Subgroups — C₃×C₅×#3012 #14276046

Order 1920.

1528 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#450	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#447	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3012	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
14	C₃×C₅×H(5,𝔽₂)	—	2	4	no	—
15	C₂×C₃×C₅×#41	—	2	1	no	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	—	2	2	no	—
21	C₂²×C₃×C₅×D₄	—	2	1	no	—
22	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
23	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
25	C₃×C₅×#135	—	2	4	no	—
26	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
30	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₃×C₅×#121	—	2	1	no	—
37	C₃×C₅×#121	—	2	2	no	—
38	C₃×C₅×#121	C₂²	1	2	yes	complemented
39	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#103	C₂²	1	2	yes	complemented
41	C₃×C₅×#102	C₂²	1	2	yes	complemented
42	C₃×C₅×#102	C₂²	1	2	yes	complemented
43	C₃×C₅×#102	C₂²	1	2	yes	complemented
44	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
45	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	complemented
46	C₃×#3012	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₂×C₅×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#452	C₂×C₃	1	2	yes	complemented
52	C₅×#450	C₂×C₃	1	2	yes	complemented
53	C₅×#449	C₂×C₃	1	2	yes	complemented
54	C₅×#447	C₂×C₃	1	2	yes	complemented
55	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂⁴×C₃×C₅	—	2	2	no	—
59	C₂⁴×C₃×C₅	—	2	1	no	—
60	C₃×C₅×#41	—	2	8	no	—
61	C₃×C₅×#41	—	2	4	no	—
62	C₃×C₅×#41	—	2	4	no	—
63	C₃×C₅×#41	—	2	2	no	—
64	C₃×C₅×#41	—	2	2	no	—
65	C₃×C₅×#41	—	2	2	no	—
66	C₃×C₅×#41	—	2	2	no	—
67	C₃×C₅×#41	—	2	2	no	—
68	C₃×C₅×#41	D₄	1	4	yes	complemented
69	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
70	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×D₄	—	2	16	no	—
73	C₂×C₃×C₅×D₄	—	2	8	no	—
74	C₂×C₃×C₅×D₄	—	2	2	no	—
75	C₂×C₃×C₅×D₄	—	2	1	no	—
76	C₂×C₃×C₅×D₄	—	2	4	no	—
77	C₂×C₃×C₅×D₄	—	2	4	no	—
78	C₂×C₃×C₅×D₄	—	2	1	no	—
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
84	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
89	C₂²×C₃×C₄×C₅	—	2	2	no	—
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₃×C₅×Q₁₆	—	2	2	no	—
96	C₃×C₅×SD₁₆	—	2	2	no	—
97	C₃×C₅×SD₁₆	—	2	2	no	—
98	C₃×C₅×SD₁₆	—	2	4	no	—
99	C₃×C₅×D₈	—	2	2	no	—
100	C₃×C₅×D₈	—	2	4	no	—
101	C₃×C₅×M₁₆	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	2	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	2	no	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₃×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#452	C₂×C₅	1	2	yes	complemented
116	C₃×#450	C₂×C₅	1	2	yes	complemented
117	C₃×#449	C₂×C₅	1	2	yes	complemented
118	C₃×#447	C₂×C₅	1	2	yes	complemented
119	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
122	C₅×H(5,𝔽₂)	—	2	4	no	—
123	C₅×H(5,𝔽₂)	—	2	4	no	—
124	C₂×C₅×#41	—	2	1	no	—
125	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
126	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂²×C₅×D₄	—	2	2	no	—
130	C₂²×C₅×D₄	—	2	1	no	—
131	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
132	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₅×AGL(1,ℤ/8)	—	2	4	no	—
134	C₅×#135	—	2	4	no	—
135	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
136	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
137	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
139	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
141	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
142	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
143	C₅×C₂²⋊Q₈	—	2	1	no	—
144	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
145	C₅×#121	—	2	1	no	—
146	C₅×#121	—	2	2	no	—
147	C₅×#121	C₂²×C₃	1	2	yes	complemented
