Subgroups — C₂×C₅×#2372 #11956867

Order 1280.

3158 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₅×#2372	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#388	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#386	C₂	1	2	yes	maximal
6	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#376	C₂	1	2	yes	maximal, complemented
8	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
11	C₂×C₅×#124	C₄	1	16	yes	complemented
12	C₂×C₅×#124	C₂²	1	8	yes	—
13	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
15	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₄²×C₅	C₂²	1	4	yes	—
18	C₂²×C₄²×C₅	C₂²	1	2	yes	—
19	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₅×#391	C₂²	1	16	yes	complemented
21	C₅×#388	C₂²	1	32	yes	complemented
22	C₅×#386	C₂²	1	16	yes	—
23	C₄×C₅×C₂²⋊C₄	C₂²	1	32	yes	complemented
24	C₅×#376	C₂²	1	16	yes	complemented
25	C₂×C₅×#95	C₂²	1	2	yes	—
26	C₂×C₅×#95	C₂²	1	4	yes	—
27	C₂×C₅×#95	C₂²	1	2	yes	—
28	C₂×C₅×#95	C₂²	1	4	yes	—
29	C₂×#2372	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂⁵×C₅	C₂³	1	2	yes	—
31	C₂²×C₅×Q₈	—	4	2	no	—
32	C₂²×C₅×Q₈	—	4	2	no	—
33	C₂²×C₅×Q₈	C₂×C₄	1	8	yes	complemented
34	C₂²×C₅×Q₈	C₂³	1	4	yes	—
35	C₂²×C₅×D₄	—	4	2	no	—
36	C₂²×C₅×D₄	—	4	2	no	—
37	C₂²×C₅×D₄	C₂×C₄	1	8	yes	—
38	C₂²×C₅×D₄	C₂³	1	4	yes	—
39	C₂³×C₄×C₅	—	2	16	no	—
40	C₂³×C₄×C₅	—	4	4	no	—
41	C₂³×C₄×C₅	C₂³	1	4	yes	—
42	C₂³×C₄×C₅	C₂³	1	8	yes	—
43	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₅	C₂³	1	2	yes	—
45	C₂³×C₄×C₅	C₂³	1	2	yes	—
46	C₂³×C₄×C₅	C₂³	1	4	yes	—
47	C₅×#124	C₂×C₄	1	64	yes	complemented
48	C₂×C₅×C₄⋊C₄	—	4	4	no	—
49	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
50	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
51	C₂×C₅×C₂²⋊C₄	—	4	4	no	—
52	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	32	yes	complemented
53	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
56	C₂×C₄²×C₅	—	2	16	no	—
57	C₂×C₄²×C₅	—	4	4	no	—
58	C₂×C₄²×C₅	C₂×C₄	1	8	yes	complemented
59	C₂×C₄²×C₅	C₂³	1	16	yes	—
60	C₂×C₄²×C₅	C₂³	1	8	yes	—
61	C₂×C₄²×C₅	C₂³	1	4	yes	—
62	C₅×#95	C₂³	1	8	yes	—
63	C₅×#95	C₂³	1	16	yes	—
64	C₅×#95	C₂³	1	8	yes	—
65	C₅×#95	C₂³	1	16	yes	—
66	C₂²×#124	C₂×C₅	1	1	yes	characteristic
67	#2372	C₂×C₅	1	16	yes	direct product factor
68	C₂×#391	C₂×C₅	1	2	yes	complemented
69	C₂×#388	C₂×C₅	1	4	yes	complemented
70	C₂×#386	C₂×C₅	1	2	yes	—
71	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
72	C₂×#376	C₂×C₅	1	2	yes	complemented
73	C₂⁴×C₅	—	2	8	no	—
74	C₂⁴×C₅	—	2	8	no	—
75	C₂⁴×C₅	—	2	4	no	—
76	C₂⁴×C₅	—	2	4	no	—
77	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
78	C₂⁴×C₅	C₂⁴	1	4	yes	—
79	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
80	C₂×C₅×Q₈	—	4	16	no	—
81	C₂×C₅×Q₈	—	4	4	no	—
82	C₂×C₅×Q₈	—	4	4	no	—
83	C₂×C₅×Q₈	C₂²×C₄	1	16	yes	complemented
84	C₂×C₅×D₄	—	4	16	no	—
85	C₂×C₅×D₄	—	4	4	no	—
86	C₂×C₅×D₄	—	4	4	no	—
87	C₂×C₅×D₄	C₂²×C₄	1	16	yes	—
88	C₂²×C₄×C₅	—	2	8	no	—
89	C₂²×C₄×C₅	—	2	8	no	—
90	C₂²×C₄×C₅	—	2	8	no	—
