Subgroups — C₃×C₅×#1631 #14274665

Order 1920.

512 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×#550	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1631	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#127	—	2	1	no	—
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×C₅×#121	—	2	2	no	—
15	C₃×C₅×#121	—	2	1	no	—
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₄×C₅×D₄	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	1	no	—
20	C₃×C₅×#106	—	2	1	no	—
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#103	—	2	1	no	—
24	C₃×C₅×#102	—	2	1	no	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#1631	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#550	C₂×C₃	1	1	yes	characteristic
28	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	4	2	no	—
35	C₃×C₅×#41	—	4	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₃×C₅×SD₁₆	—	4	4	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
57	C₃×C₄²×C₅	—	2	1	no	—
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×#550	C₂×C₅	1	1	yes	characteristic
60	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	—	2	1	no	—
67	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
69	C₅×#127	—	2	1	no	—
70	C₅×#127	C₂²×C₃	1	1	yes	characteristic
71	C₅×#121	—	2	2	no	—
72	C₅×#121	—	2	1	no	—
73	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
74	C₄×C₅×D₄	—	2	1	no	—
75	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
76	C₅×#107	—	2	1	no	—
77	C₅×#106	—	2	1	no	—
78	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
80	C₅×#103	—	2	1	no	—
81	C₅×#102	—	2	1	no	—
82	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
83	#1631	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³×C₃×C₅	—	2	1	no	—
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₃×C₅×Q₈	—	2	1	no	—
87	C₃×C₅×Q₈	—	4	2	no	—
88	C₃×C₅×Q₈	SD₁₆	1	2	yes	complemented
89	C₃×C₅×D₄	—	2	1	no	—
90	C₃×C₅×D₄	—	2	1	no	—
91	C₃×C₅×D₄	—	4	4	no	—
92	C₃×C₅×D₄	—	4	2	no	—
93	C₃×C₅×D₄	—	4	1	no	—
94	C₃×C₅×D₄	—	4	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₃×C₅×D₄	—	8	2	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	4	4	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₅×C₈	—	2	2	no	—
109	C₃×C₅×C₈	—	4	1	no	—
110	C₃×C₅×C₈	—	4	1	no	—
111	C₂×C₃×#41	—	2	1	no	—
112	C₂×C₃×SD₁₆	—	2	2	no	—
113	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
114	C₃×#127	—	2	1	no	—
115	C₃×#127	C₂²×C₅	1	1	yes	characteristic
116	C₃×#121	—	2	2	no	—
117	C₃×#121	—	2	1	no	—
118	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
119	C₃×C₄×D₄	—	2	1	no	—
120	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
121	C₃×#107	—	2	1	no	—
122	C₃×#106	—	2	1	no	—
123	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
125	C₃×#103	—	2	1	no	—
126	C₃×#102	—	2	1	no	—
127	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
128	C₅×#41	—	4	2	no	—
129	C₅×#41	—	4	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
137	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₅×SD₁₆	—	4	4	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
148	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₄²×C₅	—	2	1	no	—
152	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
153	#550	C₂×C₃×C₅	1	1	yes	characteristic
154	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
157	#331	C₂×C₃×C₅	1	1	yes	characteristic, complemented
158	Q₈⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	—	4	2	no	—
161	C₂²×C₃×C₅	—	4	1	no	—
162	C₂²×C₃×C₅	—	4	1	no	—
163	C₂²×C₃×C₅	—	4	2	no	—
164	C₂²×C₃×C₅	—	4	2	no	—
165	C₂²×C₃×C₅	—	4	1	no	—
166	C₂²×C₃×C₅	#120	1	1	yes	characteristic
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	4	1	no	—
170	C₃×C₄×C₅	—	4	1	no	—
171	C₃×C₄×C₅	—	8	1	no	—
172	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
173	C₃×C₄×C₅	#135	1	1	yes	characteristic
174	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₃×C₄×C₅	#137	1	1	yes	characteristic
176	C₃×#41	—	4	2	no	—
177	C₃×#41	—	4	2	no	—
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	—	2	2	no	—
182	C₂×C₃×D₄	—	2	1	no	—
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
185	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₃×SD₁₆	—	4	4	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
196	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
197	C₃×C₂²⋊C₄	—	2	2	no	—
198	C₃×C₂²⋊C₄	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	2	no	—
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₅×Q₈	C₃×SD₁₆	1	2	yes	complemented
206	C₅×D₄	—	2	1	no	—
207	C₅×D₄	—	2	1	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	4	no	—
210	C₅×D₄	—	4	1	no	—
211	C₅×D₄	—	4	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	4	1	no	—
214	C₅×D₄	—	8	2	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	4	4	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	4	1	no	—
227	C₅×C₈	—	4	1	no	—
228	C₂×#41	—	2	1	no	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
231	#127	—	2	1	no	—
