Subgroups — C₃×C₅×#3055 #14276089

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 692 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3055	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	—	2	1	no	—
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×M₁₆	—	2	4	no	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
24	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#123	—	2	1	no	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#121	—	2	1	no	—
29	C₃×C₅×#121	—	2	1	no	—
30	C₃×C₅×#121	C₂²	1	2	yes	—
31	C₃×C₅×#121	C₂²	1	2	yes	—
32	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#120	—	2	1	no	—
35	C₃×C₄×C₅×D₄	—	2	1	no	—
36	C₃×C₄×C₅×D₄	—	2	1	no	—
37	C₃×C₅×#117	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
40	C₃×C₅×#107	C₂²	1	2	yes	complemented
41	C₃×C₅×#106	C₂²	1	2	yes	complemented
42	C₃×C₅×#103	C₂²	1	2	yes	complemented
43	C₃×C₅×#102	C₂²	1	2	yes	complemented
44	C₃×C₅×#102	C₂²	1	2	yes	complemented
45	C₃×C₅×#102	C₂²	1	2	yes	complemented
46	C₃×#3055	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#469	C₂×C₃	1	2	yes	complemented
52	C₅×#468	C₂×C₃	1	2	yes	complemented
53	C₅×#466	C₂×C₃	1	2	yes	complemented
54	C₅×#465	C₂×C₃	1	2	yes	complemented
55	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#418	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂⁴×C₃×C₅	—	2	1	no	—
59	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
60	C₃×C₅×#41	—	2	2	no	—
61	C₃×C₅×#41	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	—	2	2	no	—
67	C₂×C₃×C₅×D₄	—	2	2	no	—
68	C₂×C₃×C₅×D₄	—	2	2	no	—
69	C₂×C₃×C₅×D₄	—	2	1	no	—
70	C₂×C₃×C₅×D₄	—	2	2	no	—
71	C₂×C₃×C₅×D₄	—	4	4	no	—
72	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
73	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	—	2	2	no	—
75	C₂²×C₃×C₄×C₅	—	2	2	no	—
76	C₂²×C₃×C₄×C₅	—	2	1	no	—
77	C₂²×C₃×C₄×C₅	—	2	1	no	—
78	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₅×SD₁₆	—	2	4	no	—
85	C₃×C₅×D₈	—	2	4	no	—
86	C₃×C₅×M₁₆	—	2	2	no	—
87	C₃×C₅×M₁₆	—	2	4	no	—
88	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
89	C₂×C₃×C₅×C₈	—	2	4	no	—
90	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
91	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	—	2	1	no	—
94	C₃×C₅×C₄⋊C₄	—	2	1	no	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
105	C₃×C₄²×C₅	—	2	1	no	—
106	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
108	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
110	C₃×#469	C₂×C₅	1	2	yes	complemented
111	C₃×#468	C₂×C₅	1	2	yes	complemented
112	C₃×#466	C₂×C₅	1	2	yes	complemented
113	C₃×#465	C₂×C₅	1	2	yes	complemented
114	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#418	C₂×C₅	1	1	yes	characteristic, complemented
116	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₅×D₄	—	2	1	no	—
119	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
121	C₅×AGL(1,ℤ/8)	—	2	4	no	—
122	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
123	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
124	C₂×C₅×M₁₆	—	2	4	no	—
125	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
128	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
129	C₅×#123	—	2	1	no	—
130	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₅×#121	—	2	1	no	—
133	C₅×#121	—	2	1	no	—
134	C₅×#121	C₂²×C₃	1	2	yes	—
135	C₅×#121	C₂²×C₃	1	2	yes	—