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₅×#103	C₂²×C₃	1	2	yes	complemented
150	C₅×#102	C₂²×C₃	1	2	yes	complemented
151	C₅×#102	C₂²×C₃	1	2	yes	complemented
152	C₅×#102	C₂²×C₃	1	2	yes	complemented
153	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
154	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	complemented
155	#3012	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³×C₃×C₅	—	2	8	no	—
157	C₂³×C₃×C₅	—	2	2	no	—
158	C₂³×C₃×C₅	—	2	1	no	—
159	C₂³×C₃×C₅	—	2	4	no	—
160	C₂³×C₃×C₅	—	2	1	no	—
161	C₂³×C₃×C₅	—	8	1	no	—
162	C₂³×C₃×C₅	—	8	1	no	—
163	C₂³×C₃×C₅	—	8	2	no	—
164	C₂³×C₃×C₅	—	8	2	no	—
165	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
166	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
167	C₃×C₅×Q₈	—	2	2	no	—
168	C₃×C₅×Q₈	—	2	1	no	—
169	C₃×C₅×Q₈	—	2	1	no	—
170	C₃×C₅×Q₈	—	2	1	no	—
171	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
172	C₃×C₅×D₄	—	2	8	no	—
173	C₃×C₅×D₄	—	2	8	no	—
174	C₃×C₅×D₄	—	2	4	no	—
175	C₃×C₅×D₄	—	2	4	no	—
176	C₃×C₅×D₄	—	2	2	no	—
177	C₃×C₅×D₄	—	2	4	no	—
178	C₃×C₅×D₄	—	2	2	no	—
179	C₃×C₅×D₄	—	2	1	no	—
180	C₃×C₅×D₄	—	2	1	no	—
181	C₃×C₅×D₄	—	2	1	no	—
182	C₃×C₅×D₄	—	4	2	no	—
183	C₃×C₅×D₄	—	8	2	no	—
184	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
185	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
186	C₂×C₃×C₄×C₅	—	2	8	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	4	no	—
189	C₂×C₃×C₄×C₅	—	2	2	no	—
190	C₂×C₃×C₄×C₅	—	2	2	no	—
191	C₂×C₃×C₄×C₅	—	2	2	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	4	2	no	—
194	C₂×C₃×C₄×C₅	—	8	1	no	—
195	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
196	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
197	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
198	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
199	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
200	C₃×C₅×C₈	—	2	1	no	—
201	C₃×C₅×C₈	—	2	1	no	—
202	C₃×C₅×C₈	—	2	2	no	—
203	C₃×H(5,𝔽₂)	—	2	4	no	—
204	C₃×H(5,𝔽₂)	—	2	4	no	—
205	C₂×C₃×#41	—	2	1	no	—
206	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
207	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
208	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
209	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
210	C₂²×C₃×D₄	—	2	2	no	—
211	C₂²×C₃×D₄	—	2	1	no	—
212	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
213	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
214	C₃×AGL(1,ℤ/8)	—	2	4	no	—
215	C₃×#135	—	2	4	no	—
216	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
217	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
218	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
219	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
220	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
221	C₂×C₃×D₈	C₂²×C₅	1	2	yes	complemented
222	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
223	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
224	C₃×C₂²⋊Q₈	—	2	1	no	—
225	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
226	C₃×#121	—	2	1	no	—
227	C₃×#121	—	2	2	no	—
228	C₃×#121	C₂²×C₅	1	2	yes	complemented
229	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
230	C₃×#103	C₂²×C₅	1	2	yes	complemented
231	C₃×#102	C₂²×C₅	1	2	yes	complemented
232	C₃×#102	C₂²×C₅	1	2	yes	complemented
233	C₃×#102	C₂²×C₅	1	2	yes	complemented
234	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
235	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	complemented
236	C₂⁴×C₅	—	2	2	no	—
237	C₂⁴×C₅	—	2	1	no	—
238	C₅×#41	—	2	8	no	—
239	C₅×#41	—	2	4	no	—
240	C₅×#41	—	2	4	no	—
241	C₅×#41	—	2	2	no	—
242	C₅×#41	—	2	2	no	—
243	C₅×#41	—	2	2	no	—
244	C₅×#41	—	2	2	no	—
245	C₅×#41	—	2	2	no	—
246	C₅×#41	C₃×D₄	1	4	yes	complemented
247	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
248	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₅×D₄	—	2	16	no	—
