Subgroups — C₃×C₅×#3097 #14276131

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#484	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#483	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic
12	C₅×#3097	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	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
18	C₃×C₅×#124	—	2	1	no	—
19	C₃×C₅×#123	—	2	2	no	—
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×D₄	—	2	2	no	—
24	C₃×C₄×C₅×D₄	—	2	1	no	—
25	C₃×C₅×#117	C₂²	1	2	yes	—
26	C₃×C₅×#117	C₂²	1	1	yes	characteristic
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#107	C₂²	1	2	yes	—
32	C₃×C₅×#107	C₂²	1	1	yes	characteristic
33	C₃×C₅×#106	C₂²	1	1	yes	characteristic
34	C₃×C₅×#106	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic
36	C₃×C₅×#103	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×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×#3097	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#536	C₂×C₃	1	1	yes	characteristic
44	C₅×#520	C₂×C₃	1	1	yes	characteristic
45	C₅×#485	C₂×C₃	1	2	yes	complemented
46	C₅×#485	C₂×C₃	1	2	yes	complemented
47	C₅×#484	C₂×C₃	1	2	yes	complemented
48	C₅×#483	C₂×C₃	1	2	yes	complemented
49	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#408	C₂×C₃	1	1	yes	characteristic
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
62	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₃×C₅×M₁₆	—	2	2	no	—
69	C₂×C₃×C₅×C₈	—	2	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₄²×C₅	—	2	2	no	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	—	2	1	no	—
90	C₃×#536	C₂×C₅	1	1	yes	characteristic
91	C₃×#520	C₂×C₅	1	1	yes	characteristic
92	C₃×#485	C₂×C₅	1	2	yes	complemented
93	C₃×#485	C₂×C₅	1	2	yes	complemented
94	C₃×#484	C₂×C₅	1	2	yes	complemented
95	C₃×#483	C₂×C₅	1	2	yes	complemented
96	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#408	C₂×C₅	1	1	yes	characteristic
101	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×C₄⋊Q₈	—	2	1	no	—
106	C₅×#124	—	2	1	no	—
107	C₅×#123	—	2	2	no	—
108	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
110	C₄×C₅×Q₈	—	2	1	no	—
111	C₄×C₅×D₄	—	2	2	no	—
112	C₄×C₅×D₄	—	2	1	no	—
113	C₅×#117	C₂²×C₃	1	1	yes	characteristic
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₅×#117	C₂²×C₃	1	2	yes	—
116	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	C₅×#107	C₂²×C₃	1	1	yes	characteristic
119	C₅×#107	C₂²×C₃	1	1	yes	characteristic
120	C₅×#107	C₂²×C₃	1	2	yes	—
121	C₅×#106	C₂²×C₃	1	1	yes	characteristic
122	C₅×#106	C₂²×C₃	1	1	yes	characteristic
123	C₅×#106	C₂²×C₃	1	2	yes	—
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#103	C₂²×C₃	1	2	yes	—
126	C₅×#103	C₂²×C₃	1	2	yes	—
127	C₅×#103	C₂²×C₃	1	2	yes	—
128	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
129	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
130	#3097	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	2	no	—
137	C₃×C₅×D₄	—	2	4	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	4	2	no	—
148	C₂×C₃×C₄×C₅	—	8	1	no	—
149	C₂×C₃×C₄×C₅	—	8	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	#41	1	2	yes	—
153	C₂×C₃×C₄×C₅	#41	1	2	yes	—
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₃×C₅×C₈	—	2	1	no	—
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
159	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	—	2	1	no	—
163	C₃×#124	—	2	1	no	—
164	C₃×#123	—	2	2	no	—
165	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
166	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
167	C₃×C₄×Q₈	—	2	1	no	—
168	C₃×C₄×D₄	—	2	2	no	—
169	C₃×C₄×D₄	—	2	1	no	—
170	C₃×#117	C₂²×C₅	1	1	yes	characteristic
171	C₃×#117	C₂²×C₅	1	1	yes	characteristic
172	C₃×#117	C₂²×C₅	1	2	yes	—
173	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	C₃×#107	C₂²×C₅	1	1	yes	characteristic
176	C₃×#107	C₂²×C₅	1	1	yes	characteristic
177	C₃×#107	C₂²×C₅	1	2	yes	—
178	C₃×#106	C₂²×C₅	1	1	yes	characteristic
179	C₃×#106	C₂²×C₅	1	1	yes	characteristic
180	C₃×#106	C₂²×C₅	1	2	yes	—
181	C₃×#103	C₂²×C₅	1	2	yes	—
182	C₃×#103	C₂²×C₅	1	2	yes	—
183	C₃×#103	C₂²×C₅	1	2	yes	—
184	C₃×#103	C₂²×C₅	1	2	yes	—
185	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
186	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
187	C₅×#41	—	2	2	no	—
188	C₅×#41	—	2	2	no	—
189	C₂×C₅×Q₈	—	2	1	no	—
190	C₂×C₅×Q₈	—	2	2	no	—