136	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₅×#120	—	2	1	no	—
139	C₄×C₅×D₄	—	2	1	no	—
140	C₄×C₅×D₄	—	2	1	no	—
141	C₅×#117	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
144	C₅×#107	C₂²×C₃	1	2	yes	complemented
145	C₅×#106	C₂²×C₃	1	2	yes	complemented
146	C₅×#103	C₂²×C₃	1	2	yes	complemented
147	C₅×#102	C₂²×C₃	1	2	yes	complemented
148	C₅×#102	C₂²×C₃	1	2	yes	complemented
149	C₅×#102	C₂²×C₃	1	2	yes	complemented
150	#3055	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
151	C₂³×C₃×C₅	—	2	2	no	—
152	C₂³×C₃×C₅	—	2	2	no	—
153	C₂³×C₃×C₅	—	2	1	no	—
154	C₂³×C₃×C₅	—	2	2	no	—
155	C₂³×C₃×C₅	—	4	1	no	—
156	C₂³×C₃×C₅	—	4	2	no	—
157	C₂³×C₃×C₅	—	4	2	no	—
158	C₂³×C₃×C₅	—	4	2	no	—
159	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
162	C₃×C₅×Q₈	—	2	1	no	—
163	C₃×C₅×Q₈	—	2	1	no	—
164	C₃×C₅×D₄	—	2	1	no	—
165	C₃×C₅×D₄	—	2	2	no	—
166	C₃×C₅×D₄	—	2	2	no	—
167	C₃×C₅×D₄	—	2	1	no	—
168	C₃×C₅×D₄	—	4	2	no	—
169	C₃×C₅×D₄	—	4	4	no	—
170	C₃×C₅×D₄	—	4	2	no	—
171	C₃×C₅×D₄	—	4	2	no	—
172	C₃×C₅×D₄	—	4	4	no	—
173	C₃×C₅×D₄	—	4	2	no	—
174	C₂×C₃×C₄×C₅	—	2	2	no	—
175	C₂×C₃×C₄×C₅	—	2	2	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	2	no	—
185	C₂×C₃×C₄×C₅	—	4	2	no	—
186	C₂×C₃×C₄×C₅	—	4	2	no	—
187	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
190	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
191	C₂×C₃×C₄×C₅	#41	1	2	yes	—
192	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₃×C₅×C₈	—	2	2	no	—
194	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
195	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
196	C₂²×C₃×D₄	—	2	1	no	—
197	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
198	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
199	C₃×AGL(1,ℤ/8)	—	2	4	no	—
200	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
201	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
202	C₂×C₃×M₁₆	—	2	4	no	—
203	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
205	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
206	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	complemented
207	C₃×#123	—	2	1	no	—
208	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
209	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
210	C₃×#121	—	2	1	no	—
211	C₃×#121	—	2	1	no	—
212	C₃×#121	C₂²×C₅	1	2	yes	—
213	C₃×#121	C₂²×C₅	1	2	yes	—
214	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
215	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
216	C₃×#120	—	2	1	no	—
217	C₃×C₄×D₄	—	2	1	no	—
218	C₃×C₄×D₄	—	2	1	no	—
219	C₃×#117	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
222	C₃×#107	C₂²×C₅	1	2	yes	complemented
223	C₃×#106	C₂²×C₅	1	2	yes	complemented
224	C₃×#103	C₂²×C₅	1	2	yes	complemented
225	C₃×#102	C₂²×C₅	1	2	yes	complemented
226	C₃×#102	C₂²×C₅	1	2	yes	complemented
227	C₃×#102	C₂²×C₅	1	2	yes	complemented
228	C₂⁴×C₅	—	2	1	no	—
229	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
230	C₅×#41	—	2	2	no	—
231	C₅×#41	—	2	2	no	—
232	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₅×D₄	—	2	1	no	—
234	C₂×C₅×D₄	—	2	1	no	—
235	C₂×C₅×D₄	—	2	1	no	—
236	C₂×C₅×D₄	—	2	2	no	—
237	C₂×C₅×D₄	—	2	2	no	—
238	C₂×C₅×D₄	—	2	2	no	—
239	C₂×C₅×D₄	—	2	1	no	—
240	C₂×C₅×D₄	—	2	2	no	—
241	C₂×C₅×D₄	—	4	4	no	—
242	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
243	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	—	2	2	no	—
