Subgroups — C₃×C₅×#3277 #14276311

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#468	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3277	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₃×C₅×#137	—	2	8	no	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
21	C₃×C₅×#124	—	2	2	no	—
22	C₃×C₅×#124	C₂²	1	2	yes	—
23	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₅×#121	—	2	2	no	—
26	C₃×C₅×#121	C₂²	1	2	yes	—
27	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
28	C₃×C₄×C₅×D₄	—	2	2	no	—
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×#103	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×C₅×#102	C₂²	1	2	yes	—
35	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₃×#3277	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
39	C₅×#548	C₂×C₃	1	2	yes	complemented
40	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
41	C₅×#468	C₂×C₃	1	2	yes	complemented
42	C₅×#464	C₂×C₃	1	2	yes	complemented
43	C₅×#451	C₂×C₃	1	2	yes	complemented
44	C₅×#449	C₂×C₃	1	2	yes	complemented
45	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×C₅×#41	—	2	4	no	—
48	C₃×C₅×#41	—	4	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	4	no	—
51	C₂×C₃×C₅×Q₈	—	4	2	no	—
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₂×C₃×C₅×D₄	—	2	2	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂²×C₃×C₄×C₅	—	2	2	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₃×C₅×Q₁₆	—	2	4	no	—
62	C₃×C₅×Q₁₆	—	4	1	no	—
63	C₃×C₅×Q₁₆	D₄	1	4	yes	complemented
64	C₃×C₅×SD₁₆	—	2	4	no	—
65	C₃×C₅×SD₁₆	—	2	4	no	—
66	C₃×C₅×D₈	—	4	1	no	—
67	C₃×C₅×M₁₆	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
80	C₃×C₄²×C₅	—	2	2	no	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
83	C₃×#548	C₂×C₅	1	2	yes	complemented
84	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#468	C₂×C₅	1	2	yes	complemented
86	C₃×#464	C₂×C₅	1	2	yes	complemented
87	C₃×#451	C₂×C₅	1	2	yes	complemented
88	C₃×#449	C₂×C₅	1	2	yes	complemented
89	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
93	C₅×#137	—	2	8	no	—
94	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
95	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
98	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
99	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
101	C₅×#124	—	2	2	no	—
102	C₅×#124	C₂²×C₃	1	2	yes	—
103	C₅×C₂²⋊Q₈	—	2	2	no	—
104	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
105	C₅×#121	—	2	2	no	—
106	C₅×#121	C₂²×C₃	1	2	yes	—
107	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
108	C₄×C₅×D₄	—	2	2	no	—
109	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
110	C₅×#107	C₂²×C₃	1	1	yes	characteristic
111	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
112	C₅×#103	C₂²×C₃	1	2	yes	—
113	C₅×#103	C₂²×C₃	1	2	yes	—
114	C₅×#102	C₂²×C₃	1	2	yes	—
115	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
116	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
117	#3277	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₃×C₅×Q₈	—	2	2	no	—
121	C₃×C₅×Q₈	—	2	2	no	—
122	C₃×C₅×Q₈	—	2	2	no	—
123	C₃×C₅×Q₈	—	4	4	no	—
124	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	4	1	no	—
128	C₃×C₅×D₄	—	4	4	no	—
129	C₃×C₅×D₄	—	4	4	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	4	no	—
136	C₂×C₃×C₄×C₅	—	4	4	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₅×C₈	—	2	2	no	—
142	C₃×C₅×C₈	—	2	1	no	—
143	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
144	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
145	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
146	C₃×#137	—	2	8	no	—
147	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
148	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
151	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
152	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
153	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
154	C₃×#124	—	2	2	no	—
155	C₃×#124	C₂²×C₅	1	2	yes	—
156	C₃×C₂²⋊Q₈	—	2	2	no	—
157	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
158	C₃×#121	—	2	2	no	—
159	C₃×#121	C₂²×C₅	1	2	yes	—
160	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
161	C₃×C₄×D₄	—	2	2	no	—
162	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
163	C₃×#107	C₂²×C₅	1	1	yes	characteristic
164	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
165	C₃×#103	C₂²×C₅	1	2	yes	—
166	C₃×#103	C₂²×C₅	1	2	yes	—
167	C₃×#102	C₂²×C₅	1	2	yes	—
168	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
