Subgroups — C₃×#10615061 #14418676

Order 1920.

712 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic
2	C₃×#65313	C₂	1	4	yes	maximal, complemented
3	C₃×#65313	C₂	1	2	yes	maximal, complemented
4	C₃×Q₈×#168	C₂	1	2	yes	maximal, complemented
5	C₃×#65288	C₂	1	2	yes	maximal
6	C₃×#65286	C₂	1	2	yes	maximal
7	C₂×C₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic
9	#10615061	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₃×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₃×C₅×#125	C₄	1	2	yes	—
13	C₃×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
17	C₃×C₅×#117	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	C₂²	1	1	yes	characteristic
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₂²×C₃×#168	C₂²	1	2	yes	—
22	C₃×C₄⋊#168	C₂²	1	4	yes	—
23	C₃×C₄⋊#168	C₂²	1	4	yes	—
24	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
25	C₃×C₄⋊#168	C₂²	1	2	yes	—
26	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
27	C₃×#3935	C₂²	1	4	yes	—
28	C₃×#3935	C₂²	1	2	yes	—
29	C₃×C₄×#168	C₂²	1	4	yes	—
30	C₃×C₄×#168	C₂²	1	2	yes	—
31	C₃×#2962	—	5	1	no	maximal, Hall
32	C₅×#533	C₂×C₃	1	1	yes	characteristic
33	#65313	C₂×C₃	1	2	yes	complemented
34	#65313	C₂×C₃	1	4	yes	complemented
35	Q₈×#168	C₂×C₃	1	2	yes	complemented
36	#65288	C₂×C₃	1	2	yes	—
37	#65286	C₂×C₃	1	2	yes	—
38	C₂×C₄⋊#168	C₂×C₃	1	1	yes	characteristic
39	C₄×#681	C₂×C₃	1	1	yes	characteristic
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
41	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
52	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂³	1	4	yes	—
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×#681	—	2	2	no	—
58	C₃×#681	Q₈	1	4	yes	complemented
59	C₂×C₃×#168	—	2	4	no	—
60	C₂×C₃×#168	C₂³	1	2	yes	—
61	C₂×C₃×#168	C₂³	1	2	yes	—
62	C₂×C₃×#168	C₂³	1	2	yes	—
63	C₂×C₃×#168	C₂³	1	2	yes	—
64	C₃×#533	D₅	1	1	yes	characteristic
65	C₃×#446	—	5	2	no	—
66	C₃×#446	—	5	4	no	—
67	C₃×C₈×Q₈	—	5	2	no	—
68	C₃×#424	—	5	2	no	—
69	C₂×C₃×C₄⋊C₈	—	5	1	no	—
70	C₃×#405	—	5	2	no	—
71	C₃×C₄×M₁₆	—	5	1	no	—
72	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	C₃×C₄	1	1	yes	characteristic
74	C₅×#125	C₃×C₄	1	2	yes	—
75	C₅×C₂²⋊Q₈	C₃×C₄	1	2	yes	—
76	C₅×C₂²⋊Q₈	C₃×C₄	1	2	yes	—
77	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
78	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
79	C₅×#117	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂×#681	C₂²×C₃	1	1	yes	characteristic
82	C₂×#681	C₂²×C₃	1	1	yes	characteristic
83	C₂²×#168	C₂²×C₃	1	2	yes	—
84	C₄⋊#168	C₂²×C₃	1	4	yes	—
85	C₄⋊#168	C₂²×C₃	1	4	yes	—
86	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
87	C₄⋊#168	C₂²×C₃	1	2	yes	—
88	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
89	#3935	C₂²×C₃	1	4	yes	—
90	#3935	C₂²×C₃	1	2	yes	—
91	C₄×#168	C₂²×C₃	1	4	yes	—
92	C₄×#168	C₂²×C₃	1	2	yes	—
93	#2962	—	5	1	no	Sylow
94	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
107	C₂×C₃×C₄×C₅	#41	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
109	C₃×#168	—	2	2	no	—
110	C₃×#168	—	2	2	no	—
111	C₃×#168	—	2	2	no	—
112	C₃×#168	C₂×Q₈	1	4	yes	—
113	C₂×C₃×M₁₆	—	5	1	no	—
114	C₂×C₃×M₁₆	—	5	1	no	—
115	C₂²×C₃×C₈	—	5	2	no	—
116	C₃×C₄⋊Q₈	Dic₅	1	1	yes	characteristic
117	C₃×C₄⋊Q₈	Dic₅	1	1	yes	characteristic
118	C₃×#125	Dic₅	1	2	yes	—
119	C₃×C₂²⋊Q₈	Dic₅	1	2	yes	—
120	C₃×C₂²⋊Q₈	Dic₅	1	2	yes	—
121	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
122	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
123	C₃×#117	C₂×D₅	1	2	yes	—
124	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
125	C₃×C₄⋊C₈	—	5	1	no	—
126	C₃×C₄⋊C₈	—	5	1	no	—
127	C₃×C₄⋊C₈	—	5	2	no	—
128	C₃×C₄⋊C₈	—	5	4	no	—
129	C₃×C₄⋊C₈	—	5	4	no	—
130	C₃×#97	—	5	2	no	—
131	C₃×#97	—	5	4	no	—
132	C₃×C₄×C₈	—	5	2	no	—
133	C₃×C₄×C₈	—	5	4	no	—
134	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
136	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
140	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
141	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