245	C₂²×C₄×C₅	—	2	2	no	—
246	C₂²×C₄×C₅	—	2	1	no	—
247	C₂²×C₄×C₅	—	2	1	no	—
248	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
254	C₅×SD₁₆	—	2	4	no	—
255	C₅×D₈	—	2	4	no	—
256	C₅×M₁₆	—	2	2	no	—
257	C₅×M₁₆	—	2	4	no	—
258	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
259	C₂×C₅×C₈	—	2	4	no	—
260	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
261	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	—	2	1	no	—
264	C₅×C₄⋊C₄	—	2	1	no	—
265	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
266	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
267	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
268	C₅×C₂²⋊C₄	—	2	1	no	—
269	C₅×C₂²⋊C₄	—	2	1	no	—
270	C₅×C₂²⋊C₄	—	2	1	no	—
271	C₅×C₂²⋊C₄	—	2	2	no	—
272	C₅×C₂²⋊C₄	—	2	2	no	—
273	C₅×C₂²⋊C₄	—	2	1	no	—
274	C₅×C₂²⋊C₄	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
277	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
278	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
279	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
280	#469	C₂×C₃×C₅	1	2	yes	complemented
281	#468	C₂×C₃×C₅	1	2	yes	complemented
282	#466	C₂×C₃×C₅	1	2	yes	complemented
283	#465	C₂×C₃×C₅	1	2	yes	complemented
284	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
285	#418	C₂×C₃×C₅	1	1	yes	characteristic, complemented
286	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
287	C₂²×C₃×C₅	—	2	1	no	—
288	C₂²×C₃×C₅	—	2	1	no	—
289	C₂²×C₃×C₅	—	2	1	no	—
290	C₂²×C₃×C₅	—	2	1	no	—
291	C₂²×C₃×C₅	—	2	1	no	—
292	C₂²×C₃×C₅	—	2	1	no	—
293	C₂²×C₃×C₅	—	2	1	no	—
294	C₂²×C₃×C₅	—	4	4	no	—
295	C₂²×C₃×C₅	—	4	1	no	—
296	C₂²×C₃×C₅	—	4	2	no	—
297	C₂²×C₃×C₅	—	4	2	no	—
298	C₂²×C₃×C₅	—	4	1	no	—
299	C₂²×C₃×C₅	—	4	1	no	—
300	C₂²×C₃×C₅	—	4	2	no	—
301	C₂²×C₃×C₅	—	8	4	no	—
302	C₂²×C₃×C₅	#121	1	2	yes	—
303	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
304	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₃×C₄×C₅	—	2	1	no	—
306	C₃×C₄×C₅	—	2	1	no	—
307	C₃×C₄×C₅	—	4	1	no	—
308	C₃×C₄×C₅	—	4	2	no	—
309	C₃×C₄×C₅	—	4	1	no	—
310	C₃×C₄×C₅	—	4	1	no	—
311	C₃×C₄×C₅	#121	1	2	yes	—
312	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
313	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
314	C₂⁴×C₃	—	2	1	no	—
315	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
316	C₃×#41	—	2	2	no	—
317	C₃×#41	—	2	2	no	—
318	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
319	C₂×C₃×D₄	—	2	1	no	—
320	C₂×C₃×D₄	—	2	1	no	—
321	C₂×C₃×D₄	—	2	1	no	—
322	C₂×C₃×D₄	—	2	2	no	—
323	C₂×C₃×D₄	—	2	2	no	—
324	C₂×C₃×D₄	—	2	2	no	—
325	C₂×C₃×D₄	—	2	1	no	—
326	C₂×C₃×D₄	—	2	2	no	—
327	C₂×C₃×D₄	—	4	4	no	—
328	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
329	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
330	C₂²×C₃×C₄	—	2	2	no	—
331	C₂²×C₃×C₄	—	2	2	no	—
332	C₂²×C₃×C₄	—	2	1	no	—
333	C₂²×C₃×C₄	—	2	1	no	—
334	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₃×SD₁₆	—	2	4	no	—
341	C₃×D₈	—	2	4	no	—
342	C₃×M₁₆	—	2	2	no	—
343	C₃×M₁₆	—	2	4	no	—
344	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
345	C₂×C₃×C₈	—	2	4	no	—
346	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
347	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
348	C₃×C₄⋊C₄	—	2	1	no	—
349	C₃×C₄⋊C₄	—	2	1	no	—
350	C₃×C₄⋊C₄	—	2	1	no	—
351	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
352	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
