Subgroups — C₅×#66140 #13106960

Order 1600.

904 conjugacy classes of subgroups.

The subgroup lattice has 403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4099	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×C₂²⋊Dic₅	C₂	1	2	yes	maximal, complemented
5	C₅×#4085	C₂	1	2	yes	maximal, complemented
6	C₅×#4084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4082	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4081	C₂	1	2	yes	maximal, complemented
9	C₅×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4070	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₅²	C₂²	1	2	yes	—
13	C₂×C₅²×D₄	—	2	4	no	—
14	C₂×C₅²×D₄	C₂²	1	2	yes	—
15	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅²×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊D₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
20	C₂×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₂²×C₅×Dic₅	C₂²	1	2	yes	complemented
22	C₂²×C₅×Dic₅	C₂²	1	2	yes	complemented
23	C₅×#711	—	2	4	no	—
24	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
26	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	—
27	C₅×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
28	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
29	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
30	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
31	C₅×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
32	C₅×#685	C₂²	1	1	yes	characteristic, complemented
33	C₅×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
34	C₅×#683	C₂²	1	2	yes	complemented
35	C₅×#683	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₅×#546	—	5	1	no	maximal
38	#66140	C₅	1	1	yes	maximal, characteristic, direct product factor
39	C₂³×C₅²	—	2	4	no	—
40	C₂³×C₅²	—	2	4	no	—
41	C₂³×C₅²	—	4	2	no	—
42	C₂³×C₅²	C₂³	1	2	yes	—
43	C₂³×C₅²	C₂³	1	2	yes	—
44	C₂³×C₅²	C₂³	1	1	yes	characteristic
45	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
46	C₅²×D₄	—	2	4	no	—
47	C₅²×D₄	—	2	2	no	—
48	C₅²×D₄	D₄	1	4	yes	complemented
49	C₂×C₄×C₅²	—	2	2	no	—
50	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
51	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
52	C₅×C₂²⋊D₅	—	2	4	no	—
53	C₅×C₂²⋊D₅	—	2	2	no	—
54	C₅×C₂²⋊D₅	—	4	2	no	—
55	C₂×C₅×Dic₅	—	2	4	no	—
56	C₂×C₅×Dic₅	—	4	2	no	—
57	C₂×C₅×Dic₅	C₂³	1	2	yes	—
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	C₄×C₅×D₅	—	2	2	no	—
63	C₅×Dic₁₀	—	2	2	no	—
64	C₂×C₅×#41	—	5	1	no	—
65	C₂²×C₅×D₄	—	2	2	no	—
66	C₂²×C₅×D₄	D₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×D₄	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#711	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	1	no	—
73	C₅×#121	—	5	2	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	#4099	C₂×C₅	1	2	yes	complemented
