Subgroups — C₃×C₅×#3084 #14276118

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#476	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
12	C₅×#3084	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#125	—	2	1	no	—
19	C₃×C₅×#125	C₂²	1	2	yes	—
20	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	—	2	2	no	—
23	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
24	C₃×C₅×#117	—	2	1	no	—
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×C₅×#117	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	2	yes	—
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×#106	C₂²	1	2	yes	—
33	C₃×C₅×#106	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	1	yes	characteristic
39	C₃×C₅×#102	C₂²	1	1	yes	characteristic
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#102	C₂²	1	1	yes	characteristic
42	C₃×#3084	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#520	C₂×C₃	1	1	yes	characteristic
45	C₅×#479	C₂×C₃	1	2	yes	complemented
46	C₅×#478	C₂×C₃	1	2	yes	complemented
47	C₅×#476	C₂×C₃	1	2	yes	complemented
48	C₅×#475	C₂×C₃	1	2	yes	complemented
49	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#417	C₂×C₃	1	1	yes	characteristic
53	C₅×#416	C₂×C₃	1	1	yes	characteristic
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	Q₈	1	4	yes	complemented
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	—	2	1	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₅×M₁₆	—	2	2	no	—
66	C₂×C₃×C₅×C₈	—	2	2	no	—
67	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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	2	no	—
84	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
85	C₃×C₄²×C₅	—	2	2	no	—
86	C₃×C₄²×C₅	—	2	1	no	—
87	C₃×C₄²×C₅	C₂³	1	2	yes	—
88	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#520	C₂×C₅	1	1	yes	characteristic
90	C₃×#479	C₂×C₅	1	2	yes	complemented
91	C₃×#478	C₂×C₅	1	2	yes	complemented
92	C₃×#476	C₂×C₅	1	2	yes	complemented
93	C₃×#475	C₂×C₅	1	2	yes	complemented
94	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#417	C₂×C₅	1	1	yes	characteristic
98	C₃×#416	C₂×C₅	1	1	yes	characteristic
99	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	2	1	no	—
103	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₅×#125	—	2	1	no	—
105	C₅×#125	C₂²×C₃	1	2	yes	—
106	C₅×C₂²⋊Q₈	—	2	2	no	—
107	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
108	C₄×C₅×D₄	—	2	2	no	—
109	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
110	C₅×#117	—	2	1	no	—
111	C₅×#117	C₂²×C₃	1	1	yes	characteristic
112	C₅×#117	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×C₄⋊C₄	—	2	1	no	—
114	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₅×#107	C₂²×C₃	1	2	yes	—
117	C₅×#106	C₂²×C₃	1	2	yes	—
118	C₅×#106	C₂²×C₃	1	2	yes	—
119	C₅×#106	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
121	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
122	C₅×#103	C₂²×C₃	1	1	yes	characteristic
123	C₅×#103	C₂²×C₃	1	1	yes	characteristic
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	1	yes	characteristic
126	C₅×#102	C₂²×C₃	1	1	yes	characteristic
127	C₅×#102	C₂²×C₃	1	2	yes	—
128	#3084	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
129	C₂³×C₃×C₅	—	2	1	no	—
130	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	1	no	—
132	C₃×C₅×Q₈	—	8	2	no	—
133	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
134	C₃×C₅×D₄	—	2	4	no	—
135	C₃×C₅×D₄	—	2	1	no	—
136	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	4	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	8	2	no	—
144	C₂×C₃×C₄×C₅	—	8	1	no	—
145	C₂×C₃×C₄×C₅	—	8	1	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
150	C₂×C₃×C₄×C₅	#41	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₃×C₅×C₈	—	2	1	no	—
153	C₃×C₅×C₈	—	2	1	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
157	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄⋊Q₈	—	2	1	no	—
159	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
160	C₃×#125	—	2	1	no	—
161	C₃×#125	C₂²×C₅	1	2	yes	—
162	C₃×C₂²⋊Q₈	—	2	2	no	—
163	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
164	C₃×C₄×D₄	—	2	2	no	—
165	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
166	C₃×#117	—	2	1	no	—
167	C₃×#117	C₂²×C₅	1	1	yes	characteristic
168	C₃×#117	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₄⋊C₄	—	2	1	no	—
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₃×#107	C₂²×C₅	1	2	yes	—
173	C₃×#106	C₂²×C₅	1	2	yes	—
174	C₃×#106	C₂²×C₅	1	2	yes	—
175	C₃×#106	C₂²×C₅	1	2	yes	—
176	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
177	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
178	C₃×#103	C₂²×C₅	1	1	yes	characteristic
