Subgroups — C₃×C₅×#3332 #14276366

Order 1920.

860 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#481	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#417	C₂	1	2	yes	maximal, complemented
12	C₅×#3332	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	—	2	1	no	—
14	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#127	—	2	1	no	—
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×#106	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	1	yes	characteristic
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×C₅×#102	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	1	yes	characteristic
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3332	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#547	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#481	C₂×C₃	1	2	yes	complemented
47	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#469	C₂×C₃	1	2	yes	complemented
49	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#449	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#417	C₂×C₃	1	2	yes	complemented
54	C₃×C₅×#41	—	2	4	no	—
55	C₃×C₅×#41	—	4	2	no	—
56	C₃×C₅×#41	—	4	4	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	1	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	—	2	2	no	—
69	C₂²×C₃×C₄×C₅	—	2	1	no	—
70	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
71	C₃×C₅×SD₁₆	—	2	2	no	—
72	C₃×C₅×D₈	—	4	2	no	—
73	C₃×C₅×M₁₆	—	4	2	no	—
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
91	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#481	C₂×C₅	1	2	yes	complemented
94	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#469	C₂×C₅	1	2	yes	complemented
96	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#449	C₂×C₅	1	2	yes	complemented
98	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#417	C₂×C₅	1	2	yes	complemented
101	C₂×C₅×#41	—	2	1	no	—
102	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
103	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
105	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
106	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₅×#127	—	2	1	no	—
108	C₅×#127	C₂²×C₃	1	1	yes	characteristic
109	C₅×#123	—	2	2	no	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×#121	—	2	2	no	—
112	C₅×#121	C₂²×C₃	1	2	yes	—
113	C₅×#121	C₂²×C₃	1	2	yes	—
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
119	C₅×#106	C₂²×C₃	1	1	yes	characteristic
120	C₅×#106	C₂²×C₃	1	2	yes	—
121	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	1	yes	characteristic
123	C₅×#103	C₂²×C₃	1	2	yes	—
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	2	yes	—
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	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
130	#3332	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
134	C₃×C₅×Q₈	—	2	1	no	—
135	C₃×C₅×Q₈	—	4	2	no	—
136	C₃×C₅×Q₈	#41	1	2	yes	complemented
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	1	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	4	4	no	—
143	C₃×C₅×D₄	—	4	4	no	—
144	C₃×C₅×D₄	—	4	2	no	—
145	C₃×C₅×D₄	—	8	1	no	—
146	C₃×C₅×D₄	—	8	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	4	4	no	—
154	C₂×C₃×C₄×C₅	—	4	4	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	2	no	—
163	C₂×C₃×#41	—	2	1	no	—
164	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
165	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
167	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
168	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₃×#127	—	2	1	no	—
170	C₃×#127	C₂²×C₅	1	1	yes	characteristic
171	C₃×#123	—	2	2	no	—
172	C₃×C₂²⋊Q₈	—	2	1	no	—
173	C₃×#121	—	2	2	no	—
174	C₃×#121	C₂²×C₅	1	2	yes	—
175	C₃×#121	C₂²×C₅	1	2	yes	—
176	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄×D₄	—	2	1	no	—
178	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
179	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
181	C₃×#106	C₂²×C₅	1	1	yes	characteristic
182	C₃×#106	C₂²×C₅	1	2	yes	—
183	C₃×C₄⋊C₈	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	2	yes	—
187	C₃×#102	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	1	yes	characteristic
189	C₃×#102	C₂²×C₅	1	2	yes	—
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
191	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
192	C₅×#41	—	2	4	no	—
193	C₅×#41	—	4	2	no	—
194	C₅×#41	—	4	4	no	—
195	C₂×C₅×Q₈	—	2	1	no	—
196	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×D₄	—	2	2	no	—
198	C₂×C₅×D₄	—	2	2	no	—
199	C₂×C₅×D₄	—	2	2	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
203	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	—	2	1	no	—
208	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
209	C₅×SD₁₆	—	2	2	no	—
210	C₅×D₈	—	4	2	no	—
211	C₅×M₁₆	—	4	2	no	—
