Subgroups — C₃×C₅×#2499 #14275533

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#397	C₂	1	4	yes	maximal
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#387	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₅×#2499	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
14	C₃×C₅×#117	—	2	4	no	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	4	yes	—
28	C₃×C₅×#95	C₂²	1	4	yes	—
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₃×#2499	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
33	C₅×#397	C₂×C₃	1	4	yes	—
34	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#387	C₂×C₃	1	4	yes	complemented
37	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
39	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
40	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	8	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₄²×C₅	—	2	4	no	—
64	C₃×C₄²×C₅	—	2	2	no	—
65	C₃×C₄²×C₅	—	2	2	no	—
66	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
68	C₃×#397	C₂×C₅	1	4	yes	—
69	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#387	C₂×C₅	1	4	yes	complemented
72	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
73	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
75	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×C₂²⋊Q₈	—	2	4	no	—
78	C₅×#117	—	2	4	no	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	4	yes	—
92	C₅×#95	C₂²×C₃	1	4	yes	—
93	C₅×#95	C₂²×C₃	1	4	yes	—
94	#2499	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	1	no	—
97	C₂³×C₃×C₅	—	2	1	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
100	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	4	4	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	8	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	#41	1	4	yes	—
122	C₂×C₃×C₄×C₅	#41	1	2	yes	—
123	C₂×C₃×C₄×C₅	#41	1	2	yes	—
124	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
126	C₃×C₂²⋊Q₈	—	2	4	no	—
127	C₃×#117	—	2	4	no	—
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	4	yes	—
141	C₃×#95	C₂²×C₅	1	4	yes	—
142	C₃×#95	C₂²×C₅	1	4	yes	—
143	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₅×Q₈	—	2	2	no	—
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
152	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₅×C₄⋊C₄	—	2	2	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	2	8	no	—
163	C₅×C₂²⋊C₄	—	2	4	no	—
164	C₅×C₂²⋊C₄	—	2	4	no	—
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₄²×C₅	—	2	4	no	—
167	C₄²×C₅	—	2	2	no	—
168	C₄²×C₅	—	2	2	no	—
169	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
170	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
171	#397	C₂×C₃×C₅	1	4	yes	—
172	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
173	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	#387	C₂×C₃×C₅	1	4	yes	complemented
175	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
177	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
187	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	4	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	#123	1	4	yes	—
196	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
197	C₂×C₃×Q₈	—	2	2	no	—
198	C₂×C₃×Q₈	—	2	2	no	—
199	C₂×C₃×Q₈	—	2	2	no	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	—	2	2	no	—
202	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
211	C₃×C₄⋊C₄	—	2	2	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	—	2	2	no	—
214	C₃×C₄⋊C₄	—	2	4	no	—
215	C₃×C₄⋊C₄	—	2	8	no	—
216	C₃×C₂²⋊C₄	—	2	4	no	—
217	C₃×C₂²⋊C₄	—	2	4	no	—
218	C₃×C₂²⋊C₄	—	2	4	no	—
219	C₃×C₄²	—	2	4	no	—
220	C₃×C₄²	—	2	2	no	—
221	C₃×C₄²	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	1	no	—
224	C₂³×C₅	—	2	1	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
228	C₅×Q₈	—	4	4	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	8	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
248	C₂×C₄×C₅	C₃×#41	1	4	yes	—
249	C₂×C₄×C₅	C₃×#41	1	2	yes	—
250	C₂×C₄×C₅	C₃×#41	1	2	yes	—
251	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
253	C₂²⋊Q₈	—	2	4	no	—
254	#117	—	2	4	no	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
259	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
260	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