79	C₂×C₂²⋊Dic₅	C₂×C₅	1	2	yes	complemented
80	#4085	C₂×C₅	1	2	yes	complemented
81	#4084	C₂×C₅	1	1	yes	characteristic, complemented
82	#4082	C₂×C₅	1	1	yes	characteristic, complemented
83	#4081	C₂×C₅	1	2	yes	complemented
84	D₄×Dic₅	C₂×C₅	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
86	#4070	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂²×C₅²	—	2	1	no	—
88	C₂²×C₅²	—	2	2	no	—
89	C₂²×C₅²	—	2	1	no	—
90	C₂²×C₅²	—	2	2	no	—
91	C₂²×C₅²	—	2	2	no	—
92	C₂²×C₅²	—	2	2	no	—
93	C₂²×C₅²	—	2	2	no	—
94	C₂²×C₅²	—	4	8	no	—
95	C₂²×C₅²	C₂×D₄	1	4	yes	—
96	C₂²×C₅²	#41	1	2	yes	complemented
97	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
98	C₂×C₅×D₅	—	2	1	no	—
99	C₂×C₅×D₅	—	2	1	no	—
100	C₂×C₅×D₅	—	2	1	no	—
101	C₄×C₅²	—	2	1	no	—
102	C₄×C₅²	C₂×D₄	1	2	yes	—
103	C₅×Dic₅	—	2	2	no	—
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	—	2	4	no	—
109	C₂⁴×C₅	C₂×D₅	1	2	yes	—
110	C₂⁴×C₅	C₂²×C₅	1	2	yes	—
111	C₅×#41	—	10	4	no	—
112	C₂×C₅×Q₈	—	5	1	no	—
113	C₂×C₅×D₄	—	2	16	no	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	—	2	4	no	—
116	C₂×C₅×D₄	—	2	4	no	—
117	C₂×C₅×D₄	—	2	2	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	5	1	no	—
120	C₂×C₅×D₄	—	5	2	no	—
121	C₂×C₅×D₄	—	5	2	no	—
122	C₂×C₅×D₄	C₂×D₅	1	2	yes	—
123	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
124	C₂×C₅×D₄	C₂×D₅	1	1	yes	characteristic
125	C₂×C₅×D₄	C₂²×C₅	1	2	yes	—
126	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₅×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	5	2	no	—
130	C₂²×C₄×C₅	—	5	2	no	—
131	C₂²×C₄×C₅	—	5	1	no	—
132	C₂²×C₄×C₅	C₂×D₅	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₂²⋊D₅	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
136	C₂×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
137	C₂²×Dic₅	C₂²×C₅	1	2	yes	complemented
138	C₂²×Dic₅	C₂²×C₅	1	2	yes	complemented
139	#711	—	2	4	no	—
140	C₂×C₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
141	C₂×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
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	1	no	—
146	C₅×C₂²⋊C₄	—	5	2	no	—
147	C₅×C₂²⋊C₄	—	5	2	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	1	no	—
152	C₄²×C₅	—	5	1	no	—
153	C₂²⋊Dic₅	C₂²×C₅	1	1	yes	characteristic
154	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	—
155	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
156	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
157	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
158	C₂²⋊Dic₅	C₂²×C₅	1	2	yes	complemented
159	#685	C₂²×C₅	1	1	yes	characteristic, complemented
160	C₄⋊Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
161	#683	C₂²×C₅	1	2	yes	complemented
