Subgroups — C₃×C₅×#1627 #14274661

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#332	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×#1627	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	—	2	1	no	—
10	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
11	C₂×C₃×C₅×D₈	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×D₄	—	2	1	no	—
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#102	—	2	1	no	—
23	C₃×C₅×#102	—	2	1	no	—
24	C₃×C₅×#102	—	2	2	no	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#1627	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#459	C₂×C₃	1	1	yes	characteristic
31	C₅×#332	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	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	4	2	no	—
37	C₂×C₃×C₅×Q₈	—	4	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	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	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₃×C₅×SD₁₆	—	4	2	no	—
46	C₃×C₅×D₈	—	4	2	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	2	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×C₄⋊C₄	D₄	1	2	yes	—
56	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#459	C₂×C₅	1	1	yes	characteristic
64	C₃×#332	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×Q₈	—	2	1	no	—
68	C₂×C₅×SD₁₆	—	2	1	no	—
69	C₂×C₅×D₈	—	2	1	no	—
70	C₅×C₄⋊Q₈	—	2	1	no	—
71	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
72	C₅×#127	C₂²×C₃	1	1	yes	characteristic
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	2	no	—
75	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
80	C₅×#102	—	2	1	no	—
81	C₅×#102	—	2	1	no	—
82	C₅×#102	—	2	2	no	—
83	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
84	#1627	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	—	4	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	4	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×Q₈	—	4	1	no	—
91	C₃×C₅×Q₈	D₈	1	2	yes	complemented
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	4	2	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	—	4	1	no	—
98	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
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	C₃×C₅×C₈	—	4	1	no	—
110	C₃×C₅×C₈	—	4	1	no	—
111	C₃×C₅×C₈	—	4	1	no	—
112	C₂²×C₃×Q₈	—	2	1	no	—
113	C₂×C₃×SD₁₆	—	2	1	no	—
114	C₂×C₃×D₈	—	2	1	no	—
115	C₃×C₄⋊Q₈	—	2	1	no	—
116	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
117	C₃×#127	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₂²⋊Q₈	—	2	1	no	—
119	C₃×C₂²⋊Q₈	—	2	2	no	—
120	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄×D₄	—	2	1	no	—
122	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
125	C₃×#102	—	2	1	no	—
126	C₃×#102	—	2	1	no	—
127	C₃×#102	—	2	2	no	—
128	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	2	2	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	—	4	2	no	—
132	C₂×C₅×Q₈	—	4	2	no	—
133	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	1	no	—
140	C₅×SD₁₆	—	4	2	no	—
141	C₅×D₈	—	4	2	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
149	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
150	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
151	C₅×C₂²⋊C₄	—	2	2	no	—
152	C₅×C₂²⋊C₄	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
155	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
156	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
157	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
158	#459	C₂×C₃×C₅	1	1	yes	characteristic
159	#332	C₂×C₃×C₅	1	1	yes	characteristic, complemented
160	Q₈⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
161	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	4	1	no	—
164	C₂²×C₃×C₅	—	4	1	no	—
165	C₂²×C₃×C₅	—	8	1	no	—
166	C₂²×C₃×C₅	—	8	1	no	—
167	C₂²×C₃×C₅	—	8	1	no	—
168	C₂²×C₃×C₅	#120	1	1	yes	characteristic
169	C₃×C₄×C₅	—	2	2	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	4	2	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	4	1	no	—
174	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
176	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₃×C₄×C₅	#137	1	1	yes	characteristic
178	C₂×C₃×Q₈	—	2	2	no	—
179	C₂×C₃×Q₈	—	2	1	no	—
180	C₂×C₃×Q₈	—	4	2	no	—
181	C₂×C₃×Q₈	—	4	2	no	—
182	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
183	C₂×C₃×D₄	—	2	1	no	—
184	C₂×C₃×D₄	—	2	1	no	—
185	C₂×C₃×D₄	—	2	1	no	—
186	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₄	—	2	2	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₃×SD₁₆	—	4	2	no	—
190	C₃×D₈	—	4	2	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	2	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	—	2	1	no	—
197	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
199	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
200	C₃×C₂²⋊C₄	—	2	2	no	—
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×C₄²	—	2	1	no	—
203	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
204	C₂³×C₅	—	2	1	no	—
205	C₂³×C₅	—	4	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	4	4	no	—
208	C₅×Q₈	—	4	1	no	—
209	C₅×Q₈	—	4	1	no	—
210	C₅×Q₈	C₃×D₈	1	2	yes	complemented
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	1	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	1	no	—
217	C₅×D₄	C₃×SD₁₆	1	2	yes	complemented
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	4	4	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₅×C₈	—	4	1	no	—
