Subgroups — C₃×C₅×#3155 #14276189

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#496	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#495	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#493	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3155	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₃×C₅×AGL(1,ℤ/8)	—	2	8	no	—
13	C₃×C₅×#135	—	2	4	no	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×D₈	—	2	4	no	—
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#127	C₂²	1	4	yes	complemented
25	C₃×C₅×#124	C₂²	1	4	yes	complemented
26	C₃×C₅×#121	—	2	4	no	—
27	C₃×C₅×#120	—	2	4	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₃×C₅×#97	C₂²	1	2	yes	complemented
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
31	C₃×#3155	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
33	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#535	C₂×C₃	1	2	yes	complemented
36	C₅×#496	C₂×C₃	1	4	yes	complemented
37	C₅×#495	C₂×C₃	1	2	yes	complemented
38	C₅×#493	C₂×C₃	1	2	yes	complemented
39	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂⁴×C₃×C₅	—	2	2	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	8	no	—
49	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×Q₁₆	—	2	2	no	—
54	C₃×C₅×SD₁₆	—	2	4	no	—
55	C₃×C₅×SD₁₆	—	2	8	no	—
56	C₃×C₅×D₈	—	2	4	no	—
57	C₃×C₅×D₈	—	2	4	no	—
58	C₃×C₅×D₈	—	2	2	no	—
59	C₃×C₅×D₈	—	2	8	no	—
60	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
61	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
67	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
68	C₃×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
70	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#535	C₂×C₅	1	2	yes	complemented
73	C₃×#496	C₂×C₅	1	4	yes	complemented
74	C₃×#495	C₂×C₅	1	2	yes	complemented
75	C₃×#493	C₂×C₅	1	2	yes	complemented
76	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
78	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
79	C₅×AGL(1,ℤ/8)	—	2	8	no	—
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
82	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
83	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
84	C₂×C₅×D₈	—	2	4	no	—
85	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
86	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
87	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
89	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₅×#127	C₂²×C₃	1	4	yes	complemented
92	C₅×#124	C₂²×C₃	1	4	yes	complemented
93	C₅×#121	—	2	4	no	—
94	C₅×#120	—	2	4	no	—
95	C₅×#117	C₂²×C₃	1	1	yes	characteristic
96	C₅×#97	C₂²×C₃	1	2	yes	complemented
97	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
98	#3155	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	4	no	—
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	4	4	no	—
102	C₂³×C₃×C₅	—	8	4	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×D₄	—	2	4	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	2	4	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	4	4	no	—
111	C₃×C₅×D₄	—	4	4	no	—
112	C₃×C₅×D₄	—	8	8	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	4	4	no	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
122	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
123	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
124	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
125	C₃×AGL(1,ℤ/8)	—	2	8	no	—
126	C₃×#135	—	2	4	no	—
127	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
128	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
129	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
130	C₂×C₃×D₈	—	2	4	no	—
131	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
132	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
133	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
135	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#127	C₂²×C₅	1	4	yes	complemented
138	C₃×#124	C₂²×C₅	1	4	yes	complemented
139	C₃×#121	—	2	4	no	—
140	C₃×#120	—	2	4	no	—
141	C₃×#117	C₂²×C₅	1	1	yes	characteristic
142	C₃×#97	C₂²×C₅	1	2	yes	complemented
143	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
144	C₂⁴×C₅	—	2	2	no	—
145	C₅×#41	—	2	4	no	—
146	C₅×#41	—	2	4	no	—
147	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	4	no	—
150	C₂×C₅×D₄	—	2	4	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	2	8	no	—
153	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
154	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
157	C₅×Q₁₆	—	2	2	no	—
158	C₅×SD₁₆	—	2	4	no	—
159	C₅×SD₁₆	—	2	8	no	—
160	C₅×D₈	—	2	4	no	—
161	C₅×D₈	—	2	4	no	—
162	C₅×D₈	—	2	2	no	—
163	C₅×D₈	—	2	8	no	—
164	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
165	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
166	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
167	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
169	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
170	C₅×C₂²⋊C₄	—	2	8	no	—
171	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
172	C₄²×C₅	C₂³×C₃	1	2	yes	—
173	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
174	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	#535	C₂×C₃×C₅	1	2	yes	complemented
