Subgroups — C₅×#17816 #11940536

Order 1280.

640 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2920	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic
4	C₅×#1572	C₂	1	4	yes	maximal, complemented
5	C₅×#1571	C₂	1	2	yes	maximal, complemented
6	C₅×#1570	C₂	1	2	yes	maximal, complemented
7	C₅×#1568	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#432	—	2	1	no	—
10	C₅×#432	—	2	1	no	—
11	C₅×#432	—	2	1	no	—
12	C₅×#432	C₂²	1	2	yes	—
13	C₅×#432	C₂²	1	2	yes	—
14	C₅×#432	C₂²	1	2	yes	—
15	C₅×#431	—	2	1	no	—
16	C₅×#431	C₄	1	2	yes	—
17	C₅×#431	C₄	1	2	yes	—
18	C₅×#431	C₂²	1	2	yes	—
19	C₅×#431	C₂²	1	1	yes	characteristic
20	C₅×#431	C₂²	1	1	yes	characteristic
21	C₅×#431	C₂²	1	2	yes	—
22	C₅×#423	C₂²	1	2	yes	—
23	C₂×C₅×C₄⋊C₈	C₄	1	2	yes	—
24	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
25	C₅×#407	—	2	1	no	—
26	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
27	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
28	C₄×C₅×M₁₆	—	2	1	no	—
29	C₂×C₅×#97	—	2	1	no	—
30	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
31	C₅×#335	C₂²	1	8	yes	complemented
32	C₅×#334	C₂²	1	8	yes	complemented
33	#17816	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂²×C₅×C₈	—	2	2	no	—
39	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
47	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
48	C₂×C₄²×C₅	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊C₈	—	2	2	no	—
53	C₅×C₄⋊C₈	—	2	2	no	—
54	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
55	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
56	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
57	C₅×C₄⋊C₈	C₂³	1	4	yes	—
58	C₅×C₄⋊C₈	C₂³	1	4	yes	—
59	C₅×C₂²⋊C₈	—	2	2	no	—
60	C₅×C₂²⋊C₈	—	2	2	no	—
61	C₅×C₂²⋊C₈	—	2	2	no	—
62	C₅×C₂²⋊C₈	—	2	2	no	—
63	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₅×C₂²⋊C₈	C₂×C₄	1	4	yes	—
66	C₅×#97	—	2	2	no	—
67	C₅×#97	—	2	2	no	—
68	C₅×#97	—	2	2	no	—
69	C₄×C₅×C₈	—	2	2	no	—
70	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
71	C₄×C₅×C₈	C₂³	1	2	yes	—
72	C₄×C₅×C₈	C₂³	1	2	yes	—
73	#2920	C₂×C₅	1	1	yes	characteristic
74	C₂×#432	C₂×C₅	1	1	yes	characteristic
75	C₂×#431	C₂×C₅	1	1	yes	characteristic
76	#1572	C₂×C₅	1	4	yes	complemented
77	#1571	C₂×C₅	1	2	yes	complemented
78	#1570	C₂×C₅	1	2	yes	complemented
79	#1568	C₂×C₅	1	4	yes	complemented
80	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	—	2	4	no	—
82	C₂²×C₄×C₅	—	4	2	no	—
83	C₂²×C₄×C₅	—	4	2	no	—
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
102	C₅×M₁₆	—	4	4	no	—
103	C₂×C₅×C₈	—	2	4	no	—
104	C₂×C₅×C₈	—	2	4	no	—
105	C₂×C₅×C₈	—	4	4	no	—
106	C₂×C₅×C₈	—	4	4	no	—
107	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
109	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
123	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
124	C₄²×C₅	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
126	#432	—	2	1	no	—
127	#432	—	2	1	no	—
128	#432	—	2	1	no	—
129	#432	C₂²×C₅	1	2	yes	—
130	#432	C₂²×C₅	1	2	yes	—
131	#432	C₂²×C₅	1	2	yes	—
132	#431	—	2	1	no	—
133	#431	C₄×C₅	1	2	yes	—
134	#431	C₄×C₅	1	2	yes	—
135	#431	C₂²×C₅	1	2	yes	—
136	#431	C₂²×C₅	1	1	yes	characteristic
137	#431	C₂²×C₅	1	1	yes	characteristic
138	#431	C₂²×C₅	1	2	yes	—
139	#423	C₂²×C₅	1	2	yes	—
140	C₂×C₄⋊C₈	C₄×C₅	1	2	yes	—
141	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
142	#407	—	2	1	no	—
143	C₂×C₂²⋊C₈	—	2	1	no	—
144	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
145	C₄×M₁₆	—	2	1	no	—
146	C₂×#97	—	2	1	no	—
147	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
148	#335	C₂²×C₅	1	8	yes	complemented
149	#334	C₂²×C₅	1	8	yes	complemented
150	C₂³×C₅	—	2	2	no	—
151	C₂³×C₅	—	2	2	no	—
152	C₂³×C₅	—	4	1	no	—
153	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅	—	2	2	no	—
157	C₂×C₄×C₅	—	2	2	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	4	1	no	—
167	C₂×C₄×C₅	—	4	1	no	—
168	C₂×C₄×C₅	—	4	1	no	—
169	C₂×C₄×C₅	—	4	1	no	—
170	C₂×C₄×C₅	—	4	1	no	—
171	C₂×C₄×C₅	—	4	1	no	—
172	C₂×C₄×C₅	—	4	1	no	—
173	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₅	#135	1	4	yes	—
183	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
186	C₅×C₈	—	2	4	no	—
187	C₅×C₈	—	2	4	no	—
188	C₅×C₈	—	4	4	no	—
189	C₅×C₈	—	4	4	no	—
190	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
192	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
193	C₂×M₁₆	—	2	2	no	—
194	C₂²×C₈	—	2	2	no	—
195	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