353	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
354	C₃×C₂²⋊C₄	—	2	1	no	—
355	C₃×C₂²⋊C₄	—	2	1	no	—
356	C₃×C₂²⋊C₄	—	2	1	no	—
357	C₃×C₂²⋊C₄	—	2	2	no	—
358	C₃×C₂²⋊C₄	—	2	2	no	—
359	C₃×C₂²⋊C₄	—	2	1	no	—
360	C₃×C₂²⋊C₄	—	2	1	no	—
361	C₃×C₄²	—	2	1	no	—
362	C₂³×C₅	—	2	2	no	—
363	C₂³×C₅	—	2	2	no	—
364	C₂³×C₅	—	2	1	no	—
365	C₂³×C₅	—	2	2	no	—
366	C₂³×C₅	—	4	1	no	—
367	C₂³×C₅	—	4	2	no	—
368	C₂³×C₅	—	4	2	no	—
369	C₂³×C₅	—	4	2	no	—
370	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
371	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
372	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
373	C₅×Q₈	—	2	1	no	—
374	C₅×Q₈	—	2	1	no	—
375	C₅×D₄	—	2	1	no	—
376	C₅×D₄	—	2	2	no	—
377	C₅×D₄	—	2	2	no	—
378	C₅×D₄	—	2	1	no	—
379	C₅×D₄	—	4	2	no	—
380	C₅×D₄	—	4	4	no	—
381	C₅×D₄	—	4	2	no	—
382	C₅×D₄	—	4	2	no	—
383	C₅×D₄	—	4	4	no	—
384	C₅×D₄	—	4	2	no	—
385	C₂×C₄×C₅	—	2	2	no	—
386	C₂×C₄×C₅	—	2	2	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	2	no	—
396	C₂×C₄×C₅	—	4	2	no	—
397	C₂×C₄×C₅	—	4	2	no	—
398	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
401	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
402	C₂×C₄×C₅	C₃×#41	1	2	yes	—
403	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
404	C₅×C₈	—	2	2	no	—
405	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
406	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
407	C₂²×D₄	—	2	1	no	—
408	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
409	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
410	AGL(1,ℤ/8)	—	2	4	no	—
411	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
412	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
413	C₂×M₁₆	—	2	4	no	—
414	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
415	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
416	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
417	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	complemented
418	#123	—	2	1	no	—
419	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
421	#121	—	2	1	no	—
422	#121	—	2	1	no	—
423	#121	C₂²×C₃×C₅	1	2	yes	—
424	#121	C₂²×C₃×C₅	1	2	yes	—
425	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
426	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
427	#120	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	#117	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	#107	C₂²×C₃×C₅	1	2	yes	complemented
434	#106	C₂²×C₃×C₅	1	2	yes	complemented
435	#103	C₂²×C₃×C₅	1	2	yes	complemented
436	#102	C₂²×C₃×C₅	1	2	yes	complemented
437	#102	C₂²×C₃×C₅	1	2	yes	complemented
438	#102	C₂²×C₃×C₅	1	2	yes	complemented
439	C₂×C₃×C₅	—	2	2	no	—
440	C₂×C₃×C₅	—	2	2	no	—
441	C₂×C₃×C₅	—	4	1	no	—
442	C₂×C₃×C₅	—	8	1	no	—
443	C₂×C₃×C₅	—	8	2	no	—
444	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
445	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
446	C₂×C₃×C₅	#575	1	1	yes	characteristic
447	C₂³×C₃	—	2	2	no	—
448	C₂³×C₃	—	2	2	no	—
449	C₂³×C₃	—	2	1	no	—
450	C₂³×C₃	—	2	2	no	—
451	C₂³×C₃	—	4	1	no	—
452	C₂³×C₃	—	4	2	no	—
453	C₂³×C₃	—	4	2	no	—
454	C₂³×C₃	—	4	2	no	—
455	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
456	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
458	C₃×Q₈	—	2	1	no	—
459	C₃×Q₈	—	2	1	no	—
460	C₃×D₄	—	2	1	no	—
461	C₃×D₄	—	2	2	no	—
462	C₃×D₄	—	2	2	no	—
463	C₃×D₄	—	2	1	no	—
464	C₃×D₄	—	4	2	no	—
