Subgroups — C₃×C₅×#3190 #14276224

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3190	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	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
19	C₃×C₅×#123	—	2	1	no	—
20	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#121	C₂²	1	1	yes	characteristic
27	C₃×C₅×#121	C₂²	1	1	yes	characteristic
28	C₃×C₅×#120	—	2	1	no	—
29	C₃×C₄×C₅×D₄	—	2	1	no	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
35	C₃×C₅×#107	C₂²	1	2	yes	complemented
36	C₃×C₅×#106	C₂²	1	2	yes	complemented
37	C₃×C₅×#103	C₂²	1	2	yes	complemented
38	C₃×C₅×#103	C₂²	1	2	yes	complemented
39	C₃×C₅×#103	C₂²	1	2	yes	complemented
40	C₃×C₅×#102	C₂²	1	2	yes	complemented
41	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₃×#3190	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#525	C₂×C₃	1	1	yes	characteristic
46	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#485	C₂×C₃	1	2	yes	complemented
48	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#467	C₂×C₃	1	2	yes	complemented
51	C₅×#465	C₂×C₃	1	2	yes	complemented
52	C₅×#452	C₂×C₃	1	2	yes	complemented
53	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#448	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
57	C₃×C₅×#41	—	4	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	4	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	—	2	1	no	—
69	C₂²×C₃×C₄×C₅	—	4	2	no	—
70	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₅×Q₁₆	—	4	2	no	—
77	C₃×C₅×SD₁₆	—	4	2	no	—
78	C₂×C₃×C₅×C₈	—	4	2	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
81	C₃×C₅×C₄⋊C₄	—	2	2	no	—
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	—	2	1	no	—
84	C₃×C₅×C₄⋊C₄	—	2	1	no	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
94	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
96	C₃×C₄²×C₅	—	2	1	no	—
97	C₃×#525	C₂×C₅	1	1	yes	characteristic
98	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#485	C₂×C₅	1	2	yes	complemented
100	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#467	C₂×C₅	1	2	yes	complemented
103	C₃×#465	C₂×C₅	1	2	yes	complemented
104	C₃×#452	C₂×C₅	1	2	yes	complemented
105	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
106	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
109	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
112	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
113	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
114	C₅×#123	—	2	1	no	—
115	C₅×C₂²⋊Q₈	—	2	1	no	—
116	C₅×C₂²⋊Q₈	—	2	1	no	—
117	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
119	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
120	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#121	C₂²×C₃	1	1	yes	characteristic
122	C₅×#121	C₂²×C₃	1	1	yes	characteristic
123	C₅×#120	—	2	1	no	—
124	C₄×C₅×D₄	—	2	1	no	—
125	C₄×C₅×D₄	—	2	1	no	—
126	C₅×#117	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	—	2	1	no	—
128	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₅×#107	C₂²×C₃	1	2	yes	complemented
131	C₅×#106	C₂²×C₃	1	2	yes	complemented
132	C₅×#103	C₂²×C₃	1	2	yes	complemented
133	C₅×#103	C₂²×C₃	1	2	yes	complemented
134	C₅×#103	C₂²×C₃	1	2	yes	complemented
135	C₅×#102	C₂²×C₃	1	2	yes	complemented
136	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
137	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
138	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
139	#3190	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³×C₃×C₅	—	2	2	no	—
141	C₂³×C₃×C₅	—	2	2	no	—
142	C₂³×C₃×C₅	—	2	1	no	—
143	C₂³×C₃×C₅	—	4	1	no	—
144	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	2	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	4	2	no	—
