Subgroups — C₅×#71605 #14297723

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#832	C₂	1	2	yes	maximal
3	C₅×#4936	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₅×#1804	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	—	2	1	no	—
9	C₃×C₄×C₅×D₄	—	2	2	no	—
10	C₃×C₄×C₅×D₄	C₄	1	4	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₅×#832	—	2	4	no	—
17	C₅×C₃⋊#95	—	2	1	no	—
18	C₅×C₃⋊#95	—	2	1	no	—
19	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
20	#71605	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	—	3	1	no	—
23	C₂×C₅×#102	—	3	2	no	—
24	C₅×#382	—	3	1	no	—
25	C₅×#340	—	3	2	no	—
26	C₂⁴×C₃×C₅	—	2	1	no	—
27	C₂×C₃×C₅×D₄	—	2	1	no	—
28	C₂×C₃×C₅×D₄	—	2	1	no	—
29	C₂×C₃×C₅×D₄	—	2	1	no	—
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	4	4	no	—
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
43	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
44	C₃×C₄²×C₅	D₄	1	2	yes	—
45	C₅×C₄⋊Dic₃	—	2	2	no	—
46	C₅×C₄⋊Dic₃	—	2	2	no	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₂×C₅×C₃⋊C₈	—	2	2	no	—
50	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
51	C₂×#832	C₂×C₅	1	2	yes	—
52	#4936	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
54	#4529	C₂×C₅	1	2	yes	complemented
55	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
56	C₂³×C₄×C₅	—	2	1	no	—
57	C₂²×C₅×C₈	—	3	2	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	Dic₃	1	4	yes	complemented
60	C₂×C₅×C₄⋊C₄	—	3	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
64	C₅×C₄⋊C₈	—	6	2	no	—
65	C₅×#102	—	6	4	no	—
66	C₅×#95	—	6	1	no	—
67	C₅×#95	—	6	1	no	—
68	#1804	—	3	1	no	Sylow
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	—	2	2	no	—
71	C₂³×C₃×C₅	—	2	2	no	—
72	C₂³×C₃×C₅	—	4	2	no	—
73	C₂³×C₃×C₅	—	4	2	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×D₄	—	2	2	no	—
76	C₃×C₅×D₄	—	2	2	no	—
77	C₃×C₅×D₄	—	2	2	no	—
78	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	4	8	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
92	C₂×C₅×Dic₃	—	4	2	no	—
93	C₂×C₅×Dic₃	—	4	2	no	—
94	C₂×C₅×Dic₃	—	4	2	no	—
95	C₅×C₃⋊C₈	—	4	2	no	—
96	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
97	C₂³×C₃×C₄	—	2	1	no	—
98	C₃×C₄×D₄	—	2	2	no	—
99	C₃×C₄×D₄	C₄×C₅	1	4	yes	complemented
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
104	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
105	#832	—	2	4	no	—
106	C₃⋊#95	—	2	1	no	—
107	C₃⋊#95	—	2	1	no	—
108	C₄⋊(C₃⋊C₈)	—	2	2	no	—
109	C₂⁴×C₅	—	2	1	no	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	Dic₆	1	2	yes	—
114	C₂×C₅×D₄	D₁₂	1	2	yes	—
115	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	4	no	—
118	C₂²×C₄×C₅	—	4	4	no	—
119	C₂²×C₄×C₅	—	6	2	no	—
120	C₂²×C₄×C₅	#67	1	1	yes	characteristic
121	C₂²×C₄×C₅	#67	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
123	C₂×C₅×C₈	—	6	2	no	—
124	C₂×C₅×C₈	—	6	2	no	—
125	C₂×C₅×C₈	—	6	2	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	6	2	no	—
128	C₅×C₄⋊C₄	—	6	2	no	—
129	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
130	C₅×C₂²⋊C₄	—	2	4	no	—
131	C₄²×C₅	C₂×Dic₃	1	2	yes	—
132	C₄²×C₅	#67	1	2	yes	—
133	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
134	C₂×C₄⋊C₈	—	3	1	no	—
135	C₂×#102	—	3	2	no	—
136	#382	—	3	1	no	—
137	#340	—	3	2	no	—
138	C₂²×C₃×C₅	—	2	4	no	—
139	C₂²×C₃×C₅	—	4	2	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	—	4	4	no	—
143	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₃×C₅	#121	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂²×C₃×C₅	#135	1	2	yes	—
147	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	2	2	no	—
150	C₃×C₄×C₅	—	4	2	no	—
