Subgroups — C₅×#82234 #14322878

Order 1920.

1200 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₅×#4977	C₂	1	2	yes	maximal, complemented
5	C₅×#4975	C₂	1	2	yes	maximal, complemented
6	C₅×#4946	C₂	1	4	yes	maximal
7	C₅×#4928	C₂	1	4	yes	maximal, complemented
8	C₅×#2317	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
11	C₃×C₅×#117	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
16	C₂×C₅×#217	C₂²	1	2	yes	—
17	C₅×#926	C₄	1	8	yes	complemented
18	C₂×C₅×C₄⋊Dic₃	—	2	4	no	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	—
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₅×C₃⋊#95	C₂²	1	8	yes	—
25	#82234	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#117	—	3	1	no	—
27	C₂×C₅×#117	D₃	1	1	yes	characteristic
28	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
29	C₅×#389	—	3	4	no	—
30	C₅×#385	—	3	4	no	—
31	C₅×#384	—	3	2	no	—
32	C₅×#382	—	3	2	no	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
36	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	—	2	4	no	—
42	C₂²×C₅×Dic₃	—	4	4	no	—
43	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
44	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₄⋊C₄	—	2	2	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₄²×C₅	—	2	4	no	—
49	C₅×#217	C₂×C₄	1	8	yes	—
50	C₅×C₄⋊Dic₃	—	2	4	no	—
51	C₅×C₄⋊Dic₃	—	2	4	no	—
52	C₅×C₄⋊Dic₃	C₂×C₄	1	8	yes	complemented
53	C₅×Dic₃⋊C₄	—	4	8	no	—
54	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
55	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
56	C₂×#926	C₂×C₅	1	1	yes	characteristic
57	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic
58	#4977	C₂×C₅	1	2	yes	complemented
59	#4975	C₂×C₅	1	2	yes	complemented
60	#4946	C₂×C₅	1	4	yes	—
61	#4928	C₂×C₅	1	4	yes	complemented
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
64	C₅×#117	—	2	4	no	—
65	C₅×#117	—	3	8	no	—
66	C₂×C₅×C₄⋊C₄	—	3	2	no	—
67	C₂×C₅×C₄⋊C₄	—	3	2	no	—
68	C₂×C₅×C₄⋊C₄	—	3	2	no	—
69	C₂×C₅×C₄⋊C₄	—	3	8	no	—
70	C₂×C₅×C₄⋊C₄	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
73	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
74	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
75	C₂×C₄²×C₅	—	3	2	no	—
76	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
77	C₅×#95	—	3	8	no	—
78	#2317	—	3	1	no	Sylow
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	2	no	—
81	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
82	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
83	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
84	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
96	C₂×C₅×Dic₃	—	2	4	no	—
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	2	8	no	—
100	C₂×C₅×Dic₃	—	4	8	no	—
101	C₂×C₅×Dic₃	C₂²×C₄	1	8	yes	—
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
104	C₃×#117	—	2	4	no	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
109	C₂×#217	C₂²×C₅	1	2	yes	—
110	#926	C₄×C₅	1	8	yes	complemented
111	C₂×C₄⋊Dic₃	—	2	4	no	—
112	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
113	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
114	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
115	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	—
116	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
117	C₃⋊#95	C₂²×C₅	1	8	yes	—
118	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	3	4	no	—
120	C₂²×C₄×C₅	—	3	4	no	—
121	C₂²×C₄×C₅	—	6	4	no	—
122	C₂²×C₄×C₅	—	12	4	no	—
123	C₂²×C₄×C₅	Dic₆	1	4	yes	—
124	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
125	C₂²×C₄×C₅	#67	1	4	yes	—
126	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
127	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	2	2	no	—
131	C₅×C₄⋊C₄	—	2	2	no	—
132	C₅×C₄⋊C₄	—	3	8	no	—
133	C₅×C₄⋊C₄	—	6	4	no	—
134	C₅×C₄⋊C₄	—	6	4	no	—
135	C₅×C₄⋊C₄	—	12	8	no	—
136	C₅×C₂²⋊C₄	—	2	4	no	—
137	C₅×C₂²⋊C₄	—	3	8	no	—
138	C₄²×C₅	—	2	4	no	—
139	C₄²×C₅	—	3	8	no	—
140	C₂×#117	—	3	1	no	—
