Subgroups — C₃×C₅×#3056 #14276090

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	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
4	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#467	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×#419	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3056	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#137	—	2	4	no	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×M₁₆	—	2	4	no	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
24	C₃×C₅×#123	—	2	1	no	—
25	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
26	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×#121	C₂²	1	1	yes	characteristic
32	C₃×C₅×#121	C₂²	1	1	yes	characteristic
33	C₃×C₅×#120	—	2	1	no	—
34	C₃×C₄×C₅×D₄	—	2	1	no	—
35	C₃×C₄×C₅×D₄	—	2	1	no	—
36	C₃×C₅×#117	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
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×#103	C₂²	1	2	yes	complemented
44	C₃×C₅×#103	C₂²	1	2	yes	complemented
45	C₃×C₅×#102	C₂²	1	2	yes	complemented
46	C₃×#3056	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₂×C₅×#137	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
50	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#470	C₂×C₃	1	2	yes	complemented
52	C₅×#468	C₂×C₃	1	2	yes	complemented
53	C₅×#467	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×#419	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	—	2	1	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	—	2	2	no	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	—	2	1	no	—
67	C₂×C₃×C₅×D₄	—	2	1	no	—
68	C₂×C₃×C₅×D₄	—	2	1	no	—
69	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	2	2	no	—
71	C₂²×C₃×C₄×C₅	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	1	no	—
74	C₂²×C₃×C₄×C₅	—	2	1	no	—
75	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
77	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₅×Q₁₆	—	2	4	no	—
82	C₃×C₅×SD₁₆	—	2	4	no	—
83	C₃×C₅×M₁₆	—	2	2	no	—
84	C₃×C₅×M₁₆	—	2	4	no	—
85	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
86	C₂×C₃×C₅×C₈	—	2	4	no	—
87	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
88	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	—	2	1	no	—
92	C₃×C₅×C₄⋊C₄	—	2	1	no	—
93	C₃×C₅×C₄⋊C₄	—	2	1	no	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
95	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
99	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
104	C₃×C₄²×C₅	—	2	1	no	—
105	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
107	C₃×#525	C₂×C₅	1	1	yes	characteristic
108	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
109	C₃×#470	C₂×C₅	1	2	yes	complemented
110	C₃×#468	C₂×C₅	1	2	yes	complemented
111	C₃×#467	C₂×C₅	1	2	yes	complemented
112	C₃×#465	C₂×C₅	1	2	yes	complemented
113	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
119	C₅×#137	—	2	4	no	—
120	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
121	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
122	C₂×C₅×M₁₆	—	2	4	no	—
123	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
125	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
127	C₅×#123	—	2	1	no	—
128	C₅×C₂²⋊Q₈	—	2	1	no	—
129	C₅×C₂²⋊Q₈	—	2	1	no	—
130	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
131	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
133	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
134	C₅×#121	C₂²×C₃	1	1	yes	characteristic
135	C₅×#121	C₂²×C₃	1	1	yes	characteristic
136	C₅×#120	—	2	1	no	—
137	C₄×C₅×D₄	—	2	1	no	—
138	C₄×C₅×D₄	—	2	1	no	—
139	C₅×#117	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₄⋊C₄	—	2	1	no	—
