Subgroups — C₅×#17793 #11940513

Order 1280.

762 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	2	yes	maximal
2	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1568	C₂	1	4	yes	maximal, complemented
4	C₅×#1567	C₂	1	2	yes	maximal, complemented
5	C₅×#1566	C₂	1	2	yes	maximal, complemented
6	C₅×#1564	C₂	1	4	yes	maximal, complemented
7	C₂³×C₅×C₈	C₄	1	2	yes	—
8	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
9	C₅×#432	—	2	2	no	—
10	C₅×#432	C₂²	1	4	yes	—
11	C₅×#431	—	2	2	no	—
12	C₅×#431	C₂²	1	4	yes	—
13	C₅×#423	C₂²	1	4	yes	—
14	C₅×#407	—	2	2	no	—
15	C₄×C₅×M₁₆	—	2	2	no	—
16	C₂×C₄×C₅×C₈	C₄	1	2	yes	—
17	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
18	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₄	1	1	yes	characteristic
21	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
25	C₅×#335	C₂²	1	8	yes	complemented
26	C₅×#334	C₂²	1	8	yes	complemented
27	#17793	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₅	Q₈	1	1	yes	characteristic
31	C₂×C₅×M₁₆	—	2	4	no	—
32	C₂²×C₅×C₈	—	2	8	no	—
33	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
34	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
36	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	D₄	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	Q₈	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	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₅×C₄⋊C₈	—	2	4	no	—
52	C₅×C₄⋊C₈	C₂³	1	8	yes	—
53	C₅×C₂²⋊C₈	—	2	4	no	—
54	C₅×C₂²⋊C₈	—	2	4	no	—
55	C₅×#97	—	2	4	no	—
56	C₄×C₅×C₈	—	2	4	no	—
57	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
60	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
61	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
62	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
63	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
64	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
65	C₄×C₅×C₈	C₂³	1	2	yes	—
66	C₄×C₅×C₈	C₂³	1	2	yes	—
67	#2920	C₂×C₅	1	2	yes	—
68	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic
69	#1568	C₂×C₅	1	4	yes	complemented
70	#1567	C₂×C₅	1	2	yes	complemented
71	#1566	C₂×C₅	1	2	yes	complemented
72	#1564	C₂×C₅	1	4	yes	complemented
73	C₂⁴×C₅	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₅	—	2	4	no	—
75	C₂²×C₄×C₅	—	2	4	no	—
76	C₂²×C₄×C₅	—	2	4	no	—
77	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
95	C₅×M₁₆	—	4	8	no	—
96	C₂×C₅×C₈	—	2	4	no	—
97	C₂×C₅×C₈	—	2	4	no	—
98	C₂×C₅×C₈	—	2	4	no	—
99	C₂×C₅×C₈	—	2	4	no	—
100	C₂×C₅×C₈	—	2	4	no	—
101	C₂×C₅×C₈	—	2	8	no	—
102	C₂×C₅×C₈	M₁₆	1	8	yes	complemented
103	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
105	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
106	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
107	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₅	C₂⁴	1	1	yes	characteristic
123	C₂³×C₈	C₄×C₅	1	2	yes	—
124	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
125	#432	—	2	2	no	—
126	#432	C₂²×C₅	1	4	yes	—
127	#431	—	2	2	no	—
128	#431	C₂²×C₅	1	4	yes	—
129	#423	C₂²×C₅	1	4	yes	—
130	#407	—	2	2	no	—
131	C₄×M₁₆	—	2	2	no	—
132	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
133	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
134	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
135	C₂×C₄×C₈	C₄×C₅	1	2	yes	—
136	C₂×C₄×C₈	C₄×C₅	1	1	yes	characteristic
137	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
138	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
140	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
141	#335	C₂²×C₅	1	8	yes	complemented
142	#334	C₂²×C₅	1	8	yes	complemented
143	C₂³×C₅	—	2	2	no	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₅	—	2	2	no	—
150	C₂×C₄×C₅	—	2	2	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	2	no	—
155	C₂×C₄×C₅	—	2	2	no	—
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	#108	1	4	yes	—
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₅	#135	1	4	yes	—
176	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
179	C₅×C₈	—	2	2	no	—
180	C₅×C₈	—	2	2	no	—
181	C₅×C₈	—	4	8	no	—
182	C₅×C₈	C₂×M₁₆	1	4	yes	—
183	C₅×C₈	C₂×M₁₆	1	4	yes	—
184	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂³×C₄	C₅×Q₈	1	1	yes	characteristic
187	C₂×M₁₆	—	2	4	no	—
188	C₂²×C₈	—	2	8	no	—
189	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
190	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
191	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
192	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
193	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
194	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
195	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
