Subgroups — C₃×C₅×#3112 #14276146

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#480	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#477	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#460	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#440	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3112	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	—	2	1	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×#124	—	2	1	no	—
16	C₃×C₅×#121	—	2	1	no	—
17	C₃×C₅×#121	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	—	2	1	no	—
23	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	—	2	1	no	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#107	C₂²	1	4	yes	—
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₃×C₅×#103	C₂²	1	4	yes	—
31	C₃×C₅×#102	C₂²	1	4	yes	—
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	—
34	C₃×#3112	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₅×#532	C₂×C₃	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#480	C₂×C₃	1	2	yes	complemented
38	C₅×#477	C₂×C₃	1	2	yes	complemented
39	C₅×#460	C₂×C₃	1	2	yes	complemented
40	C₅×#448	C₂×C₃	1	2	yes	complemented
41	C₅×#440	C₂×C₃	1	4	yes	complemented
42	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₅×#41	—	4	4	no	—
44	C₂×C₃×C₅×Q₈	—	2	4	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	1	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	—	2	1	no	—
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×SD₁₆	—	2	8	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#532	C₂×C₅	1	1	yes	characteristic
75	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#480	C₂×C₅	1	2	yes	complemented
77	C₃×#477	C₂×C₅	1	2	yes	complemented
78	C₃×#460	C₂×C₅	1	2	yes	complemented
79	C₃×#448	C₂×C₅	1	2	yes	complemented
80	C₃×#440	C₂×C₅	1	4	yes	complemented
81	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂×C₅×#41	—	2	1	no	—
83	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
85	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₅×#127	C₂²×C₃	1	1	yes	characteristic
87	C₅×#124	—	2	1	no	—
88	C₅×#121	—	2	1	no	—
89	C₅×#121	C₂²×C₃	1	2	yes	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
93	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#107	C₂²×C₃	1	4	yes	—
101	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
102	C₅×#103	C₂²×C₃	1	4	yes	—
103	C₅×#102	C₂²×C₃	1	4	yes	—
104	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
105	C₅×#97	C₂²×C₃	1	2	yes	—
106	#3112	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
109	C₃×C₅×Q₈	—	2	4	no	—
110	C₃×C₅×Q₈	—	2	2	no	—
111	C₃×C₅×Q₈	—	4	2	no	—
112	C₃×C₅×Q₈	#41	1	4	yes	complemented
113	C₃×C₅×D₄	—	2	4	no	—
114	C₃×C₅×D₄	—	4	2	no	—
115	C₃×C₅×D₄	—	4	4	no	—
116	C₃×C₅×D₄	—	4	2	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	—	4	2	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×C₅×C₈	—	2	4	no	—
133	C₂×C₃×#41	—	2	1	no	—
134	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
136	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#127	C₂²×C₅	1	1	yes	characteristic
138	C₃×#124	—	2	1	no	—
139	C₃×#121	—	2	1	no	—
140	C₃×#121	C₂²×C₅	1	2	yes	—
141	C₃×C₄×Q₈	—	2	1	no	—
142	C₃×C₄×Q₈	—	2	1	no	—
143	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
144	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
145	C₃×C₄×D₄	—	2	1	no	—
146	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
147	C₂×C₃×C₄⋊C₄	—	2	1	no	—
148	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×C₄²	—	2	1	no	—
150	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
151	C₃×#107	C₂²×C₅	1	4	yes	—
152	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
153	C₃×#103	C₂²×C₅	1	4	yes	—
154	C₃×#102	C₂²×C₅	1	4	yes	—
155	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