151	C₃×C₅×D₄	—	2	2	no	—
152	C₃×C₅×D₄	—	4	2	no	—
153	C₃×C₅×D₄	—	4	2	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	2	2	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	2	no	—
161	C₂×C₃×C₄×C₅	—	2	1	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	4	1	no	—
164	C₂×C₃×C₄×C₅	—	4	1	no	—
165	C₂×C₃×C₄×C₅	—	4	1	no	—
166	C₂×C₃×C₄×C₅	—	4	2	no	—
167	C₂×C₃×C₄×C₅	—	4	2	no	—
168	C₂×C₃×C₄×C₅	—	4	2	no	—
169	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
173	C₃×C₅×C₈	—	2	2	no	—
174	C₃×C₅×C₈	—	2	2	no	—
175	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
179	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
180	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
181	C₃×#123	—	2	1	no	—
182	C₃×C₂²⋊Q₈	—	2	1	no	—
183	C₃×C₂²⋊Q₈	—	2	1	no	—
184	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
185	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
186	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
187	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
188	C₃×#121	C₂²×C₅	1	1	yes	characteristic
189	C₃×#121	C₂²×C₅	1	1	yes	characteristic
190	C₃×#120	—	2	1	no	—
191	C₃×C₄×D₄	—	2	1	no	—
192	C₃×C₄×D₄	—	2	1	no	—
193	C₃×#117	C₂²×C₅	1	1	yes	characteristic
194	C₂×C₃×C₄⋊C₄	—	2	1	no	—
195	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
196	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×#107	C₂²×C₅	1	2	yes	complemented
198	C₃×#106	C₂²×C₅	1	2	yes	complemented
199	C₃×#103	C₂²×C₅	1	2	yes	complemented
200	C₃×#103	C₂²×C₅	1	2	yes	complemented
201	C₃×#103	C₂²×C₅	1	2	yes	complemented
202	C₃×#102	C₂²×C₅	1	2	yes	complemented
203	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
204	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
205	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
206	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
207	C₅×#41	—	4	2	no	—
208	C₂×C₅×Q₈	—	2	1	no	—
209	C₂×C₅×Q₈	—	4	2	no	—
210	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
211	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₅×D₄	—	2	1	no	—
215	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	4	2	no	—
220	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₅×Q₁₆	—	4	2	no	—
227	C₅×SD₁₆	—	4	2	no	—
228	C₂×C₅×C₈	—	4	2	no	—
229	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
230	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	1	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
237	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
238	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
239	C₅×C₂²⋊C₄	—	2	2	no	—
240	C₅×C₂²⋊C₄	—	2	2	no	—
241	C₅×C₂²⋊C₄	—	2	1	no	—
242	C₅×C₂²⋊C₄	—	2	1	no	—
243	C₅×C₂²⋊C₄	—	2	1	no	—
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₄²×C₅	—	2	1	no	—
247	#525	C₂×C₃×C₅	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
249	#485	C₂×C₃×C₅	1	2	yes	complemented
250	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
251	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
252	#467	C₂×C₃×C₅	1	2	yes	complemented
253	#465	C₂×C₃×C₅	1	2	yes	complemented
254	#452	C₂×C₃×C₅	1	2	yes	complemented
255	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
257	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂²×C₃×C₅	—	2	1	no	—
259	C₂²×C₃×C₅	—	2	1	no	—
260	C₂²×C₃×C₅	—	2	1	no	—
261	C₂²×C₃×C₅	—	2	1	no	—
262	C₂²×C₃×C₅	—	2	1	no	—
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	1	no	—
265	C₂²×C₃×C₅	—	4	4	no	—
266	C₂²×C₃×C₅	—	4	1	no	—
267	C₂²×C₃×C₅	—	4	1	no	—
268	C₂²×C₃×C₅	—	4	1	no	—
269	C₂²×C₃×C₅	#135	1	2	yes	—
270	C₂²×C₃×C₅	#137	1	2	yes	—
271	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₃×C₄×C₅	—	2	1	no	—
273	C₃×C₄×C₅	—	2	1	no	—
274	C₃×C₄×C₅	—	2	1	no	—