141	C₂×#117	C₅×D₃	1	1	yes	characteristic
142	C₂²×C₄⋊C₄	—	3	1	no	—
143	#389	—	3	4	no	—
144	#385	—	3	4	no	—
145	#384	—	3	2	no	—
146	#382	—	3	2	no	—
147	C₂²×C₃×C₅	—	2	4	no	—
148	C₂²×C₃×C₅	—	2	2	no	—
149	C₂²×C₃×C₅	—	2	2	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
152	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
155	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
156	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	—	4	2	no	—
159	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
160	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
161	C₅×Dic₃	—	2	8	no	—
162	C₅×Dic₃	—	4	4	no	—
163	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
165	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
166	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₂²×Dic₃	—	2	4	no	—
172	C₂²×Dic₃	—	4	4	no	—
173	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
174	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	2	2	no	—
177	C₃×C₂²⋊C₄	—	2	4	no	—
178	C₃×C₄²	—	2	4	no	—
179	#217	C₂×C₄×C₅	1	8	yes	—
180	C₄⋊Dic₃	—	2	4	no	—
181	C₄⋊Dic₃	—	2	4	no	—
182	C₄⋊Dic₃	C₂×C₄×C₅	1	8	yes	complemented
183	Dic₃⋊C₄	—	4	8	no	—
184	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	C₂×Dic₆	1	2	yes	—
188	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
189	C₂³×C₅	C₂×#67	1	2	yes	—
190	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	2	no	—
195	C₂×C₄×C₅	—	3	8	no	—
196	C₂×C₄×C₅	—	6	4	no	—
197	C₂×C₄×C₅	—	6	4	no	—
198	C₂×C₄×C₅	—	6	8	no	—
199	C₂×C₄×C₅	—	6	4	no	—
200	C₂×C₄×C₅	—	12	8	no	—
201	C₂×C₄×C₅	Dic₃⋊C₄	1	16	yes	complemented
202	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
203	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
204	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
205	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
206	C₂×C₄×C₅	C₂×#67	1	2	yes	—
207	C₂×C₄×C₅	C₂×#67	1	2	yes	—
208	C₂³×C₄	—	3	2	no	—
209	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
210	#117	—	2	4	no	—
211	#117	—	3	8	no	—
212	C₂×C₄⋊C₄	—	3	2	no	—
213	C₂×C₄⋊C₄	—	3	2	no	—
214	C₂×C₄⋊C₄	—	3	2	no	—
215	C₂×C₄⋊C₄	—	3	8	no	—
216	C₂×C₄⋊C₄	—	6	4	no	—
217	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	—	3	2	no	—
220	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
221	C₂×C₄²	—	3	2	no	—
222	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
223	#95	—	3	8	no	—
224	C₂×C₃×C₅	—	2	4	no	—
225	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂×C₃×C₅	#520	1	2	yes	—
227	C₂×C₃×C₅	#535	1	1	yes	characteristic
228	C₂×C₃×C₅	#536	1	1	yes	characteristic
229	C₂×C₃×C₅	#544	1	2	yes	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
233	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
234	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
235	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	C₅×C₄⋊C₄	1	16	yes	complemented
241	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
244	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
245	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
247	C₂×Dic₃	—	2	4	no	—
248	C₂×Dic₃	—	2	4	no	—
249	C₂×Dic₃	—	2	4	no	—
250	C₂×Dic₃	—	2	8	no	—
251	C₂×Dic₃	—	4	8	no	—
252	C₂×Dic₃	C₂²×C₄×C₅	1	8	yes	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	2	4	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
258	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
259	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
260	C₂²×C₅	#1009	1	2	yes	—
261	C₂²×C₅	#1010	1	2	yes	—
262	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
263	C₄×C₅	—	4	2	no	—
264	C₄×C₅	—	4	2	no	—
265	C₄×C₅	—	6	8	no	—
266	C₄×C₅	—	12	4	no	—
267	C₄×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
268	C₄×C₅	C₂×Dic₃⋊C₄	1	4	yes	—
269	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
270	C₂²×C₄	—	3	4	no	—
271	C₂²×C₄	—	3	4	no	—
272	C₂²×C₄	—	6	4	no	—
273	C₂²×C₄	—	12	4	no	—
274	C₂²×C₄	C₅×Dic₆	1	4	yes	—
275	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