156	C₃×#97	C₂²×C₅	1	2	yes	—
157	C₅×#41	—	4	4	no	—
158	C₂×C₅×Q₈	—	2	4	no	—
159	C₂×C₅×Q₈	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
172	C₅×SD₁₆	—	2	8	no	—
173	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	2	2	no	—
176	C₅×C₄⋊C₄	—	2	1	no	—
177	C₅×C₄⋊C₄	—	2	1	no	—
178	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
179	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₄²×C₅	—	2	2	no	—
183	C₄²×C₅	—	2	2	no	—
184	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
185	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
186	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
188	#532	C₂×C₃×C₅	1	1	yes	characteristic
189	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
190	#480	C₂×C₃×C₅	1	2	yes	complemented
191	#477	C₂×C₃×C₅	1	2	yes	complemented
192	#460	C₂×C₃×C₅	1	2	yes	complemented
193	#448	C₂×C₃×C₅	1	2	yes	complemented
194	#440	C₂×C₃×C₅	1	4	yes	complemented
195	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	C₂²×C₃×C₅	—	2	1	no	—
197	C₂²×C₃×C₅	—	2	1	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
202	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₃×C₄×C₅	—	2	4	no	—
204	C₃×C₄×C₅	—	2	1	no	—
205	C₃×C₄×C₅	—	2	1	no	—
206	C₃×C₄×C₅	—	2	1	no	—
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	#137	1	2	yes	—
211	C₃×C₄×C₅	C₂×#41	1	2	yes	—
212	C₃×#41	—	4	4	no	—
213	C₂×C₃×Q₈	—	2	4	no	—
214	C₂×C₃×Q₈	—	2	1	no	—
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
217	C₂×C₃×D₄	—	2	2	no	—
218	C₂×C₃×D₄	—	2	1	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	—	2	2	no	—
224	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₃×SD₁₆	—	2	8	no	—
228	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	2	2	no	—
231	C₃×C₄⋊C₄	—	2	1	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
234	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
235	C₃×C₂²⋊C₄	—	2	2	no	—
236	C₃×C₂²⋊C₄	—	2	2	no	—
237	C₃×C₄²	—	2	2	no	—
238	C₃×C₄²	—	2	2	no	—
239	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
240	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
241	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
242	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
243	C₂³×C₅	—	2	2	no	—
244	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
245	C₅×Q₈	—	2	4	no	—
246	C₅×Q₈	—	2	2	no	—
247	C₅×Q₈	—	4	2	no	—
248	C₅×Q₈	C₃×#41	1	4	yes	complemented
249	C₅×D₄	—	2	4	no	—
250	C₅×D₄	—	4	2	no	—
251	C₅×D₄	—	4	4	no	—
252	C₅×D₄	—	4	2	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	4	4	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
268	C₅×C₈	—	2	4	no	—
269	C₂×#41	—	2	1	no	—
270	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
272	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
273	#127	C₂²×C₃×C₅	1	1	yes	characteristic
274	#124	—	2	1	no	—
275	#121	—	2	1	no	—
276	#121	C₂²×C₃×C₅	1	2	yes	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
280	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
287	#107	C₂²×C₃×C₅	1	4	yes	—
288	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
289	#103	C₂²×C₃×C₅	1	4	yes	—
290	#102	C₂²×C₃×C₅	1	4	yes	—
291	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
292	#97	C₂²×C₃×C₅	1	2	yes	—
293	C₂×C₃×C₅	—	2	2	no	—
294	C₂×C₃×C₅	—	8	2	no	—
295	C₂×C₃×C₅	#525	1	1	yes	characteristic
296	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
297	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
298	C₂³×C₃	—	2	2	no	—
299	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
300	C₃×Q₈	—	2	4	no	—
301	C₃×Q₈	—	2	2	no	—
302	C₃×Q₈	—	4	2	no	—
303	C₃×Q₈	C₅×#41	1	4	yes	complemented
304	C₃×D₄	—	2	4	no	—
305	C₃×D₄	—	4	2	no	—
306	C₃×D₄	—	4	4	no	—
307	C₃×D₄	—	4	2	no	—
308	C₂×C₃×C₄	—	2	4	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	4	4	no	—