191	C₂×C₅×Q₈	—	2	2	no	—
192	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
193	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
194	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
195	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	—	2	1	no	—
199	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₅×M₁₆	—	2	2	no	—
202	C₂×C₅×C₈	—	2	2	no	—
203	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
211	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	—	2	2	no	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	#536	C₂×C₃×C₅	1	1	yes	characteristic
224	#520	C₂×C₃×C₅	1	1	yes	characteristic
225	#485	C₂×C₃×C₅	1	2	yes	complemented
226	#485	C₂×C₃×C₅	1	2	yes	complemented
227	#484	C₂×C₃×C₅	1	2	yes	complemented
228	#483	C₂×C₃×C₅	1	2	yes	complemented
229	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#408	C₂×C₃×C₅	1	1	yes	characteristic
234	C₂²×C₃×C₅	—	2	1	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	—	2	2	no	—
239	C₂²×C₃×C₅	#123	1	2	yes	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	—	4	1	no	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	—	4	1	no	—
246	C₃×C₄×C₅	—	4	1	no	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	#123	1	2	yes	—
249	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
251	C₃×#41	—	2	2	no	—
252	C₃×#41	—	2	2	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	2	2	no	—
256	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
258	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
259	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
260	C₂²×C₃×C₄	—	2	1	no	—
261	C₂²×C₃×C₄	—	2	2	no	—
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
264	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₃×M₁₆	—	2	2	no	—
266	C₂×C₃×C₈	—	2	2	no	—
267	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
269	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	2	no	—
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	2	2	no	—
283	C₃×C₂²⋊C₄	—	2	2	no	—
284	C₃×C₄²	—	2	2	no	—
285	C₃×C₄²	—	2	1	no	—
286	C₃×C₄²	—	2	1	no	—
287	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₅×Q₈	—	2	2	no	—
290	C₅×Q₈	—	2	2	no	—
291	C₅×Q₈	—	2	2	no	—
292	C₅×Q₈	—	4	2	no	—
293	C₅×D₄	—	2	4	no	—
294	C₅×D₄	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	—	8	1	no	—
305	C₂×C₄×C₅	—	8	2	no	—
306	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
307	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₃×#41	1	2	yes	—
309	C₂×C₄×C₅	C₃×#41	1	2	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	2	no	—
314	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₄⋊Q₈	—	2	1	no	—
319	#124	—	2	1	no	—
320	#123	—	2	2	no	—
321	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
322	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	1	no	—
326	#117	C₂²×C₃×C₅	1	1	yes	characteristic
327	#117	C₂²×C₃×C₅	1	2	yes	—
328	#117	C₂²×C₃×C₅	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
331	#107	C₂²×C₃×C₅	1	1	yes	characteristic
332	#107	C₂²×C₃×C₅	1	1	yes	characteristic
333	#107	C₂²×C₃×C₅	1	2	yes	—
334	#106	C₂²×C₃×C₅	1	1	yes	characteristic
335	#106	C₂²×C₃×C₅	1	1	yes	characteristic
336	#106	C₂²×C₃×C₅	1	2	yes	—
337	#103	C₂²×C₃×C₅	1	2	yes	—
338	#103	C₂²×C₃×C₅	1	2	yes	—
339	#103	C₂²×C₃×C₅	1	2	yes	—
340	#103	C₂²×C₃×C₅	1	2	yes	—
341	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
342	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
343	C₂×C₃×C₅	—	2	2	no	—
344	C₂×C₃×C₅	—	4	2	no	—
345	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
346	C₂×C₃×C₅	#577	1	1	yes	characteristic
347	C₂×C₃×C₅	#578	1	1	yes	characteristic
348	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
349	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
350	C₃×Q₈	—	2	2	no	—
351	C₃×Q₈	—	2	2	no	—
352	C₃×Q₈	—	2	2	no	—
353	C₃×Q₈	—	4	2	no	—
354	C₃×D₄	—	2	4	no	—
355	C₃×D₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	4	2	no	—
365	C₂×C₃×C₄	—	8	1	no	—
366	C₂×C₃×C₄	—	8	2	no	—
367	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₅×#41	1	2	yes	—
370	C₂×C₃×C₄	C₅×#41	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
372	C₃×C₈	—	2	1	no	—
373	C₃×C₈	—	2	1	no	—
374	C₃×C₈	—	2	2	no	—
375	C₂²×C₅	—	2	1	no	—
376	C₂²×C₅	—	2	1	no	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	C₃×#123	1	2	yes	—
