Subgroups — C₅×#20446 #11943166

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
3	C₅×#2873	C₂	1	2	yes	maximal
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₅×#1773	C₂	1	4	yes	maximal, complemented
6	C₅×#1772	C₂	1	4	yes	maximal, complemented
7	C₅×#1733	C₂	1	2	yes	maximal
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	2	yes	—
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×#108	C₄	1	8	yes	complemented
14	C₂×C₅×#108	C₂²	1	2	yes	—
15	C₂×C₅×#108	C₂²	1	2	yes	—
16	C₅×#427	C₄	1	2	yes	complemented
17	C₅×#427	C₄	1	2	yes	complemented
18	C₅×#427	C₂²	1	2	yes	—
19	C₅×#427	C₂²	1	2	yes	—
20	C₂×C₅×#107	C₄	1	2	yes	complemented
21	C₂×C₅×#106	C₄	1	2	yes	complemented
22	C₅×#405	—	2	4	no	—
23	C₅×#405	C₄	1	8	yes	complemented
24	C₅×#405	C₂²	1	8	yes	—
25	C₄×C₅×M₁₆	—	2	4	no	—
26	C₂×C₅×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
28	C₅×#339	C₂²	1	8	yes	—
29	#20446	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	2	no	—
32	C₂×C₅×M₁₆	—	2	4	no	—
33	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	—
34	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₅×M₁₆	D₄	1	2	yes	—
36	C₂×C₅×M₁₆	D₄	1	2	yes	—
37	C₂×C₅×M₁₆	Q₈	1	4	yes	—
38	C₂×C₅×M₁₆	C₂³	1	4	yes	—
39	C₂²×C₅×C₈	—	2	2	no	—
40	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
41	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	2	yes	—
49	C₅×#117	—	2	2	no	—
50	C₅×#117	—	2	2	no	—
51	C₅×#117	—	2	2	no	—
52	C₅×#117	C₂×C₄	1	4	yes	—
53	C₅×#117	C₂×C₄	1	4	yes	—
54	C₅×#117	C₂³	1	4	yes	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	C₂³	1	2	yes	—
61	C₅×#108	C₂×C₄	1	8	yes	complemented
62	C₅×#108	C₂×C₄	1	8	yes	complemented
63	C₅×#107	C₂×C₄	1	4	yes	—
64	C₅×#107	C₂×C₄	1	4	yes	—
65	C₅×#106	C₂×C₄	1	4	yes	—
66	C₅×#106	C₂×C₄	1	4	yes	—
67	C₅×#97	—	2	8	no	—
68	C₅×#97	C₂×C₄	1	8	yes	complemented
69	C₄×C₅×C₈	—	2	8	no	—
70	C₄×C₅×C₈	C₂×C₄	1	8	yes	complemented
71	C₂²×#108	C₂×C₅	1	1	yes	characteristic
72	C₂×#427	C₂×C₅	1	1	yes	characteristic
73	#2873	C₂×C₅	1	2	yes	—
74	C₂×#405	C₂×C₅	1	1	yes	characteristic
75	#1773	C₂×C₅	1	4	yes	complemented
76	#1772	C₂×C₅	1	4	yes	complemented
77	#1733	C₂×C₅	1	2	yes	—
78	C₂⁴×C₅	#41	1	1	yes	characteristic
79	C₂²×C₄×C₅	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	4	no	—
81	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₅	#41	1	1	yes	characteristic
89	C₂²×C₄×C₅	#41	1	2	yes	—
90	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₅×M₁₆	—	2	8	no	—
92	C₅×M₁₆	—	2	4	no	—
93	C₅×M₁₆	C₄⋊C₄	1	8	yes	—
94	C₅×M₁₆	C₄⋊C₄	1	8	yes	—
95	C₅×M₁₆	C₂²×C₄	1	8	yes	—
96	C₂×C₅×C₈	—	2	8	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	C₄²	1	4	yes	—
99	C₂×C₅×C₈	C₄²	1	4	yes	—
100	C₂×C₅×C₈	C₄²	1	4	yes	—
101	C₂×C₅×C₈	C₄²	1	4	yes	—
102	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
103	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
110	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
111	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
112	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
113	C₅×C₄⋊C₄	—	2	4	no	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	C₂²×C₄	1	8	yes	—
116	C₅×C₂²⋊C₄	—	2	4	no	—
117	C₅×C₂²⋊C₄	—	2	4	no	—
118	C₅×C₂²⋊C₄	—	2	4	no	—
119	C₄²×C₅	—	2	4	no	—
120	C₄²×C₅	—	2	4	no	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	C₂²×C₄	1	4	yes	—
123	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
124	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
126	C₂×#117	C₂²×C₅	1	2	yes	—
127	C₂×#117	C₂²×C₅	1	1	yes	characteristic
128	C₂×#108	C₄×C₅	1	8	yes	complemented
129	C₂×#108	C₂²×C₅	1	2	yes	—
130	C₂×#108	C₂²×C₅	1	2	yes	—
131	#427	C₄×C₅	1	2	yes	complemented
132	#427	C₄×C₅	1	2	yes	complemented
133	#427	C₂²×C₅	1	2	yes	—
