Subgroups — C₂×#10611017 #12964021

Order 1280.

2890 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	#10611017	C₂	1	16	yes	maximal, direct product factor
5	C₂×#65123	C₂	1	4	yes	maximal, complemented
6	C₂×D₅×C₂²⋊C₈	C₂	1	4	yes	maximal, complemented
7	C₂×C₈×D₂₀	C₂	1	4	yes	maximal, complemented
8	C₂³×D₂₀	C₄	1	1	yes	characteristic
9	C₂³×C₄×D₅	C₂²	1	2	yes	—
10	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×#685	C₄	1	2	yes	—
12	C₂²×C₄⋊Dic₅	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅	C₂²	1	8	yes	complemented
14	C₂×C₄×D₂₀	C₄	1	2	yes	—
15	C₂×C₄×D₂₀	C₄	1	2	yes	—
16	C₂×C₄×D₂₀	C₄	1	8	yes	—
17	C₂×C₄×D₂₀	C₂²	1	2	yes	—
18	C₂×C₄×D₂₀	C₂²	1	2	yes	—
19	C₂×C₄×D₂₀	C₂²	1	8	yes	—
20	C₅×#431	C₂²	1	8	yes	complemented
21	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
22	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊#168	C₂²	1	2	yes	—
25	C₂×#3952	C₂²	1	8	yes	complemented
26	#65214	C₂²	1	8	yes	complemented
27	C₂×C₄⋊#168	C₂²	1	2	yes	complemented
28	C₂×C₄×#168	C₂²	1	2	yes	complemented
29	#65123	C₂²	1	32	yes	complemented
30	D₅×C₂²⋊C₈	C₂²	1	32	yes	complemented
31	C₈×D₂₀	C₂²	1	32	yes	complemented
32	C₂×#2972	—	5	1	no	maximal, Sylow
33	C₂⁴×D₅	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂³×Dic₅	C₂×C₄	1	2	yes	—
38	C₂²×D₂₀	C₈	1	16	yes	complemented
39	C₂²×D₂₀	C₂×C₄	1	2	yes	—
40	C₂²×D₂₀	C₂×C₄	1	2	yes	—
41	C₂²×D₂₀	C₂×C₄	1	8	yes	—
42	C₂²×C₄×D₅	—	4	8	no	—
43	C₂²×C₄×D₅	C₂×C₄	1	8	yes	—
44	C₂²×C₄×D₅	C₂×C₄	1	4	yes	—
45	C₂²×C₄×D₅	C₂³	1	4	yes	—
46	C₂²×C₄×D₅	C₂³	1	8	yes	—
47	C₂²×C₅×C₈	C₂³	1	4	yes	—
48	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₅	C₂³	1	4	yes	—
54	C₂×#685	C₂×C₄	1	4	yes	—
55	C₂×#685	C₂×C₄	1	4	yes	—
56	C₂×#685	C₂×C₄	1	16	yes	—
57	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊Dic₅	C₂×C₄	1	8	yes	—
60	C₂²×#168	C₂³	1	4	yes	—
61	C₂×C₈×D₅	—	4	16	no	—
62	C₂×C₈×D₅	C₂³	1	32	yes	complemented
63	C₄×D₂₀	C₂×C₄	1	8	yes	—
64	C₄×D₂₀	C₂×C₄	1	8	yes	—
65	C₄×D₂₀	C₂×C₄	1	16	yes	—
66	C₄×D₂₀	C₂×C₄	1	16	yes	—
67	C₄×D₂₀	C₂³	1	8	yes	—
68	C₄×D₂₀	C₂³	1	8	yes	—
69	C₅×C₄⋊C₈	C₂³	1	8	yes	complemented
70	C₅×C₂²⋊C₈	C₂³	1	8	yes	—
71	C₄×C₅×C₈	C₂³	1	8	yes	complemented
72	C₂²⋊#168	C₂³	1	8	yes	—
73	#3952	C₂³	1	32	yes	complemented
74	C₄⋊#168	C₂³	1	8	yes	complemented
75	C₄×#168	C₂³	1	8	yes	complemented
76	C₂²×C₄×D₄	—	5	1	no	—
77	#2972	—	5	16	no	—
78	C₂×C₈×D₄	—	5	4	no	—
79	C₂×C₈×D₄	—	5	4	no	—
80	C₂×#431	—	5	1	no	—
81	C₂×#431	D₅	1	1	yes	characteristic, complemented
82	C₂²×C₂²⋊C₈	—	5	4	no	—
