Subgroups — C₃×#10602548 #14283203

Order 1920.

484 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65215	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64758	C₂	1	2	yes	maximal, complemented
5	C₃×#64757	C₂	1	2	yes	maximal
6	#10602548	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic, complemented
9	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
19	C₂×C₃×C₄×Dic₅	—	2	1	no	—
20	C₃×#3963	C₂²	1	2	yes	—
21	C₃×C₂²⋊#168	C₂²	1	2	yes	—
22	C₃×C₄⋊#168	—	2	1	no	—
23	C₃×#3935	—	2	1	no	—
24	C₃×#1509	—	5	1	no	maximal, Hall
25	C₅×#529	C₂×C₃	1	1	yes	characteristic
26	C₄×C₄⋊Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
27	#65215	C₂×C₃	1	1	yes	characteristic, complemented
28	#64758	C₂×C₃	1	2	yes	complemented
29	#64757	C₂×C₃	1	2	yes	—
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₃×C₄⋊Dic₅	—	2	4	no	—
55	C₃×C₄×Dic₅	—	4	2	no	—
56	C₂×C₃×#168	—	2	2	no	—
57	C₃×#529	D₅	1	1	yes	characteristic
58	C₃×#432	—	5	1	no	—
59	C₃×C₄×C₄⋊C₄	—	5	1	no	—
60	C₃×#328	—	5	2	no	—
61	C₃×#327	—	5	2	no	—
62	C₅×#126	—	2	1	no	—
63	C₅×#125	C₃×C₄	1	1	yes	characteristic, complemented
64	C₅×#124	C₃×C₄	1	1	yes	characteristic, complemented
65	C₅×#123	—	2	1	no	—
66	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
67	C₅×#121	C₂²×C₃	1	1	yes	characteristic
68	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
69	C₄×C₅×D₄	—	2	1	no	—
70	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic, complemented
71	C₅×#117	—	2	1	no	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₄⋊Dic₅	—	2	1	no	—
74	C₂×C₄×Dic₅	—	2	1	no	—
75	#3963	C₂²×C₃	1	2	yes	—
76	C₂²⋊#168	C₂²×C₃	1	2	yes	—
77	C₄⋊#168	—	2	1	no	—
78	#3935	—	2	1	no	—
79	#1509	—	5	1	no	Sylow
80	C₂³×C₃×C₅	—	2	1	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	4	1	no	—
83	C₃×C₅×D₄	—	4	1	no	—
84	C₃×C₅×D₄	—	4	1	no	—
85	C₃×C₅×D₄	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×Dic₅	—	2	4	no	—
101	C₂×C₃×Dic₅	—	4	2	no	—
102	C₂×C₃×Dic₅	—	4	2	no	—
103	C₃×#168	—	4	2	no	—
104	C₃×#126	—	2	1	no	—
105	C₃×#125	Dic₅	1	1	yes	characteristic, complemented
106	C₃×#124	Dic₅	1	1	yes	characteristic, complemented
107	C₃×#123	—	2	1	no	—
108	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
109	C₃×#121	C₂×D₅	1	1	yes	characteristic
110	C₃×C₄×Q₈	Dic₅	1	1	yes	characteristic, complemented
111	C₃×C₄×D₄	—	2	1	no	—
112	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic, complemented
113	C₃×#117	—	2	1	no	—
114	C₂×C₃×C₄⋊C₄	—	10	1	no	—
115	C₂×C₃×C₄²	—	10	1	no	—
116	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
117	C₃×C₄⋊C₈	—	10	1	no	—
118	C₃×C₂²⋊C₈	—	5	2	no	—
119	C₃×#97	—	10	1	no	—
120	C₃×#95	—	5	2	no	—
121	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
128	C₂²×Dic₅	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
135	C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₅×C₂²⋊C₄	—	2	1	no	—
138	C₅×C₂²⋊C₄	—	2	1	no	—
139	C₅×C₂²⋊C₄	—	2	1	no	—
140	C₄²×C₅	—	2	1	no	—
141	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
142	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
143	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
144	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
145	C₄⋊Dic₅	—	2	4	no	—
146	C₄×Dic₅	—	4	2	no	—
147	C₂×#168	—	2	2	no	—
148	#529	C₃×D₅	1	1	yes	characteristic
149	#432	—	5	1	no	—
150	C₄×C₄⋊C₄	—	5	1	no	—
151	#328	—	5	2	no	—
152	#327	—	5	2	no	—
153	C₂²×C₃×C₅	—	2	1	no	—
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	4	1	no	—
156	C₂²×C₃×C₅	—	4	1	no	—