141	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
143	C₅×#107	C₂²×C₃	1	2	yes	complemented
144	C₅×#106	C₂²×C₃	1	2	yes	complemented
145	C₅×#103	C₂²×C₃	1	2	yes	complemented
146	C₅×#103	C₂²×C₃	1	2	yes	complemented
147	C₅×#103	C₂²×C₃	1	2	yes	complemented
148	C₅×#102	C₂²×C₃	1	2	yes	complemented
149	#3056	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
150	C₂³×C₃×C₅	—	2	2	no	—
151	C₂³×C₃×C₅	—	2	2	no	—
152	C₂³×C₃×C₅	—	2	1	no	—
153	C₂³×C₃×C₅	—	4	1	no	—
154	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
157	C₃×C₅×Q₈	—	2	2	no	—
158	C₃×C₅×Q₈	—	2	1	no	—
159	C₃×C₅×Q₈	—	2	2	no	—
160	C₃×C₅×Q₈	—	2	1	no	—
161	C₃×C₅×Q₈	—	4	2	no	—
162	C₃×C₅×D₄	—	2	1	no	—
163	C₃×C₅×D₄	—	2	1	no	—
164	C₃×C₅×D₄	—	4	2	no	—
165	C₃×C₅×D₄	—	4	2	no	—
166	C₃×C₅×D₄	—	4	2	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	2	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	2	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	2	no	—
179	C₂×C₃×C₄×C₅	—	4	2	no	—
180	C₂×C₃×C₄×C₅	—	4	2	no	—
181	C₂×C₃×C₄×C₅	—	4	2	no	—
182	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
183	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
184	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
185	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
186	C₂×C₃×C₄×C₅	#41	1	2	yes	—
187	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
188	C₃×C₅×C₈	—	2	2	no	—
189	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
190	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
191	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
192	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
193	C₃×#137	—	2	4	no	—
194	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
195	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
196	C₂×C₃×M₁₆	—	2	4	no	—
197	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
198	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
199	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
201	C₃×#123	—	2	1	no	—
202	C₃×C₂²⋊Q₈	—	2	1	no	—
203	C₃×C₂²⋊Q₈	—	2	1	no	—
204	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
205	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
206	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
207	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
208	C₃×#121	C₂²×C₅	1	1	yes	characteristic
209	C₃×#121	C₂²×C₅	1	1	yes	characteristic
210	C₃×#120	—	2	1	no	—
211	C₃×C₄×D₄	—	2	1	no	—
212	C₃×C₄×D₄	—	2	1	no	—
213	C₃×#117	C₂²×C₅	1	1	yes	characteristic
214	C₂×C₃×C₄⋊C₄	—	2	1	no	—
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
217	C₃×#107	C₂²×C₅	1	2	yes	complemented
218	C₃×#106	C₂²×C₅	1	2	yes	complemented
219	C₃×#103	C₂²×C₅	1	2	yes	complemented
220	C₃×#103	C₂²×C₅	1	2	yes	complemented
221	C₃×#103	C₂²×C₅	1	2	yes	complemented
222	C₃×#102	C₂²×C₅	1	2	yes	complemented
223	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
224	C₅×#41	—	2	2	no	—
225	C₅×#41	—	2	2	no	—
226	C₂×C₅×Q₈	—	2	1	no	—
227	C₂×C₅×Q₈	—	2	2	no	—
228	C₂×C₅×Q₈	—	2	2	no	—
229	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
230	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₅×D₄	—	2	1	no	—
232	C₂×C₅×D₄	—	2	1	no	—
233	C₂×C₅×D₄	—	2	1	no	—
234	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₄×C₅	—	2	2	no	—
236	C₂²×C₄×C₅	—	2	2	no	—
237	C₂²×C₄×C₅	—	2	1	no	—
238	C₂²×C₄×C₅	—	2	1	no	—
239	C₂²×C₄×C₅	—	2	1	no	—
240	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
246	C₅×Q₁₆	—	2	4	no	—
247	C₅×SD₁₆	—	2	4	no	—
248	C₅×M₁₆	—	2	2	no	—
249	C₅×M₁₆	—	2	4	no	—
250	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