196	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
200	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
201	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
202	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
203	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
204	C₂×C₄²	C₅×Q₈	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
207	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
208	C₄⋊C₈	—	2	2	no	—
209	C₄⋊C₈	—	2	2	no	—
210	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
211	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
212	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
213	C₄⋊C₈	C₂³×C₅	1	4	yes	—
214	C₄⋊C₈	C₂³×C₅	1	4	yes	—
215	C₂²⋊C₈	—	2	2	no	—
216	C₂²⋊C₈	—	2	2	no	—
217	C₂²⋊C₈	—	2	2	no	—
218	C₂²⋊C₈	—	2	2	no	—
219	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
220	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
221	C₂²⋊C₈	C₂×C₄×C₅	1	4	yes	—
222	#97	—	2	2	no	—
223	#97	—	2	2	no	—
224	#97	—	2	2	no	—
225	C₄×C₈	—	2	2	no	—
226	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
227	C₄×C₈	C₂³×C₅	1	2	yes	—
228	C₄×C₈	C₂³×C₅	1	2	yes	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	2	1	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	4	4	no	—
237	C₂²×C₅	#427	1	2	yes	—
238	C₂²×C₅	#430	1	2	yes	—
239	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	—	2	1	no	—
244	C₄×C₅	—	2	1	no	—
245	C₄×C₅	—	2	1	no	—
246	C₄×C₅	—	2	1	no	—
247	C₄×C₅	—	2	1	no	—
248	C₄×C₅	—	2	1	no	—
249	C₄×C₅	#427	1	2	yes	—
250	C₄×C₅	#568	1	2	yes	—
251	C₄×C₅	C₂×#135	1	2	yes	—
252	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
267	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
274	M₁₆	—	4	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	4	4	no	—
278	C₂×C₈	—	4	4	no	—
279	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
280	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
281	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
282	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
283	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
284	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
285	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
286	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
287	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
290	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
291	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
292	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
293	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
294	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
295	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
296	C₄²	C₂⁴×C₅	1	1	yes	characteristic
297	C₂×C₅	—	2	2	no	—
298	C₂×C₅	—	2	2	no	—
299	C₂×C₅	—	4	1	no	—
300	C₂×C₅	#2905	1	1	yes	characteristic
301	C₂×C₅	C₂×#427	1	1	yes	characteristic
302	C₂×C₅	C₂×#430	1	1	yes	characteristic
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
307	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
308	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
327	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
328	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₅×#135	1	4	yes	—
336	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₈	—	2	4	no	—
341	C₈	—	4	4	no	—
342	C₈	—	4	4	no	—
343	C₅	#17816	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	4	4	no	—
352	C₂²	C₅×#427	1	2	yes	—
353	C₂²	C₅×#430	1	2	yes	—
354	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	C₅×#427	1	2	yes	—
365	C₄	C₅×#568	1	2	yes	—
366	C₄	C₂×C₅×#135	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	C₅×#2905	1	1	yes	characteristic
371	C₂	C₂×C₅×#427	1	1	yes	characteristic
372	C₂	C₂×C₅×#430	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₅×#1572	C₂	semidirect
5. C₅×#1571	C₂	semidirect
6. C₅×#1570	C₂	semidirect
7. C₅×#1568	C₂	semidirect
31. C₅×#335	C₂²	semidirect
32. C₅×#334	C₂²	semidirect
33. #17816	C₅	direct (N × H)
76. #1572	C₂×C₅	semidirect
77. #1571	C₂×C₅	semidirect
78. #1570	C₂×C₅	semidirect
79. #1568	C₂×C₅	semidirect
148. #335	C₂²×C₅	semidirect
149. #334	C₂²×C₅	semidirect
343. C₅	#17816	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×#2920	2
C₂×C₅×#432	2
C₂×C₅×#431	2
C₅×#1572	2
C₅×#1571	2
C₅×#1570	2
C₅×#1568	2
#17816	5

Subgroups — C5×#17816 #11940536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17816 #11940536