142	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
143	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
144	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
145	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
146	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
150	C₄²×C₅	C₂³×C₃	1	4	yes	—
151	#681	—	2	2	no	—
152	#681	C₃×Q₈	1	4	yes	complemented
153	C₂×#168	—	2	4	no	—
154	C₂×#168	C₂³×C₃	1	2	yes	—
155	C₂×#168	C₂³×C₃	1	2	yes	—
156	C₂×#168	C₂³×C₃	1	2	yes	—
157	C₂×#168	C₂³×C₃	1	2	yes	—
158	#533	C₃×D₅	1	1	yes	characteristic
159	#446	—	5	2	no	—
160	#446	—	5	4	no	—
161	C₈×Q₈	—	5	2	no	—
162	#424	—	5	2	no	—
163	C₂×C₄⋊C₈	—	5	1	no	—
164	#405	—	5	2	no	—
165	C₄×M₁₆	—	5	1	no	—
166	C₂²×C₃×C₅	—	2	1	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
169	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	4	no	—
172	C₃×C₄×C₅	—	2	1	no	—
173	C₃×C₄×C₅	—	2	1	no	—
174	C₃×C₄×C₅	—	2	4	no	—
175	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
176	C₃×C₄×C₅	#131	1	2	yes	—
177	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
178	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
179	C₂×C₃×Q₈	C₂×Dic₅	1	2	yes	—
180	C₂×C₃×Q₈	C₂×Dic₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
184	C₃×M₁₆	—	5	4	no	—
185	C₃×M₁₆	—	10	2	no	—
186	C₂×C₃×C₈	—	5	2	no	—
187	C₂×C₃×C₈	—	5	2	no	—
188	C₂×C₃×C₈	—	5	2	no	—
189	C₂×C₃×C₈	—	5	2	no	—
190	C₂×C₃×C₈	—	10	4	no	—
191	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
192	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
193	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
194	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
195	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
196	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
198	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
199	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
200	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
201	C₃×C₄²	C₂²×D₅	1	4	yes	—
202	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
203	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₅×Q₈	—	2	4	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
212	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
213	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
216	C₂×C₄×C₅	C₃×#41	1	2	yes	—
217	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
218	#168	—	2	2	no	—
219	#168	—	2	2	no	—
220	#168	—	2	2	no	—
221	#168	C₂×C₃×Q₈	1	4	yes	—
222	C₂×M₁₆	—	5	1	no	—
223	C₂×M₁₆	—	5	1	no	—
224	C₂²×C₈	—	5	2	no	—
225	C₄⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
226	C₄⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
227	#125	C₃×Dic₅	1	2	yes	—
228	C₂²⋊Q₈	C₃×Dic₅	1	2	yes	—
229	C₂²⋊Q₈	C₃×Dic₅	1	2	yes	—
230	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
231	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
232	#117	C₂×C₃×D₅	1	2	yes	—
233	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
234	C₄⋊C₈	—	5	1	no	—
235	C₄⋊C₈	—	5	1	no	—
236	C₄⋊C₈	—	5	2	no	—
237	C₄⋊C₈	—	5	4	no	—
238	C₄⋊C₈	—	5	4	no	—
239	#97	—	5	2	no	—
240	#97	—	5	4	no	—
241	C₄×C₈	—	5	2	no	—
242	C₄×C₈	—	5	4	no	—
243	C₂×C₃×C₅	—	2	2	no	—
244	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
246	C₂×C₃×C₅	#568	1	1	yes	characteristic
247	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
248	C₃×Q₈	—	2	4	no	—
249	C₃×Q₈	—	4	2	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	4	1	no	—
252	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
253	C₂×C₃×C₄	#713	1	2	yes	—
254	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
258	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
259	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
262	C₃×C₈	—	5	4	no	—
263	C₃×C₈	—	10	2	no	—
264	C₃×C₈	—	10	2	no	—
265	C₃×C₈	—	10	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	2	1	no	—
268	C₂²×C₅	C₃×C₄×Q₈	1	2	yes	—
269	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