251	C₂×C₅×C₈	—	2	4	no	—
252	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
253	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
254	C₅×C₄⋊C₄	—	2	2	no	—
255	C₅×C₄⋊C₄	—	2	2	no	—
256	C₅×C₄⋊C₄	—	2	1	no	—
257	C₅×C₄⋊C₄	—	2	1	no	—
258	C₅×C₄⋊C₄	—	2	1	no	—
259	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
260	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
261	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	2	no	—
264	C₅×C₂²⋊C₄	—	2	1	no	—
265	C₅×C₂²⋊C₄	—	2	1	no	—
266	C₅×C₂²⋊C₄	—	2	1	no	—
267	C₅×C₂²⋊C₄	—	2	1	no	—
268	C₅×C₂²⋊C₄	—	2	1	no	—
269	C₄²×C₅	—	2	1	no	—
270	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
271	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
272	#525	C₂×C₃×C₅	1	1	yes	characteristic
273	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
274	#470	C₂×C₃×C₅	1	2	yes	complemented
275	#468	C₂×C₃×C₅	1	2	yes	complemented
276	#467	C₂×C₃×C₅	1	2	yes	complemented
277	#465	C₂×C₃×C₅	1	2	yes	complemented
278	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
279	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
280	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
281	C₂²×C₃×C₅	—	2	1	no	—
282	C₂²×C₃×C₅	—	2	1	no	—
283	C₂²×C₃×C₅	—	2	1	no	—
284	C₂²×C₃×C₅	—	2	1	no	—
285	C₂²×C₃×C₅	—	2	1	no	—
286	C₂²×C₃×C₅	—	2	1	no	—
287	C₂²×C₃×C₅	—	2	1	no	—
288	C₂²×C₃×C₅	—	4	4	no	—
289	C₂²×C₃×C₅	—	4	1	no	—
290	C₂²×C₃×C₅	—	4	1	no	—
291	C₂²×C₃×C₅	—	4	1	no	—
292	C₂²×C₃×C₅	#121	1	2	yes	—
293	C₂²×C₃×C₅	#137	1	2	yes	complemented
294	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
295	C₃×C₄×C₅	—	2	1	no	—
296	C₃×C₄×C₅	—	2	1	no	—
297	C₃×C₄×C₅	—	4	1	no	—
298	C₃×C₄×C₅	—	4	2	no	—
299	C₃×C₄×C₅	—	4	1	no	—
300	C₃×C₄×C₅	—	4	2	no	—
301	C₃×C₄×C₅	—	4	1	no	—
302	C₃×C₄×C₅	#121	1	2	yes	—
303	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
304	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
305	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
306	C₃×#41	—	2	2	no	—
307	C₃×#41	—	2	2	no	—
308	C₂×C₃×Q₈	—	2	1	no	—
309	C₂×C₃×Q₈	—	2	2	no	—
310	C₂×C₃×Q₈	—	2	2	no	—
311	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
312	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
313	C₂×C₃×D₄	—	2	1	no	—
314	C₂×C₃×D₄	—	2	1	no	—
315	C₂×C₃×D₄	—	2	1	no	—
316	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
317	C₂²×C₃×C₄	—	2	2	no	—
318	C₂²×C₃×C₄	—	2	2	no	—
319	C₂²×C₃×C₄	—	2	1	no	—
320	C₂²×C₃×C₄	—	2	1	no	—
321	C₂²×C₃×C₄	—	2	1	no	—
322	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
323	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
324	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
325	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
326	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
328	C₃×Q₁₆	—	2	4	no	—
329	C₃×SD₁₆	—	2	4	no	—
330	C₃×M₁₆	—	2	2	no	—
331	C₃×M₁₆	—	2	4	no	—
332	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
333	C₂×C₃×C₈	—	2	4	no	—
334	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
335	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
336	C₃×C₄⋊C₄	—	2	2	no	—
337	C₃×C₄⋊C₄	—	2	2	no	—
338	C₃×C₄⋊C₄	—	2	1	no	—
339	C₃×C₄⋊C₄	—	2	1	no	—
340	C₃×C₄⋊C₄	—	2	1	no	—
341	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
342	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
343	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
344	C₃×C₂²⋊C₄	—	2	2	no	—
345	C₃×C₂²⋊C₄	—	2	2	no	—
346	C₃×C₂²⋊C₄	—	2	1	no	—
347	C₃×C₂²⋊C₄	—	2	1	no	—
348	C₃×C₂²⋊C₄	—	2	1	no	—
349	C₃×C₂²⋊C₄	—	2	1	no	—
350	C₃×C₂²⋊C₄	—	2	1	no	—
351	C₃×C₄²	—	2	1	no	—
352	C₂³×C₅	—	2	2	no	—
353	C₂³×C₅	—	2	2	no	—
354	C₂³×C₅	—	2	1	no	—
