Subgroups — C₃×#10613888 #14322891

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	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic
4	C₃×#65499	C₂	1	4	yes	maximal
5	C₃×#65266	C₂	1	2	yes	maximal, complemented
6	C₃×#65265	C₂	1	2	yes	maximal, complemented
7	C₃×#65262	C₂	1	4	yes	maximal, complemented
8	#10613888	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
15	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
16	C₃×#4072	—	2	4	no	—
17	C₃×#4072	C₄	1	8	yes	complemented
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
21	C₂×C₃×#683	C₂²	1	8	yes	—
22	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
24	C₃×#3963	C₂²	1	8	yes	—
25	C₃×#2317	—	5	1	no	maximal, Hall
26	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
27	C₂×#4072	C₂×C₃	1	1	yes	characteristic
28	C₂×#4072	C₂×C₃	1	1	yes	characteristic
29	#65499	C₂×C₃	1	4	yes	—
30	#65266	C₂×C₃	1	2	yes	complemented
31	#65265	C₂×C₃	1	2	yes	complemented
32	#65262	C₂×C₃	1	4	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	4	4	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₂²⋊Dic₅	—	2	4	no	—
48	C₃×C₂²⋊Dic₅	C₂×C₄	1	8	yes	—
49	C₃×C₄⋊Dic₅	—	2	2	no	—
50	C₃×C₄⋊Dic₅	—	2	2	no	—
51	C₃×C₄⋊Dic₅	C₂×C₄	1	8	yes	complemented
52	C₃×#683	—	4	8	no	—
53	C₃×C₄×Dic₅	—	2	4	no	—
54	C₃×C₄×Dic₅	C₂×C₄	1	8	yes	complemented
55	C₂×C₃×#117	—	5	1	no	—
56	C₂×C₃×#117	—	5	1	no	—
57	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic
58	C₃×#389	—	5	4	no	—
59	C₃×#385	—	5	4	no	—
60	C₃×#384	—	5	2	no	—
61	C₃×#382	—	5	2	no	—
62	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
63	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₅×C₄⋊C₄	—	2	4	no	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
68	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
69	#4072	—	2	4	no	—
70	#4072	C₃×C₄	1	8	yes	complemented
71	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
74	C₂×#683	C₂²×C₃	1	8	yes	—
75	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
76	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
77	#3963	C₂²×C₃	1	8	yes	—
78	#2317	—	5	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	4	no	—
86	C₂×C₃×C₄×C₅	—	2	8	no	—
87	C₂×C₃×C₄×C₅	—	4	8	no	—
88	C₂×C₃×C₄×C₅	C₄⋊C₄	1	16	yes	complemented
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	—	2	2	no	—
98	C₂×C₃×Dic₅	—	2	2	no	—
99	C₂×C₃×Dic₅	—	2	4	no	—
100	C₂×C₃×Dic₅	—	2	4	no	—
101	C₂×C₃×Dic₅	C₂²×C₄	1	8	yes	—
102	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
103	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
104	C₃×#117	—	5	8	no	—
105	C₃×#117	—	10	4	no	—
106	C₂×C₃×C₄⋊C₄	—	2	4	no	—
107	C₂×C₃×C₄⋊C₄	—	5	2	no	—
108	C₂×C₃×C₄⋊C₄	—	5	1	no	—
109	C₂×C₃×C₄⋊C₄	—	5	1	no	—
110	C₂×C₃×C₄⋊C₄	—	5	8	no	—
111	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
112	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
113	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
114	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
115	C₂×C₃×C₄²	—	5	2	no	—
116	C₂×C₃×C₄²	—	5	2	no	—
117	C₃×#95	—	5	8	no	—
118	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	4	4	no	—
121	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
122	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
123	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
127	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
128	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
129	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
130	C₅×C₄⋊C₄	—	2	4	no	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₂²⋊Dic₅	—	2	4	no	—
133	C₂²⋊Dic₅	C₂×C₃×C₄	1	8	yes	—
134	C₄⋊Dic₅	—	2	2	no	—
135	C₄⋊Dic₅	—	2	2	no	—
136	C₄⋊Dic₅	C₂×C₃×C₄	1	8	yes	complemented
137	#683	—	4	8	no	—
138	C₄×Dic₅	—	2	4	no	—
139	C₄×Dic₅	C₂×C₃×C₄	1	8	yes	complemented
140	C₂×#117	—	5	1	no	—
141	C₂×#117	—	5	1	no	—
