Subgroups — C₃×#10601278 #14297682

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×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3948	C₂	1	2	yes	maximal
4	C₃×#65224	C₂	1	1	yes	maximal, characteristic
5	C₃×#64771	C₂	1	2	yes	maximal
6	#10601278	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
11	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
12	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×#683	—	2	1	no	—
15	C₂×C₃×C₄×Dic₅	—	2	1	no	—
16	C₃×C₄×Dic₁₀	—	2	2	no	—
17	C₃×C₄×Dic₁₀	C₄	1	4	yes	complemented
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₃×#3948	—	2	4	no	—
20	C₃×#1803	—	5	1	no	maximal, Hall
21	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₂×#3948	C₂×C₃	1	2	yes	—
24	#65224	C₂×C₃	1	1	yes	characteristic
25	#64771	C₂×C₃	1	2	yes	—
26	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₂²×C₃×Dic₅	—	2	1	no	—
30	C₂²×C₃×Dic₅	—	2	1	no	—
31	C₂²×C₃×Dic₅	—	2	2	no	—
32	C₂×C₃×Dic₁₀	—	2	1	no	—
33	C₂×C₃×Dic₁₀	—	2	1	no	—
34	C₂×C₃×Dic₁₀	—	2	1	no	—
35	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
36	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
37	C₂×C₃×Dic₁₀	Q₈	1	2	yes	—
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
42	C₃×C₄²×C₅	D₄	1	2	yes	—
43	C₃×C₄⋊Dic₅	—	2	1	no	—
44	C₃×C₄⋊Dic₅	—	2	2	no	—
45	C₃×C₄⋊Dic₅	—	2	2	no	—
46	C₃×C₄⋊Dic₅	—	4	2	no	—
47	C₃×C₄⋊Dic₅	—	4	2	no	—
48	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
49	C₃×#683	—	2	4	no	—
50	C₃×C₄×Dic₅	—	2	4	no	—
51	C₂×C₃×C₄×Q₈	—	5	1	no	—
52	C₂×C₃×C₄⋊C₈	D₅	1	1	yes	characteristic
53	C₂×C₃×#103	—	5	2	no	—
54	C₃×#384	—	5	1	no	—
55	C₃×#340	—	5	2	no	—
56	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
58	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₄⋊Dic₅	—	2	1	no	—
60	C₂×C₄⋊Dic₅	—	2	1	no	—
61	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
62	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
63	C₂×#683	—	2	1	no	—
64	C₂×C₄×Dic₅	—	2	1	no	—
65	C₄×Dic₁₀	—	2	2	no	—
66	C₄×Dic₁₀	C₃×C₄	1	4	yes	complemented
67	C₅×C₄⋊C₈	—	2	2	no	—
68	#3948	—	2	4	no	—
69	#1803	—	5	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	C₂²⋊C₄	1	2	yes	—
74	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
75	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
76	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
77	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
83	C₂×C₃×Dic₅	—	2	2	no	—
84	C₂×C₃×Dic₅	—	2	2	no	—
85	C₂×C₃×Dic₅	—	2	2	no	—
86	C₂×C₃×Dic₅	—	2	2	no	—
87	C₂×C₃×Dic₅	—	4	1	no	—
88	C₂×C₃×Dic₅	—	4	1	no	—
89	C₂×C₃×Dic₅	—	4	2	no	—
90	C₂×C₃×Dic₅	—	4	2	no	—
91	C₂×C₃×Dic₅	—	4	2	no	—
92	C₃×Dic₁₀	—	2	2	no	—
93	C₃×Dic₁₀	—	2	2	no	—
94	C₃×Dic₁₀	—	2	2	no	—
95	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	complemented
96	C₃×C₅×C₈	—	4	2	no	—
97	C₂²×C₃×Q₈	—	5	1	no	—
98	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
99	C₃×C₄×Q₈	—	5	4	no	—
100	C₃×C₄×Q₈	—	10	2	no	—
101	C₂×C₃×C₄⋊C₄	—	5	1	no	—
102	C₂×C₃×C₄⋊C₄	—	5	2	no	—