251	C₂×C₅×D₄	—	2	8	no	—
252	C₂×C₅×D₄	—	2	2	no	—
253	C₂×C₅×D₄	—	2	1	no	—
254	C₂×C₅×D₄	—	2	4	no	—
255	C₂×C₅×D₄	—	2	4	no	—
256	C₂×C₅×D₄	—	2	1	no	—
257	C₂×C₅×D₄	—	2	2	no	—
258	C₂×C₅×D₄	—	2	2	no	—
259	C₂×C₅×D₄	—	2	1	no	—
260	C₂×C₅×D₄	—	2	2	no	—
261	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
262	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
263	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
264	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
267	C₂²×C₄×C₅	—	2	2	no	—
268	C₂²×C₄×C₅	—	2	1	no	—
269	C₂²×C₄×C₅	—	2	1	no	—
270	C₂²×C₄×C₅	—	2	1	no	—
271	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
272	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
273	C₅×Q₁₆	—	2	2	no	—
274	C₅×SD₁₆	—	2	2	no	—
275	C₅×SD₁₆	—	2	2	no	—
276	C₅×SD₁₆	—	2	4	no	—
277	C₅×D₈	—	2	2	no	—
278	C₅×D₈	—	2	4	no	—
279	C₅×M₁₆	—	2	2	no	—
280	C₂×C₅×C₈	—	2	2	no	—
281	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
284	C₅×C₄⋊C₄	—	2	1	no	—
285	C₅×C₄⋊C₄	—	2	2	no	—
286	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
287	C₅×C₂²⋊C₄	—	2	2	no	—
288	C₅×C₂²⋊C₄	—	2	2	no	—
289	C₂×H(5,𝔽₂)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
290	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
291	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
292	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
293	#452	C₂×C₃×C₅	1	2	yes	complemented
294	#450	C₂×C₃×C₅	1	2	yes	complemented
295	#449	C₂×C₃×C₅	1	2	yes	complemented
296	#447	C₂×C₃×C₅	1	2	yes	complemented
297	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
298	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic, complemented
299	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
300	C₂²×C₃×C₅	—	2	1	no	—
301	C₂²×C₃×C₅	—	2	1	no	—
302	C₂²×C₃×C₅	—	2	2	no	—
303	C₂²×C₃×C₅	—	2	4	no	—
304	C₂²×C₃×C₅	—	2	2	no	—
305	C₂²×C₃×C₅	—	2	2	no	—
306	C₂²×C₃×C₅	—	2	2	no	—
307	C₂²×C₃×C₅	—	4	2	no	—
308	C₂²×C₃×C₅	—	4	1	no	—
309	C₂²×C₃×C₅	—	4	2	no	—
310	C₂²×C₃×C₅	—	4	1	no	—
311	C₂²×C₃×C₅	—	4	1	no	—
312	C₂²×C₃×C₅	—	4	1	no	—
313	C₂²×C₃×C₅	—	4	1	no	—
314	C₂²×C₃×C₅	—	8	4	no	—
315	C₂²×C₃×C₅	—	8	8	no	—
316	C₂²×C₃×C₅	#120	1	2	yes	—
317	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
318	C₃×C₄×C₅	—	2	2	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	4	1	no	—
321	C₃×C₄×C₅	—	4	2	no	—
322	C₃×C₄×C₅	#120	1	2	yes	—
323	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
324	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×C₃	—	2	2	no	—
326	C₂⁴×C₃	—	2	1	no	—
327	C₃×#41	—	2	8	no	—
328	C₃×#41	—	2	4	no	—
329	C₃×#41	—	2	4	no	—
330	C₃×#41	—	2	2	no	—
331	C₃×#41	—	2	2	no	—
332	C₃×#41	—	2	2	no	—
333	C₃×#41	—	2	2	no	—
334	C₃×#41	—	2	2	no	—
335	C₃×#41	C₅×D₄	1	4	yes	complemented
336	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
337	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
338	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
339	C₂×C₃×D₄	—	2	16	no	—
340	C₂×C₃×D₄	—	2	8	no	—
341	C₂×C₃×D₄	—	2	2	no	—
342	C₂×C₃×D₄	—	2	1	no	—
343	C₂×C₃×D₄	—	2	4	no	—
344	C₂×C₃×D₄	—	2	4	no	—
345	C₂×C₃×D₄	—	2	1	no	—
346	C₂×C₃×D₄	—	2	2	no	—
347	C₂×C₃×D₄	—	2	2	no	—
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	—	2	2	no	—
350	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
351	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
352	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
353	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
354	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
355	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
356	C₂²×C₃×C₄	—	2	2	no	—
357	C₂²×C₃×C₄	—	2	1	no	—
358	C₂²×C₃×C₄	—	2	1	no	—
359	C₂²×C₃×C₄	—	2	1	no	—
360	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₃×Q₁₆	—	2	2	no	—
363	C₃×SD₁₆	—	2	2	no	—
364	C₃×SD₁₆	—	2	2	no	—