196	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
197	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
198	C₂×C₄²	C₅×D₄	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×Q₈	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	C₂³×C₅	1	1	yes	characteristic
205	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
207	C₄⋊C₈	—	2	4	no	—
208	C₄⋊C₈	C₂³×C₅	1	8	yes	—
209	C₂²⋊C₈	—	2	4	no	—
210	C₂²⋊C₈	—	2	4	no	—
211	#97	—	2	4	no	—
212	C₄×C₈	—	2	4	no	—
213	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
214	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
215	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
216	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
217	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
218	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
219	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
220	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
221	C₄×C₈	C₂³×C₅	1	2	yes	—
222	C₄×C₈	C₂³×C₅	1	2	yes	—
223	C₂²×C₅	—	2	8	no	—
224	C₂²×C₅	—	2	1	no	—
225	C₂²×C₅	—	2	1	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	1	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	1	no	—
230	C₂²×C₅	#423	1	2	yes	—
231	C₂²×C₅	#427	1	2	yes	—
232	C₂²×C₅	C₂×#108	1	2	yes	—
233	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	1	no	—
237	C₄×C₅	—	2	1	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	1	no	—
240	C₄×C₅	#423	1	2	yes	—
241	C₄×C₅	#427	1	2	yes	—
242	C₄×C₅	C₂×#108	1	2	yes	—
243	C₄×C₅	C₂×#108	1	2	yes	—
244	C₄×C₅	C₂²×M₁₆	1	2	yes	—
245	C₄×C₅	C₂×#135	1	2	yes	—
246	C₂⁴	C₅×C₄⋊C₄	1	1	yes	characteristic
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
268	M₁₆	—	4	8	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	4	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	C₅×M₁₆	1	8	yes	complemented
276	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
277	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
278	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
279	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
280	C₄²	C₅×C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
288	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
289	C₄²	C₂×C₅×D₄	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×Q₈	1	1	yes	characteristic
293	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
294	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
295	C₄²	C₂⁴×C₅	1	1	yes	characteristic
296	C₂×C₅	—	2	2	no	—
297	C₂×C₅	—	2	2	no	—
298	C₂×C₅	—	2	2	no	—
299	C₂×C₅	C₂×#423	1	1	yes	characteristic
300	C₂×C₅	C₂×#427	1	1	yes	characteristic
301	C₂×C₅	C₂²×#108	1	1	yes	characteristic
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
306	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
307	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
308	C₂×C₄	—	2	2	no	—
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	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	C₅×#108	1	4	yes	—
324	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
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×M₁₆	1	4	yes	—
334	C₂×C₄	C₅×#135	1	4	yes	—
335	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	4	8	no	—
341	C₈	C₂×C₅×M₁₆	1	4	yes	—
342	C₈	C₂×C₅×M₁₆	1	4	yes	—
343	C₅	#17793	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	8	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	C₅×#423	1	2	yes	—
352	C₂²	C₅×#427	1	2	yes	—
353	C₂²	C₂×C₅×#108	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	C₅×#423	1	2	yes	—
362	C₄	C₅×#427	1	2	yes	—
363	C₄	C₂×C₅×#108	1	2	yes	—
364	C₄	C₂×C₅×#108	1	2	yes	—
365	C₄	C₂²×C₅×M₁₆	1	2	yes	—
366	C₄	C₂×C₅×#135	1	2	yes	—
367	C₂	—	2	2	no	—
368	C₂	—	2	2	no	—
369	C₂	—	2	2	no	—
370	C₂	C₂×C₅×#423	1	1	yes	characteristic
371	C₂	C₂×C₅×#427	1	1	yes	characteristic
372	C₂	C₂²×C₅×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₅	C₂×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 ◁ C₄²×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1568	C₂	semidirect
4. C₅×#1567	C₂	semidirect
5. C₅×#1566	C₂	semidirect
6. C₅×#1564	C₂	semidirect
25. C₅×#335	C₂²	semidirect
26. C₅×#334	C₂²	semidirect
27. #17793	C₅	direct (N × H)
69. #1568	C₂×C₅	semidirect
70. #1567	C₂×C₅	semidirect
71. #1566	C₂×C₅	semidirect
72. #1564	C₂×C₅	semidirect
102. C₂×C₅×C₈	M₁₆	semidirect
141. #335	C₂²×C₅	semidirect
142. #334	C₂²×C₅	semidirect
275. C₂×C₈	C₅×M₁₆	semidirect
343. C₅	#17793	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
C₂²×C₄×C₅×C₈	2
C₅×#1568	2
C₅×#1567	2
C₅×#1566	2
C₅×#1564	2
#17793	5

Subgroups — C5×#17793 #11940513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17793 #11940513