Subgroups — C₃×C₅×#3117 #14276151

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#441	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#440	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3117	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₃×C₅×#126	—	2	1	no	—
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	1	yes	characteristic
19	C₃×C₅×#123	—	2	1	no	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×#121	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×Q₈	—	2	1	no	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	—	2	1	no	—
30	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	—	2	1	no	—
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#107	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	2	yes	—
36	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₃×C₅×#97	C₂²	1	2	yes	—
44	C₃×#3117	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#529	C₂×C₃	1	1	yes	characteristic
46	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#481	C₂×C₃	1	1	yes	characteristic
49	C₅×#479	C₂×C₃	1	2	yes	complemented
50	C₅×#464	C₂×C₃	1	2	yes	complemented
51	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#448	C₂×C₃	1	1	yes	characteristic
53	C₅×#441	C₂×C₃	1	2	yes	complemented
54	C₅×#440	C₂×C₃	1	2	yes	complemented
55	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×Q₈	—	2	4	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×Q₁₆	—	2	4	no	—
69	C₃×C₅×SD₁₆	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₃×C₄²×C₅	—	2	2	no	—
88	C₃×C₄²×C₅	—	2	2	no	—
89	C₃×C₄²×C₅	—	2	1	no	—
90	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×#529	C₂×C₅	1	1	yes	characteristic
95	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#481	C₂×C₅	1	1	yes	characteristic
98	C₃×#479	C₂×C₅	1	2	yes	complemented
99	C₃×#464	C₂×C₅	1	2	yes	complemented
100	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#448	C₂×C₅	1	1	yes	characteristic
102	C₃×#441	C₂×C₅	1	2	yes	complemented
103	C₃×#440	C₂×C₅	1	2	yes	complemented
104	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
107	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
108	C₅×#126	—	2	1	no	—
109	C₅×#125	C₂²×C₃	1	1	yes	characteristic
110	C₅×#124	C₂²×C₃	1	1	yes	characteristic
111	C₅×#123	—	2	1	no	—
112	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₅×#121	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×Q₈	—	2	1	no	—
115	C₄×C₅×Q₈	—	2	1	no	—
116	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
117	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
119	C₄×C₅×D₄	—	2	1	no	—
120	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
121	C₅×#117	—	2	1	no	—
122	C₂×C₅×C₄⋊C₄	—	2	1	no	—
123	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄²×C₅	—	2	1	no	—
125	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
126	C₅×#107	C₂²×C₃	1	2	yes	—
127	C₅×#106	C₂²×C₃	1	2	yes	—
128	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
129	C₅×#103	C₂²×C₃	1	2	yes	—
130	C₅×#103	C₂²×C₃	1	2	yes	—
131	C₅×#103	C₂²×C₃	1	2	yes	—
132	C₅×#102	C₂²×C₃	1	2	yes	—
133	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
135	C₅×#97	C₂²×C₃	1	2	yes	—
136	#3117	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	4	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	#41	1	4	yes	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	4	2	no	—
145	C₂×C₃×C₄×C₅	—	2	4	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₃×C₅×C₈	—	2	2	no	—
163	C₃×C₅×C₈	—	2	2	no	—
164	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
166	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
167	C₃×#126	—	2	1	no	—
168	C₃×#125	C₂²×C₅	1	1	yes	characteristic
169	C₃×#124	C₂²×C₅	1	1	yes	characteristic
170	C₃×#123	—	2	1	no	—
171	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
172	C₃×#121	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×C₄×Q₈	—	2	1	no	—
175	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
176	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
178	C₃×C₄×D₄	—	2	1	no	—
179	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₃×#117	—	2	1	no	—
181	C₂×C₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×C₄²	—	2	1	no	—
184	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
185	C₃×#107	C₂²×C₅	1	2	yes	—
186	C₃×#106	C₂²×C₅	1	2	yes	—
187	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
188	C₃×#103	C₂²×C₅	1	2	yes	—
189	C₃×#103	C₂²×C₅	1	2	yes	—
190	C₃×#103	C₂²×C₅	1	2	yes	—
191	C₃×#102	C₂²×C₅	1	2	yes	—
192	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