465	C₃×D₄	—	4	4	no	—
466	C₃×D₄	—	4	2	no	—
467	C₃×D₄	—	4	2	no	—
468	C₃×D₄	—	4	4	no	—
469	C₃×D₄	—	4	2	no	—
470	C₂×C₃×C₄	—	2	2	no	—
471	C₂×C₃×C₄	—	2	2	no	—
472	C₂×C₃×C₄	—	2	2	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	2	no	—
481	C₂×C₃×C₄	—	4	2	no	—
482	C₂×C₃×C₄	—	4	2	no	—
483	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
485	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
486	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
487	C₂×C₃×C₄	C₅×#41	1	2	yes	—
488	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
489	C₃×C₈	—	2	2	no	—
490	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
491	C₂²×C₅	—	2	1	no	—
492	C₂²×C₅	—	2	1	no	—
493	C₂²×C₅	—	2	1	no	—
494	C₂²×C₅	—	2	1	no	—
495	C₂²×C₅	—	2	1	no	—
496	C₂²×C₅	—	2	1	no	—
497	C₂²×C₅	—	2	1	no	—
498	C₂²×C₅	—	4	4	no	—
499	C₂²×C₅	—	4	2	no	—
500	C₂²×C₅	—	4	1	no	—
501	C₂²×C₅	—	4	1	no	—
502	C₂²×C₅	—	4	2	no	—
503	C₂²×C₅	—	4	1	no	—
504	C₂²×C₅	—	4	2	no	—
505	C₂²×C₅	—	8	4	no	—
506	C₂²×C₅	C₃×#121	1	2	yes	—
507	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
508	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
509	C₄×C₅	—	2	1	no	—
510	C₄×C₅	—	2	1	no	—
511	C₄×C₅	—	4	2	no	—
512	C₄×C₅	—	4	1	no	—
513	C₄×C₅	—	4	1	no	—
514	C₄×C₅	—	4	1	no	—
515	C₄×C₅	C₃×#121	1	2	yes	—
516	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
517	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
518	C₂⁴	—	2	1	no	—
519	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	2	no	—
527	C₂×D₄	—	2	2	no	—
528	C₂×D₄	—	2	2	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	4	4	no	—
532	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
533	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
539	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
540	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
541	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
542	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
543	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
544	SD₁₆	—	2	4	no	—
545	D₈	—	2	4	no	—
546	M₁₆	—	2	2	no	—
547	M₁₆	—	2	4	no	—
548	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
549	C₂×C₈	—	2	4	no	—
550	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
551	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
556	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
557	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
558	C₂²⋊C₄	—	2	1	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	1	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	2	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₃×C₅	#3055	1	1	yes	characteristic, direct product factor, Hall
567	C₂²×C₃	—	2	1	no	—
568	C₂²×C₃	—	2	1	no	—
569	C₂²×C₃	—	2	1	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	2	1	no	—
574	C₂²×C₃	—	4	4	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	—	4	2	no	—
577	C₂²×C₃	—	4	2	no	—
578	C₂²×C₃	—	4	1	no	—
579	C₂²×C₃	—	4	1	no	—
580	C₂²×C₃	—	4	2	no	—
581	C₂²×C₃	—	8	4	no	—
582	C₂²×C₃	C₅×#121	1	2	yes	—
583	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
584	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	4	1	no	—
588	C₃×C₄	—	4	2	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	C₅×#121	1	2	yes	—
592	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
593	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