169	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
170	C₅×#41	—	2	4	no	—
171	C₅×#41	—	4	2	no	—
172	C₂×C₅×Q₈	—	2	2	no	—
173	C₂×C₅×Q₈	—	2	4	no	—
174	C₂×C₅×Q₈	—	4	2	no	—
175	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
176	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
177	C₂×C₅×D₄	—	2	2	no	—
178	C₂×C₅×D₄	—	2	2	no	—
179	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
180	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	—	2	2	no	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
184	C₅×Q₁₆	—	2	4	no	—
185	C₅×Q₁₆	—	4	1	no	—
186	C₅×Q₁₆	C₃×D₄	1	4	yes	complemented
187	C₅×SD₁₆	—	2	4	no	—
188	C₅×SD₁₆	—	2	4	no	—
189	C₅×D₈	—	4	1	no	—
190	C₅×M₁₆	—	2	4	no	—
191	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
192	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	2	no	—
196	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
197	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
206	#548	C₂×C₃×C₅	1	2	yes	complemented
207	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
208	#468	C₂×C₃×C₅	1	2	yes	complemented
209	#464	C₂×C₃×C₅	1	2	yes	complemented
210	#451	C₂×C₃×C₅	1	2	yes	complemented
211	#449	C₂×C₃×C₅	1	2	yes	complemented
212	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
213	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
214	C₂²×C₃×C₅	—	2	2	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	—	2	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	2	4	no	—
223	C₃×C₄×C₅	—	2	1	no	—
224	C₃×C₄×C₅	—	2	1	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	—	4	2	no	—
227	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
229	C₃×#41	—	2	4	no	—
230	C₃×#41	—	4	2	no	—
231	C₂×C₃×Q₈	—	2	2	no	—
232	C₂×C₃×Q₈	—	2	4	no	—
233	C₂×C₃×Q₈	—	4	2	no	—
234	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
235	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
236	C₂×C₃×D₄	—	2	2	no	—
237	C₂×C₃×D₄	—	2	2	no	—
238	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
239	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	2	no	—
242	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
243	C₃×Q₁₆	—	2	4	no	—
244	C₃×Q₁₆	—	4	1	no	—
245	C₃×Q₁₆	C₅×D₄	1	4	yes	complemented
246	C₃×SD₁₆	—	2	4	no	—
247	C₃×SD₁₆	—	2	4	no	—
248	C₃×D₈	—	4	1	no	—
249	C₃×M₁₆	—	2	4	no	—
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
256	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₂²⋊C₄	—	2	2	no	—
259	C₃×C₂²⋊C₄	—	2	2	no	—
260	C₃×C₂²⋊C₄	—	2	2	no	—
261	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
262	C₃×C₄²	—	2	2	no	—
263	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	—	4	4	no	—
270	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
271	C₅×D₄	—	2	2	no	—
272	C₅×D₄	—	2	2	no	—
273	C₅×D₄	—	4	1	no	—
274	C₅×D₄	—	4	4	no	—
275	C₅×D₄	—	4	4	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	4	4	no	—
282	C₂×C₄×C₅	—	4	4	no	—
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
286	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
287	C₅×C₈	—	2	2	no	—
288	C₅×C₈	—	2	1	no	—
289	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
290	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
291	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
292	#137	—	2	8	no	—
293	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
294	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
296	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
297	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
298	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
300	#124	—	2	2	no	—
301	#124	C₂²×C₃×C₅	1	2	yes	—
302	C₂²⋊Q₈	—	2	2	no	—
303	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
304	#121	—	2	2	no	—
305	#121	C₂²×C₃×C₅	1	2	yes	—
306	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
309	#107	C₂²×C₃×C₅	1	1	yes	characteristic
310	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
311	#103	C₂²×C₃×C₅	1	2	yes	—
312	#103	C₂²×C₃×C₅	1	2	yes	—
313	#102	C₂²×C₃×C₅	1	2	yes	—
314	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
315	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂×C₃×C₅	—	4	2	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
319	C₂×C₃×C₅	#575	1	1	yes	characteristic
320	C₂×C₃×C₅	#578	1	1	yes	characteristic
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
323	C₃×Q₈	—	2	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×Q₈	—	4	4	no	—
327	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	4	1	no	—
331	C₃×D₄	—	4	4	no	—
