Subgroups — C₅×#17839 #11940559

Order 1280.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2991	C₂	1	1	yes	maximal, characteristic
2	C₅×#2990	C₂	1	1	yes	maximal, characteristic
3	C₅×#2965	C₂	1	1	yes	maximal, characteristic
4	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1574	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1572	C₂	1	2	yes	maximal, complemented
7	C₅×#1571	C₂	1	2	yes	maximal, complemented
8	C₅×#1569	C₂	1	2	yes	maximal, complemented
9	C₅×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1565	C₂	1	2	yes	maximal, complemented
11	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₅×#41	C₂²	1	1	yes	characteristic
13	C₅×#446	—	2	1	no	—
14	C₅×#446	C₄	1	1	yes	characteristic
15	C₅×#446	C₄	1	1	yes	characteristic
16	C₅×C₈×Q₈	—	2	1	no	—
17	C₅×#436	—	2	1	no	—
18	C₅×#436	—	2	2	no	—
19	C₅×#436	C₄	1	1	yes	characteristic
20	C₅×#436	C₄	1	1	yes	characteristic
21	C₅×#435	—	2	2	no	—
22	C₅×#435	C₄	1	2	yes	—
23	C₅×#435	C₄	1	2	yes	—
24	C₅×C₈×D₄	—	2	1	no	—
25	C₅×#432	C₂²	1	2	yes	—
26	C₅×#431	C₂²	1	1	yes	characteristic
27	C₅×#431	C₂²	1	1	yes	characteristic
28	C₅×#431	C₂²	1	2	yes	—
29	C₅×#431	C₂²	1	2	yes	—
30	C₅×#431	C₂²	1	1	yes	characteristic
31	C₅×#423	C₂²	1	1	yes	characteristic
32	C₅×#423	C₂²	1	1	yes	characteristic
33	C₅×#423	C₂²	1	2	yes	—
34	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
35	C₄×C₅×M₁₆	C₂²	1	2	yes	—
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×#335	C₂²	1	1	yes	characteristic
38	C₅×#335	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#335	C₂²	1	2	yes	—
41	C₅×#335	C₂²	1	2	yes	—
42	C₅×#335	C₂²	1	2	yes	—
43	C₅×#334	C₂²	1	1	yes	characteristic
44	C₅×#334	C₂²	1	1	yes	characteristic
45	C₅×#334	C₂²	1	2	yes	—
46	C₅×#334	C₂²	1	2	yes	—
47	#17839	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	Q₈	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	—	2	2	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
57	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
59	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
60	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×D₄	D₄	1	1	yes	characteristic
62	C₄×C₅×D₄	D₄	1	2	yes	—
63	C₅×#117	Q₈	1	1	yes	characteristic
64	C₅×#117	Q₈	1	2	yes	—
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	2	yes	—
67	C₅×C₄⋊C₈	—	2	2	no	—
68	C₅×C₄⋊C₈	—	2	1	no	—
69	C₅×C₄⋊C₈	—	2	1	no	—
70	C₅×C₄⋊C₈	—	2	2	no	—
71	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂³	1	2	yes	—
79	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₅×C₄⋊C₈	C₂³	1	2	yes	—
81	C₅×C₂²⋊C₈	—	2	1	no	—
82	C₅×C₂²⋊C₈	—	2	2	no	—
83	C₅×C₂²⋊C₈	—	2	1	no	—
84	C₅×C₂²⋊C₈	—	2	2	no	—
85	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₅×#97	—	2	2	no	—
89	C₅×#97	C₂×C₄	1	2	yes	—
90	C₅×#97	C₂×C₄	1	2	yes	—
91	C₄×C₅×C₈	—	2	1	no	—
92	C₄×C₅×C₈	—	2	1	no	—
93	C₄×C₅×C₈	—	2	2	no	—
94	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₄×C₅×C₈	C₂³	1	2	yes	—
99	#2991	C₂×C₅	1	1	yes	characteristic
100	#2990	C₂×C₅	1	1	yes	characteristic
101	#2965	C₂×C₅	1	1	yes	characteristic
102	#1574	C₂×C₅	1	1	yes	characteristic, complemented
103	#1574	C₂×C₅	1	1	yes	characteristic, complemented
104	#1572	C₂×C₅	1	2	yes	complemented
105	#1571	C₂×C₅	1	2	yes	complemented
106	#1569	C₂×C₅	1	2	yes	complemented
107	#1567	C₂×C₅	1	1	yes	characteristic, complemented
108	#1565	C₂×C₅	1	2	yes	complemented
109	#1564	C₂×C₅	1	1	yes	characteristic, complemented
110	C₅×#41	—	4	2	no	—
111	C₂×C₅×Q₈	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₅×D₄	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
114	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
120	C₅×M₁₆	—	2	4	no	—
121	C₅×M₁₆	—	4	2	no	—
122	C₅×M₁₆	—	8	1	no	—
123	C₅×M₁₆	—	8	2	no	—
124	C₅×M₁₆	—	8	1	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	1	no	—