355	C₂³×C₅	—	4	1	no	—
356	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
357	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
359	C₅×Q₈	—	2	2	no	—
360	C₅×Q₈	—	2	1	no	—
361	C₅×Q₈	—	2	2	no	—
362	C₅×Q₈	—	2	1	no	—
363	C₅×Q₈	—	4	2	no	—
364	C₅×D₄	—	2	1	no	—
365	C₅×D₄	—	2	1	no	—
366	C₅×D₄	—	4	2	no	—
367	C₅×D₄	—	4	2	no	—
368	C₅×D₄	—	4	2	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	2	no	—
371	C₂×C₄×C₅	—	2	2	no	—
372	C₂×C₄×C₅	—	2	1	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	4	2	no	—
382	C₂×C₄×C₅	—	4	2	no	—
383	C₂×C₄×C₅	—	4	2	no	—
384	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
385	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
386	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
388	C₂×C₄×C₅	C₃×#41	1	2	yes	—
389	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
390	C₅×C₈	—	2	2	no	—
391	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
392	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
393	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
395	#137	—	2	4	no	—
396	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
397	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
398	C₂×M₁₆	—	2	4	no	—
399	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
400	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
401	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
402	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
403	#123	—	2	1	no	—
404	C₂²⋊Q₈	—	2	1	no	—
405	C₂²⋊Q₈	—	2	1	no	—
406	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
407	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
408	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
409	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
410	#121	C₂²×C₃×C₅	1	1	yes	characteristic
411	#121	C₂²×C₃×C₅	1	1	yes	characteristic
412	#120	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	1	no	—
415	#117	C₂²×C₃×C₅	1	1	yes	characteristic
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	#107	C₂²×C₃×C₅	1	2	yes	complemented
420	#106	C₂²×C₃×C₅	1	2	yes	complemented
421	#103	C₂²×C₃×C₅	1	2	yes	complemented
422	#103	C₂²×C₃×C₅	1	2	yes	complemented
423	#103	C₂²×C₃×C₅	1	2	yes	complemented
424	#102	C₂²×C₃×C₅	1	2	yes	complemented
425	C₂×C₃×C₅	—	2	2	no	—
426	C₂×C₃×C₅	—	2	2	no	—
427	C₂×C₃×C₅	—	4	1	no	—
428	C₂×C₃×C₅	—	8	1	no	—
429	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
430	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
431	C₂×C₃×C₅	#575	1	1	yes	characteristic
432	C₂³×C₃	—	2	2	no	—
433	C₂³×C₃	—	2	2	no	—
434	C₂³×C₃	—	2	1	no	—
435	C₂³×C₃	—	4	1	no	—
436	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
439	C₃×Q₈	—	2	2	no	—
440	C₃×Q₈	—	2	1	no	—
441	C₃×Q₈	—	2	2	no	—
442	C₃×Q₈	—	2	1	no	—
443	C₃×Q₈	—	4	2	no	—
444	C₃×D₄	—	2	1	no	—
445	C₃×D₄	—	2	1	no	—
446	C₃×D₄	—	4	2	no	—
447	C₃×D₄	—	4	2	no	—
448	C₃×D₄	—	4	2	no	—
449	C₂×C₃×C₄	—	2	2	no	—
450	C₂×C₃×C₄	—	2	2	no	—
451	C₂×C₃×C₄	—	2	2	no	—
452	C₂×C₃×C₄	—	2	1	no	—
453	C₂×C₃×C₄	—	2	1	no	—
454	C₂×C₃×C₄	—	2	1	no	—
455	C₂×C₃×C₄	—	2	1	no	—
456	C₂×C₃×C₄	—	2	1	no	—
457	C₂×C₃×C₄	—	2	1	no	—
458	C₂×C₃×C₄	—	2	2	no	—
459	C₂×C₃×C₄	—	2	1	no	—
460	C₂×C₃×C₄	—	2	2	no	—
461	C₂×C₃×C₄	—	4	2	no	—
462	C₂×C₃×C₄	—	4	2	no	—
463	C₂×C₃×C₄	—	4	2	no	—
464	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
468	C₂×C₃×C₄	C₅×#41	1	2	yes	—
469	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
470	C₃×C₈	—	2	2	no	—
471	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
472	C₂²×C₅	—	2	1	no	—
473	C₂²×C₅	—	2	1	no	—
474	C₂²×C₅	—	2	1	no	—
475	C₂²×C₅	—	2	1	no	—
476	C₂²×C₅	—	2	1	no	—
477	C₂²×C₅	—	2	1	no	—
