Subgroups — C₃×#10615629 #14417630

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×#66161	C₂	1	2	yes	maximal, complemented
3	C₃×#65521	C₂	1	2	yes	maximal, complemented
4	C₃×Q₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
5	C₃×#65453	C₂	1	4	yes	maximal, complemented
6	C₃×D₈×Dic₅	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#3950	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65390	C₂	1	1	yes	maximal, characteristic, complemented
9	#10615629	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₃×C₅×#135	C₄	1	8	yes	complemented
12	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×Q₈×Dic₅	C₂²	1	4	yes	—
17	C₃×D₄×Dic₅	—	2	4	no	—
18	C₃×D₄×Dic₅	C₂²	1	4	yes	—
19	C₃×#4072	—	2	2	no	—
20	C₃×#4072	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊Dic₅	—	2	2	no	—
22	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×#681	C₂²	1	1	yes	characteristic
24	C₃×#3967	C₂²	1	4	yes	—
25	C₃×#3964	C₂²	1	4	yes	—
26	C₃×#3950	C₂²	1	2	yes	—
27	C₃×#3950	C₂²	1	2	yes	—
28	C₃×#3947	C₂²	1	2	yes	—
29	C₃×C₈×Dic₅	C₂²	1	2	yes	—
30	C₃×#2951	—	5	1	no	maximal, Hall
31	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
32	#66161	C₂×C₃	1	2	yes	complemented
33	#65521	C₂×C₃	1	2	yes	complemented
34	Q₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
35	#65453	C₂×C₃	1	4	yes	complemented
36	D₈×Dic₅	C₂×C₃	1	2	yes	complemented
37	C₂×#3950	C₂×C₃	1	1	yes	characteristic, complemented
38	#65390	C₂×C₃	1	1	yes	characteristic, complemented
39	C₃×C₅×#41	—	2	4	no	—
40	C₃×C₅×#41	C₂×C₄	1	8	yes	complemented
41	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×Dic₅	—	2	2	no	—
47	C₂²×C₃×Dic₅	—	2	4	no	—
48	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₃×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
50	C₃×C₅×D₈	C₂×C₄	1	4	yes	complemented
51	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
52	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₃×C₂²⋊Dic₅	—	2	4	no	—
55	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
56	C₃×C₄⋊Dic₅	—	2	2	no	—
57	C₃×C₄⋊Dic₅	—	2	4	no	—
58	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
59	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
60	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
61	C₃×C₄×Dic₅	—	2	4	no	—
62	C₃×C₄×Dic₅	C₂³	1	2	yes	—
63	C₃×#681	—	2	2	no	—
64	C₂×C₃×#168	C₂³	1	2	yes	—
65	C₂×C₃×#135	D₅	1	1	yes	characteristic
66	C₃×#520	—	5	2	no	—
67	C₃×#440	—	5	4	no	—
68	C₃×C₄×Q₁₆	—	5	2	no	—
69	C₃×C₄×D₈	—	5	2	no	—
70	C₂×C₃×#107	—	5	1	no	—
71	C₃×#417	—	5	2	no	—
72	C₃×#405	—	5	1	no	—
73	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
74	C₅×#135	C₃×C₄	1	8	yes	complemented
75	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
77	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
79	Q₈×Dic₅	C₂²×C₃	1	4	yes	—
80	D₄×Dic₅	—	2	4	no	—
81	D₄×Dic₅	C₂²×C₃	1	4	yes	—
82	#4072	—	2	2	no	—
83	#4072	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄⋊Dic₅	—	2	2	no	—
85	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
86	C₂×#681	C₂²×C₃	1	1	yes	characteristic
87	#3967	C₂²×C₃	1	4	yes	—
88	#3964	C₂²×C₃	1	4	yes	—
89	#3950	C₂²×C₃	1	2	yes	—
90	#3950	C₂²×C₃	1	2	yes	—
91	#3947	C₂²×C₃	1	2	yes	—
92	C₈×Dic₅	C₂²×C₃	1	2	yes	—
93	#2951	—	5	1	no	Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	2	2	no	—
97	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
98	C₃×C₅×D₄	—	2	8	no	—
99	C₃×C₅×D₄	—	2	2	no	—