275	C₃×C₄×C₅	—	4	1	no	—
276	C₃×C₄×C₅	—	4	2	no	—
277	C₃×C₄×C₅	—	4	2	no	—
278	C₃×C₄×C₅	—	4	1	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
281	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
282	C₃×#41	—	4	2	no	—
283	C₂×C₃×Q₈	—	2	1	no	—
284	C₂×C₃×Q₈	—	4	2	no	—
285	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
286	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×D₄	—	2	1	no	—
288	C₂×C₃×D₄	—	2	1	no	—
289	C₂×C₃×D₄	—	2	1	no	—
290	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₃×C₄	—	2	1	no	—
292	C₂²×C₃×C₄	—	2	1	no	—
293	C₂²×C₃×C₄	—	2	1	no	—
294	C₂²×C₃×C₄	—	4	2	no	—
295	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
296	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
297	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
301	C₃×Q₁₆	—	4	2	no	—
302	C₃×SD₁₆	—	4	2	no	—
303	C₂×C₃×C₈	—	4	2	no	—
304	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
305	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
306	C₃×C₄⋊C₄	—	2	2	no	—
307	C₃×C₄⋊C₄	—	2	2	no	—
308	C₃×C₄⋊C₄	—	2	1	no	—
309	C₃×C₄⋊C₄	—	2	1	no	—
310	C₃×C₄⋊C₄	—	2	1	no	—
311	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
312	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
313	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	—	2	2	no	—
315	C₃×C₂²⋊C₄	—	2	2	no	—
316	C₃×C₂²⋊C₄	—	2	1	no	—
317	C₃×C₂²⋊C₄	—	2	1	no	—
318	C₃×C₂²⋊C₄	—	2	1	no	—
319	C₃×C₂²⋊C₄	—	2	1	no	—
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₄²	—	2	1	no	—
322	C₂³×C₅	—	2	2	no	—
323	C₂³×C₅	—	2	2	no	—
324	C₂³×C₅	—	2	1	no	—
325	C₂³×C₅	—	4	1	no	—
326	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₅×Q₈	—	2	2	no	—
330	C₅×Q₈	—	2	2	no	—
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	—	4	2	no	—
333	C₅×D₄	—	2	2	no	—
334	C₅×D₄	—	4	2	no	—
335	C₅×D₄	—	4	2	no	—
336	C₅×D₄	—	4	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	2	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	1	no	—
341	C₂×C₄×C₅	—	2	1	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	1	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	4	1	no	—
346	C₂×C₄×C₅	—	4	1	no	—
347	C₂×C₄×C₅	—	4	1	no	—
348	C₂×C₄×C₅	—	4	2	no	—
349	C₂×C₄×C₅	—	4	2	no	—
350	C₂×C₄×C₅	—	4	2	no	—
351	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
352	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
353	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
355	C₅×C₈	—	2	2	no	—
356	C₅×C₈	—	2	2	no	—
357	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
358	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
359	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
361	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
362	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
363	#123	—	2	1	no	—
364	C₂²⋊Q₈	—	2	1	no	—
365	C₂²⋊Q₈	—	2	1	no	—
366	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
367	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
368	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
370	#121	C₂²×C₃×C₅	1	1	yes	characteristic
371	#121	C₂²×C₃×C₅	1	1	yes	characteristic
372	#120	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	#117	C₂²×C₃×C₅	1	1	yes	characteristic
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	#107	C₂²×C₃×C₅	1	2	yes	complemented
380	#106	C₂²×C₃×C₅	1	2	yes	complemented
381	#103	C₂²×C₃×C₅	1	2	yes	complemented
382	#103	C₂²×C₃×C₅	1	2	yes	complemented
383	#103	C₂²×C₃×C₅	1	2	yes	complemented
384	#102	C₂²×C₃×C₅	1	2	yes	complemented
385	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
387	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
388	C₂×C₃×C₅	—	2	2	no	—
389	C₂×C₃×C₅	—	2	2	no	—
390	C₂×C₃×C₅	—	4	1	no	—
391	C₂×C₃×C₅	—	8	1	no	—