212	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
214	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	1	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
221	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
222	C₅×C₂²⋊C₄	—	2	2	no	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
228	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
229	#547	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#481	C₂×C₃×C₅	1	2	yes	complemented
232	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#469	C₂×C₃×C₅	1	2	yes	complemented
234	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#449	C₂×C₃×C₅	1	2	yes	complemented
236	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#417	C₂×C₃×C₅	1	2	yes	complemented
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	—	4	2	no	—
247	C₂²×C₃×C₅	—	4	1	no	—
248	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
256	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
257	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
258	C₃×#41	—	2	4	no	—
259	C₃×#41	—	4	2	no	—
260	C₃×#41	—	4	4	no	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×D₄	—	2	2	no	—
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	1	no	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
270	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
271	C₂²×C₃×C₄	—	2	2	no	—
272	C₂²×C₃×C₄	—	2	2	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
275	C₃×SD₁₆	—	2	2	no	—
276	C₃×D₈	—	4	2	no	—
277	C₃×M₁₆	—	4	2	no	—
278	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	2	1	no	—
284	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
285	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
286	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
287	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	2	1	no	—
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
292	C₃×C₄²	—	2	1	no	—
293	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	2	no	—
296	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
297	C₅×Q₈	—	2	1	no	—
298	C₅×Q₈	—	4	2	no	—
299	C₅×Q₈	C₃×#41	1	2	yes	complemented
300	C₅×D₄	—	2	2	no	—
301	C₅×D₄	—	2	1	no	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	—	2	1	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	4	4	no	—
306	C₅×D₄	—	4	4	no	—
307	C₅×D₄	—	4	2	no	—
308	C₅×D₄	—	8	1	no	—
309	C₅×D₄	—	8	2	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	4	4	no	—
317	C₂×C₄×C₅	—	4	4	no	—
318	C₂×C₄×C₅	—	4	2	no	—
319	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
321	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
323	C₅×C₈	—	2	1	no	—
324	C₅×C₈	—	2	1	no	—
325	C₅×C₈	—	2	2	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
328	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
329	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
330	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
331	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
332	#127	—	2	1	no	—
333	#127	C₂²×C₃×C₅	1	1	yes	characteristic
334	#123	—	2	2	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	#121	—	2	2	no	—
337	#121	C₂²×C₃×C₅	1	2	yes	—
338	#121	C₂²×C₃×C₅	1	2	yes	—
339	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
344	#106	C₂²×C₃×C₅	1	1	yes	characteristic
345	#106	C₂²×C₃×C₅	1	2	yes	—
346	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
347	#103	C₂²×C₃×C₅	1	1	yes	characteristic
348	#103	C₂²×C₃×C₅	1	2	yes	—
349	#102	C₂²×C₃×C₅	1	2	yes	—
350	#102	C₂²×C₃×C₅	1	2	yes	—
351	#102	C₂²×C₃×C₅	1	1	yes	characteristic
352	#102	C₂²×C₃×C₅	1	2	yes	—
353	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
354	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₂×C₃×C₅	—	4	2	no	—
356	C₂×C₃×C₅	—	8	2	no	—
357	C₂×C₃×C₅	—	8	1	no	—
358	C₂×C₃×C₅	#546	1	1	yes	characteristic
359	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₂×C₃×C₅	#577	1	1	yes	characteristic
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	2	no	—
363	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×Q₈	—	4	2	no	—
366	C₃×Q₈	C₅×#41	1	2	yes	complemented
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	2	2	no	—
370	C₃×D₄	—	2	1	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	4	4	no	—
373	C₃×D₄	—	4	4	no	—
374	C₃×D₄	—	4	2	no	—
375	C₃×D₄	—	8	1	no	—
376	C₃×D₄	—	8	2	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	4	4	no	—
384	C₂×C₃×C₄	—	4	4	no	—
385	C₂×C₃×C₄	—	4	2	no	—
386	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
388	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	2	1	no	—
392	C₃×C₈	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	1	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
403	C₄×C₅	—	2	1	no	—
404	C₄×C₅	—	2	2	no	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
410	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