100	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	8	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×Dic₅	—	2	4	no	—
108	C₂×C₃×Dic₅	—	8	4	no	—
109	C₂×C₃×Dic₅	—	8	2	no	—
110	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
111	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₃×#168	—	2	2	no	—
115	C₂×C₃×#41	C₂×D₅	1	2	yes	—
116	C₃×#135	Dic₅	1	8	yes	complemented
117	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
118	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
119	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
120	C₂×C₃×M₁₆	—	5	1	no	—
121	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
122	C₃×C₄×Q₈	—	5	4	no	—
123	C₃×C₄×D₄	—	5	4	no	—
124	C₃×C₄×D₄	—	10	4	no	—
125	C₃×#117	—	5	1	no	—
126	C₃×#117	—	10	2	no	—
127	C₂×C₃×C₄⋊C₄	—	5	2	no	—
128	C₂×C₃×C₄⋊C₄	—	10	2	no	—
129	C₃×#107	—	5	2	no	—
130	C₃×#107	—	5	2	no	—
131	C₃×#103	—	5	4	no	—
132	C₃×#102	—	5	4	no	—
133	C₃×#97	—	5	2	no	—
134	C₃×C₄×C₈	—	5	2	no	—
135	C₅×#41	—	2	4	no	—
136	C₅×#41	C₂×C₃×C₄	1	8	yes	complemented
137	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂²×Dic₅	—	2	2	no	—
143	C₂²×Dic₅	—	2	4	no	—
144	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
145	C₅×SD₁₆	C₂×C₃×C₄	1	8	yes	complemented
146	C₅×D₈	C₂×C₃×C₄	1	4	yes	complemented
147	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	complemented
148	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
150	C₂²⋊Dic₅	—	2	4	no	—
151	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
152	C₄⋊Dic₅	—	2	2	no	—
153	C₄⋊Dic₅	—	2	4	no	—
154	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
155	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
156	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
157	C₄×Dic₅	—	2	4	no	—
158	C₄×Dic₅	C₂³×C₃	1	2	yes	—
159	#681	—	2	2	no	—
160	C₂×#168	C₂³×C₃	1	2	yes	—
161	C₂×#135	C₃×D₅	1	1	yes	characteristic
162	#520	—	5	2	no	—
163	#440	—	5	4	no	—
164	C₄×Q₁₆	—	5	2	no	—
165	C₄×D₈	—	5	2	no	—
166	C₂×#107	—	5	1	no	—
167	#417	—	5	2	no	—
168	#405	—	5	1	no	—
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×C₅	—	2	4	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	2	no	—
174	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
175	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₃×C₄×C₅	—	2	4	no	—
177	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
178	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
180	C₃×Dic₅	—	2	2	no	—
181	C₃×Dic₅	—	2	2	no	—
182	C₃×Dic₅	—	4	4	no	—
183	C₃×#41	—	2	4	no	—
184	C₃×#41	C₂×Dic₅	1	8	yes	complemented
185	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
186	C₂×C₃×D₄	—	2	2	no	—
187	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	10	4	no	—
190	C₂²×C₃×C₄	—	10	2	no	—
191	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
192	C₃×Q₁₆	C₂×Dic₅	1	4	yes	complemented
193	C₃×SD₁₆	C₂×Dic₅	1	8	yes	complemented
194	C₃×D₈	C₂×Dic₅	1	4	yes	complemented
195	C₃×M₁₆	—	10	2	no	—
196	C₂×C₃×C₈	—	5	2	no	—
197	C₂×C₃×C₈	C₂×Dic₅	1	4	yes	complemented
198	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
199	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
200	C₃×C₄⋊C₄	—	5	1	no	—
201	C₃×C₄⋊C₄	—	5	1	no	—
202	C₃×C₄⋊C₄	—	5	4	no	—
203	C₃×C₄⋊C₄	—	10	4	no	—
204	C₃×C₄⋊C₄	—	10	2	no	—
205	C₃×C₂²⋊C₄	—	5	2	no	—
206	C₃×C₂²⋊C₄	—	10	4	no	—
207	C₃×C₄²	—	5	2	no	—
208	C₃×C₄²	—	10	4	no	—
209	C₂³×C₅	—	2	2	no	—
210	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
211	C₅×Q₈	—	2	2	no	—
212	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
213	C₅×D₄	—	2	8	no	—
