Subgroups — C₃×C₅×#3079 #14276113

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#477	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#476	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#474	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#417	C₂	1	2	yes	maximal
10	C₅×#3079	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	—	2	1	no	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
15	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	—	2	1	no	—
21	C₃×C₄×C₅×D₄	—	2	1	no	—
22	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	—	2	1	no	—
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	—	2	1	no	—
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	4	yes	—
31	C₃×C₅×#106	C₂²	1	4	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×#103	C₂²	1	4	yes	—
35	C₃×C₅×#102	C₂²	1	4	yes	—
36	C₃×#3079	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
38	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
39	C₅×#477	C₂×C₃	1	2	yes	complemented
40	C₅×#476	C₂×C₃	1	2	yes	complemented
41	C₅×#475	C₂×C₃	1	2	yes	complemented
42	C₅×#474	C₂×C₃	1	2	yes	complemented
43	C₅×#428	C₂×C₃	1	2	yes	complemented
44	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#417	C₂×C₃	1	2	yes	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	Q₈	1	4	yes	complemented
48	C₂×C₃×C₅×Q₈	—	2	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	4	4	no	—
51	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	—	2	1	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×M₁₆	—	2	4	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
69	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₄²×C₅	—	2	1	no	—
75	C₃×C₄²×C₅	—	2	1	no	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
78	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
83	C₃×#477	C₂×C₅	1	2	yes	complemented
84	C₃×#476	C₂×C₅	1	2	yes	complemented
85	C₃×#475	C₂×C₅	1	2	yes	complemented
86	C₃×#474	C₂×C₅	1	2	yes	complemented
87	C₃×#428	C₂×C₅	1	2	yes	complemented
88	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#417	C₂×C₅	1	2	yes	—
90	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₅×Q₈	—	2	1	no	—
92	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
93	C₅×C₄⋊Q₈	—	2	1	no	—
94	C₅×C₄⋊Q₈	—	2	1	no	—
95	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
97	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
102	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₅×#117	—	2	1	no	—
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	—	2	1	no	—
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₄²×C₅	—	2	1	no	—
108	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
109	C₅×#107	C₂²×C₃	1	4	yes	—
110	C₅×#106	C₂²×C₃	1	4	yes	—
111	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
112	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
113	C₅×#103	C₂²×C₃	1	4	yes	—
114	C₅×#102	C₂²×C₃	1	4	yes	—
115	#3079	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
116	C₂³×C₃×C₅	—	2	1	no	—
117	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
118	C₃×C₅×Q₈	—	2	1	no	—
119	C₃×C₅×Q₈	—	4	4	no	—
120	C₃×C₅×Q₈	—	4	4	no	—
121	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	complemented
122	C₃×C₅×D₄	—	2	4	no	—
123	C₃×C₅×D₄	—	2	1	no	—
124	C₃×C₅×D₄	C₂×Q₈	1	2	yes	complemented
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	4	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	4	no	—
132	C₂×C₃×C₄×C₅	—	4	4	no	—
133	C₂×C₃×C₄×C₅	—	4	2	no	—
134	C₂×C₃×C₄×C₅	—	4	2	no	—
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₅×C₈	—	2	4	no	—
144	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃×Q₈	—	2	1	no	—
146	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
147	C₃×C₄⋊Q₈	—	2	1	no	—
148	C₃×C₄⋊Q₈	—	2	1	no	—
149	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
150	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
151	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
152	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×C₄×D₄	—	2	1	no	—
154	C₃×C₄×D₄	—	2	1	no	—
155	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
156	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
157	C₃×#117	—	2	1	no	—
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	—	2	1	no	—
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₄²	—	2	1	no	—
162	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
163	C₃×#107	C₂²×C₅	1	4	yes	—
164	C₃×#106	C₂²×C₅	1	4	yes	—
165	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
166	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
167	C₃×#103	C₂²×C₅	1	4	yes	—
168	C₃×#102	C₂²×C₅	1	4	yes	—
169	C₅×#41	—	2	2	no	—
170	C₅×#41	C₃×Q₈	1	4	yes	complemented
171	C₂×C₅×Q₈	—	2	2	no	—
172	C₂×C₅×Q₈	—	2	2	no	—
173	C₂×C₅×Q₈	—	4	4	no	—
174	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	2	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₅×M₁₆	—	2	4	no	—