177	#496	C₂×C₃×C₅	1	4	yes	complemented
178	#495	C₂×C₃×C₅	1	2	yes	complemented
179	#493	C₂×C₃×C₅	1	2	yes	complemented
180	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	4	no	—
184	C₂²×C₃×C₅	—	4	4	no	—
185	C₂²×C₃×C₅	—	4	8	no	—
186	C₂²×C₃×C₅	—	8	8	no	—
187	C₂²×C₃×C₅	#127	1	2	yes	—
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	#127	1	2	yes	—
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂⁴×C₃	—	2	2	no	—
195	C₃×#41	—	2	4	no	—
196	C₃×#41	—	2	4	no	—
197	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
198	C₂×C₃×D₄	—	2	2	no	—
199	C₂×C₃×D₄	—	2	4	no	—
200	C₂×C₃×D₄	—	2	4	no	—
201	C₂×C₃×D₄	—	2	2	no	—
202	C₂×C₃×D₄	—	2	8	no	—
203	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
204	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	—	2	2	no	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₃×Q₁₆	—	2	2	no	—
208	C₃×SD₁₆	—	2	4	no	—
209	C₃×SD₁₆	—	2	8	no	—
210	C₃×D₈	—	2	4	no	—
211	C₃×D₈	—	2	4	no	—
212	C₃×D₈	—	2	2	no	—
213	C₃×D₈	—	2	8	no	—
214	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
215	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
216	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
218	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
219	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
220	C₃×C₂²⋊C₄	—	2	8	no	—
221	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
222	C₃×C₄²	C₂³×C₅	1	2	yes	—
223	C₂³×C₅	—	2	4	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	4	4	no	—
226	C₂³×C₅	—	8	4	no	—
227	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
228	C₅×Q₈	—	2	2	no	—
229	C₅×Q₈	—	2	2	no	—
230	C₅×D₄	—	2	4	no	—
231	C₅×D₄	—	2	2	no	—
232	C₅×D₄	—	2	4	no	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	4	4	no	—
235	C₅×D₄	—	4	4	no	—
236	C₅×D₄	—	8	8	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	4	4	no	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
240	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
243	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
244	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
245	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
246	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
247	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
248	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
249	AGL(1,ℤ/8)	—	2	8	no	—
250	#135	—	2	4	no	—
251	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
252	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
253	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	complemented
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
256	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
257	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
259	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
260	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
261	#127	C₂²×C₃×C₅	1	4	yes	complemented
262	#124	C₂²×C₃×C₅	1	4	yes	complemented
263	#121	—	2	4	no	—
264	#120	—	2	4	no	—
265	#117	C₂²×C₃×C₅	1	1	yes	characteristic
266	#97	C₂²×C₃×C₅	1	2	yes	complemented
267	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	—	8	2	no	—
270	C₂×C₃×C₅	—	8	4	no	—
271	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
272	C₂×C₃×C₅	#576	1	2	yes	—
273	C₂³×C₃	—	2	4	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	4	4	no	—
276	C₂³×C₃	—	8	4	no	—
277	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
278	C₃×Q₈	—	2	2	no	—
279	C₃×Q₈	—	2	2	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	4	no	—
283	C₃×D₄	—	2	2	no	—
284	C₃×D₄	—	4	4	no	—
285	C₃×D₄	—	4	4	no	—
286	C₃×D₄	—	8	8	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	4	4	no	—
289	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
290	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
294	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
295	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
296	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
297	C₂²×C₅	—	2	2	no	—
298	C₂²×C₅	—	4	4	no	—
299	C₂²×C₅	—	4	8	no	—
300	C₂²×C₅	—	4	2	no	—
301	C₂²×C₅	—	4	4	no	—
302	C₂²×C₅	—	8	8	no	—
303	C₂²×C₅	C₃×#127	1	2	yes	—
304	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₄×C₅	—	2	4	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	C₃×#127	1	2	yes	—
308	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
309	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₂⁴	—	2	2	no	—
311	#41	—	2	4	no	—
312	#41	—	2	4	no	—
313	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
320	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
323	Q₁₆	—	2	2	no	—
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	2	8	no	—
326	D₈	—	2	4	no	—
327	D₈	—	2	4	no	—
328	D₈	—	2	2	no	—
329	D₈	—	2	8	no	—
330	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
331	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
332	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
334	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
335	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
338	C₄²	C₂³×C₃×C₅	1	2	yes	—
339	C₃×C₅	#3155	1	1	yes	characteristic, direct product factor, Hall