179	C₃×#103	C₂²×C₅	1	1	yes	characteristic
180	C₃×#103	C₂²×C₅	1	2	yes	—
181	C₃×#102	C₂²×C₅	1	1	yes	characteristic
182	C₃×#102	C₂²×C₅	1	1	yes	characteristic
183	C₃×#102	C₂²×C₅	1	2	yes	—
184	C₅×#41	—	2	2	no	—
185	C₅×#41	C₃×Q₈	1	4	yes	complemented
186	C₂×C₅×Q₈	—	2	2	no	—
187	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₅×D₄	—	2	1	no	—
189	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	—	2	1	no	—
191	C₂²×C₄×C₅	—	2	1	no	—
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₅×M₁₆	—	2	2	no	—
196	C₂×C₅×C₈	—	2	2	no	—
197	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
209	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
210	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
211	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	2	1	no	—
217	C₄²×C₅	C₂³×C₃	1	2	yes	—
218	#544	C₂×C₃×C₅	1	1	yes	characteristic, complemented
219	#520	C₂×C₃×C₅	1	1	yes	characteristic
220	#479	C₂×C₃×C₅	1	2	yes	complemented
221	#478	C₂×C₃×C₅	1	2	yes	complemented
222	#476	C₂×C₃×C₅	1	2	yes	complemented
223	#475	C₂×C₃×C₅	1	2	yes	complemented
224	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	#417	C₂×C₃×C₅	1	1	yes	characteristic
228	#416	C₂×C₃×C₅	1	1	yes	characteristic
229	C₂²×C₃×C₅	—	2	1	no	—
230	C₂²×C₃×C₅	—	2	1	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	1	no	—
233	C₂²×C₃×C₅	—	4	1	no	—
234	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	4	1	no	—
240	C₃×C₄×C₅	—	4	2	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₃×C₄×C₅	—	4	1	no	—
243	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
244	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
245	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₃×#41	—	2	2	no	—
247	C₃×#41	C₅×Q₈	1	4	yes	complemented
248	C₂×C₃×Q₈	—	2	2	no	—
249	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	—	2	1	no	—
255	C₂²×C₃×C₄	—	2	2	no	—
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₃×M₁₆	—	2	2	no	—
258	C₂×C₃×C₈	—	2	2	no	—
259	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	—	2	2	no	—
264	C₃×C₄⋊C₄	—	2	1	no	—
265	C₃×C₄⋊C₄	—	2	2	no	—
266	C₃×C₄⋊C₄	—	2	2	no	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
270	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
271	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
274	C₃×C₂²⋊C₄	—	2	1	no	—
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
277	C₃×C₄²	—	2	2	no	—
278	C₃×C₄²	—	2	1	no	—
279	C₃×C₄²	C₂³×C₅	1	2	yes	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₅×Q₈	—	2	1	no	—
283	C₅×Q₈	—	8	2	no	—
284	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	—
285	C₅×D₄	—	2	4	no	—
286	C₅×D₄	—	2	1	no	—
287	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	4	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	8	2	no	—
295	C₂×C₄×C₅	—	8	1	no	—
296	C₂×C₄×C₅	—	8	1	no	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
301	C₂×C₄×C₅	C₃×#41	1	2	yes	—
302	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
303	C₅×C₈	—	2	1	no	—
304	C₅×C₈	—	2	1	no	—
305	C₅×C₈	—	2	2	no	—
306	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
307	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
308	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
311	#125	—	2	1	no	—
312	#125	C₂²×C₃×C₅	1	2	yes	—
313	C₂²⋊Q₈	—	2	2	no	—
314	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
317	#117	—	2	1	no	—
318	#117	C₂²×C₃×C₅	1	1	yes	characteristic
319	#117	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
323	#107	C₂²×C₃×C₅	1	2	yes	—
324	#106	C₂²×C₃×C₅	1	2	yes	—
325	#106	C₂²×C₃×C₅	1	2	yes	—
326	#106	C₂²×C₃×C₅	1	2	yes	—
327	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
328	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
329	#103	C₂²×C₃×C₅	1	1	yes	characteristic
330	#103	C₂²×C₃×C₅	1	1	yes	characteristic
331	#103	C₂²×C₃×C₅	1	2	yes	—
332	#102	C₂²×C₃×C₅	1	1	yes	characteristic
333	#102	C₂²×C₃×C₅	1	1	yes	characteristic
334	#102	C₂²×C₃×C₅	1	2	yes	—
335	C₂×C₃×C₅	—	2	2	no	—
336	C₂×C₃×C₅	—	4	2	no	—
337	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
338	C₂×C₃×C₅	#577	1	1	yes	characteristic
339	C₂×C₃×C₅	#577	1	1	yes	characteristic
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
342	C₃×Q₈	—	2	1	no	—
343	C₃×Q₈	—	8	2	no	—
344	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
345	C₃×D₄	—	2	4	no	—
346	C₃×D₄	—	2	1	no	—
347	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	4	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	8	2	no	—
355	C₂×C₃×C₄	—	8	1	no	—
356	C₂×C₃×C₄	—	8	1	no	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
361	C₂×C₃×C₄	C₅×#41	1	2	yes	—