151	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₃×C₄×C₅	#117	1	1	yes	characteristic
153	C₃×C₄×C₅	#121	1	1	yes	characteristic
154	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
155	C₅×Dic₃	—	8	2	no	—
156	C₂⁴×C₃	—	2	1	no	—
157	C₂×C₃×D₄	—	2	1	no	—
158	C₂×C₃×D₄	—	2	1	no	—
159	C₂×C₃×D₄	—	2	1	no	—
160	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
161	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
162	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	4	4	no	—
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×Dic₃	—	2	2	no	—
170	C₃×C₄⋊C₄	—	2	1	no	—
171	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
172	C₃×C₂²⋊C₄	—	2	4	no	—
173	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
174	C₃×C₄²	C₅×D₄	1	2	yes	—
175	C₄⋊Dic₃	—	2	2	no	—
176	C₄⋊Dic₃	—	2	2	no	—
177	C₂×C₃⋊C₈	—	2	2	no	—
178	C₂×C₃⋊C₈	—	2	2	no	—
179	C₂×C₃⋊C₈	—	2	2	no	—
180	C₂³×C₅	—	2	2	no	—
181	C₂³×C₅	—	2	2	no	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	2	no	—
185	C₂³×C₅	C₂×#67	1	1	yes	characteristic
186	C₅×D₄	—	2	2	no	—
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	2	2	no	—
189	C₅×D₄	C₄⋊Dic₃	1	4	yes	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	2	no	—
193	C₂×C₄×C₅	—	4	8	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	12	2	no	—
196	C₂×C₄×C₅	—	12	2	no	—
197	C₂×C₄×C₅	—	12	2	no	—
198	C₂×C₄×C₅	#217	1	2	yes	—
199	C₂×C₄×C₅	#217	1	2	yes	—
200	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
201	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
202	C₂×C₄×C₅	#235	1	1	yes	characteristic
203	C₂×C₄×C₅	#235	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
206	C₅×C₈	—	12	2	no	—
207	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
208	C₂³×C₄	—	2	1	no	—
209	C₂²×C₈	—	3	2	no	—
210	C₄×D₄	—	2	2	no	—
211	C₄×D₄	C₅×Dic₃	1	4	yes	complemented
212	C₂×C₄⋊C₄	—	3	2	no	—
213	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
214	C₂×C₂²⋊C₄	—	2	1	no	—
215	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
216	C₄⋊C₈	—	6	2	no	—
217	#102	—	6	4	no	—
218	#95	—	6	1	no	—
219	#95	—	6	1	no	—
220	C₂×C₃×C₅	—	4	4	no	—
221	C₂×C₃×C₅	#380	1	1	yes	characteristic
222	C₂×C₃×C₅	#416	1	1	yes	characteristic
223	C₂×C₃×C₅	#418	1	1	yes	characteristic
224	C₂×C₃×C₅	#463	1	2	yes	—
225	C₂×C₃×C₅	#478	1	2	yes	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	4	2	no	—
230	C₂³×C₃	—	4	2	no	—
231	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
232	C₃×D₄	—	2	2	no	—
233	C₃×D₄	—	2	2	no	—
234	C₃×D₄	—	2	2	no	—
235	C₃×D₄	C₅×C₄⋊C₄	1	4	yes	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	4	8	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
242	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
243	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
247	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
249	C₂×Dic₃	—	4	2	no	—
250	C₂×Dic₃	—	4	2	no	—
251	C₂×Dic₃	—	4	2	no	—
252	C₃⋊C₈	—	4	2	no	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	4	2	no	—
255	C₂²×C₅	—	4	2	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	#924	1	1	yes	characteristic
259	C₂²×C₅	#930	1	1	yes	characteristic
260	C₂²×C₅	#932	1	2	yes	—
261	C₂²×C₅	#950	1	2	yes	—
262	C₂²×C₅	C₂×#217	1	1	yes	characteristic
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	2	2	no	—
265	C₄×C₅	—	4	2	no	—
266	C₄×C₅	—	24	2	no	—
267	C₄×C₅	#924	1	1	yes	characteristic
268	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
269	C₄×C₅	#926	1	1	yes	characteristic
270	C₄×C₅	#930	1	1	yes	characteristic
271	C₂⁴	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	C₅×Dic₆	1	2	yes	—
276	C₂×D₄	C₅×D₁₂	1	2	yes	—