365	C₃×SD₁₆	—	2	4	no	—
366	C₃×D₈	—	2	2	no	—
367	C₃×D₈	—	2	4	no	—
368	C₃×M₁₆	—	2	2	no	—
369	C₂×C₃×C₈	—	2	2	no	—
370	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	2	2	no	—
375	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
376	C₃×C₂²⋊C₄	—	2	2	no	—
377	C₃×C₂²⋊C₄	—	2	2	no	—
378	C₂³×C₅	—	2	8	no	—
379	C₂³×C₅	—	2	2	no	—
380	C₂³×C₅	—	2	1	no	—
381	C₂³×C₅	—	2	4	no	—
382	C₂³×C₅	—	2	1	no	—
383	C₂³×C₅	—	8	1	no	—
384	C₂³×C₅	—	8	1	no	—
385	C₂³×C₅	—	8	2	no	—
386	C₂³×C₅	—	8	2	no	—
387	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
388	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
389	C₅×Q₈	—	2	2	no	—
390	C₅×Q₈	—	2	1	no	—
391	C₅×Q₈	—	2	1	no	—
392	C₅×Q₈	—	2	1	no	—
393	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
394	C₅×D₄	—	2	8	no	—
395	C₅×D₄	—	2	8	no	—
396	C₅×D₄	—	2	4	no	—
397	C₅×D₄	—	2	4	no	—
398	C₅×D₄	—	2	2	no	—
399	C₅×D₄	—	2	4	no	—
400	C₅×D₄	—	2	2	no	—
401	C₅×D₄	—	2	1	no	—
402	C₅×D₄	—	2	1	no	—
403	C₅×D₄	—	2	1	no	—
404	C₅×D₄	—	4	2	no	—
405	C₅×D₄	—	8	2	no	—
406	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
407	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
408	C₂×C₄×C₅	—	2	8	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	4	no	—
411	C₂×C₄×C₅	—	2	2	no	—
412	C₂×C₄×C₅	—	2	2	no	—
413	C₂×C₄×C₅	—	2	2	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	4	2	no	—
416	C₂×C₄×C₅	—	8	1	no	—
417	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
418	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
419	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
420	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
421	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
422	C₅×C₈	—	2	1	no	—
423	C₅×C₈	—	2	1	no	—
424	C₅×C₈	—	2	2	no	—
425	H(5,𝔽₂)	—	2	4	no	—
426	H(5,𝔽₂)	—	2	4	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
429	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
432	C₂²×D₄	—	2	2	no	—
433	C₂²×D₄	—	2	1	no	—
434	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
435	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
436	AGL(1,ℤ/8)	—	2	4	no	—
437	#135	—	2	4	no	—
438	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
439	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
440	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
441	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
442	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
443	C₂×D₈	C₂²×C₃×C₅	1	2	yes	complemented
444	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
445	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
446	C₂²⋊Q₈	—	2	1	no	—
447	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
448	#121	—	2	1	no	—
449	#121	—	2	2	no	—
450	#121	C₂²×C₃×C₅	1	2	yes	complemented
451	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
452	#103	C₂²×C₃×C₅	1	2	yes	complemented
453	#102	C₂²×C₃×C₅	1	2	yes	complemented
454	#102	C₂²×C₃×C₅	1	2	yes	complemented
455	#102	C₂²×C₃×C₅	1	2	yes	complemented
456	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
457	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
458	C₂×C₃×C₅	—	2	2	no	—
459	C₂×C₃×C₅	—	4	2	no	—
460	C₂×C₃×C₅	—	4	4	no	—
461	C₂×C₃×C₅	—	4	2	no	—
462	C₂×C₃×C₅	—	8	1	no	—
463	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
464	C₂×C₃×C₅	#576	1	1	yes	characteristic
465	C₂×C₃×C₅	#577	1	1	yes	characteristic
466	C₂³×C₃	—	2	8	no	—
467	C₂³×C₃	—	2	2	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	4	no	—
470	C₂³×C₃	—	2	1	no	—
471	C₂³×C₃	—	8	1	no	—
472	C₂³×C₃	—	8	1	no	—
473	C₂³×C₃	—	8	2	no	—
474	C₂³×C₃	—	8	2	no	—
475	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
476	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
477	C₃×Q₈	—	2	2	no	—
478	C₃×Q₈	—	2	1	no	—
479	C₃×Q₈	—	2	1	no	—
480	C₃×Q₈	—	2	1	no	—
481	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