362	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
363	C₃×C₈	—	2	1	no	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	2	2	no	—
366	C₂²×C₅	—	2	1	no	—
367	C₂²×C₅	—	2	1	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	4	1	no	—
370	C₂²×C₅	—	4	1	no	—
371	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
372	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
373	C₄×C₅	—	2	2	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
381	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
382	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
383	#41	—	2	2	no	—
384	#41	C₃×C₅×Q₈	1	4	yes	complemented
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
394	M₁₆	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
406	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
407	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
408	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
410	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	1	no	—
416	C₄²	C₂³×C₃×C₅	1	2	yes	—
417	C₃×C₅	#3084	1	1	yes	characteristic, direct product factor, Hall
418	C₂²×C₃	—	2	1	no	—
419	C₂²×C₃	—	2	1	no	—
420	C₂²×C₃	—	2	2	no	—
421	C₂²×C₃	—	4	1	no	—
422	C₂²×C₃	—	4	1	no	—
423	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
424	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	2	no	—
427	C₃×C₄	—	2	2	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	2	no	—
430	C₃×C₄	—	4	2	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
433	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
434	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
435	C₂×C₅	—	2	2	no	—
436	C₂×C₅	—	4	2	no	—
437	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂×C₅	C₃×#577	1	1	yes	characteristic
439	C₂×C₅	C₃×#577	1	1	yes	characteristic
440	C₂³	—	2	1	no	—
441	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
442	Q₈	—	2	1	no	—
443	Q₈	—	8	2	no	—
444	Q₈	C₂×C₃×C₅×Q₈	1	2	yes	—
445	D₄	—	2	4	no	—
446	D₄	—	2	1	no	—
447	D₄	C₂×C₃×C₅×Q₈	1	2	yes	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	1	no	—
456	C₂×C₄	—	8	1	no	—
457	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
458	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
459	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
461	C₂×C₄	C₃×C₅×#41	1	2	yes	—
462	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	2	no	—
466	C₂×C₃	—	2	2	no	—
467	C₂×C₃	—	4	2	no	—
468	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
469	C₂×C₃	C₅×#577	1	1	yes	characteristic
470	C₂×C₃	C₅×#577	1	1	yes	characteristic
471	C₅	C₃×#3084	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
478	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
487	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
488	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
489	C₃	C₅×#3084	1	1	yes	characteristic, direct product factor, Sylow
490	C₂	—	2	2	no	—
491	C₂	—	4	2	no	—
492	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
493	C₂	C₃×C₅×#577	1	1	yes	characteristic
494	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
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#544	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#475	C₂	semidirect
7. C₃×C₅×#428	C₂	semidirect
8. C₂×C₃×C₅×#106	C₂	semidirect
9. C₃×C₅×#424	C₂	semidirect
12. C₅×#3084	C₃	direct (N × H)
42. C₃×#3084	C₅	direct (N × H)
43. C₅×#544	C₂×C₃	semidirect
45. C₅×#479	C₂×C₃	semidirect
46. C₅×#478	C₂×C₃	semidirect
47. C₅×#476	C₂×C₃	semidirect
48. C₅×#475	C₂×C₃	semidirect
49. C₅×#428	C₂×C₃	semidirect
50. C₂×C₅×#106	C₂×C₃	semidirect
51. C₅×#424	C₂×C₃	semidirect
55. C₃×C₅×#41	Q₈	semidirect
88. C₃×#544	C₂×C₅	semidirect
90. C₃×#479	C₂×C₅	semidirect
91. C₃×#478	C₂×C₅	semidirect
92. C₃×#476	C₂×C₅	semidirect
93. C₃×#475	C₂×C₅	semidirect
94. C₃×#428	C₂×C₅	semidirect
95. C₂×C₃×#106	C₂×C₅	semidirect
96. C₃×#424	C₂×C₅	semidirect
128. #3084	C₃×C₅	direct (N × H)
185. C₅×#41	C₃×Q₈	semidirect
218. #544	C₂×C₃×C₅	semidirect
220. #479	C₂×C₃×C₅	semidirect
221. #478	C₂×C₃×C₅	semidirect
222. #476	C₂×C₃×C₅	semidirect
223. #475	C₂×C₃×C₅	semidirect
224. #428	C₂×C₃×C₅	semidirect
225. C₂×#106	C₂×C₃×C₅	semidirect
226. #424	C₂×C₃×C₅	semidirect
247. C₃×#41	C₅×Q₈	semidirect
384. #41	C₃×C₅×Q₈	semidirect
417. C₃×C₅	#3084	direct (N × H)
471. C₅	C₃×#3084	direct (N × H)
489. C₃	C₅×#3084	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×#544	2
C₃×C₅×#520	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#428	2
C₂×C₃×C₅×#106	2
C₃×C₅×#424	2
C₃×C₅×#417	2
C₃×C₅×#416	2
C₅×#3084	3
C₃×#3084	5

Subgroups — C3×C5×#3084 #14276118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3084 #14276118