Subgroups — C₃×C₅×#3098 #14276132

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#484	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#480	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3098	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×#41	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×C₂²⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₅×#121	—	2	1	no	—
20	C₃×C₅×#121	—	2	2	no	—
21	C₃×C₅×#121	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	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
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×#107	C₂²	1	2	yes	—
32	C₃×C₅×#107	C₂²	1	2	yes	—
33	C₃×C₅×#106	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	1	yes	characteristic
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#102	C₂²	1	1	yes	characteristic
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×#3098	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#537	C₂×C₃	1	1	yes	characteristic
44	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#485	C₂×C₃	1	2	yes	complemented
46	C₅×#484	C₂×C₃	1	2	yes	complemented
47	C₅×#482	C₂×C₃	1	2	yes	complemented
48	C₅×#480	C₂×C₃	1	2	yes	complemented
49	C₅×#428	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₅×#41	—	2	2	no	—
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
63	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
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	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×M₁₆	—	2	2	no	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	2	no	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₃×C₄²×C₅	—	2	2	no	—
89	C₃×C₄²×C₅	—	2	1	no	—
90	C₃×#537	C₂×C₅	1	1	yes	characteristic
91	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#485	C₂×C₅	1	2	yes	complemented
93	C₃×#484	C₂×C₅	1	2	yes	complemented
94	C₃×#482	C₂×C₅	1	2	yes	complemented
95	C₃×#480	C₂×C₅	1	2	yes	complemented
96	C₃×#428	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×#41	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×C₂²⋊Q₈	—	2	1	no	—
106	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
107	C₅×#121	—	2	1	no	—
108	C₅×#121	—	2	2	no	—
109	C₅×#121	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	2	yes	—
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
119	C₅×#107	C₂²×C₃	1	2	yes	—
120	C₅×#107	C₂²×C₃	1	2	yes	—
121	C₅×#106	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	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
129	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
130	#3098	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
133	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	1	no	—
136	C₃×C₅×Q₈	—	2	1	no	—
137	C₃×C₅×D₄	—	2	4	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	1	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	4	2	no	—
142	C₃×C₅×D₄	—	8	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	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	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	4	2	no	—
151	C₂×C₃×C₄×C₅	—	8	1	no	—
152	C₂×C₃×C₄×C₅	—	8	2	no	—
153	C₂×C₃×C₄×C₅	—	8	1	no	—
154	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	#41	1	2	yes	—
157	C₂×C₃×C₄×C₅	#41	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₃×C₅×C₈	—	2	1	no	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	2	no	—
162	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
166	C₃×C₂²⋊Q₈	—	2	1	no	—
167	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
168	C₃×#121	—	2	1	no	—
169	C₃×#121	—	2	2	no	—
170	C₃×#121	C₂²×C₅	1	2	yes	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×D₄	—	2	2	no	—
173	C₃×C₄×D₄	—	2	1	no	—
174	C₃×#117	C₂²×C₅	1	1	yes	characteristic
175	C₃×#117	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₃×#107	C₂²×C₅	1	2	yes	—
180	C₃×#107	C₂²×C₅	1	2	yes	—
181	C₃×#107	C₂²×C₅	1	2	yes	—
182	C₃×#106	C₂²×C₅	1	2	yes	—
183	C₃×#103	C₂²×C₅	1	1	yes	characteristic
184	C₃×#103	C₂²×C₅	1	1	yes	characteristic
185	C₃×#103	C₂²×C₅	1	2	yes	—
186	C₃×#102	C₂²×C₅	1	1	yes	characteristic
187	C₃×#102	C₂²×C₅	1	1	yes	characteristic
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
191	C₅×#41	—	2	2	no	—
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	2	2	no	—
194	C₅×#41	—	2	2	no	—
195	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
196	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×D₄	—	2	1	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
200	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
201	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	—	2	2	no	—
203	C₂²×C₄×C₅	—	2	1	no	—
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₅×M₁₆	—	2	2	no	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	2	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	1	no	—
