Subgroups — C₃×C₅×#3165 #14276199

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 372 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#501	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#500	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#498	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#428	C₂	1	4	yes	maximal
7	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
8	C₅×#3165	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
11	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×#125	C₂²	1	2	yes	—
18	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	—	2	1	no	—
21	C₃×C₄×C₅×Q₈	—	2	1	no	—
22	C₃×C₅×#117	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#107	C₂²	1	8	yes	—
27	C₃×C₅×#106	C₂²	1	8	yes	—
28	C₃×C₅×#97	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₃×#3165	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#533	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
33	C₅×#501	C₂×C₃	1	4	yes	complemented
34	C₅×#500	C₂×C₃	1	2	yes	complemented
35	C₅×#498	C₂×C₃	1	2	yes	complemented
36	C₅×#428	C₂×C₃	1	4	yes	—
37	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
38	C₂×C₃×C₅×Q₈	—	2	1	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	4	4	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×M₁₆	Q₈	1	8	yes	complemented
48	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₄⋊C₄	—	2	2	no	—
52	C₃×C₅×C₄⋊C₄	—	2	2	no	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₄²×C₅	—	2	2	no	—
61	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₃×#533	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
67	C₃×#501	C₂×C₅	1	4	yes	complemented
68	C₃×#500	C₂×C₅	1	2	yes	complemented
69	C₃×#498	C₂×C₅	1	2	yes	complemented
70	C₃×#428	C₂×C₅	1	4	yes	—
71	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
72	C₂²×C₅×Q₈	—	2	1	no	—
73	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
74	C₅×C₄⋊Q₈	—	2	1	no	—
75	C₅×C₄⋊Q₈	—	2	1	no	—
76	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
77	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
78	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
80	C₅×#125	C₂²×C₃	1	2	yes	—
81	C₅×C₂²⋊Q₈	—	2	1	no	—
82	C₅×C₂²⋊Q₈	—	2	1	no	—
83	C₄×C₅×Q₈	—	2	1	no	—
84	C₄×C₅×Q₈	—	2	1	no	—
85	C₅×#117	C₂²×C₃	1	2	yes	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₅×#107	C₂²×C₃	1	8	yes	—
90	C₅×#106	C₂²×C₃	1	8	yes	—
91	C₅×#97	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
93	#3165	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	4	4	no	—
96	C₃×C₅×Q₈	—	4	2	no	—
97	C₃×C₅×Q₈	—	4	4	no	—
98	C₃×C₅×Q₈	—	4	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	4	no	—
104	C₂×C₃×C₄×C₅	—	4	4	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	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₅×C₈	C₂×Q₈	1	8	yes	complemented
113	C₂²×C₃×Q₈	—	2	1	no	—
114	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
115	C₃×C₄⋊Q₈	—	2	1	no	—
116	C₃×C₄⋊Q₈	—	2	1	no	—
117	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
118	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
119	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
120	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
121	C₃×#125	C₂²×C₅	1	2	yes	—
122	C₃×C₂²⋊Q₈	—	2	1	no	—
123	C₃×C₂²⋊Q₈	—	2	1	no	—
124	C₃×C₄×Q₈	—	2	1	no	—
125	C₃×C₄×Q₈	—	2	1	no	—
126	C₃×#117	C₂²×C₅	1	2	yes	—
127	C₂×C₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
129	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
130	C₃×#107	C₂²×C₅	1	8	yes	—
131	C₃×#106	C₂²×C₅	1	8	yes	—
132	C₃×#97	C₂²×C₅	1	2	yes	—
133	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
134	C₂×C₅×Q₈	—	2	1	no	—
135	C₂×C₅×Q₈	—	2	1	no	—
136	C₂×C₅×Q₈	—	2	2	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	4	4	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₅×M₁₆	C₃×Q₈	1	8	yes	complemented
144	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
153	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
154	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
155	C₅×C₂²⋊C₄	—	2	2	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
159	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
161	#533	C₂×C₃×C₅	1	1	yes	characteristic
162	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
163	#501	C₂×C₃×C₅	1	4	yes	complemented
164	#500	C₂×C₃×C₅	1	2	yes	complemented
165	#498	C₂×C₃×C₅	1	2	yes	complemented
166	#428	C₂×C₃×C₅	1	4	yes	—
167	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₅	—	2	1	no	—
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	C₄⋊Q₈	1	2	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₃×C₄×C₅	—	2	1	no	—
173	C₃×C₄×C₅	—	2	1	no	—
174	C₃×C₄×C₅	—	4	4	no	—
175	C₃×C₄×C₅	—	4	2	no	—
176	C₃×C₄×C₅	—	4	2	no	—
177	C₃×C₄×C₅	C₄⋊Q₈	1	2	yes	—
178	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
179	C₃×C₄×C₅	#137	1	2	yes	—
180	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
181	C₂×C₃×Q₈	—	2	1	no	—
182	C₂×C₃×Q₈	—	2	1	no	—
183	C₂×C₃×Q₈	—	2	2	no	—
184	C₂×C₃×Q₈	—	2	2	no	—
185	C₂×C₃×Q₈	—	4	4	no	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
190	C₃×M₁₆	C₅×Q₈	1	8	yes	complemented
191	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	—	2	2	no	—
194	C₃×C₄⋊C₄	—	2	2	no	—
195	C₃×C₄⋊C₄	—	2	2	no	—
196	C₃×C₄⋊C₄	—	2	2	no	—
197	C₃×C₄⋊C₄	—	2	1	no	—
198	C₃×C₄⋊C₄	—	2	1	no	—
199	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
200	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
201	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