127	C₂×C₅×C₈	—	2	2	no	—
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	2	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	4	1	no	—
133	C₂×C₅×C₈	—	8	2	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
140	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
141	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
142	C₅×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
143	C₅×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
144	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
145	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
146	C₅×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
147	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂²×C₄	1	2	yes	—
149	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₅	C₂×D₄	1	2	yes	—
151	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
152	C₄²×C₅	C₂×Q₈	1	2	yes	—
153	C₄²×C₅	C₂⁴	1	1	yes	characteristic
154	C₄×#41	C₂²×C₅	1	1	yes	characteristic
155	#446	—	2	1	no	—
156	#446	C₄×C₅	1	1	yes	characteristic
157	#446	C₄×C₅	1	1	yes	characteristic
158	C₈×Q₈	—	2	1	no	—
159	#436	—	2	1	no	—
160	#436	—	2	2	no	—
161	#436	C₄×C₅	1	1	yes	characteristic
162	#436	C₄×C₅	1	1	yes	characteristic
163	#435	—	2	2	no	—
164	#435	C₄×C₅	1	2	yes	—
165	#435	C₄×C₅	1	2	yes	—
166	C₈×D₄	—	2	1	no	—
167	#432	C₂²×C₅	1	2	yes	—
168	#431	C₂²×C₅	1	1	yes	characteristic
169	#431	C₂²×C₅	1	1	yes	characteristic
170	#431	C₂²×C₅	1	2	yes	—
171	#431	C₂²×C₅	1	2	yes	—
172	#431	C₂²×C₅	1	1	yes	characteristic
173	#423	C₂²×C₅	1	1	yes	characteristic
174	#423	C₂²×C₅	1	1	yes	characteristic
175	#423	C₂²×C₅	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
177	C₄×M₁₆	C₂²×C₅	1	2	yes	—
178	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
179	#335	C₂²×C₅	1	1	yes	characteristic
180	#335	C₂²×C₅	1	1	yes	characteristic
181	#335	C₂²×C₅	1	2	yes	—
182	#335	C₂²×C₅	1	2	yes	—
183	#335	C₂²×C₅	1	2	yes	—
184	#335	C₂²×C₅	1	2	yes	—
185	#334	C₂²×C₅	1	1	yes	characteristic
186	#334	C₂²×C₅	1	1	yes	characteristic
187	#334	C₂²×C₅	1	2	yes	—
188	#334	C₂²×C₅	1	2	yes	—
189	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
191	C₅×Q₈	—	2	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
213	C₅×C₈	—	2	1	no	—
214	C₅×C₈	—	2	2	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	—	2	2	no	—
218	C₅×C₈	—	4	1	no	—
219	C₅×C₈	—	4	2	no	—
220	C₅×C₈	—	4	1	no	—
221	C₅×C₈	—	4	2	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	4	1	no	—
224	C₅×C₈	#131	1	2	yes	—
225	C₂×#41	C₅×Q₈	1	1	yes	characteristic
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
230	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
234	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
235	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
236	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
237	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
238	C₄×D₄	C₅×D₄	1	1	yes	characteristic
239	C₄×D₄	C₅×D₄	1	2	yes	—
240	#117	C₅×Q₈	1	1	yes	characteristic
241	#117	C₅×Q₈	1	2	yes	—
242	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₅	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
249	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
250	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
251	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
252	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
253	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
255	C₄⋊C₈	C₂³×C₅	1	2	yes	—
256	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
257	C₄⋊C₈	C₂³×C₅	1	2	yes	—
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	—	2	2	no	—
262	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
263	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
264	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
265	#97	—	2	2	no	—
