Subgroups — C₅×#69588 #14297669

Order 1920.

616 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×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#810	C₂	1	2	yes	maximal
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
5	C₅×#4529	C₂	1	2	yes	maximal
6	C₅×#1803	—	3	1	no	maximal, Hall
7	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
9	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×Dic₃⋊C₄	—	2	1	no	—
14	C₂×C₄×C₅×Dic₃	—	2	1	no	—
15	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
16	C₄×C₅×Dic₆	—	2	2	no	—
17	C₄×C₅×Dic₆	C₄	1	4	yes	complemented
18	C₅×#810	—	2	4	no	—
19	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
20	#69588	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×Q₈	—	3	1	no	—
22	C₂×C₅×C₄⋊C₈	—	3	1	no	—
23	C₂×C₅×#103	—	3	2	no	—
24	C₅×#384	D₃	1	1	yes	characteristic
25	C₅×#340	—	3	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₂²×C₅×Dic₃	—	2	1	no	—
31	C₂²×C₅×Dic₃	—	2	1	no	—
32	C₂×C₅×Dic₆	—	2	1	no	—
33	C₂×C₅×Dic₆	—	2	1	no	—
34	C₂×C₅×Dic₆	—	2	1	no	—
35	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
36	C₂×C₅×Dic₆	D₄	1	2	yes	—
37	C₂×C₅×Dic₆	Q₈	1	2	yes	—
38	C₃×C₅×C₄⋊C₄	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	—	2	2	no	—
40	C₃×C₅×C₄⋊C₄	—	4	2	no	—
41	C₃×C₅×C₄⋊C₄	—	4	2	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₅×C₄⋊Dic₃	—	2	1	no	—
45	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
46	C₅×Dic₃⋊C₄	—	2	4	no	—
47	C₄×C₅×Dic₃	—	2	4	no	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₂×C₅×C₃⋊C₈	—	2	2	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic
52	C₃×#384	C₂×C₅	1	1	yes	characteristic
53	C₂×#810	C₂×C₅	1	2	yes	—
54	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
55	#4529	C₂×C₅	1	2	yes	—
56	C₂²×C₅×Q₈	—	3	1	no	—
57	C₂²×C₅×C₈	—	3	2	no	—
58	C₄×C₅×Q₈	—	3	4	no	—
59	C₄×C₅×Q₈	—	6	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	3	1	no	—
63	C₂×C₅×C₄⋊C₄	—	6	1	no	—
64	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
65	C₂×C₄²×C₅	—	6	1	no	—
66	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
67	C₅×C₄⋊C₈	—	6	2	no	—
68	C₅×#103	—	6	4	no	—
69	#1803	—	3	1	no	Sylow
70	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
71	C₂×C₃×C₄×C₅	—	2	1	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	4	2	no	—
74	C₂×C₃×C₄×C₅	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	4	2	no	—
76	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
78	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
79	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
86	C₂×C₅×Dic₃	—	2	2	no	—
87	C₂×C₅×Dic₃	—	2	2	no	—
88	C₂×C₅×Dic₃	—	2	2	no	—
89	C₂×C₅×Dic₃	—	2	2	no	—
90	C₂×C₅×Dic₃	—	4	1	no	—
91	C₂×C₅×Dic₃	—	4	1	no	—
92	C₅×Dic₆	—	2	2	no	—
93	C₅×Dic₆	—	2	2	no	—
94	C₅×Dic₆	—	2	2	no	—
95	C₅×Dic₆	C₄⋊C₄	1	4	yes	complemented
96	C₅×C₃⋊C₈	—	4	2	no	—
97	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
98	C₂×C₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
103	C₂×Dic₃⋊C₄	—	2	1	no	—
104	C₂×C₄×Dic₃	—	2	1	no	—
105	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
106	C₄×Dic₆	—	2	2	no	—
107	C₄×Dic₆	C₄×C₅	1	4	yes	complemented
