Subgroups — C₃×C₅×#3227 #14276261

Order 1920.

808 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×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#498	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#486	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#481	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#476	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3227	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₂²×C₃×C₅×Q₈	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₃×C₅×#124	—	2	1	no	—
18	C₃×C₅×#121	—	2	1	no	—
19	C₃×C₅×#121	C₂²	1	2	yes	—
20	C₃×C₄×C₅×D₄	—	2	1	no	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₃×C₅×#106	C₂²	1	8	yes	—
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
27	C₃×C₅×#102	C₂²	1	8	yes	—
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₃×#3227	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#532	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#498	C₂×C₃	1	2	yes	complemented
34	C₅×#486	C₂×C₃	1	2	yes	complemented
35	C₅×#481	C₂×C₃	1	4	yes	complemented
36	C₅×#476	C₂×C₃	1	4	yes	complemented
37	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
38	C₃×C₅×#41	—	4	4	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	4	4	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
53	C₃×C₅×C₄⋊C₄	—	2	2	no	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₅×C₂²⋊C₄	—	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×#532	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×#498	C₂×C₅	1	2	yes	complemented
68	C₃×#486	C₂×C₅	1	2	yes	complemented
69	C₃×#481	C₂×C₅	1	4	yes	complemented
70	C₃×#476	C₂×C₅	1	4	yes	complemented
71	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₅×#41	—	2	1	no	—
73	C₂²×C₅×Q₈	—	2	1	no	—
74	C₅×C₄⋊Q₈	—	2	1	no	—
75	C₅×C₄⋊Q₈	—	2	1	no	—
76	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
77	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
78	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×#127	C₂²×C₃	1	1	yes	characteristic
80	C₅×#124	—	2	1	no	—
81	C₅×#121	—	2	1	no	—
82	C₅×#121	C₂²×C₃	1	2	yes	—
83	C₄×C₅×D₄	—	2	1	no	—
84	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₅×#106	C₂²×C₃	1	8	yes	—
89	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
90	C₅×#102	C₂²×C₃	1	8	yes	—
91	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
93	#3227	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₃×C₅×Q₈	—	4	4	no	—
97	C₃×C₅×Q₈	—	4	2	no	—
98	C₃×C₅×Q₈	—	4	4	no	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	4	4	no	—
101	C₃×C₅×D₄	—	4	2	no	—
102	C₃×C₅×D₄	—	4	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	4	4	no	—
108	C₂×C₃×C₄×C₅	—	4	4	no	—
109	C₂×C₃×C₄×C₅	SD₁₆	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₅×C₈	—	2	4	no	—
117	C₂×C₃×#41	—	2	1	no	—
118	C₂²×C₃×Q₈	—	2	1	no	—
119	C₃×C₄⋊Q₈	—	2	1	no	—
120	C₃×C₄⋊Q₈	—	2	1	no	—
121	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
122	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
123	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×#127	C₂²×C₅	1	1	yes	characteristic
125	C₃×#124	—	2	1	no	—
126	C₃×#121	—	2	1	no	—
127	C₃×#121	C₂²×C₅	1	2	yes	—
128	C₃×C₄×D₄	—	2	1	no	—
129	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	—	2	1	no	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	C₃×#106	C₂²×C₅	1	8	yes	—
134	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
135	C₃×#102	C₂²×C₅	1	8	yes	—
136	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
137	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
138	C₅×#41	—	4	4	no	—
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	4	4	no	—
143	C₂×C₅×D₄	—	2	2	no	—
144	C₂×C₅×D₄	—	2	1	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	2	no	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
158	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	2	2	no	—
161	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
162	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
163	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
164	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
165	#532	C₂×C₃×C₅	1	1	yes	characteristic
166	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	#498	C₂×C₃×C₅	1	2	yes	complemented
168	#486	C₂×C₃×C₅	1	2	yes	complemented
169	#481	C₂×C₃×C₅	1	4	yes	complemented
170	#476	C₂×C₃×C₅	1	4	yes	complemented
171	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
172	C₂²×C₃×C₅	—	2	1	no	—
173	C₂²×C₃×C₅	—	2	1	no	—
174	C₂²×C₃×C₅	—	4	2	no	—
175	C₂²×C₃×C₅	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
178	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	2	1	no	—
181	C₃×C₄×C₅	—	4	2	no	—
182	C₃×C₄×C₅	—	4	4	no	—
183	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
184	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
186	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
187	C₃×#41	—	4	4	no	—
188	C₂×C₃×Q₈	—	2	1	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	4	4	no	—
192	C₂×C₃×D₄	—	2	2	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	—	2	2	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
202	C₃×C₄⋊C₄	—	2	2	no	—
203	C₃×C₄⋊C₄	—	2	2	no	—
204	C₃×C₄⋊C₄	—	2	2	no	—
205	C₃×C₄⋊C₄	—	2	1	no	—
206	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
207	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
208	C₃×C₂²⋊C₄	—	2	2	no	—
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
211	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
212	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
213	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₅×Q₈	—	4	4	no	—
217	C₅×Q₈	—	4	2	no	—
218	C₅×Q₈	—	4	4	no	—