266	#97	C₂×C₄×C₅	1	2	yes	—
267	#97	C₂×C₄×C₅	1	2	yes	—
268	C₄×C₈	—	2	1	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	—	2	2	no	—
271	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
272	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₅	1	2	yes	—
275	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
283	C₄×C₅	—	2	1	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	2	no	—
289	C₄×C₅	#430	1	2	yes	—
290	C₄×C₅	C₂×#131	1	1	yes	characteristic
291	C₄×C₅	#568	1	1	yes	characteristic
292	C₄×C₅	#576	1	1	yes	characteristic
293	C₄×C₅	#578	1	1	yes	characteristic
294	#41	—	4	2	no	—
295	C₂×Q₈	C₅×C₄⋊C₄	1	1	yes	characteristic
296	C₂×D₄	C₅×C₄⋊C₄	1	1	yes	characteristic
297	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
304	M₁₆	—	2	4	no	—
305	M₁₆	—	4	2	no	—
306	M₁₆	—	8	1	no	—
307	M₁₆	—	8	2	no	—
308	M₁₆	—	8	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	8	2	no	—
318	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
319	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
322	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
323	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
324	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
325	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
326	C₄⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
327	C₄⋊C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
328	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
329	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
330	C₂²⋊C₄	C₅×C₄⋊C₄	1	2	yes	—
331	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
332	C₄²	C₂²×C₄×C₅	1	2	yes	—
333	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
334	C₄²	C₂×C₅×D₄	1	2	yes	—
335	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
336	C₄²	C₂×C₅×Q₈	1	2	yes	—
337	C₄²	C₂⁴×C₅	1	1	yes	characteristic
338	C₂×C₅	—	4	1	no	—
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	#2906	1	1	yes	characteristic
341	C₂×C₅	#2913	1	1	yes	characteristic
342	C₂×C₅	C₂×#430	1	1	yes	characteristic
343	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
344	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
345	Q₈	—	2	2	no	—
346	D₄	—	2	2	no	—
347	D₄	—	4	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
359	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
361	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
363	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	C₅×#131	1	2	yes	—
379	C₅	#17839	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	2	no	—
386	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	C₅×#430	1	2	yes	—
394	C₄	C₂×C₅×#131	1	1	yes	characteristic
395	C₄	C₅×#568	1	1	yes	characteristic
396	C₄	C₅×#576	1	1	yes	characteristic
397	C₄	C₅×#578	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	4	2	no	—
400	C₂	C₅×#2906	1	1	yes	characteristic
401	C₂	C₅×#2913	1	1	yes	characteristic
402	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	C₂×C₅×#41	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1574	C₂	semidirect
5. C₅×#1574	C₂	semidirect
6. C₅×#1572	C₂	semidirect
7. C₅×#1571	C₂	semidirect
8. C₅×#1569	C₂	semidirect
9. C₅×#1567	C₂	semidirect
10. C₅×#1565	C₂	semidirect
11. C₅×#1564	C₂	semidirect
47. #17839	C₅	direct (N × H)
102. #1574	C₂×C₅	semidirect
103. #1574	C₂×C₅	semidirect
104. #1572	C₂×C₅	semidirect
105. #1571	C₂×C₅	semidirect
106. #1569	C₂×C₅	semidirect
107. #1567	C₂×C₅	semidirect
108. #1565	C₂×C₅	semidirect
109. #1564	C₂×C₅	semidirect
379. C₅	#17839	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×#2991	2
C₅×#2990	2
C₅×#2965	2
C₅×#1574	2
C₅×#1572	2
C₅×#1571	2
C₅×#1569	2
C₅×#1567	2
C₅×#1565	2
C₅×#1564	2
#17839	5

Subgroups — C5×#17839 #11940559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17839 #11940559