216	C₅×C₄⋊C₄	—	2	2	no	—
217	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
218	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
220	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₂²⋊C₄	—	2	2	no	—
222	C₅×C₂²⋊C₄	—	2	1	no	—
223	C₅×C₂²⋊C₄	—	2	2	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₄²×C₅	—	2	2	no	—
226	C₄²×C₅	—	2	1	no	—
227	#537	C₂×C₃×C₅	1	1	yes	characteristic
228	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
229	#485	C₂×C₃×C₅	1	2	yes	complemented
230	#484	C₂×C₃×C₅	1	2	yes	complemented
231	#482	C₂×C₃×C₅	1	2	yes	complemented
232	#480	C₂×C₃×C₅	1	2	yes	complemented
233	#428	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	C₂²×C₃×C₅	—	2	1	no	—
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	#123	1	2	yes	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	—	4	2	no	—
251	C₃×C₄×C₅	—	4	1	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	—	4	1	no	—
254	C₃×C₄×C₅	#123	1	2	yes	—
255	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
256	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₃×#41	—	2	2	no	—
258	C₃×#41	—	2	2	no	—
259	C₃×#41	—	2	2	no	—
260	C₃×#41	—	2	2	no	—
261	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
262	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
266	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	—	2	2	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	1	no	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
274	C₃×M₁₆	—	2	2	no	—
275	C₂×C₃×C₈	—	2	2	no	—
276	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
277	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
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	2	no	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
284	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
286	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	C₃×C₂²⋊C₄	—	2	1	no	—
289	C₃×C₂²⋊C₄	—	2	2	no	—
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₄²	—	2	2	no	—
292	C₃×C₄²	—	2	1	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₅×Q₈	—	2	2	no	—
297	C₅×Q₈	—	2	1	no	—
298	C₅×Q₈	—	2	1	no	—
299	C₅×D₄	—	2	4	no	—
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	2	1	no	—
303	C₅×D₄	—	4	2	no	—
304	C₅×D₄	—	8	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	4	2	no	—
313	C₂×C₄×C₅	—	8	1	no	—
314	C₂×C₄×C₅	—	8	2	no	—
315	C₂×C₄×C₅	—	8	1	no	—
316	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
317	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₃×#41	1	2	yes	—
319	C₂×C₄×C₅	C₃×#41	1	2	yes	—
320	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
321	C₅×C₈	—	2	1	no	—
322	C₅×C₈	—	2	1	no	—
323	C₅×C₈	—	2	2	no	—
324	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
325	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
327	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
330	#121	—	2	1	no	—
331	#121	—	2	2	no	—
332	#121	C₂²×C₃×C₅	1	2	yes	—
333	C₄×Q₈	—	2	1	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	—	2	1	no	—
336	#117	C₂²×C₃×C₅	1	1	yes	characteristic
337	#117	C₂²×C₃×C₅	1	2	yes	—
338	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
340	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
341	#107	C₂²×C₃×C₅	1	2	yes	—
342	#107	C₂²×C₃×C₅	1	2	yes	—
343	#107	C₂²×C₃×C₅	1	2	yes	—
344	#106	C₂²×C₃×C₅	1	2	yes	—
345	#103	C₂²×C₃×C₅	1	1	yes	characteristic
346	#103	C₂²×C₃×C₅	1	1	yes	characteristic
347	#103	C₂²×C₃×C₅	1	2	yes	—
348	#102	C₂²×C₃×C₅	1	1	yes	characteristic
349	#102	C₂²×C₃×C₅	1	1	yes	characteristic
350	#102	C₂²×C₃×C₅	1	2	yes	—
351	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
352	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
353	C₂×C₃×C₅	—	2	2	no	—
354	C₂×C₃×C₅	—	4	2	no	—
355	C₂×C₃×C₅	—	8	1	no	—
356	C₂×C₃×C₅	C₂×#123	1	1	yes	characteristic
357	C₂×C₃×C₅	#576	1	1	yes	characteristic
358	C₂×C₃×C₅	#578	1	1	yes	characteristic
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
361	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
362	C₃×Q₈	—	2	2	no	—
363	C₃×Q₈	—	2	1	no	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	2	no	—
367	C₃×D₄	—	2	1	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	4	2	no	—
370	C₃×D₄	—	8	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	8	1	no	—
380	C₂×C₃×C₄	—	8	2	no	—
381	C₂×C₃×C₄	—	8	1	no	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₅×#41	1	2	yes	—
385	C₂×C₃×C₄	C₅×#41	1	2	yes	—
386	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
387	C₃×C₈	—	2	1	no	—
388	C₃×C₈	—	2	1	no	—
389	C₃×C₈	—	2	2	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	C₃×#123	1	2	yes	—
399	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
400	C₄×C₅	—	2	2	no	—
401	C₄×C₅	—	4	2	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	2	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	—	4	1	no	—