157	C₂²×C₃×C₅	—	4	1	no	—
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂²×C₃×C₅	#137	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	2	1	no	—
163	C₃×C₄×C₅	—	2	1	no	—
164	C₃×C₄×C₅	—	2	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	—	4	1	no	—
169	C₃×C₄×C₅	#104	1	2	yes	—
170	C₃×Dic₅	—	4	4	no	—
171	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	10	2	no	—
176	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
179	C₂×C₃×C₈	—	10	2	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	—	2	1	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	10	4	no	—
185	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
186	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
187	C₃×C₂²⋊C₄	—	2	1	no	—
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	1	no	—
190	C₃×C₂²⋊C₄	—	2	1	no	—
191	C₃×C₂²⋊C₄	—	2	1	no	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	—	20	2	no	—
194	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
195	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
196	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
197	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
200	C₅×Q₈	—	4	1	no	—
201	C₅×D₄	—	4	1	no	—
202	C₅×D₄	—	4	1	no	—
203	C₅×D₄	—	4	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×Dic₅	—	2	4	no	—
219	C₂×Dic₅	—	4	2	no	—
220	C₂×Dic₅	—	4	2	no	—
221	#168	—	4	2	no	—
222	#126	—	2	1	no	—
223	#125	C₃×Dic₅	1	1	yes	characteristic, complemented
224	#124	C₃×Dic₅	1	1	yes	characteristic, complemented
225	#123	—	2	1	no	—
226	C₂²⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
227	#121	C₂×C₃×D₅	1	1	yes	characteristic
228	C₄×Q₈	C₃×Dic₅	1	1	yes	characteristic, complemented
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	C₃×Dic₅	1	1	yes	characteristic, complemented
231	#117	—	2	1	no	—
232	C₂×C₄⋊C₄	—	10	1	no	—
233	C₂×C₄²	—	10	1	no	—
234	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
235	C₄⋊C₈	—	10	1	no	—
236	C₂²⋊C₈	—	5	2	no	—
237	#97	—	10	1	no	—
238	#95	—	5	2	no	—
239	C₂×C₃×C₅	—	2	1	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	—	8	1	no	—
242	C₂×C₃×C₅	#410	1	1	yes	characteristic
243	C₂×C₃×C₅	#417	1	1	yes	characteristic
244	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
245	C₂³×C₃	—	2	1	no	—
246	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
247	C₃×Q₈	—	4	1	no	—
248	C₃×D₄	—	4	1	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	4	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	2	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	20	2	no	—
261	C₂×C₃×C₄	—	20	2	no	—
262	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
268	C₃×C₈	—	20	2	no	—
269	C₂²×C₅	—	2	1	no	—
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	4	1	no	—
272	C₂²×C₅	—	4	1	no	—
273	C₂²×C₅	—	4	1	no	—
274	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₂²×C₅	C₃×#137	1	1	yes	characteristic
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	2	1	no	—
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	4	1	no	—
284	C₄×C₅	—	4	1	no	—
285	C₄×C₅	C₃×#104	1	2	yes	—
286	Dic₅	—	4	4	no	—
287	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	10	2	no	—
292	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
293	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
295	C₂×C₈	—	10	2	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	10	4	no	—
301	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
302	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	1	no	—
