Subgroups — C₅×#21434 #11944154

Order 1280.

688 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2298	C₂	1	1	yes	maximal, characteristic
2	C₅×#1924	C₂	1	2	yes	maximal
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1917	C₂	1	2	yes	maximal, complemented
5	C₅×#1916	C₂	1	2	yes	maximal, complemented
6	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1768	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1750	C₂	1	1	yes	maximal, characteristic
9	C₅×#1750	C₂	1	1	yes	maximal, characteristic
10	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×#97	C₂²	1	1	yes	characteristic
18	C₂×C₅×#97	C₂²	1	1	yes	characteristic
19	C₂×C₅×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₅×#388	C₄	1	2	yes	—
24	C₅×#388	C₄	1	2	yes	—
25	C₅×#387	C₄	1	2	yes	—
26	C₅×#387	C₄	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₅×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	#21434	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₅×#117	—	2	2	no	—
46	C₅×#117	—	2	2	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊C₈	—	2	4	no	—
64	C₅×C₄⋊C₈	—	2	4	no	—
65	C₅×C₂²⋊C₈	—	2	4	no	—
66	C₅×C₂²⋊C₈	—	2	4	no	—
67	C₅×#97	—	2	4	no	—
68	C₅×#97	—	2	2	no	—
69	C₅×#97	—	2	2	no	—
70	C₄×C₅×C₈	—	2	4	no	—
71	C₄×C₅×C₈	—	2	2	no	—
72	C₄×C₅×C₈	—	2	2	no	—
73	C₅×#95	C₂×C₄	1	2	yes	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	C₅×#95	C₂×C₄	1	2	yes	—
76	C₅×#95	C₂×C₄	1	2	yes	—
77	C₅×#95	C₂×C₄	1	2	yes	—
78	C₅×#95	C₂×C₄	1	2	yes	—
79	#2298	C₂×C₅	1	1	yes	characteristic
80	#1924	C₂×C₅	1	2	yes	—
81	#1923	C₂×C₅	1	2	yes	—
82	#1917	C₂×C₅	1	2	yes	complemented
83	#1916	C₂×C₅	1	2	yes	complemented
84	#1768	C₂×C₅	1	1	yes	characteristic, complemented
85	#1768	C₂×C₅	1	1	yes	characteristic, complemented
86	#1750	C₂×C₅	1	1	yes	characteristic
87	#1750	C₂×C₅	1	1	yes	characteristic
88	#1744	C₂×C₅	1	1	yes	characteristic, complemented
89	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	—	2	1	no	—
92	C₂²×C₄×C₅	—	2	1	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	2	2	no	—
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	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	#41	1	4	yes	—
116	C₂×C₅×C₈	#41	1	4	yes	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₄⋊C₄	—	2	4	no	—
120	C₅×C₄⋊C₄	—	4	2	no	—
121	C₅×C₂²⋊C₄	—	2	2	no	—
122	C₅×C₂²⋊C₄	—	2	2	no	—
123	C₅×C₂²⋊C₄	—	2	4	no	—
124	C₅×C₂²⋊C₄	—	4	2	no	—
125	C₄²×C₅	—	2	4	no	—
126	C₄²×C₅	—	2	1	no	—
127	C₄²×C₅	—	2	1	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	2	2	no	—
131	C₄²×C₅	—	2	2	no	—
132	C₄²×C₅	—	4	2	no	—
133	C₄²×C₅	#41	1	2	yes	—
134	C₄²×C₅	#41	1	2	yes	—
135	C₂×#117	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
138	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
139	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
140	C₂×#97	C₂²×C₅	1	2	yes	—
141	C₂×#97	C₂²×C₅	1	1	yes	characteristic
142	C₂×#97	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
144	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	#388	C₄×C₅	1	2	yes	—
147	#388	C₄×C₅	1	2	yes	—
148	#387	C₄×C₅	1	2	yes	—
149	#387	C₄×C₅	1	2	yes	—
150	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
153	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
154	#376	C₂²×C₅	1	1	yes	characteristic
155	C₄³	C₂²×C₅	1	1	yes	characteristic
156	#336	C₂²×C₅	1	2	yes	—
157	#336	C₂²×C₅	1	2	yes	—
158	#336	C₂²×C₅	1	2	yes	—
159	#336	C₂²×C₅	1	2	yes	—
160	#336	C₂²×C₅	1	2	yes	—
161	#336	C₂²×C₅	1	2	yes	—
162	C₂³×C₅	—	2	1	no	—
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	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	—	2	2	no	—
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	1	no	—
173	C₂×C₄×C₅	—	2	1	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	#117	1	2	yes	—
191	C₂×C₄×C₅	#117	1	2	yes	—
192	C₂×C₄×C₅	#131	1	4	yes	—
193	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×#41	1	2	yes	—
196	C₂×C₄×C₅	C₂×#41	1	2	yes	—
197	C₅×C₈	—	2	4	no	—