108	#810	—	2	4	no	—
109	C₄⋊(C₃⋊C₈)	—	2	2	no	—
110	C₂×C₅×Q₈	—	3	2	no	—
111	C₂×C₅×Q₈	—	3	2	no	—
112	C₂×C₅×Q₈	—	3	2	no	—
113	C₂×C₅×Q₈	—	6	1	no	—
114	C₂×C₅×Q₈	—	6	1	no	—
115	C₂×C₅×Q₈	—	6	1	no	—
116	C₂²×C₄×C₅	—	2	2	no	—
117	C₂²×C₄×C₅	—	6	1	no	—
118	C₂²×C₄×C₅	—	6	1	no	—
119	C₂²×C₄×C₅	#67	1	1	yes	characteristic
120	C₂²×C₄×C₅	#67	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
122	C₂×C₅×C₈	—	6	2	no	—
123	C₂×C₅×C₈	—	6	2	no	—
124	C₂×C₅×C₈	—	6	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	2	2	no	—
127	C₅×C₄⋊C₄	—	3	2	no	—
128	C₅×C₄⋊C₄	—	4	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	—	6	4	no	—
131	C₅×C₄⋊C₄	—	6	1	no	—
132	C₄²×C₅	—	6	4	no	—
133	C₄²×C₅	C₄×D₃	1	2	yes	—
134	C₄²×C₅	D₁₂	1	2	yes	—
135	C₂×C₄×Q₈	—	3	1	no	—
136	C₂×C₄⋊C₈	—	3	1	no	—
137	C₂×#103	—	3	2	no	—
138	#384	C₅×D₃	1	1	yes	characteristic
139	#340	—	3	2	no	—
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	#121	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
145	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂²×C₃×C₅	#137	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	8	2	no	—
149	C₃×C₄×C₅	#103	1	4	yes	complemented
150	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₃×C₄×C₅	#117	1	1	yes	characteristic
152	C₃×C₄×C₅	#121	1	1	yes	characteristic
153	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
154	C₅×Dic₃	—	2	4	no	—
155	C₅×Dic₃	—	4	2	no	—
156	C₂²×C₃×C₄	—	2	2	no	—
157	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
160	C₂²×Dic₃	—	2	1	no	—
161	C₂²×Dic₃	—	2	1	no	—
162	C₂×Dic₆	—	2	1	no	—
163	C₂×Dic₆	—	2	1	no	—
164	C₂×Dic₆	—	2	1	no	—
165	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
166	C₂×Dic₆	C₅×D₄	1	2	yes	—
167	C₂×Dic₆	C₅×Q₈	1	2	yes	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	2	2	no	—
170	C₃×C₄⋊C₄	—	4	2	no	—
171	C₃×C₄⋊C₄	—	4	2	no	—
172	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
173	C₃×C₄²	C₅×D₄	1	2	yes	—
174	C₄⋊Dic₃	—	2	1	no	—
175	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
176	Dic₃⋊C₄	—	2	4	no	—
177	C₄×Dic₃	—	2	4	no	—
178	C₂×C₃⋊C₈	—	2	2	no	—
179	C₂×C₃⋊C₈	—	2	2	no	—
180	C₂×C₃⋊C₈	—	2	2	no	—
181	C₂³×C₅	C₂×#67	1	1	yes	characteristic
182	C₅×Q₈	—	3	4	no	—
183	C₅×Q₈	—	6	2	no	—
184	C₅×Q₈	—	6	2	no	—
185	C₅×Q₈	—	6	2	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	—	4	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	6	2	no	—
192	C₂×C₄×C₅	—	6	2	no	—
193	C₂×C₄×C₅	—	6	2	no	—
194	C₂×C₄×C₅	—	6	2	no	—
195	C₂×C₄×C₅	—	12	1	no	—
196	C₂×C₄×C₅	—	12	1	no	—
197	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
198	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
199	C₂×C₄×C₅	#214	1	2	yes	—
200	C₂×C₄×C₅	#216	1	2	yes	—
201	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
203	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	#237	1	1	yes	characteristic
205	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₅	#239	1	1	yes	characteristic
207	C₅×C₈	—	12	2	no	—
208	C₂²×Q₈	—	3	1	no	—
209	C₂²×C₈	—	3	2	no	—
210	C₄×Q₈	—	3	4	no	—
211	C₄×Q₈	—	6	2	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	3	1	no	—