134	#427	C₂²×C₅	1	2	yes	—
135	C₂×#107	C₄×C₅	1	2	yes	complemented
136	C₂×#106	C₄×C₅	1	2	yes	complemented
137	#405	—	2	4	no	—
138	#405	C₄×C₅	1	8	yes	complemented
139	#405	C₂²×C₅	1	8	yes	—
140	C₄×M₁₆	—	2	4	no	—
141	C₂×#97	C₂²×C₅	1	2	yes	—
142	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
143	#339	C₂²×C₅	1	8	yes	—
144	C₂³×C₅	—	4	2	no	—
145	C₂³×C₅	#117	1	2	yes	—
146	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
148	C₂³×C₅	C₄×Q₈	1	2	yes	—
149	C₂³×C₅	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₅	—	2	4	no	—
151	C₂×C₄×C₅	—	2	8	no	—
152	C₂×C₄×C₅	—	4	4	no	—
153	C₂×C₄×C₅	—	8	4	no	—
154	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
155	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₅	#117	1	2	yes	—
159	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
164	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
172	C₅×C₈	—	2	8	no	—
173	C₅×C₈	C₂×C₄²	1	2	yes	—
174	C₅×C₈	C₂×C₄²	1	2	yes	—
175	C₅×C₈	C₂×C₄²	1	2	yes	—
176	C₅×C₈	C₂×C₄²	1	2	yes	—
177	C₅×C₈	C₂×C₄⋊C₄	1	8	yes	—
178	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
179	C₂×M₁₆	—	2	2	no	—
180	C₂×M₁₆	—	2	4	no	—
181	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	—
182	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	—
183	C₂×M₁₆	C₅×D₄	1	2	yes	—
184	C₂×M₁₆	C₅×D₄	1	2	yes	—
185	C₂×M₁₆	C₅×Q₈	1	4	yes	—
186	C₂×M₁₆	C₂³×C₅	1	4	yes	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
189	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
194	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
195	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
196	C₂²×C₈	C₂³×C₅	1	2	yes	—
197	#117	—	2	2	no	—
198	#117	—	2	2	no	—
199	#117	—	2	2	no	—
200	#117	C₂×C₄×C₅	1	4	yes	—
201	#117	C₂×C₄×C₅	1	4	yes	—
202	#117	C₂³×C₅	1	4	yes	—
203	C₂×C₄⋊C₄	—	2	1	no	—
204	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
205	C₂×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₄²	—	2	2	no	—
208	C₂×C₄²	C₂³×C₅	1	2	yes	—
209	#108	C₂×C₄×C₅	1	8	yes	complemented
210	#108	C₂×C₄×C₅	1	8	yes	complemented
211	#107	C₂×C₄×C₅	1	4	yes	—
212	#107	C₂×C₄×C₅	1	4	yes	—
213	#106	C₂×C₄×C₅	1	4	yes	—
214	#106	C₂×C₄×C₅	1	4	yes	—
215	#97	—	2	8	no	—
216	#97	C₂×C₄×C₅	1	8	yes	complemented
217	C₄×C₈	—	2	8	no	—
218	C₄×C₈	C₂×C₄×C₅	1	8	yes	complemented
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	4	2	no	—
223	C₂²×C₅	—	4	2	no	—
224	C₂²×C₅	C₄×C₄⋊C₄	1	2	yes	—
225	C₂²×C₅	C₄×C₄⋊C₄	1	2	yes	—
226	C₂²×C₅	C₂×#117	1	1	yes	characteristic
227	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
229	C₄×C₅	—	4	4	no	—
230	C₄×C₅	—	4	8	no	—
231	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
232	C₄×C₅	C₄×C₄⋊C₄	1	2	yes	—
233	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
234	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
237	C₂⁴	C₅×#41	1	1	yes	characteristic
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
243	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
247	C₂²×C₄	C₅×#41	1	1	yes	characteristic
248	C₂²×C₄	C₅×#41	1	2	yes	—
249	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
250	M₁₆	—	2	8	no	—
251	M₁₆	—	2	4	no	—
252	M₁₆	C₅×C₄⋊C₄	1	8	yes	—
253	M₁₆	C₅×C₄⋊C₄	1	8	yes	—
254	M₁₆	C₂²×C₄×C₅	1	8	yes	—
255	C₂×C₈	—	2	8	no	—
256	C₂×C₈	—	2	4	no	—
257	C₂×C₈	C₄²×C₅	1	4	yes	—
258	C₂×C₈	C₄²×C₅	1	4	yes	—
259	C₂×C₈	C₄²×C₅	1	4	yes	—
260	C₂×C₈	C₄²×C₅	1	4	yes	—
261	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
262	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
263	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
267	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
268	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
270	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
