Subgroups — C₅×#21991 #11944711

Order 1280.

762 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#433	C₂	1	1	yes	maximal, characteristic
2	C₅×#2317	C₂	1	1	yes	maximal, characteristic
3	C₅×#2314	C₂	1	1	yes	maximal, characteristic
4	C₅×#1949	C₂	1	2	yes	maximal, complemented
5	C₅×#1947	C₂	1	2	yes	maximal, complemented
6	C₅×#1854	C₂	1	2	yes	maximal
7	C₅×#1852	C₂	1	2	yes	maximal
8	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₅×#433	C₄	1	8	yes	complemented
16	C₂×C₅×#107	C₂²	1	2	yes	—
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×#107	C₂²	1	2	yes	—
19	C₂×C₅×#106	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₅×#389	—	2	2	no	—
25	C₅×#388	—	2	2	no	—
26	C₅×#387	—	2	2	no	—
27	C₅×#385	—	2	2	no	—
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₅×#384	C₂²	1	1	yes	characteristic
31	C₅×#382	C₂²	1	1	yes	characteristic
32	C₅×#382	C₂²	1	1	yes	characteristic
33	C₅×#382	C₂²	1	1	yes	characteristic
34	C₅×#380	C₂²	1	2	yes	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	2	yes	—
39	C₅×#340	C₂²	1	2	yes	—
40	#21991	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂³×C₄×C₅	—	2	1	no	—
42	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₅×#117	—	4	2	no	—
46	C₅×#117	C₂×C₄	1	4	yes	—
47	C₅×#117	Q₈	1	4	yes	—
48	C₂×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂×C₅×C₄⋊C₄	—	2	2	no	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	—	4	2	no	—
53	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
55	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
63	C₂×C₄²×C₅	—	2	1	no	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₅×#107	—	4	2	no	—
68	C₅×#107	—	4	2	no	—
69	C₅×#107	—	4	2	no	—
70	C₅×#106	—	4	2	no	—
71	C₅×C₄⋊C₈	C₂×C₄	1	8	yes	complemented
72	C₅×C₂²⋊C₈	C₂×C₄	1	8	yes	—
73	C₅×#97	C₂×C₄	1	4	yes	complemented
74	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
75	C₅×#95	—	2	2	no	—
76	C₅×#95	—	2	2	no	—
77	C₅×#95	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₂×#433	C₂×C₅	1	1	yes	characteristic
81	#2317	C₂×C₅	1	1	yes	characteristic
82	#2314	C₂×C₅	1	1	yes	characteristic
83	#1949	C₂×C₅	1	2	yes	complemented
84	#1947	C₂×C₅	1	2	yes	complemented
85	#1854	C₂×C₅	1	2	yes	—
86	#1852	C₂×C₅	1	2	yes	—
87	#1847	C₂×C₅	1	1	yes	characteristic, complemented
88	#1845	C₂×C₅	1	1	yes	characteristic, complemented
89	#1836	C₂×C₅	1	1	yes	characteristic, complemented
90	#1835	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	1	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	1	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	1	no	—
99	C₂²×C₄×C₅	—	2	1	no	—
100	C₂²×C₄×C₅	—	4	2	no	—
101	C₂²×C₄×C₅	—	8	2	no	—
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
113	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
114	C₅×C₄⋊C₄	—	2	2	no	—
115	C₅×C₄⋊C₄	—	2	2	no	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₄⋊C₄	—	2	4	no	—
121	C₅×C₄⋊C₄	—	4	2	no	—
122	C₅×C₄⋊C₄	—	8	2	no	—
123	C₅×C₄⋊C₄	—	8	2	no	—
124	C₅×C₄⋊C₄	—	8	2	no	—
125	C₅×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	8	2	no	—
128	C₅×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
129	C₄²×C₅	—	4	2	no	—
130	C₄²×C₅	—	8	2	no	—
131	C₄²×C₅	C₂²×C₄	1	2	yes	—
132	C₄²×C₅	C₂²×C₄	1	2	yes	—
133	C₄²×C₅	C₂×Q₈	1	2	yes	—
134	C₄²×C₅	C₂×Q₈	1	2	yes	—
135	C₂×#117	C₂²×C₅	1	1	yes	characteristic
136	C₂×#117	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
138	#433	C₄×C₅	1	8	yes	complemented
139	C₂×#107	C₂²×C₅	1	2	yes	—
140	C₂×#107	C₂²×C₅	1	2	yes	—
141	C₂×#107	C₂²×C₅	1	2	yes	—
142	C₂×#106	C₂²×C₅	1	2	yes	—
143	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
144	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
145	C₂×#97	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
147	#389	—	2	2	no	—
148	#388	—	2	2	no	—
149	#387	—	2	2	no	—
150	#385	—	2	2	no	—
151	#384	C₂²×C₅	1	1	yes	characteristic
152	#384	C₂²×C₅	1	1	yes	characteristic
153	#384	C₂²×C₅	1	1	yes	characteristic
154	#382	C₂²×C₅	1	1	yes	characteristic
155	#382	C₂²×C₅	1	1	yes	characteristic
156	#382	C₂²×C₅	1	1	yes	characteristic
157	#380	C₂²×C₅	1	2	yes	—
158	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	#340	C₂²×C₅	1	2	yes	—
160	#340	C₂²×C₅	1	2	yes	—
161	#340	C₂²×C₅	1	2	yes	—
162	#340	C₂²×C₅	1	2	yes	—
163	C₂³×C₅	—	2	1	no	—
164	C₂³×C₅	—	2	1	no	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	4	no	—
176	C₂×C₄×C₅	—	2	4	no	—
177	C₂×C₄×C₅	—	4	1	no	—
178	C₂×C₄×C₅	—	4	1	no	—
179	C₂×C₄×C₅	—	4	1	no	—
180	C₂×C₄×C₅	—	4	1	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	—	4	2	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	8	4	no	—
192	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
193	C₂×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
194	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
195	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
198	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
199	C₅×C₈	—	2	4	no	—
200	C₅×C₈	—	2	4	no	—
201	C₂³×C₄	—	2	1	no	—
202	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₅	1	2	yes	—
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	#117	—	4	2	no	—
206	#117	C₂×C₄×C₅	1	4	yes	—
207	#117	C₅×Q₈	1	4	yes	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	4	2	no	—
213	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
214	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
219	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₂²⋊C₄	—	2	2	no	—
222	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	—	2	2	no	—
225	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
227	#107	—	4	2	no	—
228	#107	—	4	2	no	—
229	#107	—	4	2	no	—
230	#106	—	4	2	no	—
231	C₄⋊C₈	C₂×C₄×C₅	1	8	yes	complemented
232	C₂²⋊C₈	C₂×C₄×C₅	1	8	yes	—
233	#97	C₂×C₄×C₅	1	4	yes	complemented
234	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
235	#95	—	2	2	no	—
236	#95	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	#95	—	2	2	no	—
240	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	1	no	—
243	C₂²×C₅	—	4	1	no	—
244	C₂²×C₅	—	4	2	no	—
245	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
246	C₂²×C₅	#535	1	1	yes	characteristic
247	C₂²×C₅	#536	1	1	yes	characteristic
248	C₂²×C₅	#576	1	2	yes	—
249	C₂²×C₅	#578	1	2	yes	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	2	4	no	—
252	C₄×C₅	—	2	4	no	—
253	C₄×C₅	—	8	1	no	—
254	C₄×C₅	—	8	2	no	—
255	C₄×C₅	—	8	1	no	—
256	C₄×C₅	—	8	1	no	—
257	C₄×C₅	—	8	1	no	—
258	C₄×C₅	—	8	2	no	—
259	C₄×C₅	#520	1	2	yes	—
260	C₄×C₅	#544	1	2	yes	—
261	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	8	2	no	—
272	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
273	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
274	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
283	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	8	2	no	—
293	C₄⋊C₄	—	8	2	no	—
294	C₄⋊C₄	—	8	2	no	—
295	C₄⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
296	C₂²⋊C₄	—	4	2	no	—
297	C₂²⋊C₄	—	8	2	no	—
298	C₂²⋊C₄	C₅×C₄⋊C₄	1	8	yes	—
299	C₄²	—	4	2	no	—
300	C₄²	—	8	2	no	—
301	C₄²	C₂²×C₄×C₅	1	2	yes	—
302	C₄²	C₂²×C₄×C₅	1	2	yes	—
303	C₄²	C₂×C₅×Q₈	1	2	yes	—
304	C₄²	C₂×C₅×Q₈	1	2	yes	—
305	C₂×C₅	—	4	2	no	—
306	C₂×C₅	#2317	1	1	yes	characteristic
307	C₂×C₅	#2913	1	2	yes	—
308	C₂×C₅	#3220	1	1	yes	characteristic
309	C₂×C₅	#3223	1	1	yes	characteristic
310	C₂×C₅	#3243	1	2	yes	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
316	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	8	4	no	—
340	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
341	C₂×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
342	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
343	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
345	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
346	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
347	C₈	—	2	4	no	—
348	C₈	—	2	4	no	—
349	C₅	#21991	1	1	yes	characteristic, direct product factor, Sylow
350	C₂²	—	2	2	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₂²	C₅×#535	1	1	yes	characteristic
357	C₂²	C₅×#536	1	1	yes	characteristic
358	C₂²	C₅×#576	1	2	yes	—
359	C₂²	C₅×#578	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	4	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	2	no	—
368	C₄	—	8	1	no	—
369	C₄	C₅×#520	1	2	yes	—
370	C₄	C₅×#544	1	2	yes	—
371	C₂	—	4	2	no	—
372	C₂	C₅×#2317	1	1	yes	characteristic
373	C₂	C₅×#2913	1	2	yes	—
374	C₂	C₅×#3220	1	1	yes	characteristic
375	C₂	C₅×#3223	1	1	yes	characteristic
376	C₂	C₅×#3243	1	2	yes	—