229	C₅×C₈	—	4	1	no	—
230	C₅×C₈	—	4	1	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂×SD₁₆	—	2	1	no	—
233	C₂×D₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
236	#127	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂²⋊Q₈	—	2	1	no	—
238	C₂²⋊Q₈	—	2	2	no	—
239	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
242	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
243	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
244	#102	—	2	1	no	—
245	#102	—	2	1	no	—
246	#102	—	2	2	no	—
247	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
248	C₂×C₃×C₅	—	4	2	no	—
249	C₂×C₃×C₅	—	16	1	no	—
250	C₂×C₃×C₅	#447	1	1	yes	characteristic
251	C₂×C₃×C₅	#448	1	1	yes	characteristic
252	C₂×C₃×C₅	#454	1	1	yes	characteristic
253	C₂³×C₃	—	2	1	no	—
254	C₂³×C₃	—	4	1	no	—
255	C₃×Q₈	—	2	1	no	—
256	C₃×Q₈	—	4	4	no	—
257	C₃×Q₈	—	4	1	no	—
258	C₃×Q₈	—	4	1	no	—
259	C₃×Q₈	C₅×D₈	1	2	yes	complemented
260	C₃×D₄	—	2	1	no	—
261	C₃×D₄	—	4	2	no	—
262	C₃×D₄	—	4	1	no	—
263	C₃×D₄	—	4	1	no	—
264	C₃×D₄	—	4	1	no	—
265	C₃×D₄	—	4	1	no	—
266	C₃×D₄	C₅×SD₁₆	1	2	yes	complemented
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	4	4	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	—	4	1	no	—
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₃×C₈	—	4	1	no	—
278	C₃×C₈	—	4	1	no	—
279	C₃×C₈	—	4	1	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	4	1	no	—
282	C₂²×C₅	—	4	1	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	1	no	—
285	C₂²×C₅	—	8	1	no	—
286	C₂²×C₅	C₃×#120	1	1	yes	characteristic
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	1	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
293	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
294	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₄×C₅	C₃×#137	1	1	yes	characteristic
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	SD₁₆	—	4	2	no	—
308	D₈	—	4	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
316	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
317	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
322	C₃×C₅	#1627	1	1	yes	characteristic, direct product factor, Hall
323	C₂²×C₃	—	2	2	no	—
324	C₂²×C₃	—	4	1	no	—
325	C₂²×C₃	—	4	1	no	—
326	C₂²×C₃	—	8	1	no	—
327	C₂²×C₃	—	8	1	no	—
328	C₂²×C₃	—	8	1	no	—
329	C₂²×C₃	C₅×#120	1	1	yes	characteristic
330	C₃×C₄	—	2	2	no	—
331	C₃×C₄	—	2	1	no	—
332	C₃×C₄	—	4	2	no	—
333	C₃×C₄	—	4	1	no	—
334	C₃×C₄	—	4	1	no	—
335	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
336	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
337	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₃×C₄	C₅×#137	1	1	yes	characteristic
339	C₂×C₅	—	4	2	no	—
340	C₂×C₅	—	16	1	no	—
341	C₂×C₅	C₃×#447	1	1	yes	characteristic
342	C₂×C₅	C₃×#448	1	1	yes	characteristic
343	C₂×C₅	C₃×#454	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	4	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	Q₈	C₃×C₅×D₈	1	2	yes	complemented
351	D₄	—	2	1	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	1	no	—
357	D₄	C₃×C₅×SD₁₆	1	2	yes	complemented
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
366	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	1	no	—
371	C₂×C₃	—	4	2	no	—
372	C₂×C₃	—	16	1	no	—
373	C₂×C₃	C₅×#447	1	1	yes	characteristic
374	C₂×C₃	C₅×#448	1	1	yes	characteristic
375	C₂×C₃	C₅×#454	1	1	yes	characteristic
376	C₅	C₃×#1627	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	C₃×C₅×#120	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
390	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
391	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₄	C₃×C₅×#137	1	1	yes	characteristic
393	C₃	C₅×#1627	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	4	2	no	—
395	C₂	—	16	1	no	—
396	C₂	C₃×C₅×#447	1	1	yes	characteristic
397	C₂	C₃×C₅×#448	1	1	yes	characteristic
398	C₂	C₃×C₅×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₃×C₅×#459	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
1. C₃×C₅×D₄×Q₈	C₂	semidirect
2. C₃×C₅×#486	C₂	semidirect
3. C₃×C₅×#460	C₂	semidirect
5. C₃×C₅×#332	C₂	semidirect
6. C₃×C₅×Q₈⋊C₈	C₂	semidirect
7. C₃×C₅×D₄⋊C₈	C₂	semidirect
8. C₅×#1627	C₃	direct (N × H)
26. C₃×#1627	C₅	direct (N × H)
27. C₅×D₄×Q₈	C₂×C₃	semidirect
28. C₅×#486	C₂×C₃	semidirect
29. C₅×#460	C₂×C₃	semidirect
31. C₅×#332	C₂×C₃	semidirect
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
33. C₅×D₄⋊C₈	C₂×C₃	semidirect
60. C₃×D₄×Q₈	C₂×C₅	semidirect
61. C₃×#486	C₂×C₅	semidirect
62. C₃×#460	C₂×C₅	semidirect
64. C₃×#332	C₂×C₅	semidirect
65. C₃×Q₈⋊C₈	C₂×C₅	semidirect
66. C₃×D₄⋊C₈	C₂×C₅	semidirect
84. #1627	C₃×C₅	direct (N × H)
91. C₃×C₅×Q₈	D₈	semidirect
98. C₃×C₅×D₄	SD₁₆	semidirect
155. D₄×Q₈	C₂×C₃×C₅	semidirect
156. #486	C₂×C₃×C₅	semidirect
157. #460	C₂×C₃×C₅	semidirect
159. #332	C₂×C₃×C₅	semidirect
160. Q₈⋊C₈	C₂×C₃×C₅	semidirect
161. D₄⋊C₈	C₂×C₃×C₅	semidirect
210. C₅×Q₈	C₃×D₈	semidirect
217. C₅×D₄	C₃×SD₁₆	semidirect
259. C₃×Q₈	C₅×D₈	semidirect
266. C₃×D₄	C₅×SD₁₆	semidirect
322. C₃×C₅	#1627	direct (N × H)
350. Q₈	C₃×C₅×D₈	semidirect
357. D₄	C₃×C₅×SD₁₆	semidirect
376. C₅	C₃×#1627	direct (N × H)
393. C₃	C₅×#1627	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×D₄×Q₈	2
C₃×C₅×#486	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#332	2
C₃×C₅×Q₈⋊C₈	2
C₃×C₅×D₄⋊C₈	2
C₅×#1627	3
C₃×#1627	5

Subgroups — C3×C5×#1627 #14274661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1627 #14274661