202	C₃×C₂²⋊C₄	—	2	2	no	—
203	C₃×C₄²	—	2	2	no	—
204	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
205	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
206	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
207	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
208	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
209	C₅×Q₈	—	4	4	no	—
210	C₅×Q₈	—	4	2	no	—
211	C₅×Q₈	—	4	4	no	—
212	C₅×Q₈	—	4	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	4	no	—
218	C₂×C₄×C₅	—	4	4	no	—
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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×Q₈	1	4	yes	—
225	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
226	C₅×C₈	C₂×C₃×Q₈	1	8	yes	complemented
227	C₂²×Q₈	—	2	1	no	—
228	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
229	C₄⋊Q₈	—	2	1	no	—
230	C₄⋊Q₈	—	2	1	no	—
231	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
232	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
233	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
234	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
235	#125	C₂²×C₃×C₅	1	2	yes	—
236	C₂²⋊Q₈	—	2	1	no	—
237	C₂²⋊Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	#117	C₂²×C₃×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
243	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
244	#107	C₂²×C₃×C₅	1	8	yes	—
245	#106	C₂²×C₃×C₅	1	8	yes	—
246	#97	C₂²×C₃×C₅	1	2	yes	—
247	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
252	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
253	C₃×Q₈	—	4	4	no	—
254	C₃×Q₈	—	4	2	no	—
255	C₃×Q₈	—	4	4	no	—
256	C₃×Q₈	—	4	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	2	2	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	4	4	no	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
269	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
270	C₃×C₈	C₂×C₅×Q₈	1	8	yes	complemented
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	C₃×C₄⋊Q₈	1	2	yes	—
274	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	4	4	no	—
278	C₄×C₅	—	4	2	no	—
279	C₄×C₅	—	4	2	no	—
280	C₄×C₅	C₃×C₄⋊Q₈	1	2	yes	—
281	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
282	C₄×C₅	C₃×#137	1	2	yes	—
283	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
291	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
292	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
293	M₁₆	C₃×C₅×Q₈	1	8	yes	complemented
294	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
303	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
304	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
308	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
309	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
310	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
311	C₃×C₅	#3165	1	1	yes	characteristic, direct product factor, Hall
312	C₂²×C₃	—	2	1	no	—
313	C₂²×C₃	—	2	1	no	—
314	C₂²×C₃	C₅×C₄⋊Q₈	1	2	yes	—
315	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	4	4	no	—
319	C₃×C₄	—	4	2	no	—
320	C₃×C₄	—	4	2	no	—
321	C₃×C₄	C₅×C₄⋊Q₈	1	2	yes	—
322	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
323	C₃×C₄	C₅×#137	1	2	yes	—
324	C₃×C₄	C₂²×C₅×Q₈	1	2	yes	—
325	C₂×C₅	—	2	2	no	—
326	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
327	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
328	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
329	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
330	Q₈	—	4	4	no	—
331	Q₈	—	4	4	no	—
332	Q₈	—	4	2	no	—
333	Q₈	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
344	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
346	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
347	C₈	C₂×C₃×C₅×Q₈	1	8	yes	complemented
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
350	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
352	C₅	C₃×#3165	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	C₃×C₅×C₄⋊Q₈	1	2	yes	—
356	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	C₃×C₅×C₄⋊Q₈	1	2	yes	—
363	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
364	C₄	C₃×C₅×#137	1	2	yes	—
365	C₄	C₂²×C₃×C₅×Q₈	1	2	yes	—
366	C₃	C₅×#3165	1	1	yes	characteristic, direct product factor, Sylow
367	C₂	—	2	2	no	—
368	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
369	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
370	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#501	C₂	semidirect
4. C₃×C₅×#500	C₂	semidirect
5. C₃×C₅×#498	C₂	semidirect
8. C₅×#3165	C₃	direct (N × H)
30. C₃×#3165	C₅	direct (N × H)
33. C₅×#501	C₂×C₃	semidirect
34. C₅×#500	C₂×C₃	semidirect
35. C₅×#498	C₂×C₃	semidirect
47. C₃×C₅×M₁₆	Q₈	semidirect
67. C₃×#501	C₂×C₅	semidirect
68. C₃×#500	C₂×C₅	semidirect
69. C₃×#498	C₂×C₅	semidirect
93. #3165	C₃×C₅	direct (N × H)
112. C₃×C₅×C₈	C₂×Q₈	semidirect
143. C₅×M₁₆	C₃×Q₈	semidirect
163. #501	C₂×C₃×C₅	semidirect
164. #500	C₂×C₃×C₅	semidirect
165. #498	C₂×C₃×C₅	semidirect
190. C₃×M₁₆	C₅×Q₈	semidirect
226. C₅×C₈	C₂×C₃×Q₈	semidirect
270. C₃×C₈	C₂×C₅×Q₈	semidirect
293. M₁₆	C₃×C₅×Q₈	semidirect
311. C₃×C₅	#3165	direct (N × H)
347. C₈	C₂×C₃×C₅×Q₈	semidirect
352. C₅	C₃×#3165	direct (N × H)
366. C₃	C₅×#3165	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
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#501	2
C₃×C₅×#500	2
C₃×C₅×#498	2
C₃×C₅×#428	2
C₃×C₄×C₅×M₁₆	2
C₅×#3165	3
C₃×#3165	5

Subgroups — C3×C5×#3165 #14276199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3165 #14276199