162	#683	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₄×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
164	#546	—	5	1	no	Sylow
165	C₂×C₅²	—	2	2	no	—
166	C₂×C₅²	—	2	4	no	—
167	C₂×C₅²	—	4	2	no	—
168	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₅²	C₂×#41	1	1	yes	characteristic
170	C₂×C₅²	H(5,𝔽₂)	1	1	yes	characteristic
171	C₅×D₅	—	4	1	no	—
172	C₂³×C₅	—	2	16	no	—
173	C₂³×C₅	—	2	4	no	—
174	C₂³×C₅	—	2	4	no	—
175	C₂³×C₅	—	2	4	no	—
176	C₂³×C₅	—	2	4	no	—
177	C₂³×C₅	—	2	2	no	—
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	4	no	—
180	C₂³×C₅	—	4	8	no	—
181	C₂³×C₅	—	4	2	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	—	4	8	no	—
184	C₂³×C₅	—	5	1	no	—
185	C₂³×C₅	C₂²×D₅	1	2	yes	—
186	C₂³×C₅	C₂²×D₅	1	1	yes	characteristic
187	C₂³×C₅	C₂²×D₅	1	2	yes	—
188	C₂³×C₅	C₂³×C₅	1	2	yes	—
189	C₂³×C₅	C₂³×C₅	1	2	yes	—
190	C₂³×C₅	C₂³×C₅	1	1	yes	characteristic
191	C₂²×D₅	C₂³×C₅	1	1	yes	characteristic
192	C₅×Q₈	—	10	2	no	—
193	C₅×D₄	—	2	16	no	—
194	C₅×D₄	—	2	8	no	—
195	C₅×D₄	—	2	4	no	—
196	C₅×D₄	—	2	4	no	—
197	C₅×D₄	—	2	2	no	—
198	C₅×D₄	—	2	2	no	—
199	C₅×D₄	—	2	8	no	—
200	C₅×D₄	—	10	2	no	—
201	C₅×D₄	—	10	4	no	—
202	C₅×D₄	—	20	2	no	—
203	C₅×D₄	C₂²⋊D₅	1	4	yes	complemented
204	C₅×D₄	C₅×D₄	1	4	yes	complemented
205	C₂×C₄×C₅	—	2	8	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	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	—	5	2	no	—
215	C₂×C₄×C₅	—	10	4	no	—
216	C₂×C₄×C₅	—	10	2	no	—
217	C₂×C₄×C₅	—	20	2	no	—
218	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
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	—	2	4	no	—
226	C₂×Dic₅	—	4	2	no	—
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	C₂×Dic₅	C₂³×C₅	1	2	yes	—
231	C₂×Dic₅	C₂³×C₅	1	1	yes	characteristic
232	C₄×D₅	—	2	2	no	—
233	Dic₁₀	—	2	2	no	—
234	C₂×#41	—	5	1	no	—
235	C₂²×D₄	C₅×D₅	1	1	yes	characteristic, complemented
236	#124	—	5	1	no	—
237	#123	—	5	2	no	—
238	C₂²⋊Q₈	—	5	1	no	—
239	#121	—	5	1	no	—
240	#121	—	5	2	no	—
241	#120	—	5	2	no	—
242	C₄×D₄	—	5	1	no	—
243	C₄×D₄	—	5	1	no	—
244	C₂×C₂²⋊C₄	—	5	2	no	—
245	C₅²	#546	1	1	yes	characteristic, complemented, Sylow
246	C₂²×C₅	—	2	4	no	—
247	C₂²×C₅	—	2	4	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	2	2	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	1	no	—
256	C₂²×C₅	—	2	8	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	2	2	no	—
259	C₂²×C₅	—	2	2	no	—
260	C₂²×C₅	—	2	2	no	—
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	4	no	—
264	C₂²×C₅	—	2	8	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	4	no	—
270	C₂²×C₅	—	4	8	no	—
271	C₂²×C₅	—	4	8	no	—
272	C₂²×C₅	—	4	32	no	—
273	C₂²×C₅	—	10	1	no	—
274	C₂²×C₅	—	10	1	no	—
275	C₂²×C₅	—	10	1	no	—
276	C₂²×C₅	#711	1	2	yes	complemented
277	C₂²×C₅	C₂×C₂²⋊D₅	1	4	yes	—