232	#127	C₂²×C₃×C₅	1	1	yes	characteristic
233	#121	—	2	2	no	—
234	#121	—	2	1	no	—
235	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
236	C₄×D₄	—	2	1	no	—
237	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
238	#107	—	2	1	no	—
239	#106	—	2	1	no	—
240	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
241	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
242	#103	—	2	1	no	—
243	#102	—	2	1	no	—
244	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
245	C₂×C₃×C₅	—	8	1	no	—
246	C₂×C₃×C₅	—	8	2	no	—
247	C₂×C₃×C₅	#450	1	1	yes	characteristic
248	C₂×C₃×C₅	#452	1	1	yes	characteristic
249	C₂×C₃×C₅	#453	1	1	yes	characteristic
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	—	2	2	no	—
252	C₃×Q₈	—	2	1	no	—
253	C₃×Q₈	—	4	2	no	—
254	C₃×Q₈	C₅×SD₁₆	1	2	yes	complemented
255	C₃×D₄	—	2	1	no	—
256	C₃×D₄	—	2	1	no	—
257	C₃×D₄	—	4	2	no	—
258	C₃×D₄	—	4	4	no	—
259	C₃×D₄	—	4	1	no	—
260	C₃×D₄	—	4	1	no	—
261	C₃×D₄	—	4	1	no	—
262	C₃×D₄	—	4	1	no	—
263	C₃×D₄	—	8	2	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	4	4	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	C₃×C₈	—	2	2	no	—
275	C₃×C₈	—	4	1	no	—
276	C₃×C₈	—	4	1	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	4	1	no	—
279	C₂²×C₅	—	4	1	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	C₃×#120	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	1	no	—
286	C₄×C₅	—	4	1	no	—
287	C₄×C₅	—	4	1	no	—
288	C₄×C₅	—	8	1	no	—
289	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
290	C₄×C₅	C₃×#135	1	1	yes	characteristic
291	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₄×C₅	C₃×#137	1	1	yes	characteristic
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
302	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	SD₁₆	—	4	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
313	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
318	C₃×C₅	#1631	1	1	yes	characteristic, direct product factor, Hall
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	4	2	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	C₅×#120	1	1	yes	characteristic
326	C₃×C₄	—	2	2	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	—	4	1	no	—
330	C₃×C₄	—	8	1	no	—
331	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
332	C₃×C₄	C₅×#135	1	1	yes	characteristic
333	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₃×C₄	C₅×#137	1	1	yes	characteristic
335	C₂×C₅	—	8	1	no	—
336	C₂×C₅	—	8	2	no	—
337	C₂×C₅	C₃×#450	1	1	yes	characteristic
338	C₂×C₅	C₃×#452	1	1	yes	characteristic
339	C₂×C₅	C₃×#453	1	1	yes	characteristic
340	C₂³	—	2	1	no	—
341	C₂³	—	2	2	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	C₃×C₅×SD₁₆	1	2	yes	complemented
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
363	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	4	1	no	—
367	C₂×C₃	—	8	1	no	—
368	C₂×C₃	—	8	2	no	—
369	C₂×C₃	C₅×#450	1	1	yes	characteristic
370	C₂×C₃	C₅×#452	1	1	yes	characteristic
371	C₂×C₃	C₅×#453	1	1	yes	characteristic
372	C₅	C₃×#1631	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₃×C₅×#120	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	1	no	—
385	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
386	C₄	C₃×C₅×#135	1	1	yes	characteristic
387	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₄	C₃×C₅×#137	1	1	yes	characteristic
389	C₃	C₅×#1631	1	1	yes	characteristic, direct product factor, Sylow
390	C₂	—	8	1	no	—
391	C₂	—	8	2	no	—
392	C₂	C₃×C₅×#450	1	1	yes	characteristic
393	C₂	C₃×C₅×#452	1	1	yes	characteristic
394	C₂	C₃×C₅×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₃×C₅×#550	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#492	C₂	semidirect
3. C₃×C₅×#477	C₂	semidirect
4. C₃×C₅×#476	C₂	semidirect
5. C₃×C₅×#331	C₂	semidirect
6. C₃×C₅×Q₈⋊C₈	C₂	semidirect
7. C₃×C₅×D₄⋊C₈	C₂	semidirect
8. C₅×#1631	C₃	direct (N × H)
26. C₃×#1631	C₅	direct (N × H)
28. C₅×#492	C₂×C₃	semidirect
29. C₅×#477	C₂×C₃	semidirect
30. C₅×#476	C₂×C₃	semidirect
31. C₅×#331	C₂×C₃	semidirect
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
33. C₅×D₄⋊C₈	C₂×C₃	semidirect
60. C₃×#492	C₂×C₅	semidirect
61. C₃×#477	C₂×C₅	semidirect
62. C₃×#476	C₂×C₅	semidirect
63. C₃×#331	C₂×C₅	semidirect
64. C₃×Q₈⋊C₈	C₂×C₅	semidirect
65. C₃×D₄⋊C₈	C₂×C₅	semidirect
83. #1631	C₃×C₅	direct (N × H)
88. C₃×C₅×Q₈	SD₁₆	semidirect
154. #492	C₂×C₃×C₅	semidirect
155. #477	C₂×C₃×C₅	semidirect
156. #476	C₂×C₃×C₅	semidirect
157. #331	C₂×C₃×C₅	semidirect
158. Q₈⋊C₈	C₂×C₃×C₅	semidirect
159. D₄⋊C₈	C₂×C₃×C₅	semidirect
205. C₅×Q₈	C₃×SD₁₆	semidirect
254. C₃×Q₈	C₅×SD₁₆	semidirect
318. C₃×C₅	#1631	direct (N × H)
344. Q₈	C₃×C₅×SD₁₆	semidirect
372. C₅	C₃×#1631	direct (N × H)
389. C₃	C₅×#1631	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×#550	2
C₃×C₅×#492	2
C₃×C₅×#477	2
C₃×C₅×#476	2
C₃×C₅×#331	2
C₃×C₅×Q₈⋊C₈	2
C₃×C₅×D₄⋊C₈	2
C₅×#1631	3
C₃×#1631	5

Subgroups — C3×C5×#1631 #14274665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1631 #14274665