214	C₅×D₄	—	2	2	no	—
215	C₅×D₄	C₂²×C₃×C₄	1	4	yes	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	8	no	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₃×#41	1	2	yes	—
221	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
222	C₂×Dic₅	—	2	4	no	—
223	C₂×Dic₅	—	8	4	no	—
224	C₂×Dic₅	—	8	2	no	—
225	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
226	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
227	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
228	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
229	#168	—	2	2	no	—
230	C₂×#41	C₂×C₃×D₅	1	2	yes	—
231	#135	C₃×Dic₅	1	8	yes	complemented
232	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
233	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
234	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
235	C₂×M₁₆	—	5	1	no	—
236	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
237	C₄×Q₈	—	5	4	no	—
238	C₄×D₄	—	5	4	no	—
239	C₄×D₄	—	10	4	no	—
240	#117	—	5	1	no	—
241	#117	—	10	2	no	—
242	C₂×C₄⋊C₄	—	5	2	no	—
243	C₂×C₄⋊C₄	—	10	2	no	—
244	#107	—	5	2	no	—
245	#107	—	5	2	no	—
246	#103	—	5	4	no	—
247	#102	—	5	4	no	—
248	#97	—	5	2	no	—
249	C₄×C₈	—	5	2	no	—
250	C₂×C₃×C₅	—	2	2	no	—
251	C₂×C₃×C₅	—	4	4	no	—
252	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂×C₃×C₅	#576	1	1	yes	characteristic
254	C₂×C₃×C₅	#578	1	1	yes	characteristic
255	C₂³×C₃	—	2	2	no	—
256	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
257	C₃×Q₈	—	2	2	no	—
258	C₃×Q₈	C₂²×Dic₅	1	4	yes	—
259	C₃×D₄	—	2	8	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	C₂²×Dic₅	1	4	yes	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	2	8	no	—
264	C₂×C₃×C₄	—	5	2	no	—
265	C₂×C₃×C₄	—	5	2	no	—
266	C₂×C₃×C₄	—	10	4	no	—
267	C₂×C₃×C₄	—	40	4	no	—
268	C₂×C₃×C₄	—	40	2	no	—
269	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
270	C₂×C₃×C₄	#711	1	2	yes	—
271	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
272	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
273	C₃×C₈	—	10	2	no	—
274	C₃×C₈	C₂²×Dic₅	1	2	yes	—
275	C₃×C₈	C₂²×Dic₅	1	2	yes	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	4	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
282	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
285	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
286	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
287	Dic₅	—	2	2	no	—
288	Dic₅	—	2	2	no	—
289	Dic₅	—	4	4	no	—
290	#41	—	2	4	no	—
291	#41	C₂×C₃×Dic₅	1	8	yes	complemented
292	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	10	4	no	—
297	C₂²×C₄	—	10	2	no	—
298	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
299	Q₁₆	C₂×C₃×Dic₅	1	4	yes	complemented
300	SD₁₆	C₂×C₃×Dic₅	1	8	yes	complemented
301	D₈	C₂×C₃×Dic₅	1	4	yes	complemented
302	M₁₆	—	10	2	no	—
303	C₂×C₈	—	5	2	no	—
304	C₂×C₈	C₂×C₃×Dic₅	1	4	yes	complemented
305	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
307	C₄⋊C₄	—	5	1	no	—
308	C₄⋊C₄	—	5	1	no	—
309	C₄⋊C₄	—	5	4	no	—
310	C₄⋊C₄	—	10	4	no	—
311	C₄⋊C₄	—	10	2	no	—
312	C₂²⋊C₄	—	5	2	no	—
313	C₂²⋊C₄	—	10	4	no	—
314	C₄²	—	5	2	no	—
315	C₄²	—	10	4	no	—
316	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	4	no	—
320	C₂²×C₃	—	4	2	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	D₄×Dic₅	1	2	yes	—
323	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	10	2	no	—
326	C₃×C₄	—	10	2	no	—
327	C₃×C₄	—	20	4	no	—
328	C₃×C₄	D₄×Dic₅	1	2	yes	—
329	C₃×C₄	C₂×#711	1	1	yes	characteristic