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	20	2	no	—
310	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
311	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
312	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
313	C₄²	C₃×C₂²⋊D₅	1	1	yes	characteristic
314	C₃×C₅	#1509	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	1	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	4	1	no	—
318	C₂²×C₃	—	4	1	no	—
319	C₂²×C₃	—	4	1	no	—
320	C₂²×C₃	#4095	1	1	yes	characteristic
321	C₂²×C₃	#4097	1	1	yes	characteristic
322	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	4	1	no	—
331	C₃×C₄	—	20	4	no	—
332	C₃×C₄	#3969	1	2	yes	—
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	1	no	—
335	C₂×C₅	—	8	1	no	—
336	C₂×C₅	C₃×#410	1	1	yes	characteristic
337	C₂×C₅	C₃×#417	1	1	yes	characteristic
338	C₂×C₅	C₂×C₃×#104	1	1	yes	characteristic
339	C₂³	—	2	1	no	—
340	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
341	Q₈	—	4	1	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	1	no	—
344	D₄	—	4	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	10	4	no	—
354	C₂×C₄	—	20	2	no	—
355	C₂×C₄	—	20	2	no	—
356	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
357	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
358	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
359	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
361	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
362	C₈	—	20	2	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	8	1	no	—
366	C₂×C₃	#65521	1	1	yes	characteristic
367	C₂×C₃	C₂×#3969	1	1	yes	characteristic
368	C₂×C₃	#65529	1	1	yes	characteristic
369	C₅	C₃×#1509	1	1	yes	characteristic, complemented, Sylow
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	C₃×#4095	1	1	yes	characteristic
376	C₂²	C₃×#4097	1	1	yes	characteristic
377	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	4	1	no	—
385	C₄	—	4	1	no	—
386	C₄	—	20	4	no	—
387	C₄	C₃×#3969	1	2	yes	—
388	C₃	#10602548	1	1	yes	characteristic, direct product factor, Sylow
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	8	1	no	—
392	C₂	C₃×#65521	1	1	yes	characteristic
393	C₂	C₂×C₃×#3969	1	1	yes	characteristic
394	C₂	C₃×#65529	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₂²⋊Dic₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₂²
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#1509
LCS	G ▷ C₂×C₄×C₅ ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×C₄⋊Dic₅	C₂	semidirect
3. C₃×#65215	C₂	semidirect
4. C₃×#64758	C₂	semidirect
6. #10602548	C₃	direct (N × H)
8. C₃×C₅×#125	C₄	semidirect
9. C₃×C₅×#124	C₄	semidirect
13. C₃×C₄×C₅×Q₈	C₄	semidirect
15. C₃×C₄×C₅×D₄	C₄	semidirect
26. C₄×C₄⋊Dic₅	C₂×C₃	semidirect
27. #65215	C₂×C₃	semidirect
28. #64758	C₂×C₃	semidirect
63. C₅×#125	C₃×C₄	semidirect
64. C₅×#124	C₃×C₄	semidirect
68. C₄×C₅×Q₈	C₃×C₄	semidirect
70. C₄×C₅×D₄	C₃×C₄	semidirect
105. C₃×#125	Dic₅	semidirect
106. C₃×#124	Dic₅	semidirect
110. C₃×C₄×Q₈	Dic₅	semidirect
112. C₃×C₄×D₄	Dic₅	semidirect
223. #125	C₃×Dic₅	semidirect
224. #124	C₃×Dic₅	semidirect
228. C₄×Q₈	C₃×Dic₅	semidirect
230. C₄×D₄	C₃×Dic₅	semidirect
314. C₃×C₅	#1509	semidirect
369. C₅	C₃×#1509	semidirect
388. C₃	#10602548	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×#529	2
C₃×C₄×C₄⋊Dic₅	2
C₃×#65215	2
C₃×#64758	2
C₃×#64757	2
#10602548	3
C₃×#1509	5

Subgroups — C3×#10602548 #14283203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602548 #14283203