103	C₂×C₃×C₄⋊C₄	—	10	1	no	—
104	C₂×C₃×C₄⋊C₄	—	10	1	no	—
105	C₂×C₃×C₄⋊C₄	—	10	1	no	—
106	C₂×C₃×C₄²	—	10	1	no	—
107	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	2	2	no	—
109	C₃×#103	—	10	4	no	—
110	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
113	C₂²×Dic₅	—	2	1	no	—
114	C₂²×Dic₅	—	2	1	no	—
115	C₂²×Dic₅	—	2	2	no	—
116	C₂×Dic₁₀	—	2	1	no	—
117	C₂×Dic₁₀	—	2	1	no	—
118	C₂×Dic₁₀	—	2	1	no	—
119	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
120	C₂×Dic₁₀	C₃×D₄	1	2	yes	—
121	C₂×Dic₁₀	C₃×Q₈	1	2	yes	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
126	C₄²×C₅	C₃×D₄	1	2	yes	—
127	C₄⋊Dic₅	—	2	1	no	—
128	C₄⋊Dic₅	—	2	2	no	—
129	C₄⋊Dic₅	—	2	2	no	—
130	C₄⋊Dic₅	—	4	2	no	—
131	C₄⋊Dic₅	—	4	2	no	—
132	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
133	#683	—	2	4	no	—
134	C₄×Dic₅	—	2	4	no	—
135	C₂×C₄×Q₈	—	5	1	no	—
136	C₂×C₄⋊C₈	C₃×D₅	1	1	yes	characteristic
137	C₂×#103	—	5	2	no	—
138	#384	—	5	1	no	—
139	#340	—	5	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	#103	1	4	yes	complemented
149	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₃×C₄×C₅	#117	1	1	yes	characteristic
151	C₃×C₄×C₅	#121	1	1	yes	characteristic
152	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
153	C₃×Dic₅	—	2	4	no	—
154	C₃×Dic₅	—	4	2	no	—
155	C₃×Dic₅	—	8	2	no	—
156	C₂×C₃×Q₈	—	5	2	no	—
157	C₂×C₃×Q₈	—	5	2	no	—
158	C₂×C₃×Q₈	—	5	2	no	—
159	C₂×C₃×Q₈	—	10	1	no	—
160	C₂×C₃×Q₈	—	10	1	no	—
161	C₂×C₃×Q₈	—	10	1	no	—
162	C₂²×C₃×C₄	—	10	1	no	—
163	C₂²×C₃×C₄	—	10	1	no	—
164	C₂²×C₃×C₄	—	10	2	no	—
165	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
166	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₃×C₄⋊C₄	—	5	2	no	—
172	C₃×C₄⋊C₄	—	10	4	no	—
173	C₃×C₄⋊C₄	—	10	1	no	—
174	C₃×C₄⋊C₄	—	10	2	no	—
175	C₃×C₄⋊C₄	—	10	2	no	—
176	C₃×C₄⋊C₄	—	20	2	no	—
177	C₃×C₄⋊C₄	—	20	2	no	—
178	C₃×C₄²	—	10	4	no	—
179	C₃×C₄²	C₄×D₅	1	2	yes	—
180	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
181	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
187	C₂×C₄×C₅	C₃×Q₁₆	1	2	yes	—
188	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
189	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
193	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
194	C₂×Dic₅	—	2	2	no	—
195	C₂×Dic₅	—	2	2	no	—
196	C₂×Dic₅	—	2	2	no	—
197	C₂×Dic₅	—	2	2	no	—
198	C₂×Dic₅	—	4	1	no	—
199	C₂×Dic₅	—	4	1	no	—
200	C₂×Dic₅	—	4	2	no	—
201	C₂×Dic₅	—	4	2	no	—
202	C₂×Dic₅	—	4	2	no	—
203	Dic₁₀	—	2	2	no	—
204	Dic₁₀	—	2	2	no	—
205	Dic₁₀	—	2	2	no	—
206	Dic₁₀	C₃×C₄⋊C₄	1	4	yes	complemented
207	C₅×C₈	—	4	2	no	—
208	C₂²×Q₈	—	5	1	no	—
209	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
210	C₄×Q₈	—	5	4	no	—
211	C₄×Q₈	—	10	2	no	—
212	C₂×C₄⋊C₄	—	5	1	no	—
213	C₂×C₄⋊C₄	—	5	2	no	—
214	C₂×C₄⋊C₄	—	10	1	no	—
215	C₂×C₄⋊C₄	—	10	1	no	—
216	C₂×C₄⋊C₄	—	10	1	no	—
217	C₂×C₄²	—	10	1	no	—
218	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
219	C₄⋊C₈	—	2	2	no	—
220	#103	—	10	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×D₂₀	1	1	yes	characteristic