330	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
331	C₂×C₅	—	2	2	no	—
332	C₂×C₅	—	4	4	no	—
333	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
334	C₂×C₅	C₃×#576	1	1	yes	characteristic
335	C₂×C₅	C₃×#578	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
338	Q₈	—	2	2	no	—
339	Q₈	C₂²×C₃×Dic₅	1	4	yes	—
340	D₄	—	2	8	no	—
341	D₄	—	2	2	no	—
342	D₄	C₂²×C₃×Dic₅	1	4	yes	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	5	2	no	—
346	C₂×C₄	—	5	2	no	—
347	C₂×C₄	—	10	4	no	—
348	C₂×C₄	—	40	4	no	—
349	C₂×C₄	—	40	2	no	—
350	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
351	C₂×C₄	C₃×#711	1	2	yes	—
352	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
353	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
354	C₈	—	10	2	no	—
355	C₈	C₂²×C₃×Dic₅	1	2	yes	—
356	C₈	C₂²×C₃×Dic₅	1	2	yes	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	4	4	no	—
359	C₂×C₃	#66103	1	1	yes	characteristic
360	C₂×C₃	#66105	1	1	yes	characteristic
361	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
362	C₅	C₃×#2951	1	1	yes	characteristic, complemented, Sylow
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	C₃×D₄×Dic₅	1	2	yes	—
369	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	10	2	no	—
372	C₄	—	10	2	no	—
373	C₄	—	20	4	no	—
374	C₄	C₃×D₄×Dic₅	1	2	yes	—
375	C₄	C₂×C₃×#711	1	1	yes	characteristic
376	C₄	C₂³×C₃×Dic₅	1	1	yes	characteristic
377	C₃	#10615629	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	4	4	no	—
380	C₂	C₃×#66103	1	1	yes	characteristic
381	C₂	C₃×#66105	1	1	yes	characteristic
382	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₂×C₃×C₅×#135	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#135	D₅
hypocenter	C₅	C₃×#2951
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#135

Complements

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

N	H ≅ G/N	type
2. C₃×#66161	C₂	semidirect
3. C₃×#65521	C₂	semidirect
4. C₃×Q₁₆×Dic₅	C₂	semidirect
5. C₃×#65453	C₂	semidirect
6. C₃×D₈×Dic₅	C₂	semidirect
7. C₂×C₃×#3950	C₂	semidirect
8. C₃×#65390	C₂	semidirect
9. #10615629	C₃	direct (N × H)
11. C₃×C₅×#135	C₄	semidirect
32. #66161	C₂×C₃	semidirect
33. #65521	C₂×C₃	semidirect
34. Q₁₆×Dic₅	C₂×C₃	semidirect
35. #65453	C₂×C₃	semidirect
36. D₈×Dic₅	C₂×C₃	semidirect
37. C₂×#3950	C₂×C₃	semidirect
38. #65390	C₂×C₃	semidirect
40. C₃×C₅×#41	C₂×C₄	semidirect
48. C₃×C₅×Q₁₆	C₂×C₄	semidirect
49. C₃×C₅×SD₁₆	C₂×C₄	semidirect
50. C₃×C₅×D₈	C₂×C₄	semidirect
51. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
74. C₅×#135	C₃×C₄	semidirect
116. C₃×#135	Dic₅	semidirect
136. C₅×#41	C₂×C₃×C₄	semidirect
144. C₅×Q₁₆	C₂×C₃×C₄	semidirect
145. C₅×SD₁₆	C₂×C₃×C₄	semidirect
146. C₅×D₈	C₂×C₃×C₄	semidirect
147. C₂×C₅×C₈	C₂×C₃×C₄	semidirect
184. C₃×#41	C₂×Dic₅	semidirect
192. C₃×Q₁₆	C₂×Dic₅	semidirect
193. C₃×SD₁₆	C₂×Dic₅	semidirect
194. C₃×D₈	C₂×Dic₅	semidirect
197. C₂×C₃×C₈	C₂×Dic₅	semidirect
231. #135	C₃×Dic₅	semidirect
291. #41	C₂×C₃×Dic₅	semidirect
299. Q₁₆	C₂×C₃×Dic₅	semidirect
300. SD₁₆	C₂×C₃×Dic₅	semidirect
301. D₈	C₂×C₃×Dic₅	semidirect
304. C₂×C₈	C₂×C₃×Dic₅	semidirect
316. C₃×C₅	#2951	semidirect
362. C₅	C₃×#2951	semidirect
377. C₃	#10615629	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×C₅×#135	2
C₃×#66161	2
C₃×#65521	2
C₃×Q₁₆×Dic₅	2
C₃×#65453	2
C₃×D₈×Dic₅	2
C₂×C₃×#3950	2
C₃×#65390	2
#10615629	3
C₃×#2951	5

Subgroups — C3×#10615629 #14417630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615629 #14417630