185	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
192	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
193	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
194	C₅×C₂²⋊C₄	—	2	1	no	—
195	C₅×C₂²⋊C₄	—	2	1	no	—
196	C₅×C₂²⋊C₄	—	2	1	no	—
197	C₄²×C₅	—	2	1	no	—
198	C₄²×C₅	—	2	1	no	—
199	C₄²×C₅	—	2	1	no	—
200	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
201	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
202	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
203	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
204	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic
206	#477	C₂×C₃×C₅	1	2	yes	complemented
207	#476	C₂×C₃×C₅	1	2	yes	complemented
208	#475	C₂×C₃×C₅	1	2	yes	complemented
209	#474	C₂×C₃×C₅	1	2	yes	complemented
210	#428	C₂×C₃×C₅	1	2	yes	complemented
211	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
212	#417	C₂×C₃×C₅	1	2	yes	—
213	C₂²×C₃×C₅	—	2	1	no	—
214	C₂²×C₃×C₅	—	2	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	—	4	1	no	—
218	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	—	2	1	no	—
222	C₃×C₄×C₅	—	2	1	no	—
223	C₃×C₄×C₅	—	4	1	no	—
224	C₃×C₄×C₅	—	4	4	no	—
225	C₃×C₄×C₅	—	4	1	no	—
226	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
227	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
228	C₃×C₄×C₅	#137	1	2	yes	—
229	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₃×#41	—	2	2	no	—
232	C₃×#41	C₅×Q₈	1	4	yes	complemented
233	C₂×C₃×Q₈	—	2	2	no	—
234	C₂×C₃×Q₈	—	2	2	no	—
235	C₂×C₃×Q₈	—	4	4	no	—
236	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₃×D₄	—	2	1	no	—
238	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	1	no	—
242	C₂²×C₃×C₄	—	2	1	no	—
243	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₃×M₁₆	—	2	4	no	—
247	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	2	no	—
251	C₃×C₄⋊C₄	—	2	1	no	—
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₂²⋊C₄	—	2	1	no	—
258	C₃×C₂²⋊C₄	—	2	1	no	—
259	C₃×C₄²	—	2	1	no	—
260	C₃×C₄²	—	2	1	no	—
261	C₃×C₄²	—	2	1	no	—
262	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
263	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
264	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
265	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
266	C₂³×C₅	—	2	1	no	—
267	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₅×Q₈	—	2	1	no	—
269	C₅×Q₈	—	4	4	no	—
270	C₅×Q₈	—	4	4	no	—
271	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	complemented
272	C₅×D₄	—	2	4	no	—
273	C₅×D₄	—	2	1	no	—
274	C₅×D₄	C₂×C₃×Q₈	1	2	yes	complemented
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	4	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	4	no	—
282	C₂×C₄×C₅	—	4	4	no	—
283	C₂×C₄×C₅	—	4	2	no	—
284	C₂×C₄×C₅	—	4	2	no	—
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
291	C₂×C₄×C₅	C₃×#41	1	2	yes	—
292	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₅×C₈	—	2	4	no	—
294	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
295	C₂²×Q₈	—	2	1	no	—
296	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
297	C₄⋊Q₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	1	no	—
299	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
300	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
301	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
302	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	C₂²×C₃×C₅	1	1	yes	characteristic
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
313	#107	C₂²×C₃×C₅	1	4	yes	—
314	#106	C₂²×C₃×C₅	1	4	yes	—
315	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
316	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
317	#103	C₂²×C₃×C₅	1	4	yes	—
318	#102	C₂²×C₃×C₅	1	4	yes	—
319	C₂×C₃×C₅	—	2	2	no	—
320	C₂×C₃×C₅	—	4	2	no	—
321	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
322	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
324	C₂³×C₃	—	2	1	no	—
325	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
326	C₃×Q₈	—	2	1	no	—
327	C₃×Q₈	—	4	4	no	—
328	C₃×Q₈	—	4	4	no	—
329	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	complemented
330	C₃×D₄	—	2	4	no	—
331	C₃×D₄	—	2	1	no	—
332	C₃×D₄	C₂×C₅×Q₈	1	2	yes	complemented
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	4	no	—
340	C₂×C₃×C₄	—	4	4	no	—
341	C₂×C₃×C₄	—	4	2	no	—
342	C₂×C₃×C₄	—	4	2	no	—
343	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
349	C₂×C₃×C₄	C₅×#41	1	2	yes	—
350	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
351	C₃×C₈	—	2	4	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	—	2	1	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	4	1	no	—
356	C₂²×C₅	—	4	1	no	—
357	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
358	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	1	no	—
361	C₄×C₅	—	2	2	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	—	4	4	no	—
364	C₄×C₅	—	4	1	no	—