229	C₃×Q₈	—	5	4	no	—
230	C₃×Q₈	—	10	2	no	—
231	C₃×Q₈	—	10	2	no	—
232	C₃×Q₈	—	10	2	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	10	2	no	—
236	C₂×C₃×C₄	—	10	2	no	—
237	C₂×C₃×C₄	—	10	2	no	—
238	C₂×C₃×C₄	—	10	2	no	—
239	C₂×C₃×C₄	—	20	1	no	—
240	C₂×C₃×C₄	—	20	1	no	—
241	C₂×C₃×C₄	—	20	2	no	—
242	C₂×C₃×C₄	—	20	2	no	—
243	C₂×C₃×C₄	—	20	2	no	—
244	C₂×C₃×C₄	#677	1	2	yes	—
245	C₂×C₃×C₄	Dic₂₀	1	2	yes	—
246	C₂×C₃×C₄	#685	1	2	yes	—
247	C₂×C₃×C₄	#685	1	2	yes	—
248	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
249	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
250	C₂×C₃×C₄	#711	1	1	yes	characteristic
251	C₂×C₃×C₄	Q₈×D₅	1	1	yes	characteristic
252	C₂×C₃×C₄	#713	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
254	C₃×C₈	—	4	2	no	—
255	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₅	C₃×#121	1	1	yes	characteristic
257	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
258	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
259	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
260	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₅	C₃×#137	1	1	yes	characteristic
262	C₄×C₅	—	2	2	no	—
263	C₄×C₅	C₃×#103	1	4	yes	complemented
264	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
265	C₄×C₅	C₃×#117	1	1	yes	characteristic
266	C₄×C₅	C₃×#121	1	1	yes	characteristic
267	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
268	Dic₅	—	2	4	no	—
269	Dic₅	—	4	2	no	—
270	Dic₅	—	8	2	no	—
271	C₂×Q₈	—	5	2	no	—
272	C₂×Q₈	—	5	2	no	—
273	C₂×Q₈	—	5	2	no	—
274	C₂×Q₈	—	10	1	no	—
275	C₂×Q₈	—	10	1	no	—
276	C₂×Q₈	—	10	1	no	—
277	C₂²×C₄	—	10	1	no	—
278	C₂²×C₄	—	10	1	no	—
279	C₂²×C₄	—	10	2	no	—
280	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
281	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₄⋊C₄	—	5	2	no	—
287	C₄⋊C₄	—	10	4	no	—
288	C₄⋊C₄	—	10	1	no	—
289	C₄⋊C₄	—	10	2	no	—
290	C₄⋊C₄	—	10	2	no	—
291	C₄⋊C₄	—	20	2	no	—
292	C₄⋊C₄	—	20	2	no	—
293	C₄²	—	10	4	no	—
294	C₄²	C₃×C₄×D₅	1	2	yes	—
295	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
296	C₃×C₅	#1803	1	1	yes	characteristic, complemented, Hall
297	C₂²×C₃	#4041	1	1	yes	characteristic
298	C₂²×C₃	#4043	1	1	yes	characteristic
299	C₂²×C₃	C₂×#677	1	1	yes	characteristic
300	C₂²×C₃	C₂×Dic₂₀	1	1	yes	characteristic
301	C₂²×C₃	#4054	1	1	yes	characteristic
302	C₂²×C₃	#4055	1	1	yes	characteristic
303	C₂²×C₃	C₂×#685	1	1	yes	characteristic
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	10	4	no	—
306	C₃×C₄	—	20	2	no	—
307	C₃×C₄	—	40	2	no	—
308	C₃×C₄	#3948	1	4	yes	complemented
309	C₃×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
310	C₃×C₄	#4038	1	1	yes	characteristic
311	C₃×C₄	#4084	1	1	yes	characteristic
312	C₃×C₄	#4092	1	1	yes	characteristic
313	C₂×C₅	C₃×#380	1	1	yes	characteristic
314	C₂×C₅	C₂×C₃×#103	1	1	yes	characteristic
315	C₂×C₅	C₃×#417	1	1	yes	characteristic
316	C₂×C₅	C₃×#460	1	1	yes	characteristic
317	C₂×C₅	C₃×#462	1	1	yes	characteristic
