Subgroups — C₅×#22629 #11945349

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#1939	C₂	1	2	yes	maximal, complemented
3	C₅×#1917	C₂	1	4	yes	maximal, complemented
4	C₅×#1797	C₂	1	2	yes	maximal
5	C₅×#1797	C₂	1	1	yes	maximal, characteristic
6	C₅×#1770	C₂	1	2	yes	maximal, complemented
7	C₅×#1749	C₂	1	2	yes	maximal
8	C₄×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#97	C₂²	1	4	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
20	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
22	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×#95	C₄	1	2	yes	—
27	C₅×#336	C₂²	1	4	yes	—
28	C₅×#336	C₂²	1	2	yes	—
29	C₅×#336	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	4	yes	—
31	#22629	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₅×C₈	C₂³	1	2	yes	—
38	C₂²×C₅×C₈	C₂³	1	4	yes	—
39	C₂²×C₅×C₈	C₂³	1	2	yes	—
40	C₂×C₅×C₄⋊C₄	—	2	4	no	—
41	C₂×C₅×C₄⋊C₄	—	2	4	no	—
42	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₅	—	2	4	no	—
49	C₂×C₄²×C₅	—	4	4	no	—
50	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅	C₂³	1	2	yes	—
55	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂³	1	2	yes	—
57	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₅×C₄⋊C₈	—	2	4	no	—
59	C₅×C₄⋊C₈	—	4	4	no	—
60	C₅×C₂²⋊C₈	—	2	2	no	—
61	C₅×C₂²⋊C₈	—	2	4	no	—
62	C₅×C₂²⋊C₈	Q₈	1	4	yes	—
63	C₅×#97	—	4	4	no	—
64	C₄×C₅×C₈	—	2	4	no	—
65	C₅×#95	C₂×C₄	1	2	yes	—
66	C₅×#95	C₂×C₄	1	2	yes	—
67	C₅×#95	C₂×C₄	1	2	yes	—
68	C₅×#95	C₂×C₄	1	2	yes	—
69	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
70	#1939	C₂×C₅	1	2	yes	complemented
71	#1917	C₂×C₅	1	4	yes	complemented
72	#1797	C₂×C₅	1	1	yes	characteristic
73	#1797	C₂×C₅	1	2	yes	—
74	#1770	C₂×C₅	1	2	yes	complemented
75	#1749	C₂×C₅	1	2	yes	—
76	C₄×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
77	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅	—	2	2	no	—
79	C₂²×C₄×C₅	—	2	2	no	—
80	C₂²×C₄×C₅	—	2	2	no	—
81	C₂²×C₄×C₅	—	2	2	no	—
82	C₂²×C₄×C₅	—	2	4	no	—
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	2	4	no	—
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	4	no	—
87	C₂²×C₄×C₅	—	4	2	no	—
88	C₂²×C₄×C₅	—	4	2	no	—
89	C₂²×C₄×C₅	—	4	1	no	—
90	C₂²×C₄×C₅	—	4	2	no	—
91	C₂²×C₄×C₅	M₁₆	1	4	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₅	#41	1	2	yes	—
103	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₂×C₅×C₈	—	2	2	no	—
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	4	no	—
109	C₂×C₅×C₈	—	2	4	no	—
110	C₂×C₅×C₈	—	2	4	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
113	C₅×C₄⋊C₄	—	2	4	no	—
114	C₅×C₄⋊C₄	—	2	4	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	M₁₆	1	4	yes	—
119	C₄²×C₅	—	2	2	no	—
120	C₄²×C₅	—	2	2	no	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	—	2	4	no	—
123	C₄²×C₅	—	2	4	no	—
124	C₄²×C₅	—	4	2	no	—
125	C₄²×C₅	—	4	2	no	—
126	C₄²×C₅	#41	1	4	yes	—
127	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
128	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
129	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄²	C₂²×C₅	1	2	yes	—
131	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
133	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
135	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
136	C₂×#97	C₂²×C₅	1	4	yes	—
137	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
138	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
139	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
140	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
141	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
142	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
143	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×#95	C₄×C₅	1	2	yes	—
145	#336	C₂²×C₅	1	2	yes	—
146	#336	C₂²×C₅	1	4	yes	—
147	#336	C₂²×C₅	1	2	yes	—
148	#336	C₂²×C₅	1	4	yes	—
149	C₂³×C₅	—	2	1	no	—
150	C₂³×C₅	—	2	1	no	—
151	C₂³×C₅	—	2	1	no	—
152	C₂³×C₅	—	2	1	no	—
153	C₂³×C₅	C₄×Q₈	1	2	yes	—
154	C₂³×C₅	C₂×M₁₆	1	2	yes	—
155	C₂³×C₅	#131	1	2	yes	—
156	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	1	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	1	no	—
161	C₂×C₄×C₅	—	2	1	no	—
162	C₂×C₄×C₅	—	2	1	no	—
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	4	no	—
166	C₂×C₄×C₅	—	2	4	no	—
167	C₂×C₄×C₅	—	2	8	no	—
168	C₂×C₄×C₅	—	2	1	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	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	4	4	no	—
181	C₂×C₄×C₅	—	4	8	no	—
182	C₂×C₄×C₅	—	4	8	no	—
183	C₂×C₄×C₅	#117	1	2	yes	—
184	C₂×C₄×C₅	#117	1	2	yes	—
185	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
186	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
188	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
189	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×#41	1	2	yes	—
193	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
194	C₅×C₈	—	2	4	no	—