83	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂³×D₅	—	4	4	no	—
85	C₂³×D₅	—	4	4	no	—
86	C₂³×D₅	C₂×C₈	1	16	yes	complemented
87	C₂³×D₅	C₂²×C₄	1	4	yes	—
88	C₂³×D₅	C₂²×C₄	1	8	yes	—
89	C₂²×C₄×C₅	—	2	4	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	C₂×C₈	1	8	yes	complemented
92	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₅	—	4	4	no	—
103	C₂²×Dic₅	C₂²×C₄	1	4	yes	—
104	C₂²×Dic₅	C₂²×C₄	1	8	yes	—
105	C₂×D₂₀	C₂×C₈	1	16	yes	complemented
106	C₂×D₂₀	C₂×C₈	1	16	yes	complemented
107	C₂×D₂₀	C₂×C₈	1	64	yes	complemented
108	C₂×D₂₀	C₂²×C₄	1	8	yes	—
109	C₂×D₂₀	C₂²×C₄	1	8	yes	—
110	C₂×C₄×D₅	—	2	16	no	—
111	C₂×C₄×D₅	—	4	16	no	—
112	C₂×C₄×D₅	—	4	16	no	—
113	C₂×C₄×D₅	—	4	8	no	—
114	C₂×C₄×D₅	C₂²×C₄	1	8	yes	—
115	C₂×C₄×D₅	C₂²×C₄	1	16	yes	—
116	C₂×C₄×D₅	C₂⁴	1	8	yes	—
117	C₂×C₅×C₈	—	2	8	no	—
118	C₂×C₅×C₈	C₂⁴	1	8	yes	—
119	C₄²×C₅	C₂²×C₄	1	4	yes	—
120	C₄²×C₅	C₂²×C₄	1	4	yes	—
121	C₄²×C₅	C₂²×C₄	1	2	yes	—
122	C₄²×C₅	C₂²×C₄	1	2	yes	—
123	C₄²×C₅	C₂⁴	1	2	yes	—
124	C₄²×C₅	C₂⁴	1	2	yes	—
125	#685	C₂²×C₄	1	16	yes	—
126	#685	C₂²×C₄	1	16	yes	—
127	C₄⋊Dic₅	C₂²×C₄	1	8	yes	—
128	C₄⋊Dic₅	C₂²×C₄	1	8	yes	—
129	C₂×#168	—	2	8	no	—
130	C₂×#168	C₂⁴	1	8	yes	—
131	C₈×D₅	—	4	32	no	—
132	C₂³×D₄	—	5	1	no	—
133	C₂⁴×C₄	—	5	2	no	—
134	C₂³×C₈	—	5	8	no	—
135	C₂×C₄×D₄	—	5	2	no	—
136	C₂×C₄×D₄	—	5	2	no	—
137	C₂×C₄×D₄	—	5	8	no	—
138	C₂×C₄×D₄	—	5	2	no	—
139	C₂×C₄×D₄	—	5	2	no	—
140	C₂×C₄×D₄	—	5	8	no	—
141	C₂²×C₄⋊C₄	—	5	1	no	—
142	C₂²×C₂²⋊C₄	—	5	2	no	—
143	C₂²×C₄²	C₂×D₅	1	1	yes	characteristic
144	C₈×D₄	—	5	32	no	—
145	C₈×D₄	—	5	32	no	—
146	#431	—	5	8	no	—
147	#431	C₂×D₅	1	8	yes	complemented
148	C₂×C₄⋊C₈	—	5	2	no	—
149	C₂×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
150	C₂×C₂²⋊C₈	—	5	2	no	—
151	C₂×C₂²⋊C₈	—	5	8	no	—
152	C₂×C₂²⋊C₈	—	5	32	no	—
153	C₂×C₂²⋊C₈	C₂×D₅	1	2	yes	—
154	C₂×C₄×C₈	—	5	2	no	—
155	C₂×C₄×C₈	C₂×D₅	1	2	yes	complemented
156	C₂³×C₅	—	2	2	no	—
157	C₂³×C₅	—	2	2	no	—
158	C₂³×C₅	C₂²×C₈	1	4	yes	—
159	C₂³×C₅	C₂³×C₄	1	2	yes	—
160	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₂²×D₅	—	2	8	no	—
162	C₂²×D₅	—	2	8	no	—
163	C₂²×D₅	—	4	8	no	—
164	C₂²×D₅	—	4	32	no	—
165	C₂²×D₅	—	4	8	no	—
166	C₂²×D₅	C₂²×C₈	1	16	yes	—
167	C₂²×D₅	C₂²×C₈	1	32	yes	complemented
168	C₂²×D₅	C₂³×C₄	1	8	yes	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	4	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	4	4	no	—
175	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
176	C₂×C₄×C₅	C₂²×C₈	1	4	yes	—
