₂²⋊D₅	C₂	semidirect
2. C₂×C₅×#711	C₂	semidirect
3. C₅²×#120	C₂	semidirect
4. C₅×#4099	C₂	semidirect
5. C₅×#4086	C₂	semidirect
6. C₅×#4085	C₂	semidirect
7. C₅×#4083	C₂	semidirect
8. C₅×#4031	C₂	semidirect
9. C₅×#4030	C₂	semidirect
10. C₅×#4028	C₂	semidirect
11. C₅×#4023	C₂	semidirect
15. C₂×C₅²×D₄	C₂²	semidirect
20. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
22. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
24. C₂²×C₅×Dic₅	C₂²	semidirect
26. C₂×C₅×D₂₀	C₂²	semidirect
27. C₂×C₄×C₅×D₅	C₂²	semidirect
28. C₂×C₅×Dic₁₀	C₂²	semidirect
30. C₅²×C₂²⋊C₄	C₂²	semidirect
32. C₅×C₂²⋊Dic₅	C₂²	semidirect
33. C₅×#685	C₂²	semidirect
34. C₅×#685	C₂²	semidirect
35. C₅×#683	C₂²	semidirect
36. C₄×C₅×Dic₅	C₂²	semidirect
38. #65926	C₅	direct (N × H)
59. C₂×C₅×Dic₅	D₄	semidirect
69. C₂²×C₂²⋊D₅	C₂×C₅	semidirect
70. C₂×#711	C₂×C₅	semidirect
79. C₅×#120	D₅	semidirect
80. C₅×#120	C₂×C₅	semidirect
82. #4099	C₂×C₅	semidirect
83. #4086	C₂×C₅	semidirect
84. #4085	C₂×C₅	semidirect
85. #4083	C₂×C₅	semidirect
86. #4031	C₂×C₅	semidirect
87. #4030	C₂×C₅	semidirect
88. #4028	C₂×C₅	semidirect
89. #4023	C₂×C₅	semidirect
129. C₂×C₅×D₄	C₂×D₅	semidirect
131. C₂×C₅×D₄	C₂²×C₅	semidirect
139. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
140. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
141. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
143. C₂²×Dic₅	C₂²×C₅	semidirect
145. C₂×D₂₀	C₂²×C₅	semidirect
146. C₂×C₄×D₅	C₂²×C₅	semidirect
147. C₂×Dic₁₀	C₂²×C₅	semidirect
156. C₅×C₂²⋊C₄	C₂×D₅	semidirect
158. C₅×C₂²⋊C₄	C₂²×C₅	semidirect
161. C₂²⋊Dic₅	C₂²×C₅	semidirect
162. #685	C₂²×C₅	semidirect
163. #685	C₂²×C₅	semidirect
164. #683	C₂²×C₅	semidirect
165. C₄×Dic₅	C₂²×C₅	semidirect
231. C₂×Dic₅	C₅×D₄	semidirect
248. #120	C₅×D₅	semidirect
250. C₅²	#535	semidirect
317. C₂×D₄	C₂×C₅×D₅	semidirect
327. C₂²⋊C₄	C₂×C₅×D₅	semidirect
377. C₅	#65926	direct (N × H)
378. C₅	C₅×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₂²⋊D₅	2
C₂×C₅×#711	2
C₅²×#120	2
C₅×#4099	2
C₅×#4086	2
C₅×#4085	2
C₅×#4083	2
C₅×#4031	2
C₅×#4030	2
C₅×#4028	2
C₅×#4023	2
C₅×#535	5
#65926	5

Subgroups — C5×#65926 #13106741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#65926 #13106741