195	C₅×C₈	—	4	2	no	—
196	C₅×C₈	—	4	4	no	—
197	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
198	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
199	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
201	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₅	1	2	yes	—
203	C₂²×C₈	C₂³×C₅	1	4	yes	—
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
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	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₄²	—	2	4	no	—
214	C₂×C₄²	—	4	4	no	—
215	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
219	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₅	1	2	yes	—
221	C₂×C₄²	C₂³×C₅	1	2	yes	—
222	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
223	C₄⋊C₈	—	2	4	no	—
224	C₄⋊C₈	—	4	4	no	—
225	C₂²⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	2	4	no	—
227	C₂²⋊C₈	C₅×Q₈	1	4	yes	—
228	#97	—	4	4	no	—
229	C₄×C₈	—	2	4	no	—
230	#95	C₂×C₄×C₅	1	2	yes	—
231	#95	C₂×C₄×C₅	1	2	yes	—
232	#95	C₂×C₄×C₅	1	2	yes	—
233	#95	C₂×C₄×C₅	1	2	yes	—
234	C₂²×C₅	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	2	2	no	—
239	C₂²×C₅	—	2	2	no	—
240	C₂²×C₅	#446	1	4	yes	—
241	C₂²×C₅	C₂×#117	1	1	yes	characteristic
242	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
243	C₂²×C₅	#518	1	1	yes	characteristic
244	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
245	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
246	C₂²×C₅	C₂×#131	1	1	yes	characteristic
247	C₂²×C₅	#568	1	1	yes	characteristic
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	2	no	—
250	C₄×C₅	—	2	2	no	—
251	C₄×C₅	—	2	4	no	—
252	C₄×C₅	—	4	1	no	—
253	C₄×C₅	—	4	2	no	—
254	C₄×C₅	—	4	2	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	#432	1	4	yes	—
257	C₄×C₅	#553	1	2	yes	—
258	C₄×C₅	#554	1	2	yes	—
259	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	1	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₅×M₁₆	1	4	yes	—
274	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
276	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
277	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
284	C₂²×C₄	C₅×#41	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	4	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	C₅×#41	1	4	yes	—
309	C₂×C₅	—	2	4	no	—
310	C₂×C₅	#2345	1	1	yes	characteristic
311	C₂×C₅	C₂×#432	1	1	yes	characteristic
312	C₂×C₅	#2924	1	1	yes	characteristic
313	C₂×C₅	C₂×#446	1	1	yes	characteristic
314	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
315	C₂×C₅	#2974	1	1	yes	characteristic
316	C₂×C₅	#2975	1	1	yes	characteristic
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	C₄×C₅×Q₈	1	2	yes	—
322	C₂³	C₂×C₅×M₁₆	1	2	yes	—
323	C₂³	C₅×#131	1	2	yes	—
324	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	8	no	—
351	C₂×C₄	C₅×#117	1	2	yes	—
352	C₂×C₄	C₅×#117	1	2	yes	—
353	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
354	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
355	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
356	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
357	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
358	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
359	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
360	C₂×C₄	C₂×C₅×#41	1	2	yes	—
361	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
362	C₈	—	2	4	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	4	no	—
365	C₅	#22629	1	1	yes	characteristic, direct product factor, Sylow
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	C₅×#446	1	4	yes	—
373	C₂²	C₂×C₅×#117	1	1	yes	characteristic
374	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
375	C₂²	C₅×#518	1	1	yes	characteristic
376	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
377	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
378	C₂²	C₂×C₅×#131	1	1	yes	characteristic
379	C₂²	C₅×#568	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	C₅×#432	1	4	yes	—
389	C₄	C₅×#553	1	2	yes	—
390	C₄	C₅×#554	1	2	yes	—
391	C₂	—	2	4	no	—
392	C₂	C₅×#2345	1	1	yes	characteristic
393	C₂	C₂×C₅×#432	1	1	yes	characteristic
394	C₂	C₅×#2924	1	1	yes	characteristic
395	C₂	C₂×C₅×#446	1	1	yes	characteristic
396	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic
397	C₂	C₅×#2974	1	1	yes	characteristic
398	C₂	C₅×#2975	1	1	yes	characteristic

	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
2. C₅×#1939	C₂	semidirect
3. C₅×#1917	C₂	semidirect
6. C₅×#1770	C₂	semidirect
31. #22629	C₅	direct (N × H)
70. #1939	C₂×C₅	semidirect
71. #1917	C₂×C₅	semidirect
74. #1770	C₂×C₅	semidirect
365. C₅	#22629	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×C₄×C₅×C₄⋊C₄	2
C₅×#1939	2
C₅×#1917	2
C₅×#1797	2
C₅×#1770	2
C₅×#1749	2
C₄×C₅×C₂²⋊C₈	2
#22629	5

Subgroups — C5×#22629 #11945349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22629 #11945349