318	C₂×C₅	C₃×#475	1	1	yes	characteristic
319	C₂×C₅	C₃×#477	1	1	yes	characteristic
320	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
321	Q₈	—	5	4	no	—
322	Q₈	—	10	2	no	—
323	Q₈	—	10	2	no	—
324	Q₈	—	10	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	10	2	no	—
328	C₂×C₄	—	10	2	no	—
329	C₂×C₄	—	10	2	no	—
330	C₂×C₄	—	10	2	no	—
331	C₂×C₄	—	20	1	no	—
332	C₂×C₄	—	20	1	no	—
333	C₂×C₄	—	20	2	no	—
334	C₂×C₄	—	20	2	no	—
335	C₂×C₄	—	20	2	no	—
336	C₂×C₄	C₃×#677	1	2	yes	—
337	C₂×C₄	C₃×Dic₂₀	1	2	yes	—
338	C₂×C₄	C₃×#685	1	2	yes	—
339	C₂×C₄	C₃×#685	1	2	yes	—
340	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
341	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
342	C₂×C₄	C₃×#711	1	1	yes	characteristic
343	C₂×C₄	C₃×Q₈×D₅	1	1	yes	characteristic
344	C₂×C₄	C₃×#713	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
346	C₈	—	4	2	no	—
347	C₂×C₃	#65137	1	1	yes	characteristic
348	C₂×C₃	#65138	1	1	yes	characteristic
349	C₂×C₃	#65139	1	1	yes	characteristic
350	C₂×C₃	#65140	1	1	yes	characteristic
351	C₂×C₃	#65276	1	1	yes	characteristic
352	C₂×C₃	C₂×#3948	1	1	yes	characteristic
353	C₂×C₃	#65422	1	1	yes	characteristic
354	C₅	C₃×#1803	1	1	yes	characteristic, complemented, Sylow
355	C₂²	C₃×#4041	1	1	yes	characteristic
356	C₂²	C₃×#4043	1	1	yes	characteristic
357	C₂²	C₂×C₃×#677	1	1	yes	characteristic
358	C₂²	C₂×C₃×Dic₂₀	1	1	yes	characteristic
359	C₂²	C₃×#4054	1	1	yes	characteristic
360	C₂²	C₃×#4055	1	1	yes	characteristic
361	C₂²	C₂×C₃×#685	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	10	4	no	—
364	C₄	—	20	2	no	—
365	C₄	—	40	2	no	—
366	C₄	C₃×#3948	1	4	yes	complemented
367	C₄	C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
368	C₄	C₃×#4038	1	1	yes	characteristic
369	C₄	C₃×#4084	1	1	yes	characteristic
370	C₄	C₃×#4092	1	1	yes	characteristic
371	C₃	#10601278	1	1	yes	characteristic, direct product factor, Sylow
372	C₂	C₃×#65137	1	1	yes	characteristic
373	C₂	C₃×#65138	1	1	yes	characteristic
374	C₂	C₃×#65139	1	1	yes	characteristic
375	C₂	C₃×#65140	1	1	yes	characteristic
376	C₂	C₃×#65276	1	1	yes	characteristic
377	C₂	C₂×C₃×#3948	1	1	yes	characteristic
378	C₂	C₃×#65422	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₂₀
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×C₄⋊C₈	D₅
hypocenter	C₅	C₃×#1803
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
6. #10601278	C₃	direct (N × H)
17. C₃×C₄×Dic₁₀	C₄	semidirect
66. C₄×Dic₁₀	C₃×C₄	semidirect
95. C₃×Dic₁₀	C₄⋊C₄	semidirect
148. C₃×C₄×C₅	#103	semidirect
206. Dic₁₀	C₃×C₄⋊C₄	semidirect
263. C₄×C₅	C₃×#103	semidirect
296. C₃×C₅	#1803	semidirect
308. C₃×C₄	#3948	semidirect
354. C₅	C₃×#1803	semidirect
366. C₄	C₃×#3948	semidirect
371. C₃	#10601278	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×Dic₁₀	2
C₂×C₃×C₅×C₄⋊C₈	2
C₂×C₃×#3948	2
C₃×#65224	2
C₃×#64771	2
#10601278	3
C₃×#1803	5

Subgroups — C3×#10601278 #14297682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10601278 #14297682