91	C₂²×C₄×C₅	—	2	4	no	—
92	C₂²×C₄×C₅	—	2	4	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	8	no	—
96	C₂²×C₄×C₅	—	2	8	no	—
97	C₂²×C₄×C₅	—	2	8	no	—
98	C₂²×C₄×C₅	—	2	32	no	—
99	C₂²×C₄×C₅	—	4	8	no	—
100	C₂²×C₄×C₅	—	4	32	no	—
101	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
104	C₂²×C₄×C₅	#41	1	16	yes	—
105	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
108	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
110	C₅×C₄⋊C₄	—	4	8	no	—
111	C₅×C₂²⋊C₄	—	2	32	no	—
112	C₅×C₂²⋊C₄	—	4	8	no	—
113	C₅×C₂²⋊C₄	C₂²×C₄	1	64	yes	complemented
114	C₄²×C₅	—	2	32	no	—
115	C₄²×C₅	—	4	8	no	—
116	C₄²×C₅	C₂²×C₄	1	16	yes	complemented
117	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
118	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
119	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
120	C₂×#124	C₄×C₅	1	16	yes	complemented
121	C₂×#124	C₂²×C₅	1	8	yes	—
122	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
124	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
125	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
126	C₂²×C₄²	C₂²×C₅	1	4	yes	—
127	C₂²×C₄²	C₂²×C₅	1	2	yes	—
128	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
129	#391	C₂²×C₅	1	16	yes	complemented
130	#388	C₂²×C₅	1	32	yes	complemented
131	#386	C₂²×C₅	1	16	yes	—
132	C₄×C₂²⋊C₄	C₂²×C₅	1	32	yes	complemented
133	#376	C₂²×C₅	1	16	yes	complemented
134	C₂×#95	C₂²×C₅	1	2	yes	—
135	C₂×#95	C₂²×C₅	1	4	yes	—
136	C₂×#95	C₂²×C₅	1	2	yes	—
137	C₂×#95	C₂²×C₅	1	4	yes	—
138	C₂³×C₅	—	2	32	no	—
139	C₂³×C₅	—	2	16	no	—
140	C₂³×C₅	—	2	8	no	—
141	C₂³×C₅	—	2	8	no	—
142	C₂³×C₅	—	2	4	no	—
143	C₂³×C₅	—	2	4	no	—
144	C₂³×C₅	—	4	8	no	—
145	C₂³×C₅	—	4	8	no	—
146	C₂³×C₅	—	4	16	no	—
147	C₂³×C₅	C₂³×C₄	1	8	yes	—
148	C₂³×C₅	C₂³×C₄	1	2	yes	—
149	C₂³×C₅	C₂×#41	1	8	yes	—
150	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
152	C₂³×C₅	C₂⁵	1	1	yes	characteristic
153	C₅×Q₈	—	4	16	no	—
154	C₅×D₄	—	4	16	no	—
155	C₂×C₄×C₅	—	2	16	no	—
156	C₂×C₄×C₅	—	2	8	no	—
157	C₂×C₄×C₅	—	2	16	no	—
158	C₂×C₄×C₅	—	2	32	no	—
159	C₂×C₄×C₅	—	2	8	no	—
160	C₂×C₄×C₅	—	2	8	no	—
161	C₂×C₄×C₅	—	2	8	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	2	4	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	8	no	—
167	C₂×C₄×C₅	—	2	8	no	—
168	C₂×C₄×C₅	—	2	8	no	—
169	C₂×C₄×C₅	—	4	32	no	—
170	C₂×C₄×C₅	—	4	16	no	—
171	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
172	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
173	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
174	C₂×C₄×C₅	C₂×#41	1	16	yes	—
175	C₂⁵	C₂³×C₅	1	2	yes	—
176	C₂²×Q₈	—	4	2	no	—
177	C₂²×Q₈	—	4	2	no	—
178	C₂²×Q₈	C₂×C₄×C₅	1	8	yes	complemented
179	C₂²×Q₈	C₂³×C₅	1	4	yes	—
180	C₂²×D₄	—	4	2	no	—
181	C₂²×D₄	—	4	2	no	—
182	C₂²×D₄	C₂×C₄×C₅	1	8	yes	—
183	C₂²×D₄	C₂³×C₅	1	4	yes	—
184	C₂³×C₄	—	2	16	no	—
185	C₂³×C₄	—	4	4	no	—
186	C₂³×C₄	C₂³×C₅	1	4	yes	—
187	C₂³×C₄	C₂³×C₅	1	8	yes	—
188	C₂³×C₄	C₂³×C₅	1	2	yes	—
189	C₂³×C₄	C₂³×C₅	1	2	yes	—