270	C₄×C₅	—	2	1	no	—
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	2	1	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	2	4	no	—
275	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
276	C₄×C₅	C₃×#131	1	2	yes	—
277	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
278	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
279	C₂×Q₈	C₂×C₃×Dic₅	1	2	yes	—
280	C₂×Q₈	C₂×C₃×Dic₅	1	2	yes	—
281	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
283	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
284	M₁₆	—	5	4	no	—
285	M₁₆	—	10	2	no	—
286	C₂×C₈	—	5	2	no	—
287	C₂×C₈	—	5	2	no	—
288	C₂×C₈	—	5	2	no	—
289	C₂×C₈	—	5	2	no	—
290	C₂×C₈	—	10	4	no	—
291	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
292	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
293	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
294	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
295	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
296	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
297	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
298	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
299	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
300	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
301	C₄²	C₂²×C₃×D₅	1	4	yes	—
302	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
303	C₃×C₅	#2962	1	1	yes	characteristic, complemented, Hall
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	Q₈×Dic₅	1	2	yes	—
307	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	Q₈×Dic₅	1	2	yes	—
314	C₃×C₄	#4094	1	2	yes	—
315	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
316	C₃×C₄	C₂×#713	1	1	yes	characteristic
317	C₂×C₅	—	2	2	no	—
318	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
319	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
320	C₂×C₅	C₃×#568	1	1	yes	characteristic
321	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
327	C₂×C₄	C₃×#713	1	2	yes	—
328	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
332	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
333	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
334	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
335	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
336	C₈	—	5	4	no	—
337	C₈	—	10	2	no	—
338	C₈	—	10	2	no	—
339	C₈	—	10	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	C₂×Q₈×Dic₅	1	1	yes	characteristic
342	C₂×C₃	C₂×#4094	1	1	yes	characteristic
343	C₂×C₃	#66153	1	1	yes	characteristic
344	C₅	C₃×#2962	1	1	yes	characteristic, complemented, Sylow
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	C₃×Q₈×Dic₅	1	2	yes	—
348	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
349	C₄	—	2	1	no	—
350	C₄	—	2	4	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	4	no	—
354	C₄	C₃×Q₈×Dic₅	1	2	yes	—
355	C₄	C₃×#4094	1	2	yes	—
356	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
357	C₄	C₂×C₃×#713	1	1	yes	characteristic
358	C₃	#10615061	1	1	yes	characteristic, direct product factor, Sylow
359	C₂	—	2	2	no	—
360	C₂	C₂×C₃×Q₈×Dic₅	1	1	yes	characteristic
361	C₂	C₂×C₃×#4094	1	1	yes	characteristic
362	C₂	C₃×#66153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#533	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#533	D₅
hypocenter	C₅	C₃×#2962
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
2. C₃×#65313	C₂	semidirect
3. C₃×#65313	C₂	semidirect
4. C₃×Q₈×#168	C₂	semidirect
9. #10615061	C₃	direct (N × H)
33. #65313	C₂×C₃	semidirect
34. #65313	C₂×C₃	semidirect
35. Q₈×#168	C₂×C₃	semidirect
58. C₃×#681	Q₈	semidirect
152. #681	C₃×Q₈	semidirect
303. C₃×C₅	#2962	semidirect
344. C₅	C₃×#2962	semidirect
358. C₃	#10615061	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#533	2
C₃×#65313	2
C₃×Q₈×#168	2
C₃×#65288	2
C₃×#65286	2
C₂×C₃×C₄⋊#168	2
C₃×C₄×#681	2
#10615061	3
C₃×#2962	5

Subgroups — C3×#10615061 #14418676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615061 #14418676