Subgroups — C₅×#21981 #11944701

Order 1280.

966 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
2	C₅×#2285	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#384	C₂	1	1	yes	maximal, characteristic
4	C₅×#1948	C₂	1	4	yes	maximal, complemented
5	C₅×#1853	C₂	1	4	yes	maximal
6	C₅×#1844	C₂	1	2	yes	maximal, complemented
7	C₅×#1834	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#117	—	2	1	no	—
9	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₅×#431	C₄	1	8	yes	complemented
14	C₂×C₅×#106	C₂²	1	8	yes	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
18	C₅×#384	—	2	1	no	—
19	C₅×#384	—	2	1	no	—
20	C₅×#384	C₂²	1	2	yes	—
21	C₅×#384	C₂²	1	2	yes	—
22	C₅×#384	C₂²	1	1	yes	characteristic
23	C₅×#384	C₂²	1	1	yes	characteristic
24	C₅×#382	—	2	1	no	—
25	C₅×#380	—	2	1	no	—
26	C₅×#380	C₂²	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	—	2	1	no	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₅×#340	C₂²	1	8	yes	—
30	#21981	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂³×C₄×C₅	—	2	2	no	—
32	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂²×C₅×C₈	C₂³	1	4	yes	—
36	C₅×#117	—	4	4	no	—
37	C₂×C₅×C₄⋊C₄	—	2	1	no	—
38	C₂×C₅×C₄⋊C₄	—	2	1	no	—
39	C₂×C₅×C₄⋊C₄	—	2	1	no	—
40	C₂×C₅×C₄⋊C₄	—	2	1	no	—
41	C₂×C₅×C₄⋊C₄	—	2	2	no	—
42	C₂×C₅×C₄⋊C₄	—	2	2	no	—
43	C₂×C₅×C₄⋊C₄	—	2	2	no	—
44	C₂×C₅×C₄⋊C₄	—	2	2	no	—
45	C₂×C₅×C₄⋊C₄	—	2	2	no	—
46	C₂×C₅×C₄⋊C₄	—	4	4	no	—
47	C₂×C₅×C₄⋊C₄	—	4	4	no	—
48	C₂×C₅×C₄⋊C₄	—	4	4	no	—
49	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
52	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₄²×C₅	—	2	2	no	—
54	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	Q₈	1	4	yes	—
58	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₅×#106	—	4	8	no	—
61	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
62	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
63	C₄×C₅×C₈	C₂×C₄	1	8	yes	complemented
64	C₅×#95	—	2	2	no	—
65	C₅×#95	—	2	2	no	—
66	C₂×#431	C₂×C₅	1	1	yes	characteristic
67	#2285	C₂×C₅	1	1	yes	characteristic
68	C₂×#384	C₂×C₅	1	1	yes	characteristic
69	#1948	C₂×C₅	1	4	yes	complemented
70	#1853	C₂×C₅	1	4	yes	—
71	#1844	C₂×C₅	1	2	yes	complemented
72	#1834	C₂×C₅	1	2	yes	complemented
73	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₅	—	2	2	no	—
75	C₂²×C₄×C₅	—	2	2	no	—
76	C₂²×C₄×C₅	—	2	2	no	—
77	C₂²×C₄×C₅	—	2	2	no	—
78	C₂²×C₄×C₅	—	2	2	no	—
79	C₂²×C₄×C₅	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	4	no	—
81	C₂²×C₄×C₅	—	4	4	no	—
82	C₂²×C₄×C₅	—	4	4	no	—
83	C₂²×C₄×C₅	—	4	4	no	—
84	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₅	SD₁₆	1	4	yes	—
87	C₂²×C₄×C₅	SD₁₆	1	4	yes	—
88	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₂×C₅×C₈	—	2	4	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	C₂²×C₄	1	8	yes	—
99	C₅×C₄⋊C₄	—	2	8	no	—
100	C₅×C₄⋊C₄	—	2	4	no	—
101	C₅×C₄⋊C₄	—	2	4	no	—
102	C₅×C₄⋊C₄	—	4	4	no	—
103	C₅×C₄⋊C₄	—	4	4	no	—
104	C₅×C₄⋊C₄	—	4	4	no	—
105	C₅×C₄⋊C₄	—	4	4	no	—
106	C₅×C₄⋊C₄	—	4	2	no	—
107	C₅×C₄⋊C₄	—	4	2	no	—
108	C₅×C₄⋊C₄	—	4	2	no	—
109	C₅×C₄⋊C₄	—	4	4	no	—
110	C₅×C₄⋊C₄	—	4	2	no	—
111	C₅×C₂²⋊C₄	—	4	4	no	—
112	C₄²×C₅	—	4	4	no	—
113	C₄²×C₅	C₄⋊C₄	1	4	yes	—
114	C₄²×C₅	C₄⋊C₄	1	4	yes	—
115	C₄²×C₅	C₂²×C₄	1	2	yes	—
116	C₄²×C₅	C₂²×C₄	1	2	yes	—
117	C₄²×C₅	C₂×Q₈	1	2	yes	—
118	C₄²×C₅	C₂×Q₈	1	2	yes	—
119	C₂×#117	—	2	1	no	—
120	C₂²×C₄⋊C₄	—	2	1	no	—
121	C₂²×C₄⋊C₄	—	2	1	no	—
122	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
124	#431	C₄×C₅	1	8	yes	complemented
125	C₂×#106	C₂²×C₅	1	8	yes	—
126	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
127	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
128	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
129	#384	—	2	1	no	—
130	#384	—	2	1	no	—