219	C₅×D₄	—	2	4	no	—
220	C₅×D₄	—	4	4	no	—
221	C₅×D₄	—	4	2	no	—
222	C₅×D₄	—	4	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	4	4	no	—
228	C₂×C₄×C₅	—	4	4	no	—
229	C₂×C₄×C₅	C₃×SD₁₆	1	4	yes	—
230	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
236	C₅×C₈	—	2	4	no	—
237	C₂×#41	—	2	1	no	—
238	C₂²×Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
242	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
243	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
244	#127	C₂²×C₃×C₅	1	1	yes	characteristic
245	#124	—	2	1	no	—
246	#121	—	2	1	no	—
247	#121	C₂²×C₃×C₅	1	2	yes	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
252	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
253	#106	C₂²×C₃×C₅	1	8	yes	—
254	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
255	#102	C₂²×C₃×C₅	1	8	yes	—
256	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
257	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₃×C₅	—	2	2	no	—
259	C₂×C₃×C₅	—	8	2	no	—
260	C₂×C₃×C₅	#536	1	1	yes	characteristic
261	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
262	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂³×C₃	—	2	2	no	—
264	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
265	C₃×Q₈	—	4	4	no	—
266	C₃×Q₈	—	4	2	no	—
267	C₃×Q₈	—	4	4	no	—
268	C₃×D₄	—	2	4	no	—
269	C₃×D₄	—	4	4	no	—
270	C₃×D₄	—	4	2	no	—
271	C₃×D₄	—	4	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	2	no	—
274	C₂×C₃×C₄	—	2	2	no	—
275	C₂×C₃×C₄	—	2	4	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	—	4	4	no	—
278	C₂×C₃×C₄	C₅×SD₁₆	1	4	yes	—
279	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
285	C₃×C₈	—	2	4	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	4	2	no	—
289	C₂²×C₅	—	4	2	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	C₂×C₃×SD₁₆	1	2	yes	—
292	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	4	4	no	—
297	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
298	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
299	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
300	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
301	#41	—	4	4	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	4	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
315	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
321	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
325	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
326	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
327	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
328	C₃×C₅	#3227	1	1	yes	characteristic, direct product factor, Hall
329	C₂²×C₃	—	2	1	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	4	2	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
335	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
341	C₃×C₄	C₂×C₅×SD₁₆	1	2	yes	—
342	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
343	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
344	C₂×C₅	—	2	2	no	—
345	C₂×C₅	—	8	2	no	—
346	C₂×C₅	C₃×#536	1	1	yes	characteristic
347	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
348	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂³	—	2	2	no	—
350	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
351	Q₈	—	4	4	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	C₃×C₅×SD₁₆	1	4	yes	—
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	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
371	C₈	—	2	4	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	8	2	no	—
374	C₂×C₃	C₅×#536	1	1	yes	characteristic
375	C₂×C₃	C₂²×C₅×SD₁₆	1	1	yes	characteristic
376	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
377	C₅	C₃×#3227	1	1	yes	characteristic, direct product factor, Sylow
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	C₂×C₃×C₅×SD₁₆	1	2	yes	—
384	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	4	no	—
389	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
390	C₄	C₂×C₃×C₅×SD₁₆	1	2	yes	—
391	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
393	C₃	C₅×#3227	1	1	yes	characteristic, direct product factor, Sylow
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	C₃×C₅×#536	1	1	yes	characteristic
397	C₂	C₂²×C₃×C₅×SD₁₆	1	1	yes	characteristic
398	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#532	C₂
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
2. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#498	C₂	semidirect
4. C₃×C₅×#486	C₂	semidirect
5. C₃×C₅×#481	C₂	semidirect
6. C₃×C₅×#476	C₂	semidirect
7. C₃×C₅×#431	C₂	semidirect
8. C₅×#3227	C₃	direct (N × H)
30. C₃×#3227	C₅	direct (N × H)
32. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
33. C₅×#498	C₂×C₃	semidirect
34. C₅×#486	C₂×C₃	semidirect
35. C₅×#481	C₂×C₃	semidirect
36. C₅×#476	C₂×C₃	semidirect
37. C₅×#431	C₂×C₃	semidirect
66. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
67. C₃×#498	C₂×C₅	semidirect
68. C₃×#486	C₂×C₅	semidirect
69. C₃×#481	C₂×C₅	semidirect
70. C₃×#476	C₂×C₅	semidirect
71. C₃×#431	C₂×C₅	semidirect
93. #3227	C₃×C₅	direct (N × H)
166. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
167. #498	C₂×C₃×C₅	semidirect
168. #486	C₂×C₃×C₅	semidirect
169. #481	C₂×C₃×C₅	semidirect
170. #476	C₂×C₃×C₅	semidirect
171. #431	C₂×C₃×C₅	semidirect
328. C₃×C₅	#3227	direct (N × H)
377. C₅	C₃×#3227	direct (N × H)
393. C₃	C₅×#3227	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×#532	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#498	2
C₃×C₅×#486	2
C₃×C₅×#481	2
C₃×C₅×#476	2
C₃×C₅×#431	2
C₅×#3227	3
C₃×#3227	5

Subgroups — C3×C5×#3227 #14276261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3227 #14276261