365	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
366	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
367	C₄×C₅	C₃×#137	1	2	yes	—
368	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
369	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
370	#41	—	2	2	no	—
371	#41	C₃×C₅×Q₈	1	4	yes	complemented
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	4	4	no	—
375	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
385	M₁₆	—	2	4	no	—
386	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
393	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
394	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	2	1	no	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
402	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
403	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₃×C₅	#3079	1	1	yes	characteristic, direct product factor, Hall
406	C₂²×C₃	—	2	1	no	—
407	C₂²×C₃	—	2	1	no	—
408	C₂²×C₃	—	2	2	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	—	4	1	no	—
411	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
412	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	4	1	no	—
417	C₃×C₄	—	4	4	no	—
418	C₃×C₄	—	4	1	no	—
419	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
420	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
421	C₃×C₄	C₅×#137	1	2	yes	—
422	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
423	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
424	C₂×C₅	—	2	2	no	—
425	C₂×C₅	—	4	2	no	—
426	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
427	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
428	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
431	Q₈	—	2	1	no	—
432	Q₈	—	4	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	C₂×C₃×C₅×Q₈	1	2	yes	complemented
435	D₄	—	2	4	no	—
436	D₄	—	2	1	no	—
437	D₄	C₂×C₃×C₅×Q₈	1	2	yes	complemented
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
449	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
452	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
453	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
454	C₂×C₄	C₃×C₅×#41	1	2	yes	—
455	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
456	C₈	—	2	4	no	—
457	C₂×C₃	—	2	2	no	—
458	C₂×C₃	—	4	2	no	—
459	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
460	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
462	C₅	C₃×#3079	1	1	yes	characteristic, direct product factor, Sylow
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
469	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
477	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
478	C₄	C₃×C₅×#137	1	2	yes	—
479	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
480	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
481	C₃	C₅×#3079	1	1	yes	characteristic, direct product factor, Sylow
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
485	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
486	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	C₂×C₃×C₅×#41	C₂²
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
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#477	C₂	semidirect
4. C₃×C₅×#476	C₂	semidirect
5. C₃×C₅×#475	C₂	semidirect
6. C₃×C₅×#474	C₂	semidirect
7. C₃×C₅×#428	C₂	semidirect
8. C₃×C₅×#423	C₂	semidirect
10. C₅×#3079	C₃	direct (N × H)
36. C₃×#3079	C₅	direct (N × H)
37. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
39. C₅×#477	C₂×C₃	semidirect
40. C₅×#476	C₂×C₃	semidirect
41. C₅×#475	C₂×C₃	semidirect
42. C₅×#474	C₂×C₃	semidirect
43. C₅×#428	C₂×C₃	semidirect
44. C₅×#423	C₂×C₃	semidirect
47. C₃×C₅×#41	Q₈	semidirect
81. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
83. C₃×#477	C₂×C₅	semidirect
84. C₃×#476	C₂×C₅	semidirect
85. C₃×#475	C₂×C₅	semidirect
86. C₃×#474	C₂×C₅	semidirect
87. C₃×#428	C₂×C₅	semidirect
88. C₃×#423	C₂×C₅	semidirect
115. #3079	C₃×C₅	direct (N × H)
121. C₃×C₅×Q₈	C₂×Q₈	semidirect
124. C₃×C₅×D₄	C₂×Q₈	semidirect
170. C₅×#41	C₃×Q₈	semidirect
204. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
206. #477	C₂×C₃×C₅	semidirect
207. #476	C₂×C₃×C₅	semidirect
208. #475	C₂×C₃×C₅	semidirect
209. #474	C₂×C₃×C₅	semidirect
210. #428	C₂×C₃×C₅	semidirect
211. #423	C₂×C₃×C₅	semidirect
232. C₃×#41	C₅×Q₈	semidirect
271. C₅×Q₈	C₂×C₃×Q₈	semidirect
274. C₅×D₄	C₂×C₃×Q₈	semidirect
329. C₃×Q₈	C₂×C₅×Q₈	semidirect
332. C₃×D₄	C₂×C₅×Q₈	semidirect
371. #41	C₃×C₅×Q₈	semidirect
405. C₃×C₅	#3079	direct (N × H)
434. Q₈	C₂×C₃×C₅×Q₈	semidirect
437. D₄	C₂×C₃×C₅×Q₈	semidirect
462. C₅	C₃×#3079	direct (N × H)
481. C₃	C₅×#3079	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×C₄⋊Q₈	2
C₃×C₄×C₅×#41	2
C₃×C₅×#477	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#474	2
C₃×C₅×#428	2
C₃×C₅×#423	2
C₃×C₅×#417	2
C₅×#3079	3
C₃×#3079	5

Subgroups — C3×C5×#3079 #14276113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3079 #14276113