190	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂³×C₄	C₂³×C₅	1	4	yes	—
192	#124	C₂×C₄×C₅	1	64	yes	complemented
193	C₂×C₄⋊C₄	—	4	4	no	—
194	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
195	C₂×C₂²⋊C₄	—	2	16	no	—
196	C₂×C₂²⋊C₄	—	4	4	no	—
197	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	32	yes	complemented
198	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
199	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
200	C₂×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
201	C₂×C₄²	—	2	16	no	—
202	C₂×C₄²	—	4	4	no	—
203	C₂×C₄²	C₂×C₄×C₅	1	8	yes	complemented
204	C₂×C₄²	C₂³×C₅	1	16	yes	—
205	C₂×C₄²	C₂³×C₅	1	8	yes	—
206	C₂×C₄²	C₂³×C₅	1	4	yes	—
207	#95	C₂³×C₅	1	8	yes	—
208	#95	C₂³×C₅	1	16	yes	—
209	#95	C₂³×C₅	1	8	yes	—
210	#95	C₂³×C₅	1	16	yes	—
211	C₂²×C₅	—	2	16	no	—
212	C₂²×C₅	—	2	8	no	—
213	C₂²×C₅	—	4	32	no	—
214	C₂²×C₅	—	4	4	no	—
215	C₂²×C₅	—	4	4	no	—
216	C₂²×C₅	—	4	8	no	—
217	C₂²×C₅	C₄×#41	1	8	yes	—
218	C₂²×C₅	#518	1	4	yes	—
219	C₂²×C₅	#551	1	8	yes	—
220	C₂²×C₅	#555	1	8	yes	—
221	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
222	C₂²×C₅	C₂²×#41	1	4	yes	—
223	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
225	C₄×C₅	—	2	8	no	—
226	C₄×C₅	—	2	4	no	—
227	C₄×C₅	—	2	8	no	—
228	C₄×C₅	—	2	16	no	—
229	C₄×C₅	—	4	8	no	—
230	C₂⁴	—	2	8	no	—
231	C₂⁴	—	2	8	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	—	2	4	no	—
234	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
235	C₂⁴	C₂⁴×C₅	1	4	yes	—
236	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
237	C₂×Q₈	—	4	16	no	—
238	C₂×Q₈	—	4	4	no	—
239	C₂×Q₈	—	4	4	no	—
240	C₂×Q₈	C₂²×C₄×C₅	1	16	yes	complemented
241	C₂×D₄	—	4	16	no	—
242	C₂×D₄	—	4	4	no	—
243	C₂×D₄	—	4	4	no	—
244	C₂×D₄	C₂²×C₄×C₅	1	16	yes	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	8	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	32	no	—
256	C₂²×C₄	—	4	8	no	—
257	C₂²×C₄	—	4	32	no	—
258	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
259	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
261	C₂²×C₄	C₅×#41	1	16	yes	—
262	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
263	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
265	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
267	C₄⋊C₄	—	4	8	no	—
268	C₂²⋊C₄	—	2	32	no	—
269	C₂²⋊C₄	—	4	8	no	—
270	C₂²⋊C₄	C₂²×C₄×C₅	1	64	yes	complemented
271	C₄²	—	2	32	no	—
272	C₄²	—	4	8	no	—
273	C₄²	C₂²×C₄×C₅	1	16	yes	complemented
274	C₂×C₅	—	4	8	no	—
275	C₂×C₅	#2372	1	8	yes	direct product factor
276	C₂×C₅	C₂×C₄×#41	1	2	yes	—
277	C₂×C₅	C₂×#518	1	1	yes	characteristic
278	C₂×C₅	C₂×#551	1	2	yes	—
279	C₂×C₅	C₂×#555	1	2	yes	—
280	C₂³	—	2	32	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	8	no	—
283	C₂³	—	2	8	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	4	no	—
286	C₂³	—	4	8	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	16	no	—
289	C₂³	C₂³×C₄×C₅	1	8	yes	—
290	C₂³	C₂³×C₄×C₅	1	2	yes	—
291	C₂³	C₂×C₅×#41	1	8	yes	—
292	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