392	C₂×C₃×C₅	#534	1	1	yes	characteristic
393	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
394	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
395	C₂³×C₃	—	2	2	no	—
396	C₂³×C₃	—	2	2	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	4	1	no	—
399	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
400	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
402	C₃×Q₈	—	2	2	no	—
403	C₃×Q₈	—	2	2	no	—
404	C₃×Q₈	—	2	2	no	—
405	C₃×Q₈	—	4	2	no	—
406	C₃×D₄	—	2	2	no	—
407	C₃×D₄	—	4	2	no	—
408	C₃×D₄	—	4	2	no	—
409	C₃×D₄	—	4	2	no	—
410	C₂×C₃×C₄	—	2	2	no	—
411	C₂×C₃×C₄	—	2	2	no	—
412	C₂×C₃×C₄	—	2	2	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	2	2	no	—
418	C₂×C₃×C₄	—	4	1	no	—
419	C₂×C₃×C₄	—	4	1	no	—
420	C₂×C₃×C₄	—	4	1	no	—
421	C₂×C₃×C₄	—	4	2	no	—
422	C₂×C₃×C₄	—	4	2	no	—
423	C₂×C₃×C₄	—	4	2	no	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₃×C₈	—	2	2	no	—
429	C₃×C₈	—	2	2	no	—
430	C₂²×C₅	—	2	1	no	—
431	C₂²×C₅	—	2	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	1	no	—
434	C₂²×C₅	—	2	1	no	—
435	C₂²×C₅	—	2	1	no	—
436	C₂²×C₅	—	2	1	no	—
437	C₂²×C₅	—	4	4	no	—
438	C₂²×C₅	—	4	1	no	—
439	C₂²×C₅	—	4	1	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	C₃×#135	1	2	yes	—
442	C₂²×C₅	C₃×#137	1	2	yes	—
443	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
444	C₄×C₅	—	2	1	no	—
445	C₄×C₅	—	2	1	no	—
446	C₄×C₅	—	2	1	no	—
447	C₄×C₅	—	4	2	no	—
448	C₄×C₅	—	4	1	no	—
449	C₄×C₅	—	4	1	no	—
450	C₄×C₅	—	4	1	no	—
451	C₄×C₅	—	4	2	no	—
452	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
453	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
454	#41	—	4	2	no	—
455	C₂×Q₈	—	2	1	no	—
456	C₂×Q₈	—	4	2	no	—
457	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
458	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	4	2	no	—
467	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
471	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
472	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
473	Q₁₆	—	4	2	no	—
474	SD₁₆	—	4	2	no	—
475	C₂×C₈	—	4	2	no	—
476	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
477	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
484	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
485	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₃×C₅	#3190	1	1	yes	characteristic, direct product factor, Hall
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	—	4	4	no	—
503	C₂²×C₃	—	4	1	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	C₅×#135	1	2	yes	—
507	C₂²×C₃	C₅×#137	1	2	yes	—
508	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	1	no	—
511	C₃×C₄	—	2	1	no	—
512	C₃×C₄	—	4	1	no	—
513	C₃×C₄	—	4	2	no	—
514	C₃×C₄	—	4	2	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	—	4	1	no	—
517	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
518	C₂×C₅	—	2	2	no	—
519	C₂×C₅	—	2	2	no	—
520	C₂×C₅	—	4	1	no	—
521	C₂×C₅	—	8	1	no	—
522	C₂×C₅	C₃×#534	1	1	yes	characteristic
523	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
524	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
525	C₂³	—	2	2	no	—
526	C₂³	—	2	2	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
530	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
531	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
532	Q₈	—	2	2	no	—
533	Q₈	—	2	2	no	—
534	Q₈	—	2	2	no	—
535	Q₈	—	4	2	no	—
536	D₄	—	2	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
555	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
556	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
557	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₂×C₃	—	2	2	no	—
561	C₂×C₃	—	2	2	no	—
562	C₂×C₃	—	4	1	no	—
563	C₂×C₃	—	8	1	no	—
564	C₂×C₃	C₅×#534	1	1	yes	characteristic