482	C₃×D₄	—	2	8	no	—
483	C₃×D₄	—	2	8	no	—
484	C₃×D₄	—	2	4	no	—
485	C₃×D₄	—	2	4	no	—
486	C₃×D₄	—	2	2	no	—
487	C₃×D₄	—	2	4	no	—
488	C₃×D₄	—	2	2	no	—
489	C₃×D₄	—	2	1	no	—
490	C₃×D₄	—	2	1	no	—
491	C₃×D₄	—	2	1	no	—
492	C₃×D₄	—	4	2	no	—
493	C₃×D₄	—	8	2	no	—
494	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
495	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
496	C₂×C₃×C₄	—	2	8	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	4	no	—
499	C₂×C₃×C₄	—	2	2	no	—
500	C₂×C₃×C₄	—	2	2	no	—
501	C₂×C₃×C₄	—	2	2	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	4	2	no	—
504	C₂×C₃×C₄	—	8	1	no	—
505	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
506	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
507	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
508	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
509	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
510	C₃×C₈	—	2	1	no	—
511	C₃×C₈	—	2	1	no	—
512	C₃×C₈	—	2	2	no	—
513	C₂²×C₅	—	2	1	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	2	no	—
516	C₂²×C₅	—	2	2	no	—
517	C₂²×C₅	—	2	2	no	—
518	C₂²×C₅	—	2	4	no	—
519	C₂²×C₅	—	2	2	no	—
520	C₂²×C₅	—	4	2	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	2	no	—
523	C₂²×C₅	—	4	1	no	—
524	C₂²×C₅	—	4	1	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	4	1	no	—
527	C₂²×C₅	—	8	4	no	—
528	C₂²×C₅	—	8	8	no	—
529	C₂²×C₅	C₃×#120	1	2	yes	—
530	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
531	C₄×C₅	—	2	2	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	4	2	no	—
534	C₄×C₅	—	4	1	no	—
535	C₄×C₅	C₃×#120	1	2	yes	—
536	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
537	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	1	no	—
540	#41	—	2	8	no	—
541	#41	—	2	4	no	—
542	#41	—	2	4	no	—
543	#41	—	2	2	no	—
544	#41	—	2	2	no	—
545	#41	—	2	2	no	—
546	#41	—	2	2	no	—
547	#41	—	2	2	no	—
548	#41	C₃×C₅×D₄	1	4	yes	complemented
549	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
550	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
552	C₂×D₄	—	2	16	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	4	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
564	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
565	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
566	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
567	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
568	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
574	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
575	Q₁₆	—	2	2	no	—
576	SD₁₆	—	2	2	no	—
577	SD₁₆	—	2	2	no	—
578	SD₁₆	—	2	4	no	—
579	D₈	—	2	2	no	—
580	D₈	—	2	4	no	—
581	M₁₆	—	2	2	no	—
582	C₂×C₈	—	2	2	no	—
583	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₃×C₅	#3012	1	1	yes	characteristic, direct product factor, Hall
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	2	no	—
595	C₂²×C₃	—	2	4	no	—
596	C₂²×C₃	—	2	2	no	—
597	C₂²×C₃	—	2	2	no	—
598	C₂²×C₃	—	2	2	no	—
599	C₂²×C₃	—	4	2	no	—
600	C₂²×C₃	—	4	1	no	—
601	C₂²×C₃	—	4	2	no	—
602	C₂²×C₃	—	4	1	no	—
603	C₂²×C₃	—	4	1	no	—
604	C₂²×C₃	—	4	1	no	—
605	C₂²×C₃	—	4	1	no	—
606	C₂²×C₃	—	8	4	no	—
607	C₂²×C₃	—	8	8	no	—
608	C₂²×C₃	C₅×#120	1	2	yes	—
609	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
610	C₃×C₄	—	2	2	no	—
611	C₃×C₄	—	2	2	no	—
612	C₃×C₄	—	4	1	no	—
613	C₃×C₄	—	4	2	no	—
614	C₃×C₄	C₅×#120	1	2	yes	—
615	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
616	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
617	C₂×C₅	—	2	2	no	—
618	C₂×C₅	—	4	2	no	—
619	C₂×C₅	—	4	4	no	—
620	C₂×C₅	—	4	2	no	—
621	C₂×C₅	—	8	1	no	—
622	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
623	C₂×C₅	C₃×#576	1	1	yes	characteristic
624	C₂×C₅	C₃×#577	1	1	yes	characteristic
625	C₂³	—	2	8	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	8	1	no	—