193	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
194	C₃×#97	C₂²×C₅	1	2	yes	—
195	C₂×C₅×Q₈	—	2	4	no	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₄×C₅	—	2	1	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	2	4	no	—
208	C₅×SD₁₆	—	2	4	no	—
209	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
210	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
211	C₅×C₄⋊C₄	—	2	2	no	—
212	C₅×C₄⋊C₄	—	2	2	no	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
219	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₂²⋊C₄	—	2	1	no	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	1	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₄²×C₅	—	2	2	no	—
227	C₄²×C₅	—	2	2	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
230	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
231	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
232	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
233	#529	C₂×C₃×C₅	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#481	C₂×C₃×C₅	1	1	yes	characteristic
237	#479	C₂×C₃×C₅	1	2	yes	complemented
238	#464	C₂×C₃×C₅	1	2	yes	complemented
239	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	#448	C₂×C₃×C₅	1	1	yes	characteristic
241	#441	C₂×C₃×C₅	1	2	yes	complemented
242	#440	C₂×C₃×C₅	1	2	yes	complemented
243	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	—	4	1	no	—
249	C₂²×C₃×C₅	#137	1	2	yes	—
250	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₃×C₄×C₅	—	2	4	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	—	4	1	no	—
258	C₃×C₄×C₅	—	4	1	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	C₂×#41	1	2	yes	—
262	C₂×C₃×Q₈	—	2	4	no	—
263	C₂×C₃×Q₈	—	2	1	no	—
264	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₃×Q₁₆	—	2	4	no	—
275	C₃×SD₁₆	—	2	4	no	—
276	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
277	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	—	2	2	no	—
279	C₃×C₄⋊C₄	—	2	2	no	—
280	C₃×C₄⋊C₄	—	2	1	no	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	2	1	no	—
284	C₃×C₄⋊C₄	—	2	1	no	—
285	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
286	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
287	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	2	1	no	—
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	1	no	—
293	C₃×C₄²	—	2	2	no	—
294	C₃×C₄²	—	2	2	no	—
295	C₃×C₄²	—	2	1	no	—
296	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
297	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
298	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
299	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
300	C₂³×C₅	—	2	1	no	—
301	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
302	C₅×Q₈	—	2	4	no	—
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	C₃×#41	1	4	yes	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	4	2	no	—
308	C₂×C₄×C₅	—	2	4	no	—
309	C₂×C₄×C₅	—	2	2	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	4	1	no	—
317	C₂×C₄×C₅	—	4	2	no	—
318	C₂×C₄×C₅	—	4	2	no	—
319	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	2	2	no	—
327	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
328	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
329	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
330	#126	—	2	1	no	—
331	#125	C₂²×C₃×C₅	1	1	yes	characteristic
332	#124	C₂²×C₃×C₅	1	1	yes	characteristic
333	#123	—	2	1	no	—
334	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	#121	C₂²×C₃×C₅	1	1	yes	characteristic
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
339	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
340	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
348	#107	C₂²×C₃×C₅	1	2	yes	—
349	#106	C₂²×C₃×C₅	1	2	yes	—
350	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
351	#103	C₂²×C₃×C₅	1	2	yes	—
352	#103	C₂²×C₃×C₅	1	2	yes	—
353	#103	C₂²×C₃×C₅	1	2	yes	—
354	#102	C₂²×C₃×C₅	1	2	yes	—
355	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
356	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
357	#97	C₂²×C₃×C₅	1	2	yes	—
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	—	8	1	no	—
360	C₂×C₃×C₅	#525	1	1	yes	characteristic
361	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
362	C₂×C₃×C₅	#575	1	1	yes	characteristic
363	C₂³×C₃	—	2	1	no	—
364	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
365	C₃×Q₈	—	2	4	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	2	2	no	—
368	C₃×Q₈	C₅×#41	1	4	yes	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	4	2	no	—