381	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	4	1	no	—
384	C₄×C₅	—	4	2	no	—
385	C₄×C₅	—	4	1	no	—
386	C₄×C₅	—	4	1	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	C₃×#123	1	2	yes	—
390	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
391	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
392	#41	—	2	2	no	—
393	#41	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
398	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
399	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
400	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
405	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
406	M₁₆	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
410	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
416	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
418	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
419	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₃×C₅	#3097	1	1	yes	characteristic, direct product factor, Hall
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	C₅×#123	1	2	yes	—
435	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	2	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	C₅×#123	1	2	yes	—
444	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
445	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
446	C₂×C₅	—	2	2	no	—
447	C₂×C₅	—	4	2	no	—
448	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
449	C₂×C₅	C₃×#577	1	1	yes	characteristic
450	C₂×C₅	C₃×#578	1	1	yes	characteristic
451	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
452	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
453	Q₈	—	2	2	no	—
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	4	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	2	no	—
470	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
471	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₃×C₅×#41	1	2	yes	—
473	C₂×C₄	C₃×C₅×#41	1	2	yes	—
474	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
475	C₈	—	2	1	no	—
476	C₈	—	2	1	no	—
477	C₈	—	2	2	no	—
478	C₂×C₃	—	2	2	no	—
479	C₂×C₃	—	4	2	no	—
480	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
481	C₂×C₃	C₅×#577	1	1	yes	characteristic
482	C₂×C₃	C₅×#578	1	1	yes	characteristic
483	C₅	C₃×#3097	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	C₃×C₅×#123	1	2	yes	—
490	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	1	no	—
498	C₄	C₃×C₅×#123	1	2	yes	—
499	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
500	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
501	C₃	C₅×#3097	1	1	yes	characteristic, direct product factor, Sylow
502	C₂	—	2	2	no	—
503	C₂	—	4	2	no	—
504	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
505	C₂	C₃×C₅×#577	1	1	yes	characteristic
506	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
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
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#484	C₂	semidirect
6. C₃×C₅×#483	C₂	semidirect
7. C₃×C₅×#428	C₂	semidirect
8. C₃×C₅×#427	C₂	semidirect
9. C₃×C₅×#419	C₂	semidirect
10. C₂×C₃×C₅×#103	C₂	semidirect
12. C₅×#3097	C₃	direct (N × H)
42. C₃×#3097	C₅	direct (N × H)
45. C₅×#485	C₂×C₃	semidirect
46. C₅×#485	C₂×C₃	semidirect
47. C₅×#484	C₂×C₃	semidirect
48. C₅×#483	C₂×C₃	semidirect
49. C₅×#428	C₂×C₃	semidirect
50. C₅×#427	C₂×C₃	semidirect
51. C₅×#419	C₂×C₃	semidirect
52. C₂×C₅×#103	C₂×C₃	semidirect
92. C₃×#485	C₂×C₅	semidirect
93. C₃×#485	C₂×C₅	semidirect
94. C₃×#484	C₂×C₅	semidirect
95. C₃×#483	C₂×C₅	semidirect
96. C₃×#428	C₂×C₅	semidirect
97. C₃×#427	C₂×C₅	semidirect
98. C₃×#419	C₂×C₅	semidirect
99. C₂×C₃×#103	C₂×C₅	semidirect
130. #3097	C₃×C₅	direct (N × H)
225. #485	C₂×C₃×C₅	semidirect
226. #485	C₂×C₃×C₅	semidirect
227. #484	C₂×C₃×C₅	semidirect
228. #483	C₂×C₃×C₅	semidirect
229. #428	C₂×C₃×C₅	semidirect
230. #427	C₂×C₃×C₅	semidirect
231. #419	C₂×C₃×C₅	semidirect
232. C₂×#103	C₂×C₃×C₅	semidirect
428. C₃×C₅	#3097	direct (N × H)
483. C₅	C₃×#3097	direct (N × H)
501. C₃	C₅×#3097	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×#536	2
C₃×C₅×#520	2
C₃×C₅×#485	2
C₃×C₅×#484	2
C₃×C₅×#483	2
C₃×C₅×#428	2
C₃×C₅×#427	2
C₃×C₅×#419	2
C₂×C₃×C₅×#103	2
C₃×C₅×#408	2
C₅×#3097	3
C₃×#3097	5

Subgroups — C3×C5×#3097 #14276131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3097 #14276131