278	C₂²×C₅	C₂×C₅×D₄	1	4	yes	—
279	C₂²×C₅	C₅×#41	1	2	yes	complemented
280	C₂²×C₅	C₂³×D₅	1	1	yes	characteristic
281	C₂²×C₅	C₂⁴×C₅	1	1	yes	characteristic
282	C₂×D₅	—	2	1	no	—
283	C₂×D₅	—	2	1	no	—
284	C₂×D₅	—	2	1	no	—
285	C₄×C₅	—	2	4	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	4	no	—
289	C₄×C₅	—	10	1	no	—
290	C₄×C₅	—	10	1	no	—
291	C₄×C₅	—	10	2	no	—
292	C₄×C₅	—	10	1	no	—
293	C₄×C₅	—	10	2	no	—
294	C₄×C₅	C₂×C₂²⋊D₅	1	2	yes	—
295	C₄×C₅	C₂×C₅×D₄	1	2	yes	—
296	Dic₅	—	2	2	no	—
297	Dic₅	—	2	1	no	—
298	Dic₅	—	2	1	no	—
299	Dic₅	—	2	1	no	—
300	Dic₅	—	2	2	no	—
301	C₂⁴	C₂×C₅×D₅	1	2	yes	—
302	#41	—	10	4	no	—
303	C₂×Q₈	—	5	1	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	5	1	no	—
306	C₂×D₄	—	5	2	no	—
307	C₂×D₄	—	5	2	no	—
308	C₂×D₄	C₂×C₅×D₅	1	2	yes	—
309	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
310	C₂×D₄	C₂×C₅×D₅	1	1	yes	characteristic
311	C₂²×C₄	—	5	2	no	—
312	C₂²×C₄	—	5	2	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	C₂×C₅×D₅	1	1	yes	characteristic
315	C₄⋊C₄	—	5	1	no	—
316	C₄⋊C₄	—	5	1	no	—
317	C₄⋊C₄	—	5	2	no	—
318	C₂²⋊C₄	—	5	1	no	—
319	C₂²⋊C₄	—	5	2	no	—
320	C₂²⋊C₄	—	5	2	no	—
321	C₂²⋊C₄	—	5	2	no	—
322	C₂²⋊C₄	—	5	2	no	—
323	C₂²⋊C₄	—	5	2	no	—
324	C₂²⋊C₄	—	5	1	no	—
325	C₄²	—	5	1	no	—
326	C₂×C₅	—	2	8	no	—
327	C₂×C₅	—	2	2	no	—
328	C₂×C₅	—	2	4	no	—
329	C₂×C₅	—	2	2	no	—
330	C₂×C₅	—	2	4	no	—
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	2	2	no	—
333	C₂×C₅	—	2	2	no	—
334	C₂×C₅	—	4	8	no	—
335	C₂×C₅	—	4	8	no	—
336	C₂×C₅	—	4	2	no	—
337	C₂×C₅	—	4	2	no	—
338	C₂×C₅	—	20	1	no	—
339	C₂×C₅	C₂×#711	1	1	yes	characteristic
340	C₂×C₅	#4144	1	1	yes	characteristic
341	C₂×C₅	C₂²×C₂²⋊D₅	1	1	yes	characteristic
342	C₂×C₅	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₂×C₅	C₂×C₅×#41	1	1	yes	characteristic
344	C₂×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic
345	D₅	—	4	1	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	5	1	no	—
350	C₂³	C₂²×C₅×D₅	1	2	yes	—
351	C₂³	C₂²×C₅×D₅	1	1	yes	characteristic
352	C₂³	C₂²×C₅×D₅	1	2	yes	—
353	Q₈	—	10	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	2	2	no	—
356	D₄	—	10	2	no	—
357	D₄	—	10	4	no	—
358	D₄	—	20	2	no	—
359	D₄	C₅×C₂²⋊D₅	1	4	yes	complemented
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	5	1	no	—
362	C₂×C₄	—	5	1	no	—
363	C₂×C₄	—	5	2	no	—
364	C₂×C₄	—	5	1	no	—
365	C₂×C₄	—	5	2	no	—
366	C₂×C₄	—	10	4	no	—
367	C₂×C₄	—	10	2	no	—
368	C₂×C₄	—	20	2	no	—
369	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
371	C₅	—	2	2	no	—
372	C₅	#66140	1	1	yes	characteristic, direct product factor
373	C₅	C₅×#546	1	1	yes	characteristic, complemented
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	8	no	—
382	C₂²	—	10	1	no	—
383	C₂²	—	10	1	no	—
384	C₂²	—	10	1	no	—