631	C₂³	—	8	1	no	—
632	C₂³	—	8	2	no	—
633	C₂³	—	8	2	no	—
634	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
635	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
636	Q₈	—	2	2	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	2	1	no	—
639	Q₈	—	2	1	no	—
640	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
641	D₄	—	2	8	no	—
642	D₄	—	2	8	no	—
643	D₄	—	2	4	no	—
644	D₄	—	2	4	no	—
645	D₄	—	2	2	no	—
646	D₄	—	2	4	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	1	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	4	2	no	—
652	D₄	—	8	2	no	—
653	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
654	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
665	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
666	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
667	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
668	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
669	C₈	—	2	1	no	—
670	C₈	—	2	1	no	—
671	C₈	—	2	2	no	—
672	C₂×C₃	—	2	2	no	—
673	C₂×C₃	—	4	2	no	—
674	C₂×C₃	—	4	4	no	—
675	C₂×C₃	—	4	2	no	—
676	C₂×C₃	—	8	1	no	—
677	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
678	C₂×C₃	C₅×#576	1	1	yes	characteristic
679	C₂×C₃	C₅×#577	1	1	yes	characteristic
680	C₅	C₃×#3012	1	1	yes	characteristic, direct product factor, Sylow
681	C₂²	—	2	1	no	—
682	C₂²	—	2	1	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	4	2	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	8	4	no	—
696	C₂²	—	8	8	no	—
697	C₂²	C₃×C₅×#120	1	2	yes	—
698	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
699	C₄	—	2	2	no	—
700	C₄	—	2	2	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	2	no	—
703	C₄	C₃×C₅×#120	1	2	yes	—
704	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
705	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
706	C₃	C₅×#3012	1	1	yes	characteristic, direct product factor, Sylow
707	C₂	—	2	2	no	—
708	C₂	—	4	2	no	—
709	C₂	—	4	4	no	—
710	C₂	—	4	2	no	—
711	C₂	—	8	1	no	—
712	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
713	C₂	C₃×C₅×#576	1	1	yes	characteristic
714	C₂	C₃×C₅×#577	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 ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₃×C₅×#135	C₂	semidirect
4. C₃×C₅×#537	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₃×C₅×#450	C₂	semidirect
7. C₃×C₅×#449	C₂	semidirect
8. C₃×C₅×#447	C₂	semidirect
9. C₃×C₅×#417	C₂	semidirect
10. C₂×C₃×C₅×#102	C₂	semidirect
11. C₃×C₅×#408	C₂	semidirect
12. C₅×#3012	C₃	direct (N × H)
19. C₂×C₃×C₅×#41	C₂²	semidirect
26. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
27. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
28. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
29. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
30. C₂×C₃×C₅×D₈	C₂²	semidirect
31. C₂×C₃×C₅×D₈	C₂²	semidirect
32. C₂×C₃×C₅×M₁₆	C₂²	semidirect
33. C₂²×C₃×C₅×C₈	C₂²	semidirect
35. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
38. C₃×C₅×#121	C₂²	semidirect
39. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
40. C₃×C₅×#103	C₂²	semidirect
41. C₃×C₅×#102	C₂²	semidirect
42. C₃×C₅×#102	C₂²	semidirect
43. C₃×C₅×#102	C₂²	semidirect
44. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
45. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
46. C₃×#3012	C₅	direct (N × H)
47. C₂×C₅×H(5,𝔽₂)	C₂×C₃	semidirect
48. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
49. C₂×C₅×#135	C₂×C₃	semidirect
50. C₅×#537	C₂×C₃	semidirect
51. C₅×#452	C₂×C₃	semidirect
52. C₅×#450	C₂×C₃	semidirect
53. C₅×#449	C₂×C₃	semidirect
54. C₅×#447	C₂×C₃	semidirect
55. C₅×#417	C₂×C₃	semidirect
56. C₂×C₅×#102	C₂×C₃	semidirect
57. C₅×#408	C₂×C₃	semidirect
68. C₃×C₅×#41	D₄	semidirect
85. C₂×C₃×C₅×D₄	D₄	semidirect