177	C₂×C₄×C₅	C₂²×C₈	1	16	yes	complemented
178	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
181	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₅	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
185	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
186	C₂×Dic₅	—	2	8	no	—
187	C₂×Dic₅	—	4	8	no	—
188	C₂×Dic₅	C₂³×C₄	1	8	yes	—
189	D₂₀	C₂²×C₈	1	32	yes	complemented
190	D₂₀	C₂²×C₈	1	32	yes	complemented
191	C₄×D₅	—	2	16	no	—
192	C₄×D₅	—	2	16	no	—
193	C₄×D₅	—	4	16	no	—
194	C₅×C₈	—	2	8	no	—
195	#168	—	2	8	no	—
196	C₂⁵	—	5	2	no	—
197	C₂²×D₄	—	5	16	no	—
198	C₂²×D₄	—	5	2	no	—
199	C₂²×D₄	—	5	2	no	—
200	C₂²×D₄	—	5	8	no	—
201	C₂³×C₄	—	5	2	no	—
202	C₂³×C₄	—	5	4	no	—
203	C₂³×C₄	—	5	4	no	—
204	C₂³×C₄	—	5	8	no	—
205	C₂³×C₄	—	5	8	no	—
206	C₂³×C₄	—	20	8	no	—
207	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂³×C₄	C₄×D₅	1	1	yes	characteristic
209	C₂³×C₄	C₂²×D₅	1	1	yes	characteristic
210	C₂²×C₈	—	5	4	no	—
211	C₂²×C₈	—	5	32	no	—
212	C₂²×C₈	—	20	16	no	—
213	C₂²×C₈	C₂²×D₅	1	4	yes	—
214	C₄×D₄	—	5	8	no	—
215	C₄×D₄	—	5	8	no	—
216	C₄×D₄	—	5	16	no	—
217	C₄×D₄	—	5	16	no	—
218	C₄×D₄	—	5	8	no	—
219	C₄×D₄	—	5	8	no	—
220	C₂×C₄⋊C₄	—	5	2	no	—
221	C₂×C₄⋊C₄	—	5	2	no	—
222	C₂×C₄⋊C₄	—	5	8	no	—
223	C₂×C₂²⋊C₄	—	5	4	no	—
224	C₂×C₂²⋊C₄	—	5	4	no	—
225	C₂×C₂²⋊C₄	—	5	16	no	—
226	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₅	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₅	1	4	yes	—
229	C₂×C₄²	C₂²×D₅	1	4	yes	—
230	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
231	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
232	C₄⋊C₈	—	5	8	no	—
233	C₄⋊C₈	C₂²×D₅	1	8	yes	complemented
234	C₂²⋊C₈	—	5	8	no	—
235	C₂²⋊C₈	—	5	32	no	—
236	C₂²⋊C₈	C₂²×D₅	1	8	yes	—
237	C₄×C₈	—	5	8	no	—
238	C₄×C₈	C₂²×D₅	1	8	yes	complemented
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	—	2	8	no	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	#518	1	2	yes	—
243	C₂²×C₅	C₂³×C₈	1	4	yes	—
244	C₂²×C₅	C₂³×C₈	1	2	yes	—
245	C₂²×C₅	#568	1	2	yes	—
246	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
247	C₂×D₅	—	2	8	no	—
248	C₂×D₅	—	2	32	no	—
249	C₂×D₅	—	2	8	no	—
250	C₂×D₅	—	4	32	no	—
251	C₂×D₅	C₂³×C₈	1	16	yes	—
252	C₄×C₅	—	2	2	no	—
253	C₄×C₅	—	2	2	no	—
254	C₄×C₅	—	2	2	no	—
255	C₄×C₅	#518	1	2	yes	—
256	C₄×C₅	C₂³×C₈	1	4	yes	—
257	C₄×C₅	C₂³×C₈	1	4	yes	—
258	C₄×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
259	Dic₅	—	2	8	no	—
260	C₂⁴	—	5	4	no	—
261	C₂⁴	—	5	8	no	—
262	C₂⁴	—	5	16	no	—
263	C₂⁴	—	20	4	no	—