276	C₂²×C₄	C₅×#67	1	4	yes	—
277	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
278	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
279	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	3	8	no	—
284	C₄⋊C₄	—	6	4	no	—
285	C₄⋊C₄	—	6	4	no	—
286	C₄⋊C₄	—	12	8	no	—
287	C₂²⋊C₄	—	2	4	no	—
288	C₂²⋊C₄	—	3	8	no	—
289	C₄²	—	2	4	no	—
290	C₄²	—	3	8	no	—
291	C₃×C₅	#2317	1	1	yes	characteristic, complemented, Hall
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	2	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	4	no	—
296	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
297	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
298	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
299	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
300	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
301	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	—	4	2	no	—
304	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
305	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
306	Dic₃	—	2	8	no	—
307	Dic₃	—	4	4	no	—
308	C₂×C₅	—	2	4	no	—
309	C₂×C₅	#5519	1	2	yes	—
310	C₂×C₅	#5523	1	2	yes	—
311	C₂×C₅	C₂²×Dic₃⋊C₄	1	1	yes	characteristic
312	C₂×C₅	#5825	1	1	yes	characteristic
313	C₂×C₅	#5830	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₂×C₅×Dic₆	1	2	yes	—
317	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
318	C₂³	C₂×C₅×#67	1	2	yes	—
319	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	3	8	no	—
325	C₂×C₄	—	6	4	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	—	6	8	no	—
328	C₂×C₄	—	6	4	no	—
329	C₂×C₄	—	12	8	no	—
330	C₂×C₄	C₅×Dic₃⋊C₄	1	16	yes	complemented
331	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
332	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
333	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
334	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
335	C₂×C₄	C₂×C₅×#67	1	2	yes	—
336	C₂×C₄	C₂×C₅×#67	1	2	yes	—
337	C₂×C₃	—	2	4	no	—
338	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
339	C₂×C₃	C₅×#520	1	2	yes	—
340	C₂×C₃	C₅×#535	1	1	yes	characteristic
341	C₂×C₃	C₅×#536	1	1	yes	characteristic
342	C₂×C₃	C₅×#544	1	2	yes	—
343	C₅	#82234	1	1	yes	characteristic, direct product factor, Sylow
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
349	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
350	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
351	C₂²	C₅×#1009	1	2	yes	—
352	C₂²	C₅×#1010	1	2	yes	—
353	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	6	8	no	—
357	C₄	—	12	4	no	—
358	C₄	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
359	C₄	C₂×C₅×Dic₃⋊C₄	1	4	yes	—
360	C₃	C₅×#2317	1	1	yes	characteristic, complemented, Sylow
361	C₂	—	2	4	no	—
362	C₂	C₅×#5519	1	2	yes	—
363	C₂	C₅×#5523	1	2	yes	—
364	C₂	C₂²×C₅×Dic₃⋊C₄	1	1	yes	characteristic
365	C₂	C₅×#5825	1	1	yes	characteristic
366	C₂	C₅×#5830	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#2317
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
4. C₅×#4977	C₂	semidirect
5. C₅×#4975	C₂	semidirect
7. C₅×#4928	C₂	semidirect
17. C₅×#926	C₄	semidirect
25. #82234	C₅	direct (N × H)
52. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
54. C₄×C₅×Dic₃	C₂×C₄	semidirect
58. #4977	C₂×C₅	semidirect
59. #4975	C₂×C₅	semidirect
61. #4928	C₂×C₅	semidirect
89. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
110. #926	C₄×C₅	semidirect
182. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
184. C₄×Dic₃	C₂×C₄×C₅	semidirect
201. C₂×C₄×C₅	Dic₃⋊C₄	semidirect
240. C₂×C₃×C₄	C₅×C₄⋊C₄	semidirect
291. C₃×C₅	#2317	semidirect
330. C₂×C₄	C₅×Dic₃⋊C₄	semidirect
343. C₅	#82234	direct (N × H)
360. C₃	C₅×#2317	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₂²×C₅×C₄⋊Dic₃	2
C₅×#4977	2
C₅×#4975	2
C₅×#4946	2
C₅×#4928	2
C₅×#2317	3
#82234	5

Subgroups — C5×#82234 #14322878

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82234 #14322878