131	#384	C₂²×C₅	1	1	yes	characteristic
132	#384	C₂²×C₅	1	2	yes	—
133	#384	C₂²×C₅	1	1	yes	characteristic
134	#384	C₂²×C₅	1	2	yes	—
135	#382	—	2	1	no	—
136	#380	—	2	1	no	—
137	#380	C₂²×C₅	1	2	yes	—
138	C₄×C₄⋊C₄	—	2	1	no	—
139	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	#340	C₂²×C₅	1	8	yes	—
141	C₂³×C₅	—	2	1	no	—
142	C₂³×C₅	—	2	1	no	—
143	C₂³×C₅	—	2	1	no	—
144	C₂³×C₅	—	2	1	no	—
145	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
146	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
147	C₂³×C₅	C₂×SD₁₆	1	2	yes	—
148	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₅	—	2	1	no	—
150	C₂×C₄×C₅	—	2	1	no	—
151	C₂×C₄×C₅	—	2	1	no	—
152	C₂×C₄×C₅	—	2	1	no	—
153	C₂×C₄×C₅	—	2	4	no	—
154	C₂×C₄×C₅	—	2	4	no	—
155	C₂×C₄×C₅	—	2	8	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	—	4	2	no	—
158	C₂×C₄×C₅	—	4	2	no	—
159	C₂×C₄×C₅	—	4	2	no	—
160	C₂×C₄×C₅	—	4	2	no	—
161	C₂×C₄×C₅	—	4	4	no	—
162	C₂×C₄×C₅	—	4	4	no	—
163	C₂×C₄×C₅	—	4	2	no	—
164	C₂×C₄×C₅	—	4	2	no	—
165	C₂×C₄×C₅	—	8	8	no	—
166	C₂×C₄×C₅	#106	1	16	yes	complemented
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
173	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₅	#137	1	2	yes	—
178	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
181	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
182	C₅×C₈	—	2	8	no	—
183	C₂³×C₄	—	2	2	no	—
184	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂²×C₈	C₂³×C₅	1	4	yes	—
188	#117	—	4	4	no	—
189	C₂×C₄⋊C₄	—	2	2	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₄⋊C₄	—	2	2	no	—
192	C₂×C₄⋊C₄	—	2	2	no	—
193	C₂×C₄⋊C₄	—	2	2	no	—
194	C₂×C₄⋊C₄	—	2	1	no	—
195	C₂×C₄⋊C₄	—	2	1	no	—
196	C₂×C₄⋊C₄	—	2	1	no	—
197	C₂×C₄⋊C₄	—	2	1	no	—
198	C₂×C₄⋊C₄	—	4	4	no	—
199	C₂×C₄⋊C₄	—	4	4	no	—
200	C₂×C₄⋊C₄	—	4	4	no	—
201	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
202	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
203	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
204	C₂×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₄²	—	2	2	no	—
206	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
207	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
208	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₅×Q₈	1	4	yes	—
210	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
211	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
212	#106	—	4	8	no	—
213	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
214	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
215	C₄×C₈	C₂×C₄×C₅	1	8	yes	complemented
216	#95	—	2	2	no	—
217	#95	—	2	2	no	—
218	C₂²×C₅	—	2	2	no	—
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	2	no	—
224	C₂²×C₅	C₂×#106	1	4	yes	—
225	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₅	#535	1	1	yes	characteristic
227	C₂²×C₅	#536	1	1	yes	characteristic
228	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
229	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
230	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₂²×C₅	C₂×#137	1	1	yes	characteristic
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	8	2	no	—
235	C₄×C₅	—	8	4	no	—
236	C₄×C₅	—	8	2	no	—
237	C₄×C₅	C₂×#106	1	4	yes	—
238	C₄×C₅	C₂×#106	1	4	yes	—
239	C₄×C₅	#428	1	4	yes	—
240	C₄×C₅	#520	1	2	yes	—
241	C₄×C₅	#544	1	2	yes	—
242	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	4	no	—
252	C₂²×C₄	—	4	4	no	—
253	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
254	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
255	C₂²×C₄	C₅×SD₁₆	1	4	yes	—
256	C₂²×C₄	C₅×SD₁₆	1	4	yes	—
257	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
258	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