565	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
566	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
567	C₅	C₃×#3190	1	1	yes	characteristic, direct product factor, Sylow
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	C₃×C₅×#135	1	2	yes	—
580	C₂²	C₃×C₅×#137	1	2	yes	—
581	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
591	C₃	C₅×#3190	1	1	yes	characteristic, direct product factor, Sylow
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	4	1	no	—
595	C₂	—	8	1	no	—
596	C₂	C₃×C₅×#534	1	1	yes	characteristic
597	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
598	C₂	C₂×C₃×C₅×#137	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
2. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#480	C₂	semidirect
6. C₃×C₅×#467	C₂	semidirect
7. C₃×C₅×#465	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₅×#451	C₂	semidirect
10. C₃×C₅×#448	C₂	semidirect
11. C₂×C₃×C₅×C₂²⋊C₈	C₂	semidirect
12. C₅×#3190	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
35. C₃×C₅×#107	C₂²	semidirect
36. C₃×C₅×#106	C₂²	semidirect
37. C₃×C₅×#103	C₂²	semidirect
38. C₃×C₅×#103	C₂²	semidirect
39. C₃×C₅×#103	C₂²	semidirect
40. C₃×C₅×#102	C₂²	semidirect
44. C₃×#3190	C₅	direct (N × H)
46. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
47. C₅×#485	C₂×C₃	semidirect
48. C₅×#483	C₂×C₃	semidirect
49. C₅×#480	C₂×C₃	semidirect
50. C₅×#467	C₂×C₃	semidirect
51. C₅×#465	C₂×C₃	semidirect
52. C₅×#452	C₂×C₃	semidirect
53. C₅×#451	C₂×C₃	semidirect
54. C₅×#448	C₂×C₃	semidirect
55. C₂×C₅×C₂²⋊C₈	C₂×C₃	semidirect
98. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
99. C₃×#485	C₂×C₅	semidirect
100. C₃×#483	C₂×C₅	semidirect
101. C₃×#480	C₂×C₅	semidirect
102. C₃×#467	C₂×C₅	semidirect
103. C₃×#465	C₂×C₅	semidirect
104. C₃×#452	C₂×C₅	semidirect
105. C₃×#451	C₂×C₅	semidirect
106. C₃×#448	C₂×C₅	semidirect
107. C₂×C₃×C₂²⋊C₈	C₂×C₅	semidirect
111. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
112. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
130. C₅×#107	C₂²×C₃	semidirect
131. C₅×#106	C₂²×C₃	semidirect
132. C₅×#103	C₂²×C₃	semidirect
133. C₅×#103	C₂²×C₃	semidirect
134. C₅×#103	C₂²×C₃	semidirect
135. C₅×#102	C₂²×C₃	semidirect
139. #3190	C₃×C₅	direct (N × H)
178. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
179. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
197. C₃×#107	C₂²×C₅	semidirect
198. C₃×#106	C₂²×C₅	semidirect
199. C₃×#103	C₂²×C₅	semidirect
200. C₃×#103	C₂²×C₅	semidirect
201. C₃×#103	C₂²×C₅	semidirect
202. C₃×#102	C₂²×C₅	semidirect
248. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
249. #485	C₂×C₃×C₅	semidirect
250. #483	C₂×C₃×C₅	semidirect
251. #480	C₂×C₃×C₅	semidirect
252. #467	C₂×C₃×C₅	semidirect
253. #465	C₂×C₃×C₅	semidirect
254. #452	C₂×C₃×C₅	semidirect
255. #451	C₂×C₃×C₅	semidirect
256. #448	C₂×C₃×C₅	semidirect
257. C₂×C₂²⋊C₈	C₂×C₃×C₅	semidirect
360. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
361. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
379. #107	C₂²×C₃×C₅	semidirect
380. #106	C₂²×C₃×C₅	semidirect
381. #103	C₂²×C₃×C₅	semidirect
382. #103	C₂²×C₃×C₅	semidirect
383. #103	C₂²×C₃×C₅	semidirect
384. #102	C₂²×C₃×C₅	semidirect
494. C₃×C₅	#3190	direct (N × H)
567. C₅	C₃×#3190	direct (N × H)
591. C₃	C₅×#3190	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×#525	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#485	2
C₃×C₅×#483	2
C₃×C₅×#480	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#448	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₅×#3190	3
C₃×#3190	5

Subgroups — C3×C5×#3190 #14276224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3190 #14276224