263	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
264	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
266	#95	C₂²×C₃×C₅	1	2	yes	—
267	#95	C₂²×C₃×C₅	1	4	yes	—
268	#95	C₂²×C₃×C₅	1	4	yes	—
269	#95	C₂²×C₃×C₅	1	4	yes	—
270	C₂×C₃×C₅	—	4	2	no	—
271	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
272	C₂×C₃×C₅	#532	1	1	yes	characteristic
273	C₂×C₃×C₅	#536	1	1	yes	characteristic
274	C₂×C₃×C₅	#552	1	2	yes	—
275	C₂×C₃×C₅	#556	1	2	yes	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	1	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
281	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
282	C₃×Q₈	—	4	4	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	8	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₅×#41	1	4	yes	—
303	C₂×C₃×C₄	C₅×#41	1	2	yes	—
304	C₂×C₃×C₄	C₅×#41	1	2	yes	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
311	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
312	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
313	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
314	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	4	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	—	4	2	no	—
319	C₄×C₅	—	4	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	C₃×#123	1	4	yes	—
323	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
330	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
331	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
332	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
335	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	2	4	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₄²	—	2	4	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₃×C₅	#2499	1	1	yes	characteristic, direct product factor, Hall
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
358	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
359	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	C₅×#123	1	4	yes	—
368	C₂×C₅	—	4	2	no	—
369	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
370	C₂×C₅	C₃×#532	1	1	yes	characteristic
371	C₂×C₅	C₃×#536	1	1	yes	characteristic
372	C₂×C₅	C₃×#552	1	2	yes	—
373	C₂×C₅	C₃×#556	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
379	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
380	Q₈	—	4	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
400	C₂×C₄	C₃×C₅×#41	1	4	yes	—
401	C₂×C₄	C₃×C₅×#41	1	2	yes	—
402	C₂×C₄	C₃×C₅×#41	1	2	yes	—
403	C₂×C₃	—	4	2	no	—
404	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
405	C₂×C₃	C₅×#532	1	1	yes	characteristic
406	C₂×C₃	C₅×#536	1	1	yes	characteristic
407	C₂×C₃	C₅×#552	1	2	yes	—
408	C₂×C₃	C₅×#556	1	2	yes	—
409	C₅	C₃×#2499	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
417	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
418	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
419	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	C₃×C₅×#123	1	4	yes	—
428	C₃	C₅×#2499	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	4	2	no	—
430	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
431	C₂	C₃×C₅×#532	1	1	yes	characteristic
432	C₂	C₃×C₅×#536	1	1	yes	characteristic
433	C₂	C₃×C₅×#552	1	2	yes	—
434	C₂	C₃×C₅×#556	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
7. C₃×C₅×#384	C₂	semidirect
8. C₃×C₅×#382	C₂	semidirect
10. C₅×#2499	C₃	direct (N × H)
30. C₃×#2499	C₅	direct (N × H)
34. C₅×#391	C₂×C₃	semidirect
35. C₅×#391	C₂×C₃	semidirect
36. C₅×#387	C₂×C₃	semidirect
37. C₅×#384	C₂×C₃	semidirect
38. C₅×#382	C₂×C₃	semidirect
69. C₃×#391	C₂×C₅	semidirect
70. C₃×#391	C₂×C₅	semidirect
71. C₃×#387	C₂×C₅	semidirect
72. C₃×#384	C₂×C₅	semidirect
73. C₃×#382	C₂×C₅	semidirect
94. #2499	C₃×C₅	direct (N × H)
172. #391	C₂×C₃×C₅	semidirect
173. #391	C₂×C₃×C₅	semidirect
174. #387	C₂×C₃×C₅	semidirect
175. #384	C₂×C₃×C₅	semidirect
176. #382	C₂×C₃×C₅	semidirect
349. C₃×C₅	#2499	direct (N × H)
409. C₅	C₃×#2499	direct (N × H)
428. C₃	C₅×#2499	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×C₂²⋊Q₈	2
C₂×C₃×C₅×#117	2
C₃×C₅×#397	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#384	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2499	3
C₃×#2499	5

Subgroups — C3×C5×#2499 #14275533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2499 #14275533