264	C₂⁴	—	20	4	no	—
265	C₂⁴	C₂×C₄×D₅	1	1	yes	characteristic
266	C₂×D₄	—	5	8	no	—
267	C₂×D₄	—	5	8	no	—
268	C₂×D₄	—	5	16	no	—
269	C₂×D₄	—	5	16	no	—
270	C₂×D₄	—	5	64	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	5	4	no	—
274	C₂²×C₄	—	5	8	no	—
275	C₂²×C₄	—	5	8	no	—
276	C₂²×C₄	—	5	8	no	—
277	C₂²×C₄	—	5	16	no	—
278	C₂²×C₄	—	10	16	no	—
279	C₂²×C₄	—	20	16	no	—
280	C₂²×C₄	—	20	16	no	—
281	C₂²×C₄	—	20	8	no	—
282	C₂²×C₄	—	20	4	no	—
283	C₂²×C₄	C₈×D₅	1	8	yes	complemented
284	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₅	1	2	yes	—
286	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₅	1	4	yes	—
289	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₅	1	4	yes	—
292	C₂²×C₄	C₂³×D₅	1	2	yes	—
293	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	—	5	8	no	—
296	C₂×C₈	—	10	8	no	—
297	C₂×C₈	—	20	32	no	—
298	C₂×C₈	C₂³×D₅	1	8	yes	—
299	C₄⋊C₄	—	5	8	no	—
300	C₄⋊C₄	—	5	8	no	—
301	C₂²⋊C₄	—	5	16	no	—
302	C₂²⋊C₄	—	5	16	no	—
303	C₄²	C₂×C₄×D₅	1	4	yes	—
304	C₄²	C₂×C₄×D₅	1	4	yes	—
305	C₄²	C₂×C₄×D₅	1	2	yes	—
306	C₄²	C₂×C₄×D₅	1	2	yes	—
307	C₄²	C₂³×D₅	1	2	yes	—
308	C₄²	C₂³×D₅	1	2	yes	—
309	C₂×C₅	—	2	4	no	—
310	C₂×C₅	#2972	1	4	yes	complemented
311	C₂×C₅	C₂×#518	1	1	yes	characteristic
312	C₂×C₅	C₂⁴×C₈	1	1	yes	characteristic
313	C₂×C₅	C₂×#568	1	1	yes	characteristic
314	D₅	—	2	16	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	5	16	no	—
318	C₂³	—	5	8	no	—
319	C₂³	—	5	32	no	—
320	C₂³	—	10	8	no	—
321	C₂³	—	10	8	no	—
322	C₂³	—	20	8	no	—
323	C₂³	—	20	32	no	—
324	C₂³	—	20	8	no	—
325	C₂³	C₂×C₈×D₅	1	4	yes	—
326	C₂³	C₂²×C₄×D₅	1	2	yes	—
327	C₂³	C₂²×C₄×D₅	1	1	yes	characteristic
328	D₄	—	5	32	no	—
329	D₄	—	5	32	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	5	8	no	—
337	C₂×C₄	—	10	8	no	—
338	C₂×C₄	—	10	16	no	—
339	C₂×C₄	—	10	16	no	—
340	C₂×C₄	—	20	16	no	—
341	C₂×C₄	—	20	8	no	—
342	C₂×C₄	C₂×C₈×D₅	1	4	yes	—
343	C₂×C₄	C₂×C₈×D₅	1	4	yes	—
344	C₂×C₄	C₂×C₈×D₅	1	16	yes	complemented
345	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
346	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
347	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
348	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
349	C₂×C₄	C₂²×C₄×D₅	1	2	yes	—
350	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
351	C₂×C₄	#4149	1	4	yes	—
352	C₂×C₄	C₂⁴×D₅	1	1	yes	characteristic
353	C₈	—	2	8	no	—
354	C₈	—	10	8	no	—
355	C₅	C₂×#2972	1	1	yes	characteristic, complemented, Sylow