271	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	2	4	no	—
274	C₄⋊C₄	C₂²×C₄×C₅	1	8	yes	—
275	C₂²⋊C₄	—	2	4	no	—
276	C₂²⋊C₄	—	2	4	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	2	no	—
281	C₄²	C₂²×C₄×C₅	1	4	yes	—
282	C₂×C₅	—	2	1	no	—
283	C₂×C₅	—	2	1	no	—
284	C₂×C₅	—	2	2	no	—
285	C₂×C₅	—	2	2	no	—
286	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₅	#2957	1	2	yes	—
288	C₂³	—	4	2	no	—
289	C₂³	C₅×#117	1	2	yes	—
290	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
291	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
292	C₂³	C₄×C₅×Q₈	1	2	yes	—
293	C₂³	C₂×C₅×#41	1	1	yes	characteristic
294	C₂×C₄	—	2	4	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	8	4	no	—
298	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
299	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
300	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
301	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
302	C₂×C₄	C₅×#117	1	2	yes	—
303	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
304	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
305	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
306	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
307	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
308	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
309	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
310	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
311	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
312	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
315	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
316	C₈	—	2	8	no	—
317	C₈	C₂×C₄²×C₅	1	2	yes	—
318	C₈	C₂×C₄²×C₅	1	2	yes	—
319	C₈	C₂×C₄²×C₅	1	2	yes	—
320	C₈	C₂×C₄²×C₅	1	2	yes	—
321	C₈	C₂×C₅×C₄⋊C₄	1	8	yes	—
322	C₅	#20446	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	C₄×C₅×C₄⋊C₄	1	2	yes	—
329	C₂²	C₄×C₅×C₄⋊C₄	1	2	yes	—
330	C₂²	C₂×C₅×#117	1	1	yes	characteristic
331	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
332	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
333	C₄	—	4	4	no	—
334	C₄	—	4	8	no	—
335	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
336	C₄	C₄×C₅×C₄⋊C₄	1	2	yes	—
337	C₄	C₂²×C₄²×C₅	1	1	yes	characteristic
338	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
339	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
340	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
341	C₂	—	2	1	no	—
342	C₂	—	2	2	no	—
343	C₂	—	2	2	no	—
344	C₂	—	2	1	no	—
345	C₂	C₂×C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
346	C₂	C₅×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₄	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1773	C₂	semidirect
6. C₅×#1772	C₂	semidirect
13. C₂×C₅×#108	C₄	semidirect
16. C₅×#427	C₄	semidirect
17. C₅×#427	C₄	semidirect
20. C₂×C₅×#107	C₄	semidirect
21. C₂×C₅×#106	C₄	semidirect
23. C₅×#405	C₄	semidirect
29. #20446	C₅	direct (N × H)
61. C₅×#108	C₂×C₄	semidirect
62. C₅×#108	C₂×C₄	semidirect
68. C₅×#97	C₂×C₄	semidirect
70. C₄×C₅×C₈	C₂×C₄	semidirect
75. #1773	C₂×C₅	semidirect
76. #1772	C₂×C₅	semidirect
128. C₂×#108	C₄×C₅	semidirect
131. #427	C₄×C₅	semidirect
132. #427	C₄×C₅	semidirect
135. C₂×#107	C₄×C₅	semidirect
136. C₂×#106	C₄×C₅	semidirect
138. #405	C₄×C₅	semidirect
209. #108	C₂×C₄×C₅	semidirect
210. #108	C₂×C₄×C₅	semidirect
216. #97	C₂×C₄×C₅	semidirect
218. C₄×C₈	C₂×C₄×C₅	semidirect
322. C₅	#20446	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×C₅×#108	2
C₂×C₅×#427	2
C₅×#2873	2
C₂×C₅×#405	2
C₅×#1773	2
C₅×#1772	2
C₅×#1733	2
#20446	5

Subgroups — C5×#20446 #11943166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20446 #11943166