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	4	2	no	—
342	C₂²×C₃	—	4	4	no	—
343	C₂²×C₃	—	4	4	no	—
344	C₂²×C₃	—	4	8	no	—
345	C₂²×C₃	—	8	8	no	—
346	C₂²×C₃	C₅×#127	1	2	yes	—
347	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
348	C₃×C₄	—	2	4	no	—
349	C₃×C₄	—	4	2	no	—
350	C₃×C₄	C₅×#127	1	2	yes	—
351	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
352	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	8	4	no	—
355	C₂×C₅	—	8	2	no	—
356	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
357	C₂×C₅	C₃×#576	1	2	yes	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	8	4	no	—
362	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	2	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	2	2	no	—
367	D₄	—	2	4	no	—
368	D₄	—	2	2	no	—
369	D₄	—	4	4	no	—
370	D₄	—	4	4	no	—
371	D₄	—	8	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
375	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
376	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
377	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
379	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
380	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
381	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
382	C₂×C₃	—	2	2	no	—
383	C₂×C₃	—	8	4	no	—
384	C₂×C₃	—	8	2	no	—
385	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
386	C₂×C₃	C₅×#576	1	2	yes	—
387	C₅	C₃×#3155	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	4	no	—
392	C₂²	—	4	8	no	—
393	C₂²	—	8	8	no	—
394	C₂²	C₃×C₅×#127	1	2	yes	—
395	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	C₃×C₅×#127	1	2	yes	—
399	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
400	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
401	C₃	C₅×#3155	1	1	yes	characteristic, direct product factor, Sylow
402	C₂	—	2	2	no	—
403	C₂	—	8	4	no	—
404	C₂	—	8	2	no	—
405	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
406	C₂	C₃×C₅×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₂²×C₃×C₅×D₈	C₂	semidirect
4. C₃×C₅×#535	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₃×C₅×#495	C₂	semidirect
7. C₃×C₅×#493	C₂	semidirect
8. C₃×C₅×#405	C₂	semidirect
9. C₅×#3155	C₃	direct (N × H)
14. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
15. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
16. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
20. C₂×C₃×C₅×D₈	C₂²	semidirect
21. C₂×C₃×C₅×D₈	C₂²	semidirect
24. C₃×C₅×#127	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
29. C₃×C₅×#97	C₂²	semidirect
30. C₃×C₄×C₅×C₈	C₂²	semidirect
31. C₃×#3155	C₅	direct (N × H)
32. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
33. C₂×C₅×#135	C₂×C₃	semidirect
34. C₂²×C₅×D₈	C₂×C₃	semidirect
35. C₅×#535	C₂×C₃	semidirect
36. C₅×#496	C₂×C₃	semidirect
37. C₅×#495	C₂×C₃	semidirect
38. C₅×#493	C₂×C₃	semidirect
39. C₅×#405	C₂×C₃	semidirect
60. C₃×C₅×M₁₆	D₄	semidirect
61. C₂×C₃×C₅×C₈	D₄	semidirect
69. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
70. C₂×C₃×#135	C₂×C₅	semidirect
71. C₂²×C₃×D₈	C₂×C₅	semidirect
72. C₃×#535	C₂×C₅	semidirect
73. C₃×#496	C₂×C₅	semidirect
74. C₃×#495	C₂×C₅	semidirect
75. C₃×#493	C₂×C₅	semidirect
76. C₃×#405	C₂×C₅	semidirect
81. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
82. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
83. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
87. C₂×C₅×D₈	C₂²×C₃	semidirect
88. C₂×C₅×D₈	C₂²×C₃	semidirect
91. C₅×#127	C₂²×C₃	semidirect
92. C₅×#124	C₂²×C₃	semidirect
96. C₅×#97	C₂²×C₃	semidirect
97. C₄×C₅×C₈	C₂²×C₃	semidirect
98. #3155	C₃×C₅	direct (N × H)
127. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
128. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
129. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
133. C₂×C₃×D₈	C₂²×C₅	semidirect
134. C₂×C₃×D₈	C₂²×C₅	semidirect
137. C₃×#127	C₂²×C₅	semidirect
138. C₃×#124	C₂²×C₅	semidirect
142. C₃×#97	C₂²×C₅	semidirect
143. C₃×C₄×C₈	C₂²×C₅	semidirect
164. C₅×M₁₆	C₃×D₄	semidirect
165. C₂×C₅×C₈	C₃×D₄	semidirect
173. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
174. C₂×#135	C₂×C₃×C₅	semidirect
175. C₂²×D₈	C₂×C₃×C₅	semidirect
176. #535	C₂×C₃×C₅	semidirect
177. #496	C₂×C₃×C₅	semidirect
178. #495	C₂×C₃×C₅	semidirect
179. #493	C₂×C₃×C₅	semidirect
180. #405	C₂×C₃×C₅	semidirect
214. C₃×M₁₆	C₅×D₄	semidirect
215. C₂×C₃×C₈	C₅×D₄	semidirect
251. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
252. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
253. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
257. C₂×D₈	C₂²×C₃×C₅	semidirect
258. C₂×D₈	C₂²×C₃×C₅	semidirect
261. #127	C₂²×C₃×C₅	semidirect
262. #124	C₂²×C₃×C₅	semidirect
266. #97	C₂²×C₃×C₅	semidirect
267. C₄×C₈	C₂²×C₃×C₅	semidirect
330. M₁₆	C₃×C₅×D₄	semidirect
331. C₂×C₈	C₃×C₅×D₄	semidirect
339. C₃×C₅	#3155	direct (N × H)
387. C₅	C₃×#3155	direct (N × H)
401. C₃	C₅×#3155	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#135	2
C₂²×C₃×C₅×D₈	2
C₃×C₅×#535	2
C₃×C₅×#496	2
C₃×C₅×#495	2
C₃×C₅×#493	2
C₃×C₅×#405	2
C₅×#3155	3
C₃×#3155	5

Subgroups — C3×C5×#3155 #14276189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3155 #14276189