406	C₄×C₅	C₃×#123	1	2	yes	—
407	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
408	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
414	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
418	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
419	C₂×D₄	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	1	no	—
424	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
425	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
426	M₁₆	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
429	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
430	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
436	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
438	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	1	no	—
445	C₃×C₅	#3098	1	1	yes	characteristic, direct product factor, Hall
446	C₂²×C₃	—	2	1	no	—
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	4	1	no	—
452	C₂²×C₃	—	4	1	no	—
453	C₂²×C₃	—	4	1	no	—
454	C₂²×C₃	C₅×#123	1	2	yes	—
455	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	4	1	no	—
458	C₃×C₄	—	4	2	no	—
459	C₃×C₄	—	4	1	no	—
460	C₃×C₄	—	4	2	no	—
461	C₃×C₄	—	4	1	no	—
462	C₃×C₄	C₅×#123	1	2	yes	—
463	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
464	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	4	2	no	—
467	C₂×C₅	—	8	1	no	—
468	C₂×C₅	C₂×C₃×#123	1	1	yes	characteristic
469	C₂×C₅	C₃×#576	1	1	yes	characteristic
470	C₂×C₅	C₃×#578	1	1	yes	characteristic
471	C₂³	—	2	1	no	—
472	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
473	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	8	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	—	8	2	no	—
493	C₂×C₄	—	8	1	no	—
494	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
495	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
496	C₂×C₄	C₃×C₅×#41	1	2	yes	—
497	C₂×C₄	C₃×C₅×#41	1	2	yes	—
498	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
499	C₈	—	2	1	no	—
500	C₈	—	2	1	no	—
501	C₈	—	2	2	no	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	4	2	no	—
504	C₂×C₃	—	8	1	no	—
505	C₂×C₃	C₂×C₅×#123	1	1	yes	characteristic
506	C₂×C₃	C₅×#576	1	1	yes	characteristic
507	C₂×C₃	C₅×#578	1	1	yes	characteristic
508	C₅	C₃×#3098	1	1	yes	characteristic, direct product factor, Sylow
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	1	no	—
515	C₂²	—	4	1	no	—
516	C₂²	—	4	1	no	—
517	C₂²	C₃×C₅×#123	1	2	yes	—
518	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
519	C₄	—	2	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	1	no	—
525	C₄	C₃×C₅×#123	1	2	yes	—
526	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
527	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
528	C₃	C₅×#3098	1	1	yes	characteristic, direct product factor, Sylow
529	C₂	—	2	2	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	1	no	—
532	C₂	C₂×C₃×C₅×#123	1	1	yes	characteristic
533	C₂	C₃×C₅×#576	1	1	yes	characteristic
534	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	C₃×C₅×#537	C₂
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
2. C₃×C₅×#520	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#482	C₂	semidirect
6. C₃×C₅×#480	C₂	semidirect
7. C₃×C₅×#428	C₂	semidirect
8. C₂×C₃×C₅×#107	C₂	semidirect
9. C₃×C₅×#417	C₂	semidirect
10. C₃×C₅×#416	C₂	semidirect
11. C₃×C₅×#408	C₂	semidirect
12. C₅×#3098	C₃	direct (N × H)
42. C₃×#3098	C₅	direct (N × H)
44. C₅×#520	C₂×C₃	semidirect
45. C₅×#485	C₂×C₃	semidirect
46. C₅×#484	C₂×C₃	semidirect
47. C₅×#482	C₂×C₃	semidirect
48. C₅×#480	C₂×C₃	semidirect
49. C₅×#428	C₂×C₃	semidirect
50. C₂×C₅×#107	C₂×C₃	semidirect
51. C₅×#417	C₂×C₃	semidirect
52. C₅×#416	C₂×C₃	semidirect
53. C₅×#408	C₂×C₃	semidirect
91. C₃×#520	C₂×C₅	semidirect
92. C₃×#485	C₂×C₅	semidirect
93. C₃×#484	C₂×C₅	semidirect
94. C₃×#482	C₂×C₅	semidirect
95. C₃×#480	C₂×C₅	semidirect
96. C₃×#428	C₂×C₅	semidirect
97. C₂×C₃×#107	C₂×C₅	semidirect
98. C₃×#417	C₂×C₅	semidirect
99. C₃×#416	C₂×C₅	semidirect
100. C₃×#408	C₂×C₅	semidirect
130. #3098	C₃×C₅	direct (N × H)
228. #520	C₂×C₃×C₅	semidirect
229. #485	C₂×C₃×C₅	semidirect
230. #484	C₂×C₃×C₅	semidirect
231. #482	C₂×C₃×C₅	semidirect
232. #480	C₂×C₃×C₅	semidirect
233. #428	C₂×C₃×C₅	semidirect
234. C₂×#107	C₂×C₃×C₅	semidirect
235. #417	C₂×C₃×C₅	semidirect
236. #416	C₂×C₃×C₅	semidirect
237. #408	C₂×C₃×C₅	semidirect
445. C₃×C₅	#3098	direct (N × H)
508. C₅	C₃×#3098	direct (N × H)
528. C₃	C₅×#3098	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×#537	2
C₃×C₅×#520	2
C₃×C₅×#485	2
C₃×C₅×#484	2
C₃×C₅×#482	2
C₃×C₅×#480	2
C₃×C₅×#428	2
C₂×C₃×C₅×#107	2
C₃×C₅×#417	2
C₃×C₅×#416	2
C₃×C₅×#408	2
C₅×#3098	3
C₃×#3098	5

Subgroups — C3×C5×#3098 #14276132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3098 #14276132