198	C₅×C₈	—	2	4	no	—
199	C₅×C₈	—	4	2	no	—
200	C₅×C₈	—	4	2	no	—
201	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₅	1	2	yes	—
203	C₂²×C₈	C₂³×C₅	1	2	yes	—
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	C₂²×C₈	C₂³×C₅	1	2	yes	—
206	#117	—	2	2	no	—
207	#117	—	2	2	no	—
208	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
210	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
216	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
217	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
224	C₄⋊C₈	—	2	4	no	—
225	C₄⋊C₈	—	2	4	no	—
226	C₂²⋊C₈	—	2	4	no	—
227	C₂²⋊C₈	—	2	4	no	—
228	#97	—	2	4	no	—
229	#97	—	2	2	no	—
230	#97	—	2	2	no	—
231	C₄×C₈	—	2	4	no	—
232	C₄×C₈	—	2	2	no	—
233	C₄×C₈	—	2	2	no	—
234	#95	C₂×C₄×C₅	1	2	yes	—
235	#95	C₂×C₄×C₅	1	2	yes	—
236	#95	C₂×C₄×C₅	1	2	yes	—
237	#95	C₂×C₄×C₅	1	2	yes	—
238	#95	C₂×C₄×C₅	1	2	yes	—
239	#95	C₂×C₄×C₅	1	2	yes	—
240	C₂²×C₅	—	4	1	no	—
241	C₂²×C₅	—	4	1	no	—
242	C₂²×C₅	—	4	2	no	—
243	C₂²×C₅	—	4	2	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	C₂×#117	1	1	yes	characteristic
246	C₂²×C₅	C₄×#41	1	1	yes	characteristic
247	C₂²×C₅	C₄×#41	1	1	yes	characteristic
248	C₂²×C₅	C₂×#131	1	2	yes	—
249	C₂²×C₅	#568	1	2	yes	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	2	2	no	—
252	C₄×C₅	—	2	4	no	—
253	C₄×C₅	—	4	1	no	—
254	C₄×C₅	—	4	1	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	—	4	2	no	—
257	C₄×C₅	—	4	2	no	—
258	C₄×C₅	—	4	1	no	—
259	C₄×C₅	#529	1	2	yes	—
260	C₄×C₅	#529	1	2	yes	—
261	C₂⁴	C₂²×C₄×C₅	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	1	no	—
266	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
268	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
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	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	C₅×#41	1	4	yes	—
287	C₂×C₈	C₅×#41	1	4	yes	—
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	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	4	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₄²	—	2	4	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	4	2	no	—
304	C₄²	C₅×#41	1	2	yes	—
305	C₄²	C₅×#41	1	2	yes	—
306	C₂×C₅	—	8	1	no	—
307	C₂×C₅	#2298	1	1	yes	characteristic
308	C₂×C₅	#2922	1	1	yes	characteristic
309	C₂×C₅	#2923	1	1	yes	characteristic
310	C₂×C₅	#2968	1	2	yes	—
311	C₂×C₅	#2969	1	2	yes	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	C₅×#117	1	2	yes	—
341	C₂×C₄	C₅×#117	1	2	yes	—
342	C₂×C₄	C₅×#131	1	4	yes	—
343	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×#41	1	2	yes	—
346	C₂×C₄	C₂×C₅×#41	1	2	yes	—
347	C₈	—	2	4	no	—
348	C₈	—	2	4	no	—
349	C₈	—	4	2	no	—
350	C₈	—	4	2	no	—
351	C₅	#21434	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	C₂×C₅×#117	1	1	yes	characteristic
358	C₂²	C₄×C₅×#41	1	1	yes	characteristic
359	C₂²	C₄×C₅×#41	1	1	yes	characteristic
360	C₂²	C₂×C₅×#131	1	2	yes	—
361	C₂²	C₅×#568	1	2	yes	—
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	4	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	C₅×#529	1	2	yes	—
372	C₄	C₅×#529	1	2	yes	—
373	C₂	—	8	1	no	—
374	C₂	C₅×#2298	1	1	yes	characteristic
375	C₂	C₅×#2922	1	1	yes	characteristic
376	C₂	C₅×#2923	1	1	yes	characteristic
377	C₂	C₅×#2968	1	2	yes	—
378	C₂	C₅×#2969	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₅×#1917	C₂	semidirect
5. C₅×#1916	C₂	semidirect
6. C₅×#1768	C₂	semidirect
7. C₅×#1768	C₂	semidirect
10. C₅×#1744	C₂	semidirect
11. C₄×C₅×#97	C₂	semidirect
39. #21434	C₅	direct (N × H)
82. #1917	C₂×C₅	semidirect
83. #1916	C₂×C₅	semidirect
84. #1768	C₂×C₅	semidirect
85. #1768	C₂×C₅	semidirect
88. #1744	C₂×C₅	semidirect
89. C₄×#97	C₂×C₅	semidirect
351. C₅	#21434	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#2298	2
C₅×#1924	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1768	2
C₅×#1750	2
C₅×#1744	2
C₄×C₅×#97	2
#21434	5

Subgroups — C5×#21434 #11944154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21434 #11944154