594	C₂×C₅	—	2	2	no	—
595	C₂×C₅	—	2	2	no	—
596	C₂×C₅	—	4	1	no	—
597	C₂×C₅	—	8	2	no	—
598	C₂×C₅	—	8	1	no	—
599	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
600	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
601	C₂×C₅	C₃×#575	1	1	yes	characteristic
602	C₂³	—	2	2	no	—
603	C₂³	—	2	2	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
611	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
612	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	D₄	—	2	1	no	—
616	D₄	—	2	2	no	—
617	D₄	—	2	2	no	—
618	D₄	—	2	1	no	—
619	D₄	—	4	4	no	—
620	D₄	—	4	2	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	4	no	—
623	D₄	—	4	2	no	—
624	D₄	—	4	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	2	no	—
638	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
639	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
640	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
641	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
642	C₂×C₄	C₃×C₅×#41	1	2	yes	—
643	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
644	C₈	—	2	2	no	—
645	C₈	C₂×C₃×C₅×D₄	1	4	yes	complemented
646	C₂×C₃	—	2	2	no	—
647	C₂×C₃	—	2	2	no	—
648	C₂×C₃	—	4	1	no	—
649	C₂×C₃	—	8	2	no	—
650	C₂×C₃	—	8	1	no	—
651	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
652	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
653	C₂×C₃	C₅×#575	1	1	yes	characteristic
654	C₅	C₃×#3055	1	1	yes	characteristic, direct product factor, Sylow
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	8	4	no	—
670	C₂²	C₃×C₅×#121	1	2	yes	—
671	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	complemented
672	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	C₃×C₅×#121	1	2	yes	—
680	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
681	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
682	C₃	C₅×#3055	1	1	yes	characteristic, direct product factor, Sylow
683	C₂	—	2	2	no	—
684	C₂	—	2	2	no	—
685	C₂	—	4	1	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	1	no	—
688	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
689	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
690	C₂	C₃×C₅×#575	1	1	yes	characteristic

	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 ◁ C₂³×C₃×C₄×C₅ ◁ 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. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₃×C₅×#525	C₂	semidirect
4. C₂×C₃×C₅×#121	C₂	semidirect
5. C₃×C₅×#469	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#466	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#428	C₂	semidirect
10. C₃×C₅×#418	C₂	semidirect
11. C₃×C₅×#417	C₂	semidirect
12. C₅×#3055	C₃	direct (N × H)
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
19. C₂×C₃×C₅×D₈	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
26. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
27. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
32. C₃×C₅×#121	C₂²	semidirect
33. C₃×C₅×#121	C₂²	semidirect
40. C₃×C₅×#107	C₂²	semidirect
41. C₃×C₅×#106	C₂²	semidirect
42. C₃×C₅×#103	C₂²	semidirect
43. C₃×C₅×#102	C₂²	semidirect
44. C₃×C₅×#102	C₂²	semidirect
45. C₃×C₅×#102	C₂²	semidirect
46. C₃×#3055	C₅	direct (N × H)
47. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
48. C₂²×C₅×M₁₆	C₂×C₃	semidirect
49. C₅×#525	C₂×C₃	semidirect
50. C₂×C₅×#121	C₂×C₃	semidirect
51. C₅×#469	C₂×C₃	semidirect