142	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
143	#389	—	5	4	no	—
144	#385	—	5	4	no	—
145	#384	—	5	2	no	—
146	#382	—	5	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	4	no	—
158	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
159	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
160	C₃×Dic₅	—	2	8	no	—
161	C₃×Dic₅	—	4	2	no	—
162	C₃×Dic₅	—	4	2	no	—
163	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	4	4	no	—
166	C₂²×C₃×C₄	—	5	4	no	—
167	C₂²×C₃×C₄	—	5	2	no	—
168	C₂²×C₃×C₄	—	5	2	no	—
169	C₂²×C₃×C₄	Dic₁₀	1	4	yes	—
170	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
171	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
172	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
173	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
175	C₃×C₄⋊C₄	—	2	4	no	—
176	C₃×C₄⋊C₄	—	2	4	no	—
177	C₃×C₄⋊C₄	—	5	8	no	—
178	C₃×C₄⋊C₄	—	10	2	no	—
179	C₃×C₄⋊C₄	—	10	2	no	—
180	C₃×C₄⋊C₄	—	20	8	no	—
181	C₃×C₂²⋊C₄	—	5	8	no	—
182	C₃×C₂²⋊C₄	—	10	4	no	—
183	C₃×C₄²	—	5	8	no	—
184	C₃×C₄²	—	10	4	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
188	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
189	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
190	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	8	no	—
193	C₂×C₄×C₅	—	4	8	no	—
194	C₂×C₄×C₅	C₃×C₄⋊C₄	1	16	yes	complemented
195	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
196	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
197	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
200	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
201	C₂×Dic₅	—	2	4	no	—
202	C₂×Dic₅	—	2	4	no	—
203	C₂×Dic₅	—	2	2	no	—
204	C₂×Dic₅	—	2	2	no	—
205	C₂×Dic₅	—	2	4	no	—
206	C₂×Dic₅	—	2	4	no	—
207	C₂×Dic₅	C₂²×C₃×C₄	1	8	yes	—
208	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
209	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
210	#117	—	5	8	no	—
211	#117	—	10	4	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	5	2	no	—
214	C₂×C₄⋊C₄	—	5	1	no	—
215	C₂×C₄⋊C₄	—	5	1	no	—
216	C₂×C₄⋊C₄	—	5	8	no	—
217	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
219	C₂×C₂²⋊C₄	—	5	2	no	—
220	C₂×C₂²⋊C₄	—	5	2	no	—
221	C₂×C₄²	—	5	2	no	—
222	C₂×C₄²	—	5	2	no	—
223	#95	—	5	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	C₂×Dic₁₀	1	2	yes	—
233	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
234	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
235	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
236	C₂×C₃×C₄	—	2	8	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	4	8	no	—
239	C₂×C₃×C₄	—	5	8	no	—
240	C₂×C₃×C₄	—	10	4	no	—
241	C₂×C₃×C₄	—	10	4	no	—
242	C₂×C₃×C₄	—	10	4	no	—
243	C₂×C₃×C₄	—	10	4	no	—
244	C₂×C₃×C₄	—	10	2	no	—
245	C₂×C₃×C₄	—	10	2	no	—
246	C₂×C₃×C₄	#683	1	16	yes	complemented
247	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
248	C₂×C₃×C₄	C₂×Dic₁₀	1	2	yes	—
249	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
251	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
252	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	2	2	no	—
255	C₂²×C₅	—	2	2	no	—
256	C₂²×C₅	—	2	4	no	—
257	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
258	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
259	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
260	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
261	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
265	C₄×C₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
266	Dic₅	—	2	8	no	—
267	Dic₅	—	4	2	no	—
268	Dic₅	—	4	2	no	—
269	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	5	4	no	—
273	C₂²×C₄	—	5	2	no	—
274	C₂²×C₄	—	5	2	no	—
275	C₂²×C₄	C₃×Dic₁₀	1	4	yes	—
276	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
277	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