215	C₂×C₄⋊C₄	—	6	1	no	—
216	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
217	C₂×C₄²	—	6	1	no	—
218	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
219	C₄⋊C₈	—	6	2	no	—
220	#103	—	6	4	no	—
221	C₂×C₃×C₅	#380	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
223	C₂×C₃×C₅	#417	1	1	yes	characteristic
224	C₂×C₃×C₅	#460	1	1	yes	characteristic
225	C₂×C₃×C₅	#462	1	1	yes	characteristic
226	C₂×C₃×C₅	#475	1	1	yes	characteristic
227	C₂×C₃×C₅	#477	1	1	yes	characteristic
228	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
235	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
236	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
237	C₂×C₃×C₄	C₅×Q₁₆	1	2	yes	—
238	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
242	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
243	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
244	C₂×Dic₃	—	2	2	no	—
245	C₂×Dic₃	—	2	2	no	—
246	C₂×Dic₃	—	2	2	no	—
247	C₂×Dic₃	—	2	2	no	—
248	C₂×Dic₃	—	4	1	no	—
249	C₂×Dic₃	—	4	1	no	—
250	Dic₆	—	2	2	no	—
251	Dic₆	—	2	2	no	—
252	Dic₆	—	2	2	no	—
253	Dic₆	C₅×C₄⋊C₄	1	4	yes	complemented
254	C₃⋊C₈	—	4	2	no	—
255	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
256	C₂²×C₅	#932	1	1	yes	characteristic
257	C₂²×C₅	C₂×#214	1	1	yes	characteristic
258	C₂²×C₅	#938	1	1	yes	characteristic
259	C₂²×C₅	#942	1	1	yes	characteristic
260	C₂²×C₅	C₂×#216	1	1	yes	characteristic
261	C₂²×C₅	#946	1	1	yes	characteristic
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	—	6	4	no	—
264	C₄×C₅	—	8	2	no	—
265	C₄×C₅	—	12	2	no	—
266	C₄×C₅	#810	1	4	yes	complemented
267	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₅	#892	1	1	yes	characteristic
269	C₄×C₅	#895	1	1	yes	characteristic
270	C₄×C₅	#897	1	1	yes	characteristic
271	C₂×Q₈	—	3	2	no	—
272	C₂×Q₈	—	3	2	no	—
273	C₂×Q₈	—	3	2	no	—
274	C₂×Q₈	—	6	1	no	—
275	C₂×Q₈	—	6	1	no	—
276	C₂×Q₈	—	6	1	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	6	1	no	—
279	C₂²×C₄	—	6	1	no	—
280	C₂²×C₄	C₅×#67	1	1	yes	characteristic
281	C₂²×C₄	C₅×#67	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
283	C₂×C₈	—	6	2	no	—
284	C₂×C₈	—	6	2	no	—
285	C₂×C₈	—	6	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	3	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	6	4	no	—
292	C₄⋊C₄	—	6	1	no	—
293	C₄²	—	6	4	no	—
294	C₄²	C₄×C₅×D₃	1	2	yes	—
295	C₄²	C₅×D₁₂	1	2	yes	—
296	C₃×C₅	#1803	1	1	yes	characteristic, complemented, Hall
297	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₃	C₅×#121	1	1	yes	characteristic
299	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
302	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₂²×C₃	C₅×#137	1	1	yes	characteristic
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	8	2	no	—
306	C₃×C₄	C₅×#103	1	4	yes	complemented
307	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
308	C₃×C₄	C₅×#117	1	1	yes	characteristic
309	C₃×C₄	C₅×#121	1	1	yes	characteristic
310	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
311	Dic₃	—	2	4	no	—
312	Dic₃	—	4	2	no	—
313	C₂×C₅	#4966	1	1	yes	characteristic
314	C₂×C₅	C₂×#810	1	1	yes	characteristic