	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 ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1949	C₂	semidirect
5. C₅×#1947	C₂	semidirect
8. C₅×#1847	C₂	semidirect
9. C₅×#1845	C₂	semidirect
10. C₅×#1836	C₂	semidirect
11. C₅×#1835	C₂	semidirect
15. C₅×#433	C₄	semidirect
40. #21991	C₅	direct (N × H)
71. C₅×C₄⋊C₈	C₂×C₄	semidirect
73. C₅×#97	C₂×C₄	semidirect
74. C₄×C₅×C₈	C₂×C₄	semidirect
83. #1949	C₂×C₅	semidirect
84. #1947	C₂×C₅	semidirect
87. #1847	C₂×C₅	semidirect
88. #1845	C₂×C₅	semidirect
89. #1836	C₂×C₅	semidirect
90. #1835	C₂×C₅	semidirect
138. #433	C₄×C₅	semidirect
231. C₄⋊C₈	C₂×C₄×C₅	semidirect
233. #97	C₂×C₄×C₅	semidirect
234. C₄×C₈	C₂×C₄×C₅	semidirect
349. C₅	#21991	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×#433	2
C₅×#2317	2
C₅×#2314	2
C₅×#1949	2
C₅×#1947	2
C₅×#1854	2
C₅×#1852	2
C₅×#1847	2
C₅×#1845	2
C₅×#1836	2
C₅×#1835	2
#21991	5

Subgroups — C5×#21991 #11944711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21991 #11944711