293	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
294	C₂³	C₂⁵×C₅	1	1	yes	characteristic
295	Q₈	—	4	16	no	—
296	D₄	—	4	16	no	—
297	C₂×C₄	—	2	16	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	16	no	—
300	C₂×C₄	—	2	32	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	4	32	no	—
312	C₂×C₄	—	4	16	no	—
313	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
314	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
315	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
316	C₂×C₄	C₂×C₅×#41	1	16	yes	—
317	C₅	C₂×#2372	1	1	yes	characteristic, direct product factor, Sylow
318	C₂²	—	2	16	no	—
319	C₂²	—	2	8	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	4	8	no	—
323	C₂²	—	4	32	no	—
324	C₂²	C₄×C₅×#41	1	8	yes	—
325	C₂²	C₅×#518	1	4	yes	—
326	C₂²	C₅×#551	1	8	yes	—
327	C₂²	C₅×#555	1	8	yes	—
328	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
329	C₂²	C₂²×C₅×#41	1	4	yes	—
330	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
332	C₄	—	2	8	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	8	no	—
335	C₄	—	2	16	no	—
336	C₄	—	4	8	no	—
337	C₂	—	4	8	no	—
338	C₂	C₅×#2372	1	8	yes	direct product factor
339	C₂	C₂×C₄×C₅×#41	1	2	yes	—
340	C₂	C₂×C₅×#518	1	1	yes	characteristic
341	C₂	C₂×C₅×#551	1	2	yes	—
342	C₂	C₂×C₅×#555	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2372	C₂	direct (N × H)
3. C₂×C₅×#391	C₂	semidirect
4. C₂×C₅×#388	C₂	semidirect
6. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
7. C₂×C₅×#376	C₂	semidirect
11. C₂×C₅×#124	C₄	semidirect
20. C₅×#391	C₂²	semidirect
21. C₅×#388	C₂²	semidirect
23. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
24. C₅×#376	C₂²	semidirect
29. C₂×#2372	C₅	direct (N × H)
33. C₂²×C₅×Q₈	C₂×C₄	semidirect
47. C₅×#124	C₂×C₄	semidirect
52. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
58. C₂×C₄²×C₅	C₂×C₄	semidirect
67. #2372	C₂×C₅	direct (N × H)
68. C₂×#391	C₂×C₅	semidirect
69. C₂×#388	C₂×C₅	semidirect
71. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
72. C₂×#376	C₂×C₅	semidirect
83. C₂×C₅×Q₈	C₂²×C₄	semidirect
113. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
116. C₄²×C₅	C₂²×C₄	semidirect
120. C₂×#124	C₄×C₅	semidirect
129. #391	C₂²×C₅	semidirect
130. #388	C₂²×C₅	semidirect
132. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
133. #376	C₂²×C₅	semidirect
178. C₂²×Q₈	C₂×C₄×C₅	semidirect
192. #124	C₂×C₄×C₅	semidirect
197. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
203. C₂×C₄²	C₂×C₄×C₅	semidirect
240. C₂×Q₈	C₂²×C₄×C₅	semidirect
270. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
273. C₄²	C₂²×C₄×C₅	semidirect
275. C₂×C₅	#2372	direct (N × H)
317. C₅	C₂×#2372	direct (N × H)
338. C₂	C₅×#2372	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×#124	2
C₅×#2372	2
C₂×C₅×#391	2
C₂×C₅×#388	2
C₂×C₅×#386	2
C₂×C₄×C₅×C₂²⋊C₄	2
C₂×C₅×#376	2
C₂×#2372	5

Subgroups — C2×C5×#2372 #11956867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2372 #11956867