315	C₂×C₅	#4987	1	1	yes	characteristic
316	C₂×C₅	#5075	1	1	yes	characteristic
317	C₂×C₅	#5090	1	1	yes	characteristic
318	C₂×C₅	#5091	1	1	yes	characteristic
319	C₂×C₅	#5094	1	1	yes	characteristic
320	C₂³	C₂×C₅×#67	1	1	yes	characteristic
321	Q₈	—	3	4	no	—
322	Q₈	—	6	2	no	—
323	Q₈	—	6	2	no	—
324	Q₈	—	6	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	6	2	no	—
333	C₂×C₄	—	6	2	no	—
334	C₂×C₄	—	12	1	no	—
335	C₂×C₄	—	12	1	no	—
336	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
337	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
338	C₂×C₄	C₅×#214	1	2	yes	—
339	C₂×C₄	C₅×#216	1	2	yes	—
340	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
341	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
342	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
343	C₂×C₄	C₅×#237	1	1	yes	characteristic
344	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
345	C₂×C₄	C₅×#239	1	1	yes	characteristic
346	C₈	—	12	2	no	—
347	C₂×C₃	C₅×#380	1	1	yes	characteristic
348	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
349	C₂×C₃	C₅×#417	1	1	yes	characteristic
350	C₂×C₃	C₅×#460	1	1	yes	characteristic
351	C₂×C₃	C₅×#462	1	1	yes	characteristic
352	C₂×C₃	C₅×#475	1	1	yes	characteristic
353	C₂×C₃	C₅×#477	1	1	yes	characteristic
354	C₅	#69588	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
356	C₂²	C₅×#932	1	1	yes	characteristic
357	C₂²	C₂×C₅×#214	1	1	yes	characteristic
358	C₂²	C₅×#938	1	1	yes	characteristic
359	C₂²	C₅×#942	1	1	yes	characteristic
360	C₂²	C₂×C₅×#216	1	1	yes	characteristic
361	C₂²	C₅×#946	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	6	4	no	—
364	C₄	—	8	2	no	—
365	C₄	—	12	2	no	—
366	C₄	C₅×#810	1	4	yes	complemented
367	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
368	C₄	C₅×#892	1	1	yes	characteristic
369	C₄	C₅×#895	1	1	yes	characteristic
370	C₄	C₅×#897	1	1	yes	characteristic
371	C₃	C₅×#1803	1	1	yes	characteristic, complemented, Sylow
372	C₂	C₅×#4966	1	1	yes	characteristic
373	C₂	C₂×C₅×#810	1	1	yes	characteristic
374	C₂	C₅×#4987	1	1	yes	characteristic
375	C₂	C₅×#5075	1	1	yes	characteristic
376	C₂	C₅×#5090	1	1	yes	characteristic
377	C₂	C₅×#5091	1	1	yes	characteristic
378	C₂	C₅×#5094	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	C₃×C₅×#384	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#384	D₃
hypocenter	C₃	C₅×#1803
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₅×#384

Complements

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

N	H ≅ G/N	type
17. C₄×C₅×Dic₆	C₄	semidirect
20. #69588	C₅	direct (N × H)
95. C₅×Dic₆	C₄⋊C₄	semidirect
107. C₄×Dic₆	C₄×C₅	semidirect
149. C₃×C₄×C₅	#103	semidirect
253. Dic₆	C₅×C₄⋊C₄	semidirect
266. C₄×C₅	#810	semidirect
296. C₃×C₅	#1803	semidirect
306. C₃×C₄	C₅×#103	semidirect
354. C₅	#69588	direct (N × H)
366. C₄	C₅×#810	semidirect
371. C₃	C₅×#1803	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Dic₆	2
C₃×C₅×#384	2
C₂×C₅×#810	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4529	2
C₅×#1803	3
#69588	5

Subgroups — C5×#69588 #14297669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69588 #14297669