277	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	6	2	no	—
282	C₂²×C₄	C₅×#67	1	1	yes	characteristic
283	C₂²×C₄	C₅×#67	1	1	yes	characteristic
284	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
285	C₂×C₈	—	6	2	no	—
286	C₂×C₈	—	6	2	no	—
287	C₂×C₈	—	6	2	no	—
288	C₄⋊C₄	—	2	1	no	—
289	C₄⋊C₄	—	6	2	no	—
290	C₄⋊C₄	—	6	2	no	—
291	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
292	C₂²⋊C₄	—	2	4	no	—
293	C₄²	C₂×C₅×Dic₃	1	2	yes	—
294	C₄²	C₅×#67	1	2	yes	—
295	C₃×C₅	#1804	1	1	yes	characteristic, complemented, Hall
296	C₂²×C₃	—	2	4	no	—
297	C₂²×C₃	—	4	2	no	—
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	4	4	no	—
300	C₂²×C₃	—	4	4	no	—
301	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
302	C₂²×C₃	C₅×#121	1	1	yes	characteristic
303	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
304	C₂²×C₃	C₅×#135	1	2	yes	—
305	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	2	2	no	—
308	C₃×C₄	—	4	2	no	—
309	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
310	C₃×C₄	C₅×#117	1	1	yes	characteristic
311	C₃×C₄	C₅×#121	1	1	yes	characteristic
312	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
313	Dic₃	—	8	2	no	—
314	C₂×C₅	—	4	4	no	—
315	C₂×C₅	#5009	1	2	yes	—
316	C₂×C₅	#5016	1	2	yes	—
317	C₂×C₅	#5212	1	1	yes	characteristic
318	C₂×C₅	#5215	1	1	yes	characteristic
319	C₂×C₅	#5233	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	C₂×C₅×#67	1	1	yes	characteristic
326	D₄	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	C₅×C₄⋊Dic₃	1	4	yes	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	12	2	no	—
336	C₂×C₄	—	12	2	no	—
337	C₂×C₄	—	12	2	no	—
338	C₂×C₄	C₅×#217	1	2	yes	—
339	C₂×C₄	C₅×#217	1	2	yes	—
340	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
342	C₂×C₄	C₅×#235	1	1	yes	characteristic
343	C₂×C₄	C₅×#235	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
346	C₈	—	12	2	no	—
347	C₂×C₃	—	4	4	no	—
348	C₂×C₃	C₅×#380	1	1	yes	characteristic
349	C₂×C₃	C₅×#416	1	1	yes	characteristic
350	C₂×C₃	C₅×#418	1	1	yes	characteristic
351	C₂×C₃	C₅×#463	1	2	yes	—
352	C₂×C₃	C₅×#478	1	2	yes	—
353	C₅	#71605	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	4	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	C₅×#924	1	1	yes	characteristic
360	C₂²	C₅×#930	1	1	yes	characteristic
361	C₂²	C₅×#932	1	2	yes	—
362	C₂²	C₅×#950	1	2	yes	—
363	C₂²	C₂×C₅×#217	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	24	2	no	—
368	C₄	C₅×#924	1	1	yes	characteristic
369	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
370	C₄	C₅×#926	1	1	yes	characteristic
371	C₄	C₅×#930	1	1	yes	characteristic
372	C₃	C₅×#1804	1	1	yes	characteristic, complemented, Sylow
373	C₂	—	4	4	no	—
374	C₂	C₅×#5009	1	2	yes	—
375	C₂	C₅×#5016	1	2	yes	—
376	C₂	C₅×#5212	1	1	yes	characteristic
377	C₂	C₅×#5215	1	1	yes	characteristic
378	C₂	C₅×#5233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#1804
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
3. C₅×#4936	C₂	semidirect
4. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₅×#4529	C₂	semidirect
10. C₃×C₄×C₅×D₄	C₄	semidirect
20. #71605	C₅	direct (N × H)
52. #4936	C₂×C₅	semidirect
53. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
54. #4529	C₂×C₅	semidirect
59. C₄×C₅×D₄	Dic₃	semidirect
99. C₃×C₄×D₄	C₄×C₅	semidirect
211. C₄×D₄	C₅×Dic₃	semidirect
295. C₃×C₅	#1804	semidirect
353. C₅	#71605	direct (N × H)
372. C₃	C₅×#1804	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#832	2
C₅×#4936	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4529	2
C₅×#1804	3
#71605	5

Subgroups — C5×#71605 #14297723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71605 #14297723