316	C₂×C₃×C₄	—	4	2	no	—
317	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
323	C₃×C₈	—	2	4	no	—
324	C₂²×C₅	—	2	1	no	—
325	C₂²×C₅	—	2	1	no	—
326	C₂²×C₅	—	4	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	2	no	—
329	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
330	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	2	4	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	4	2	no	—
337	C₄×C₅	—	4	2	no	—
338	C₄×C₅	C₃×#137	1	2	yes	—
339	C₄×C₅	C₂×C₃×#41	1	2	yes	—
340	#41	—	4	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
355	SD₁₆	—	2	8	no	—
356	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
362	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
368	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
369	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
370	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
371	C₃×C₅	#3112	1	1	yes	characteristic, direct product factor, Hall
372	C₂²×C₃	—	2	1	no	—
373	C₂²×C₃	—	2	1	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	2	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
378	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
379	C₃×C₄	—	2	4	no	—
380	C₃×C₄	—	2	1	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	4	2	no	—
385	C₃×C₄	—	4	2	no	—
386	C₃×C₄	C₅×#137	1	2	yes	—
387	C₃×C₄	C₂×C₅×#41	1	2	yes	—
388	C₂×C₅	—	2	2	no	—
389	C₂×C₅	—	8	2	no	—
390	C₂×C₅	C₃×#525	1	1	yes	characteristic
391	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	C₃×C₅×#41	1	4	yes	complemented
399	D₄	—	2	4	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	8	2	no	—
421	C₂×C₃	C₅×#525	1	1	yes	characteristic
422	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
424	C₅	C₃×#3112	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
431	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
432	C₄	—	2	4	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	C₃×C₅×#137	1	2	yes	—
440	C₄	C₂×C₃×C₅×#41	1	2	yes	—
441	C₃	C₅×#3112	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	8	2	no	—
444	C₂	C₃×C₅×#525	1	1	yes	characteristic
445	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
446	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×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
3. C₃×C₅×#480	C₂	semidirect
4. C₃×C₅×#477	C₂	semidirect
5. C₃×C₅×#460	C₂	semidirect
6. C₃×C₅×#448	C₂	semidirect
7. C₃×C₅×#440	C₂	semidirect
8. C₃×C₅×#432	C₂	semidirect
9. C₅×#3112	C₃	direct (N × H)
34. C₃×#3112	C₅	direct (N × H)
36. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
37. C₅×#480	C₂×C₃	semidirect
38. C₅×#477	C₂×C₃	semidirect
39. C₅×#460	C₂×C₃	semidirect
40. C₅×#448	C₂×C₃	semidirect
41. C₅×#440	C₂×C₃	semidirect
42. C₅×#432	C₂×C₃	semidirect
75. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
76. C₃×#480	C₂×C₅	semidirect
77. C₃×#477	C₂×C₅	semidirect
78. C₃×#460	C₂×C₅	semidirect
79. C₃×#448	C₂×C₅	semidirect
80. C₃×#440	C₂×C₅	semidirect
81. C₃×#432	C₂×C₅	semidirect
106. #3112	C₃×C₅	direct (N × H)
112. C₃×C₅×Q₈	#41	semidirect
189. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
190. #480	C₂×C₃×C₅	semidirect
191. #477	C₂×C₃×C₅	semidirect
192. #460	C₂×C₃×C₅	semidirect
193. #448	C₂×C₃×C₅	semidirect
194. #440	C₂×C₃×C₅	semidirect
195. #432	C₂×C₃×C₅	semidirect
248. C₅×Q₈	C₃×#41	semidirect
303. C₃×Q₈	C₅×#41	semidirect
371. C₃×C₅	#3112	direct (N × H)
398. Q₈	C₃×C₅×#41	semidirect
424. C₅	C₃×#3112	direct (N × H)
441. C₃	C₅×#3112	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×#532	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#480	2
C₃×C₅×#477	2
C₃×C₅×#460	2
C₃×C₅×#448	2
C₃×C₅×#440	2
C₃×C₅×#432	2
C₅×#3112	3
C₃×#3112	5

Subgroups — C3×C5×#3112 #14276146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3112 #14276146