478	C₂²×C₅	—	2	1	no	—
479	C₂²×C₅	—	4	4	no	—
480	C₂²×C₅	—	4	1	no	—
481	C₂²×C₅	—	4	1	no	—
482	C₂²×C₅	—	4	1	no	—
483	C₂²×C₅	C₃×#121	1	2	yes	—
484	C₂²×C₅	C₃×#137	1	2	yes	complemented
485	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
486	C₄×C₅	—	2	1	no	—
487	C₄×C₅	—	2	1	no	—
488	C₄×C₅	—	4	1	no	—
489	C₄×C₅	—	4	2	no	—
490	C₄×C₅	—	4	1	no	—
491	C₄×C₅	—	4	1	no	—
492	C₄×C₅	—	4	2	no	—
493	C₄×C₅	C₃×#121	1	2	yes	—
494	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
495	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
496	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
503	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
517	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
518	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
519	Q₁₆	—	2	4	no	—
520	SD₁₆	—	2	4	no	—
521	M₁₆	—	2	2	no	—
522	M₁₆	—	2	4	no	—
523	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
524	C₂×C₈	—	2	4	no	—
525	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
526	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
533	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
534	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
535	C₂²⋊C₄	—	2	2	no	—
536	C₂²⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₃×C₅	#3056	1	1	yes	characteristic, direct product factor, Hall
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	2	1	no	—
546	C₂²×C₃	—	2	1	no	—
547	C₂²×C₃	—	2	1	no	—
548	C₂²×C₃	—	2	1	no	—
549	C₂²×C₃	—	2	1	no	—
550	C₂²×C₃	—	2	1	no	—
551	C₂²×C₃	—	4	4	no	—
552	C₂²×C₃	—	4	1	no	—
553	C₂²×C₃	—	4	1	no	—
554	C₂²×C₃	—	4	1	no	—
555	C₂²×C₃	C₅×#121	1	2	yes	—
556	C₂²×C₃	C₅×#137	1	2	yes	complemented
557	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	4	1	no	—
561	C₃×C₄	—	4	2	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	—	4	2	no	—
564	C₃×C₄	—	4	1	no	—
565	C₃×C₄	C₅×#121	1	2	yes	—
566	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
567	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
568	C₂×C₅	—	2	2	no	—
569	C₂×C₅	—	2	2	no	—
570	C₂×C₅	—	4	1	no	—
571	C₂×C₅	—	8	1	no	—
572	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
573	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
574	C₂×C₅	C₃×#575	1	1	yes	characteristic
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
580	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
581	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
582	Q₈	—	2	2	no	—
583	Q₈	—	2	1	no	—
584	Q₈	—	2	2	no	—
585	Q₈	—	2	1	no	—
586	Q₈	—	4	2	no	—
587	D₄	—	2	1	no	—
588	D₄	—	2	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
608	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
609	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
610	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
611	C₂×C₄	C₃×C₅×#41	1	2	yes	—
612	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
613	C₈	—	2	2	no	—
614	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
615	C₂×C₃	—	2	2	no	—
616	C₂×C₃	—	2	2	no	—
617	C₂×C₃	—	4	1	no	—
618	C₂×C₃	—	8	1	no	—
619	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
620	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
621	C₂×C₃	C₅×#575	1	1	yes	characteristic
622	C₅	C₃×#3056	1	1	yes	characteristic, direct product factor, Sylow
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	C₃×C₅×#121	1	2	yes	—
635	C₂²	C₃×C₅×#137	1	2	yes	complemented
636	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	C₃×C₅×#121	1	2	yes	—
645	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
646	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
647	C₃	C₅×#3056	1	1	yes	characteristic, direct product factor, Sylow