278	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
279	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	5	8	no	—
284	C₄⋊C₄	—	10	2	no	—
285	C₄⋊C₄	—	10	2	no	—
286	C₄⋊C₄	—	20	8	no	—
287	C₂²⋊C₄	—	5	8	no	—
288	C₂²⋊C₄	—	10	4	no	—
289	C₄²	—	5	8	no	—
290	C₄²	—	10	4	no	—
291	C₃×C₅	#2317	1	1	yes	characteristic, complemented, Hall
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	2	2	no	—
295	C₂²×C₃	—	2	2	no	—
296	C₂²×C₃	C₂×#683	1	4	yes	—
297	C₂²×C₃	C₂²×Dic₁₀	1	1	yes	characteristic
298	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
299	C₂²×C₃	#4144	1	2	yes	—
300	C₂²×C₃	#4147	1	2	yes	—
301	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
302	C₃×C₄	—	4	4	no	—
303	C₃×C₄	—	10	8	no	—
304	C₃×C₄	—	20	2	no	—
305	C₃×C₄	—	20	2	no	—
306	C₃×C₄	C₂×#683	1	4	yes	—
307	C₃×C₄	C₂×#683	1	4	yes	—
308	C₂×C₅	—	2	4	no	—
309	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
310	C₂×C₅	C₃×#520	1	2	yes	—
311	C₂×C₅	C₃×#535	1	1	yes	characteristic
312	C₂×C₅	C₃×#536	1	1	yes	characteristic
313	C₂×C₅	C₃×#544	1	2	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	C₂×C₃×Dic₁₀	1	2	yes	—
317	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
318	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
319	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	8	no	—
323	C₂×C₄	—	5	8	no	—
324	C₂×C₄	—	10	4	no	—
325	C₂×C₄	—	10	4	no	—
326	C₂×C₄	—	10	4	no	—
327	C₂×C₄	—	10	4	no	—
328	C₂×C₄	—	10	2	no	—
329	C₂×C₄	—	10	2	no	—
330	C₂×C₄	C₃×#683	1	16	yes	complemented
331	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
332	C₂×C₄	C₂×C₃×Dic₁₀	1	2	yes	—
333	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
334	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
335	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
336	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
337	C₂×C₃	—	2	4	no	—
338	C₂×C₃	#65834	1	2	yes	—
339	C₂×C₃	#65838	1	2	yes	—
340	C₂×C₃	C₂²×#683	1	1	yes	characteristic
341	C₂×C₃	#66139	1	1	yes	characteristic
342	C₂×C₃	#66150	1	1	yes	characteristic
343	C₅	C₃×#2317	1	1	yes	characteristic, complemented, Sylow
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	4	no	—
348	C₂²	C₂×C₃×#683	1	4	yes	—
349	C₂²	C₂²×C₃×Dic₁₀	1	1	yes	characteristic
350	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
351	C₂²	C₃×#4144	1	2	yes	—
352	C₂²	C₃×#4147	1	2	yes	—
353	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
354	C₄	—	4	4	no	—
355	C₄	—	10	8	no	—
356	C₄	—	20	2	no	—
357	C₄	—	20	2	no	—
358	C₄	C₂×C₃×#683	1	4	yes	—
359	C₄	C₂×C₃×#683	1	4	yes	—
360	C₃	#10613888	1	1	yes	characteristic, direct product factor, Sylow
361	C₂	—	2	4	no	—
362	C₂	C₃×#65834	1	2	yes	—
363	C₂	C₃×#65838	1	2	yes	—
364	C₂	C₂²×C₃×#683	1	1	yes	characteristic
365	C₂	C₃×#66139	1	1	yes	characteristic
366	C₂	C₃×#66150	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#2317
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
5. C₃×#65266	C₂	semidirect
6. C₃×#65265	C₂	semidirect
7. C₃×#65262	C₂	semidirect
8. #10613888	C₃	direct (N × H)
17. C₃×#4072	C₄	semidirect
30. #65266	C₂×C₃	semidirect
31. #65265	C₂×C₃	semidirect
32. #65262	C₂×C₃	semidirect
51. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
54. C₃×C₄×Dic₅	C₂×C₄	semidirect
70. #4072	C₃×C₄	semidirect
88. C₂×C₃×C₄×C₅	C₄⋊C₄	semidirect
136. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
139. C₄×Dic₅	C₂×C₃×C₄	semidirect
194. C₂×C₄×C₅	C₃×C₄⋊C₄	semidirect
246. C₂×C₃×C₄	#683	semidirect
291. C₃×C₅	#2317	semidirect
330. C₂×C₄	C₃×#683	semidirect
343. C₅	C₃×#2317	semidirect
360. C₃	#10613888	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×#4072	2
C₃×#65499	2
C₃×#65266	2
C₃×#65265	2
C₃×#65262	2
#10613888	3
C₃×#2317	5

Subgroups — C3×#10613888 #14322891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613888 #14322891