52. C₅×#468	C₂×C₃	semidirect
53. C₅×#466	C₂×C₃	semidirect
54. C₅×#465	C₂×C₃	semidirect
55. C₅×#428	C₂×C₃	semidirect
56. C₅×#418	C₂×C₃	semidirect
57. C₅×#417	C₂×C₃	semidirect
88. C₃×C₅×M₁₆	D₄	semidirect
106. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
107. C₂²×C₃×M₁₆	C₂×C₅	semidirect
108. C₃×#525	C₂×C₅	semidirect
109. C₂×C₃×#121	C₂×C₅	semidirect
110. C₃×#469	C₂×C₅	semidirect
111. C₃×#468	C₂×C₅	semidirect
112. C₃×#466	C₂×C₅	semidirect
113. C₃×#465	C₂×C₅	semidirect
114. C₃×#428	C₂×C₅	semidirect
115. C₃×#418	C₂×C₅	semidirect
116. C₃×#417	C₂×C₅	semidirect
122. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
123. C₂×C₅×D₈	C₂²×C₃	semidirect
127. C₂×C₅×M₁₆	C₂²×C₃	semidirect
128. C₂²×C₅×C₈	C₂²×C₃	semidirect
130. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
131. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
136. C₅×#121	C₂²×C₃	semidirect
137. C₅×#121	C₂²×C₃	semidirect
144. C₅×#107	C₂²×C₃	semidirect
145. C₅×#106	C₂²×C₃	semidirect
146. C₅×#103	C₂²×C₃	semidirect
147. C₅×#102	C₂²×C₃	semidirect
148. C₅×#102	C₂²×C₃	semidirect
149. C₅×#102	C₂²×C₃	semidirect
150. #3055	C₃×C₅	direct (N × H)
194. C₃×C₅×C₈	C₂×D₄	semidirect
200. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
201. C₂×C₃×D₈	C₂²×C₅	semidirect
205. C₂×C₃×M₁₆	C₂²×C₅	semidirect
206. C₂²×C₃×C₈	C₂²×C₅	semidirect
208. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
209. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
214. C₃×#121	C₂²×C₅	semidirect
215. C₃×#121	C₂²×C₅	semidirect
222. C₃×#107	C₂²×C₅	semidirect
223. C₃×#106	C₂²×C₅	semidirect
224. C₃×#103	C₂²×C₅	semidirect
225. C₃×#102	C₂²×C₅	semidirect
226. C₃×#102	C₂²×C₅	semidirect
227. C₃×#102	C₂²×C₅	semidirect
258. C₅×M₁₆	C₃×D₄	semidirect
276. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
277. C₂²×M₁₆	C₂×C₃×C₅	semidirect
278. #525	C₂×C₃×C₅	semidirect
279. C₂×#121	C₂×C₃×C₅	semidirect
280. #469	C₂×C₃×C₅	semidirect
281. #468	C₂×C₃×C₅	semidirect
282. #466	C₂×C₃×C₅	semidirect
283. #465	C₂×C₃×C₅	semidirect
284. #428	C₂×C₃×C₅	semidirect
285. #418	C₂×C₃×C₅	semidirect
286. #417	C₂×C₃×C₅	semidirect
303. C₂²×C₃×C₅	AGL(1,ℤ/8)	semidirect
344. C₃×M₁₆	C₅×D₄	semidirect
405. C₅×C₈	C₂×C₃×D₄	semidirect
411. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
412. C₂×D₈	C₂²×C₃×C₅	semidirect
416. C₂×M₁₆	C₂²×C₃×C₅	semidirect
417. C₂²×C₈	C₂²×C₃×C₅	semidirect
419. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
420. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
425. #121	C₂²×C₃×C₅	semidirect
426. #121	C₂²×C₃×C₅	semidirect
433. #107	C₂²×C₃×C₅	semidirect
434. #106	C₂²×C₃×C₅	semidirect
435. #103	C₂²×C₃×C₅	semidirect
436. #102	C₂²×C₃×C₅	semidirect
437. #102	C₂²×C₃×C₅	semidirect
438. #102	C₂²×C₃×C₅	semidirect
490. C₃×C₈	C₂×C₅×D₄	semidirect
507. C₂²×C₅	C₃×AGL(1,ℤ/8)	semidirect
548. M₁₆	C₃×C₅×D₄	semidirect
566. C₃×C₅	#3055	direct (N × H)
583. C₂²×C₃	C₅×AGL(1,ℤ/8)	semidirect
645. C₈	C₂×C₃×C₅×D₄	semidirect
654. C₅	C₃×#3055	direct (N × H)
671. C₂²	C₃×C₅×AGL(1,ℤ/8)	semidirect
682. C₃	C₅×#3055	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
C₂²×C₃×C₅×M₁₆	2
C₃×C₅×#525	2
C₂×C₃×C₅×#121	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#428	2
C₃×C₅×#418	2
C₃×C₅×#417	2
C₅×#3055	3
C₃×#3055	5

Subgroups — C3×C5×#3055 #14276089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3055 #14276089