371	C₂×C₃×C₄	—	2	4	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	4	1	no	—
380	C₂×C₃×C₄	—	4	2	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
388	C₃×C₈	—	2	2	no	—
389	C₃×C₈	—	2	2	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	4	1	no	—
395	C₂²×C₅	C₃×#137	1	2	yes	—
396	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	2	4	no	—
402	C₄×C₅	—	2	1	no	—
403	C₄×C₅	—	4	1	no	—
404	C₄×C₅	—	4	2	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	C₂×C₃×#41	1	2	yes	—
408	C₂×Q₈	—	2	4	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
411	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
420	Q₁₆	—	2	4	no	—
421	SD₁₆	—	2	4	no	—
422	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
423	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
432	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
433	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
443	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
444	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
445	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
446	C₃×C₅	#3117	1	1	yes	characteristic, direct product factor, Hall
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	4	1	no	—
450	C₂²×C₃	—	4	1	no	—
451	C₂²×C₃	—	4	1	no	—
452	C₂²×C₃	C₅×#137	1	2	yes	—
453	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
454	C₃×C₄	—	2	4	no	—
455	C₃×C₄	—	2	1	no	—
456	C₃×C₄	—	2	1	no	—
457	C₃×C₄	—	2	1	no	—
458	C₃×C₄	—	2	1	no	—
459	C₃×C₄	—	2	1	no	—
460	C₃×C₄	—	4	1	no	—
461	C₃×C₄	—	4	1	no	—
462	C₃×C₄	—	4	2	no	—
463	C₃×C₄	—	4	1	no	—
464	C₃×C₄	C₂×C₅×#41	1	2	yes	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	8	1	no	—
467	C₂×C₅	C₃×#525	1	1	yes	characteristic
468	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
469	C₂×C₅	C₃×#575	1	1	yes	characteristic
470	C₂³	—	2	1	no	—
471	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
472	Q₈	—	2	4	no	—
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	C₃×C₅×#41	1	4	yes	—
476	D₄	—	2	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
491	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
492	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
493	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
494	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₂×C₃	—	2	2	no	—
498	C₂×C₃	—	8	1	no	—
499	C₂×C₃	C₅×#525	1	1	yes	characteristic
500	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
501	C₂×C₃	C₅×#575	1	1	yes	characteristic
502	C₅	C₃×#3117	1	1	yes	characteristic, direct product factor, Sylow
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	C₃×C₅×#137	1	2	yes	—
509	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
510	C₄	—	2	4	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	C₂×C₃×C₅×#41	1	2	yes	—
521	C₃	C₅×#3117	1	1	yes	characteristic, direct product factor, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	8	1	no	—
524	C₂	C₃×C₅×#525	1	1	yes	characteristic
525	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
526	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×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#479	C₂	semidirect
6. C₃×C₅×#464	C₂	semidirect
7. C₃×C₅×#451	C₂	semidirect
9. C₃×C₅×#441	C₂	semidirect
10. C₃×C₅×#440	C₂	semidirect
11. C₃×C₅×#432	C₂	semidirect
12. C₅×#3117	C₃	direct (N × H)
44. C₃×#3117	C₅	direct (N × H)
46. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
47. C₅×#484	C₂×C₃	semidirect
49. C₅×#479	C₂×C₃	semidirect
50. C₅×#464	C₂×C₃	semidirect
51. C₅×#451	C₂×C₃	semidirect
53. C₅×#441	C₂×C₃	semidirect
54. C₅×#440	C₂×C₃	semidirect
55. C₅×#432	C₂×C₃	semidirect
95. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
96. C₃×#484	C₂×C₅	semidirect
98. C₃×#479	C₂×C₅	semidirect
99. C₃×#464	C₂×C₅	semidirect
100. C₃×#451	C₂×C₅	semidirect
102. C₃×#441	C₂×C₅	semidirect
103. C₃×#440	C₂×C₅	semidirect
104. C₃×#432	C₂×C₅	semidirect
136. #3117	C₃×C₅	direct (N × H)
234. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
235. #484	C₂×C₃×C₅	semidirect
237. #479	C₂×C₃×C₅	semidirect
238. #464	C₂×C₃×C₅	semidirect
239. #451	C₂×C₃×C₅	semidirect
241. #441	C₂×C₃×C₅	semidirect
242. #440	C₂×C₃×C₅	semidirect
243. #432	C₂×C₃×C₅	semidirect
446. C₃×C₅	#3117	direct (N × H)
502. C₅	C₃×#3117	direct (N × H)
521. C₃	C₅×#3117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#484	2
C₃×C₅×#481	2
C₃×C₅×#479	2
C₃×C₅×#464	2
C₃×C₅×#451	2
C₃×C₅×#448	2
C₃×C₅×#441	2
C₃×C₅×#440	2
C₃×C₅×#432	2
C₅×#3117	3
C₃×#3117	5

Subgroups — C3×C5×#3117 #14276151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3117 #14276151