265	C₂×C₈	—	2	4	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	C₂²×C₄×C₅	1	8	yes	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	2	4	no	—
271	C₄⋊C₄	—	4	4	no	—
272	C₄⋊C₄	—	4	4	no	—
273	C₄⋊C₄	—	4	4	no	—
274	C₄⋊C₄	—	4	4	no	—
275	C₄⋊C₄	—	4	2	no	—
276	C₄⋊C₄	—	4	2	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₄⋊C₄	—	4	2	no	—
279	C₄⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	4	no	—
281	C₄²	—	4	4	no	—
282	C₄²	C₅×C₄⋊C₄	1	4	yes	—
283	C₄²	C₅×C₄⋊C₄	1	4	yes	—
284	C₄²	C₂²×C₄×C₅	1	2	yes	—
285	C₄²	C₂²×C₄×C₅	1	2	yes	—
286	C₄²	C₂×C₅×Q₈	1	2	yes	—
287	C₄²	C₂×C₅×Q₈	1	2	yes	—
288	C₂×C₅	—	2	4	no	—
289	C₂×C₅	#2317	1	1	yes	characteristic
290	C₂×C₅	C₂²×#106	1	1	yes	characteristic
291	C₂×C₅	C₂×#428	1	1	yes	characteristic
292	C₂×C₅	#3206	1	1	yes	characteristic
293	C₂×C₅	#3208	1	1	yes	characteristic
294	C₂×C₅	#3227	1	1	yes	characteristic
295	C₂×C₅	#3229	1	1	yes	characteristic
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
301	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
302	C₂³	C₂×C₅×SD₁₆	1	2	yes	—
303	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	8	8	no	—
321	C₂×C₄	C₅×#106	1	16	yes	complemented
322	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
323	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
324	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
325	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
326	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
327	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
328	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
329	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
330	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
331	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
332	C₂×C₄	C₅×#137	1	2	yes	—
333	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
335	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
336	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
337	C₈	—	2	8	no	—
338	C₅	#21981	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²	—	2	2	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	C₂×C₅×#106	1	4	yes	—
346	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
347	C₂²	C₅×#535	1	1	yes	characteristic
348	C₂²	C₅×#536	1	1	yes	characteristic
349	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
350	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
351	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂²	C₂×C₅×#137	1	1	yes	characteristic
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	8	2	no	—
356	C₄	—	8	4	no	—
357	C₄	—	8	2	no	—
358	C₄	C₂×C₅×#106	1	4	yes	—
359	C₄	C₂×C₅×#106	1	4	yes	—
360	C₄	C₅×#428	1	4	yes	—
361	C₄	C₅×#520	1	2	yes	—
362	C₄	C₅×#544	1	2	yes	—
363	C₂	—	2	4	no	—
364	C₂	C₅×#2317	1	1	yes	characteristic
365	C₂	C₂²×C₅×#106	1	1	yes	characteristic
366	C₂	C₂×C₅×#428	1	1	yes	characteristic
367	C₂	C₅×#3206	1	1	yes	characteristic
368	C₂	C₅×#3208	1	1	yes	characteristic
369	C₂	C₅×#3227	1	1	yes	characteristic
370	C₂	C₅×#3229	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1948	C₂	semidirect
6. C₅×#1844	C₂	semidirect
7. C₅×#1834	C₂	semidirect
13. C₅×#431	C₄	semidirect
30. #21981	C₅	direct (N × H)
61. C₅×C₄⋊C₈	C₂×C₄	semidirect
63. C₄×C₅×C₈	C₂×C₄	semidirect
69. #1948	C₂×C₅	semidirect
71. #1844	C₂×C₅	semidirect
72. #1834	C₂×C₅	semidirect
124. #431	C₄×C₅	semidirect
166. C₂×C₄×C₅	#106	semidirect
213. C₄⋊C₈	C₂×C₄×C₅	semidirect
215. C₄×C₈	C₂×C₄×C₅	semidirect
321. C₂×C₄	C₅×#106	semidirect
338. C₅	#21981	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#431	2
C₅×#2285	2
C₂×C₅×#384	2
C₅×#1948	2
C₅×#1853	2
C₅×#1844	2
C₅×#1834	2
#21981	5

Subgroups — C5×#21981 #11944701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21981 #11944701