356	C₂²	—	2	2	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	5	16	no	—
360	C₂²	—	10	8	no	—
361	C₂²	—	10	32	no	—
362	C₂²	—	10	8	no	—
363	C₂²	—	20	32	no	—
364	C₂²	#65855	1	2	yes	—
365	C₂²	C₂²×C₈×D₅	1	4	yes	—
366	C₂²	C₂²×C₈×D₅	1	2	yes	—
367	C₂²	#66079	1	2	yes	—
368	C₂²	C₂³×C₄×D₅	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	10	8	no	—
373	C₄	#65855	1	2	yes	—
374	C₄	C₂²×C₈×D₅	1	4	yes	—
375	C₄	C₂²×C₈×D₅	1	4	yes	—
376	C₄	C₂×#4149	1	2	yes	—
377	C₂	—	2	4	no	—
378	C₂	—	10	16	no	—
379	C₂	#10611017	1	4	yes	direct product factor
380	C₂	C₂×#65855	1	1	yes	characteristic
381	C₂	C₂³×C₈×D₅	1	1	yes	characteristic
382	C₂	C₂×#66079	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅
commutator	C₂×C₅	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₅
Fitting	C₂×C₅×#431	C₂
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂³×D₂₀	C₄
cosocle	C₂×C₄×C₅	C₂⁵
hypercenter	C₂×#431	D₅
hypocenter	C₅	C₂×#2972
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#431	C₂	semidirect
3. C₂×#65214	C₂	semidirect
4. #10611017	C₂	direct (N × H)
5. C₂×#65123	C₂	semidirect
6. C₂×D₅×C₂²⋊C₈	C₂	semidirect
7. C₂×C₈×D₂₀	C₂	semidirect
13. C₂²×C₈×D₅	C₂²	semidirect
20. C₅×#431	C₂²	semidirect
21. C₂×C₅×C₄⋊C₈	C₂²	semidirect
23. C₂×C₄×C₅×C₈	C₂²	semidirect
25. C₂×#3952	C₂²	semidirect
26. #65214	C₂²	semidirect
27. C₂×C₄⋊#168	C₂²	semidirect
28. C₂×C₄×#168	C₂²	semidirect
29. #65123	C₂²	semidirect
30. D₅×C₂²⋊C₈	C₂²	semidirect
31. C₈×D₂₀	C₂²	semidirect
38. C₂²×D₂₀	C₈	semidirect
62. C₂×C₈×D₅	C₂³	semidirect
69. C₅×C₄⋊C₈	C₂³	semidirect
71. C₄×C₅×C₈	C₂³	semidirect
73. #3952	C₂³	semidirect
74. C₄⋊#168	C₂³	semidirect
75. C₄×#168	C₂³	semidirect
81. C₂×#431	D₅	semidirect
86. C₂³×D₅	C₂×C₈	semidirect
91. C₂²×C₄×C₅	C₂×C₈	semidirect
105. C₂×D₂₀	C₂×C₈	semidirect
106. C₂×D₂₀	C₂×C₈	semidirect
107. C₂×D₂₀	C₂×C₈	semidirect
147. #431	C₂×D₅	semidirect
149. C₂×C₄⋊C₈	C₂×D₅	semidirect
155. C₂×C₄×C₈	C₂×D₅	semidirect
167. C₂²×D₅	C₂²×C₈	semidirect
177. C₂×C₄×C₅	C₂²×C₈	semidirect
189. D₂₀	C₂²×C₈	semidirect
190. D₂₀	C₂²×C₈	semidirect
233. C₄⋊C₈	C₂²×D₅	semidirect
238. C₄×C₈	C₂²×D₅	semidirect
283. C₂²×C₄	C₈×D₅	semidirect
310. C₂×C₅	#2972	semidirect
344. C₂×C₄	C₂×C₈×D₅	semidirect
355. C₅	C₂×#2972	semidirect
379. C₂	#10611017	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₂₀	2
C₂×C₅×#431	2
C₂×#65214	2
#10611017	2
C₂×#65123	2
C₂×D₅×C₂²⋊C₈	2
C₂×C₈×D₂₀	2
C₂×#2972	5

Subgroups — C2×#10611017 #12964021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10611017 #12964021