385	C₂²	C₅×#711	1	2	yes	complemented
386	C₂²	C₂×C₅×C₂²⋊D₅	1	4	yes	—
387	C₂²	C₂³×C₅×D₅	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	10	1	no	—
390	C₄	—	10	1	no	—
391	C₄	—	10	2	no	—
392	C₄	—	10	1	no	—
393	C₄	—	10	2	no	—
394	C₄	C₂×C₅×C₂²⋊D₅	1	2	yes	—
395	C₂	—	2	2	no	—
396	C₂	—	2	4	no	—
397	C₂	—	4	2	no	—
398	C₂	—	20	1	no	—
399	C₂	C₂×C₅×#711	1	1	yes	characteristic
400	C₂	C₅×#4144	1	1	yes	characteristic
401	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	C₂²×C₅²×D₄	C₂
socle	C₂²×C₅²	C₂⁴
hypercenter	C₂²×C₅×D₄	D₅
hypocenter	C₅	C₅×#546
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅²×D₄	C₂	semidirect
2. C₂×C₅×#711	C₂	semidirect
3. C₅×#4099	C₂	semidirect
4. C₂×C₅×C₂²⋊Dic₅	C₂	semidirect
5. C₅×#4085	C₂	semidirect
6. C₅×#4084	C₂	semidirect
7. C₅×#4082	C₂	semidirect
8. C₅×#4081	C₂	semidirect
9. C₅×D₄×Dic₅	C₂	semidirect
10. C₄×C₅×C₂²⋊D₅	C₂	semidirect
11. C₅×#4070	C₂	semidirect
19. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
20. C₂×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₂²×C₅×Dic₅	C₂²	semidirect
22. C₂²×C₅×Dic₅	C₂²	semidirect
24. C₂×C₄×C₅×D₅	C₂²	semidirect
25. C₂×C₅×Dic₁₀	C₂²	semidirect
28. C₅×C₂²⋊Dic₅	C₂²	semidirect
29. C₅×C₂²⋊Dic₅	C₂²	semidirect
30. C₅×C₂²⋊Dic₅	C₂²	semidirect
31. C₅×C₂²⋊Dic₅	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. #66140	C₅	direct (N × H)
48. C₅²×D₄	D₄	semidirect
66. C₂²×C₅×D₄	D₅	semidirect
67. C₂²×C₅×D₄	C₂×C₅	semidirect
68. C₂×#711	C₂×C₅	semidirect
78. #4099	C₂×C₅	semidirect
79. C₂×C₂²⋊Dic₅	C₂×C₅	semidirect
80. #4085	C₂×C₅	semidirect
81. #4084	C₂×C₅	semidirect
82. #4082	C₂×C₅	semidirect
83. #4081	C₂×C₅	semidirect
84. D₄×Dic₅	C₂×C₅	semidirect
85. C₄×C₂²⋊D₅	C₂×C₅	semidirect
86. #4070	C₂×C₅	semidirect
96. C₂²×C₅²	#41	semidirect
135. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
136. C₂×C₂²⋊D₅	C₂²×C₅	semidirect
137. C₂²×Dic₅	C₂²×C₅	semidirect
138. C₂²×Dic₅	C₂²×C₅	semidirect
140. C₂×C₄×D₅	C₂²×C₅	semidirect
141. C₂×Dic₁₀	C₂²×C₅	semidirect
155. C₂²⋊Dic₅	C₂²×C₅	semidirect
156. C₂²⋊Dic₅	C₂²×C₅	semidirect
157. C₂²⋊Dic₅	C₂²×C₅	semidirect
158. C₂²⋊Dic₅	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
203. C₅×D₄	C₂²⋊D₅	semidirect
204. C₅×D₄	C₅×D₄	semidirect
235. C₂²×D₄	C₅×D₅	semidirect
245. C₅²	#546	semidirect
276. C₂²×C₅	#711	semidirect
279. C₂²×C₅	C₅×#41	semidirect
359. D₄	C₅×C₂²⋊D₅	semidirect
372. C₅	#66140	direct (N × H)
373. C₅	C₅×#546	semidirect
385. C₂²	C₅×#711	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅²×D₄	2
C₂×C₅×#711	2
C₅×#4099	2
C₂×C₅×C₂²⋊Dic₅	2
C₅×#4085	2
C₅×#4084	2
C₅×#4082	2
C₅×#4081	2
C₅×D₄×Dic₅	2
C₄×C₅×C₂²⋊D₅	2
C₅×#4070	2
C₅×#546	5
#66140	5

Subgroups — C5×#66140 #13106960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#66140 #13106960