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	4	1	no	—
651	C₂	—	8	1	no	—
652	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
653	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
654	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
prime radical	C₃×C₅×#525	C₂
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×#137	C₂	semidirect
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
4. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₅×#470	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#467	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#428	C₂	semidirect
10. C₃×C₅×#419	C₂	semidirect
11. C₃×C₅×#417	C₂	semidirect
12. C₅×#3056	C₃	direct (N × H)
17. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
40. C₃×C₅×#107	C₂²	semidirect
41. C₃×C₅×#106	C₂²	semidirect
42. C₃×C₅×#103	C₂²	semidirect
43. C₃×C₅×#103	C₂²	semidirect
44. C₃×C₅×#103	C₂²	semidirect
45. C₃×C₅×#102	C₂²	semidirect
46. C₃×#3056	C₅	direct (N × H)
47. C₂×C₅×#137	C₂×C₃	semidirect
48. C₂²×C₅×M₁₆	C₂×C₃	semidirect
50. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
51. C₅×#470	C₂×C₃	semidirect
52. C₅×#468	C₂×C₃	semidirect
53. C₅×#467	C₂×C₃	semidirect
54. C₅×#465	C₂×C₃	semidirect
55. C₅×#428	C₂×C₃	semidirect
56. C₅×#419	C₂×C₃	semidirect
57. C₅×#417	C₂×C₃	semidirect
85. C₃×C₅×M₁₆	D₄	semidirect
105. C₂×C₃×#137	C₂×C₅	semidirect
106. C₂²×C₃×M₁₆	C₂×C₅	semidirect
108. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
109. C₃×#470	C₂×C₅	semidirect
110. C₃×#468	C₂×C₅	semidirect
111. C₃×#467	C₂×C₅	semidirect
112. C₃×#465	C₂×C₅	semidirect
113. C₃×#428	C₂×C₅	semidirect
114. C₃×#419	C₂×C₅	semidirect
115. C₃×#417	C₂×C₅	semidirect
120. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
121. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
143. C₅×#107	C₂²×C₃	semidirect
144. C₅×#106	C₂²×C₃	semidirect
145. C₅×#103	C₂²×C₃	semidirect
146. C₅×#103	C₂²×C₃	semidirect
147. C₅×#103	C₂²×C₃	semidirect
148. C₅×#102	C₂²×C₃	semidirect
149. #3056	C₃×C₅	direct (N × H)
194. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
195. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
217. C₃×#107	C₂²×C₅	semidirect
218. C₃×#106	C₂²×C₅	semidirect
219. C₃×#103	C₂²×C₅	semidirect
220. C₃×#103	C₂²×C₅	semidirect
221. C₃×#103	C₂²×C₅	semidirect
222. C₃×#102	C₂²×C₅	semidirect
250. C₅×M₁₆	C₃×D₄	semidirect
270. C₂×#137	C₂×C₃×C₅	semidirect
271. C₂²×M₁₆	C₂×C₃×C₅	semidirect
273. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
274. #470	C₂×C₃×C₅	semidirect
275. #468	C₂×C₃×C₅	semidirect
276. #467	C₂×C₃×C₅	semidirect
277. #465	C₂×C₃×C₅	semidirect
278. #428	C₂×C₃×C₅	semidirect
279. #419	C₂×C₃×C₅	semidirect
280. #417	C₂×C₃×C₅	semidirect
293. C₂²×C₃×C₅	#137	semidirect
332. C₃×M₁₆	C₅×D₄	semidirect
396. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
397. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
419. #107	C₂²×C₃×C₅	semidirect
420. #106	C₂²×C₃×C₅	semidirect
421. #103	C₂²×C₃×C₅	semidirect
422. #103	C₂²×C₃×C₅	semidirect
423. #103	C₂²×C₃×C₅	semidirect
424. #102	C₂²×C₃×C₅	semidirect
484. C₂²×C₅	C₃×#137	semidirect
523. M₁₆	C₃×C₅×D₄	semidirect
543. C₃×C₅	#3056	direct (N × H)
556. C₂²×C₃	C₅×#137	semidirect
622. C₅	C₃×#3056	direct (N × H)
635. C₂²	C₃×C₅×#137	semidirect
647. C₃	C₅×#3056	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×#137	2
C₂²×C₃×C₅×M₁₆	2
C₃×C₅×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#428	2
C₃×C₅×#419	2
C₃×C₅×#417	2
C₅×#3056	3
C₃×#3056	5

Subgroups — C3×C5×#3056 #14276090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3056 #14276090