411	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
412	#41	—	2	4	no	—
413	#41	—	4	2	no	—
414	#41	—	4	4	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
423	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
424	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
429	SD₁₆	—	2	2	no	—
430	D₈	—	4	2	no	—
431	M₁₆	—	4	2	no	—
432	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
433	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
439	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
440	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
441	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	2	no	—
445	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
446	C₄²	—	2	1	no	—
447	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
448	C₃×C₅	#3332	1	1	yes	characteristic, direct product factor, Hall
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	4	2	no	—
453	C₂²×C₃	—	4	1	no	—
454	C₂²×C₃	—	4	1	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	4	2	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	1	no	—
462	C₃×C₄	—	4	1	no	—
463	C₃×C₄	—	4	2	no	—
464	C₃×C₄	—	4	1	no	—
465	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
466	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
467	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₅	—	4	2	no	—
469	C₂×C₅	—	8	1	no	—
470	C₂×C₅	—	8	2	no	—
471	C₂×C₅	C₃×#546	1	1	yes	characteristic
472	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂×C₅	C₃×#577	1	1	yes	characteristic
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
477	Q₈	—	2	1	no	—
478	Q₈	—	4	2	no	—
479	Q₈	C₃×C₅×#41	1	2	yes	complemented
480	D₄	—	2	1	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	8	1	no	—
489	D₄	—	8	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
501	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
503	C₈	—	2	1	no	—
504	C₈	—	2	1	no	—
505	C₈	—	2	2	no	—
506	C₂×C₃	—	4	2	no	—
507	C₂×C₃	—	8	2	no	—
508	C₂×C₃	—	8	1	no	—
509	C₂×C₃	C₅×#546	1	1	yes	characteristic
510	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
511	C₂×C₃	C₅×#577	1	1	yes	characteristic
512	C₅	C₃×#3332	1	1	yes	characteristic, direct product factor, Sylow
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	1	no	—
522	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
530	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
531	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
532	C₃	C₅×#3332	1	1	yes	characteristic, direct product factor, Sylow
533	C₂	—	4	2	no	—
534	C₂	—	8	2	no	—
535	C₂	—	8	1	no	—
536	C₂	C₃×C₅×#546	1	1	yes	characteristic
537	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
538	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
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#550	C₂	semidirect
2. C₃×C₅×#547	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×C₅×#481	C₂	semidirect
5. C₃×C₅×#475	C₂	semidirect
6. C₃×C₅×#469	C₂	semidirect
7. C₃×C₅×#459	C₂	semidirect
8. C₃×C₅×#449	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×#436	C₂	semidirect
11. C₃×C₅×#417	C₂	semidirect
12. C₅×#3332	C₃	direct (N × H)
42. C₃×#3332	C₅	direct (N × H)
43. C₅×#550	C₂×C₃	semidirect
44. C₅×#547	C₂×C₃	semidirect
45. C₅×#486	C₂×C₃	semidirect
46. C₅×#481	C₂×C₃	semidirect
47. C₅×#475	C₂×C₃	semidirect
48. C₅×#469	C₂×C₃	semidirect
49. C₅×#459	C₂×C₃	semidirect
50. C₅×#449	C₂×C₃	semidirect
51. C₄×C₅×SD₁₆	C₂×C₃	semidirect
52. C₅×#436	C₂×C₃	semidirect
53. C₅×#417	C₂×C₃	semidirect
90. C₃×#550	C₂×C₅	semidirect
91. C₃×#547	C₂×C₅	semidirect
92. C₃×#486	C₂×C₅	semidirect
93. C₃×#481	C₂×C₅	semidirect
94. C₃×#475	C₂×C₅	semidirect
95. C₃×#469	C₂×C₅	semidirect
96. C₃×#459	C₂×C₅	semidirect
97. C₃×#449	C₂×C₅	semidirect
98. C₃×C₄×SD₁₆	C₂×C₅	semidirect
99. C₃×#436	C₂×C₅	semidirect
100. C₃×#417	C₂×C₅	semidirect
130. #3332	C₃×C₅	direct (N × H)
136. C₃×C₅×Q₈	#41	semidirect
228. #550	C₂×C₃×C₅	semidirect
229. #547	C₂×C₃×C₅	semidirect
230. #486	C₂×C₃×C₅	semidirect
231. #481	C₂×C₃×C₅	semidirect
232. #475	C₂×C₃×C₅	semidirect
233. #469	C₂×C₃×C₅	semidirect
234. #459	C₂×C₃×C₅	semidirect
235. #449	C₂×C₃×C₅	semidirect
236. C₄×SD₁₆	C₂×C₃×C₅	semidirect
237. #436	C₂×C₃×C₅	semidirect
238. #417	C₂×C₃×C₅	semidirect
299. C₅×Q₈	C₃×#41	semidirect
366. C₃×Q₈	C₅×#41	semidirect
448. C₃×C₅	#3332	direct (N × H)
479. Q₈	C₃×C₅×#41	semidirect
512. C₅	C₃×#3332	direct (N × H)
532. C₃	C₅×#3332	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×#550	2
C₃×C₅×#547	2
C₃×C₅×#486	2
C₃×C₅×#481	2
C₃×C₅×#475	2
C₃×C₅×#469	2
C₃×C₅×#459	2
C₃×C₅×#449	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#436	2
C₃×C₅×#417	2
C₅×#3332	3
C₃×#3332	5

Subgroups — C3×C5×#3332 #14276366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3332 #14276366