332	C₃×D₄	—	4	4	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	4	4	no	—
339	C₂×C₃×C₄	—	4	4	no	—
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
344	C₃×C₈	—	2	2	no	—
345	C₃×C₈	—	2	1	no	—
346	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
347	C₂²×C₅	—	2	2	no	—
348	C₂²×C₅	—	2	2	no	—
349	C₂²×C₅	—	2	2	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	4	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
361	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	#41	—	2	4	no	—
363	#41	—	4	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	4	2	no	—
367	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
368	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
372	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
376	Q₁₆	—	2	4	no	—
377	Q₁₆	—	4	1	no	—
378	Q₁₆	C₃×C₅×D₄	1	4	yes	complemented
379	SD₁₆	—	2	4	no	—
380	SD₁₆	—	2	4	no	—
381	D₈	—	4	1	no	—
382	M₁₆	—	2	4	no	—
383	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
384	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
385	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
389	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₃×C₅	#3277	1	1	yes	characteristic, direct product factor, Hall
398	C₂²×C₃	—	2	2	no	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	—	2	2	no	—
406	C₃×C₄	—	2	4	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂×C₅	—	4	2	no	—
414	C₂×C₅	—	8	2	no	—
415	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
416	C₂×C₅	C₃×#575	1	1	yes	characteristic
417	C₂×C₅	C₃×#578	1	1	yes	characteristic
418	C₂³	—	2	2	no	—
419	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
420	Q₈	—	2	2	no	—
421	Q₈	—	2	2	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	4	4	no	—
424	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	4	no	—
429	D₄	—	4	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
438	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
440	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
441	C₈	—	2	2	no	—
442	C₈	—	2	1	no	—
443	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
444	C₂×C₃	—	4	2	no	—
445	C₂×C₃	—	8	2	no	—
446	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
447	C₂×C₃	C₅×#575	1	1	yes	characteristic
448	C₂×C₃	C₅×#578	1	1	yes	characteristic
449	C₅	C₃×#3277	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
464	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
465	C₃	C₅×#3277	1	1	yes	characteristic, direct product factor, Sylow
466	C₂	—	4	2	no	—
467	C₂	—	8	2	no	—
468	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
469	C₂	C₃×C₅×#575	1	1	yes	characteristic
470	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
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. C₂×C₃×C₅×#137	C₂	semidirect
2. C₃×C₅×#548	C₂	semidirect
3. C₃×C₅×#495	C₂	semidirect
4. C₃×C₅×#468	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×C₅×#451	C₂	semidirect
7. C₃×C₅×#449	C₂	semidirect
8. C₃×C₄×C₅×Q₁₆	C₂	semidirect
9. C₃×C₅×#436	C₂	semidirect
10. C₅×#3277	C₃	direct (N × H)
37. C₃×#3277	C₅	direct (N × H)
38. C₂×C₅×#137	C₂×C₃	semidirect
39. C₅×#548	C₂×C₃	semidirect
40. C₅×#495	C₂×C₃	semidirect
41. C₅×#468	C₂×C₃	semidirect
42. C₅×#464	C₂×C₃	semidirect
43. C₅×#451	C₂×C₃	semidirect
44. C₅×#449	C₂×C₃	semidirect
45. C₄×C₅×Q₁₆	C₂×C₃	semidirect
46. C₅×#436	C₂×C₃	semidirect
63. C₃×C₅×Q₁₆	D₄	semidirect
82. C₂×C₃×#137	C₂×C₅	semidirect
83. C₃×#548	C₂×C₅	semidirect
84. C₃×#495	C₂×C₅	semidirect
85. C₃×#468	C₂×C₅	semidirect
86. C₃×#464	C₂×C₅	semidirect
87. C₃×#451	C₂×C₅	semidirect
88. C₃×#449	C₂×C₅	semidirect
89. C₃×C₄×Q₁₆	C₂×C₅	semidirect
90. C₃×#436	C₂×C₅	semidirect
117. #3277	C₃×C₅	direct (N × H)
186. C₅×Q₁₆	C₃×D₄	semidirect
205. C₂×#137	C₂×C₃×C₅	semidirect
206. #548	C₂×C₃×C₅	semidirect
207. #495	C₂×C₃×C₅	semidirect
208. #468	C₂×C₃×C₅	semidirect
209. #464	C₂×C₃×C₅	semidirect
210. #451	C₂×C₃×C₅	semidirect
211. #449	C₂×C₃×C₅	semidirect
212. C₄×Q₁₆	C₂×C₃×C₅	semidirect
213. #436	C₂×C₃×C₅	semidirect
245. C₃×Q₁₆	C₅×D₄	semidirect
378. Q₁₆	C₃×C₅×D₄	semidirect
397. C₃×C₅	#3277	direct (N × H)
449. C₅	C₃×#3277	direct (N × H)
465. C₃	C₅×#3277	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×#137	2
C₃×C₅×#548	2
C₃×C₅×#495	2
C₃×C₅×#468	2
C₃×C₅×#464	2
C₃×C₅×#451	2
C₃×C₅×#449	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×#436	2
C₅×#3277	3
C₃×#3277	5

Subgroups — C3×C5×#3277 #14276311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3277 #14276311