111. C₂×C₃×H(5,𝔽₂)	C₂×C₅	semidirect
112. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
113. C₂×C₃×#135	C₂×C₅	semidirect
114. C₃×#537	C₂×C₅	semidirect
115. C₃×#452	C₂×C₅	semidirect
116. C₃×#450	C₂×C₅	semidirect
117. C₃×#449	C₂×C₅	semidirect
118. C₃×#447	C₂×C₅	semidirect
119. C₃×#417	C₂×C₅	semidirect
120. C₂×C₃×#102	C₂×C₅	semidirect
121. C₃×#408	C₂×C₅	semidirect
128. C₂×C₅×#41	C₂²×C₃	semidirect
135. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
136. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
137. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
138. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
139. C₂×C₅×D₈	C₂²×C₃	semidirect
140. C₂×C₅×D₈	C₂²×C₃	semidirect
141. C₂×C₅×M₁₆	C₂²×C₃	semidirect
142. C₂²×C₅×C₈	C₂²×C₃	semidirect
144. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
147. C₅×#121	C₂²×C₃	semidirect
148. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
149. C₅×#103	C₂²×C₃	semidirect
150. C₅×#102	C₂²×C₃	semidirect
151. C₅×#102	C₂²×C₃	semidirect
152. C₅×#102	C₂²×C₃	semidirect
153. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
154. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
155. #3012	C₃×C₅	direct (N × H)
209. C₂×C₃×#41	C₂²×C₅	semidirect
216. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
217. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
218. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
219. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
220. C₂×C₃×D₈	C₂²×C₅	semidirect
221. C₂×C₃×D₈	C₂²×C₅	semidirect
222. C₂×C₃×M₁₆	C₂²×C₅	semidirect
223. C₂²×C₃×C₈	C₂²×C₅	semidirect
225. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
228. C₃×#121	C₂²×C₅	semidirect
229. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
230. C₃×#103	C₂²×C₅	semidirect
231. C₃×#102	C₂²×C₅	semidirect
232. C₃×#102	C₂²×C₅	semidirect
233. C₃×#102	C₂²×C₅	semidirect
234. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
235. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
246. C₅×#41	C₃×D₄	semidirect
263. C₂×C₅×D₄	C₃×D₄	semidirect
289. C₂×H(5,𝔽₂)	C₂×C₃×C₅	semidirect
290. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
291. C₂×#135	C₂×C₃×C₅	semidirect
292. #537	C₂×C₃×C₅	semidirect
293. #452	C₂×C₃×C₅	semidirect
294. #450	C₂×C₃×C₅	semidirect
295. #449	C₂×C₃×C₅	semidirect
296. #447	C₂×C₃×C₅	semidirect
297. #417	C₂×C₃×C₅	semidirect
298. C₂×#102	C₂×C₃×C₅	semidirect
299. #408	C₂×C₃×C₅	semidirect
335. C₃×#41	C₅×D₄	semidirect
352. C₂×C₃×D₄	C₅×D₄	semidirect
431. C₂×#41	C₂²×C₃×C₅	semidirect
438. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
439. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
440. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
441. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
442. C₂×D₈	C₂²×C₃×C₅	semidirect
443. C₂×D₈	C₂²×C₃×C₅	semidirect
444. C₂×M₁₆	C₂²×C₃×C₅	semidirect
445. C₂²×C₈	C₂²×C₃×C₅	semidirect
447. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
450. #121	C₂²×C₃×C₅	semidirect
451. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
452. #103	C₂²×C₃×C₅	semidirect
453. #102	C₂²×C₃×C₅	semidirect
454. #102	C₂²×C₃×C₅	semidirect
455. #102	C₂²×C₃×C₅	semidirect
456. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
457. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
548. #41	C₃×C₅×D₄	semidirect
565. C₂×D₄	C₃×C₅×D₄	semidirect
591. C₃×C₅	#3012	direct (N × H)
680. C₅	C₃×#3012	direct (N × H)
706. C₃	C₅×#3012	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×H(5,𝔽₂)	2
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#135	2
C₃×C₅×#537	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#417	2
C₂×C₃×C₅×#102	2
C₃×C₅×#408	2
C₅×#3012	3
C₃×#3012	5

Subgroups — C3×C5×#3012 #14276046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3012 #14276046