Subgroups — C₃×C₅×#3038 #14276072

Order 1920.

1168 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#460	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#459	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#418	C₂	1	2	yes	maximal, complemented
8	C₅×#3038	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	—	2	2	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₃×C₅×AGL(1,ℤ/8)	—	2	8	no	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₃×C₅×#127	—	2	1	no	—
17	C₃×C₅×#127	—	2	1	no	—
18	C₃×C₅×#127	C₂²	1	4	yes	—
19	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
20	C₃×C₄×C₅×D₄	—	2	2	no	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
22	C₃×C₅×#117	—	2	1	no	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	—	2	1	no	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	complemented
27	C₃×C₅×#102	C₂²	1	8	yes	complemented
28	C₃×#3038	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
30	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
31	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#460	C₂×C₃	1	4	yes	complemented
33	C₅×#459	C₂×C₃	1	4	yes	complemented
34	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#418	C₂×C₃	1	2	yes	complemented
36	C₂⁴×C₃×C₅	—	2	2	no	—
37	C₃×C₅×#41	—	2	2	no	—
38	C₃×C₅×#41	D₄	1	4	yes	complemented
39	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	4	no	—
42	C₂×C₃×C₅×D₄	—	2	4	no	—
43	C₂×C₃×C₅×D₄	—	2	4	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	4	8	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×SD₁₆	—	2	8	no	—
54	C₃×C₅×D₈	—	2	8	no	—
55	C₃×C₅×M₁₆	—	2	4	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
61	C₃×C₄²×C₅	—	2	1	no	—
62	C₃×C₄²×C₅	—	2	2	no	—
63	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	2	yes	—
66	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
67	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#460	C₂×C₅	1	4	yes	complemented
70	C₃×#459	C₂×C₅	1	4	yes	complemented
71	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#418	C₂×C₅	1	2	yes	complemented
73	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₅×D₄	—	2	2	no	—
75	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
76	C₅×AGL(1,ℤ/8)	—	2	8	no	—
77	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
78	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
79	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
80	C₅×#127	—	2	1	no	—
81	C₅×#127	—	2	1	no	—
82	C₅×#127	C₂²×C₃	1	4	yes	—
83	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
86	C₅×#117	—	2	1	no	—
87	C₅×#117	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
90	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
91	C₅×#102	C₂²×C₃	1	8	yes	complemented
92	#3038	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
93	C₂³×C₃×C₅	—	2	1	no	—
94	C₂³×C₃×C₅	—	2	4	no	—
95	C₂³×C₃×C₅	—	4	8	no	—
96	C₂³×C₃×C₅	—	4	4	no	—
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₃×C₅×Q₈	—	2	1	no	—
99	C₃×C₅×Q₈	C₂×D₄	1	2	yes	complemented
100	C₃×C₅×D₄	—	2	4	no	—
101	C₃×C₅×D₄	—	2	4	no	—
102	C₃×C₅×D₄	—	2	1	no	—
103	C₃×C₅×D₄	—	2	4	no	—
104	C₃×C₅×D₄	—	4	8	no	—
105	C₃×C₅×D₄	—	4	4	no	—
106	C₃×C₅×D₄	—	4	8	no	—
107	C₃×C₅×D₄	C₂×D₄	1	2	yes	complemented
108	C₂×C₃×C₄×C₅	—	2	1	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	4	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	#41	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₃×C₅×C₈	—	2	4	no	—
120	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×D₄	—	2	2	no	—
122	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
123	C₃×AGL(1,ℤ/8)	—	2	8	no	—
124	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
125	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
126	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
127	C₃×#127	—	2	1	no	—
128	C₃×#127	—	2	1	no	—
129	C₃×#127	C₂²×C₅	1	4	yes	—
130	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
131	C₃×C₄×D₄	—	2	2	no	—
132	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
133	C₃×#117	—	2	1	no	—
134	C₃×#117	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₄²	—	2	1	no	—
136	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	complemented
138	C₃×#102	C₂²×C₅	1	8	yes	complemented
139	C₂⁴×C₅	—	2	2	no	—
140	C₅×#41	—	2	2	no	—
141	C₅×#41	C₃×D₄	1	4	yes	complemented
142	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	—	2	4	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	4	no	—
147	C₂×C₅×D₄	—	2	4	no	—
148	C₂×C₅×D₄	—	2	4	no	—
149	C₂×C₅×D₄	—	4	8	no	—
150	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
151	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₅×SD₁₆	—	2	8	no	—
157	C₅×D₈	—	2	8	no	—
158	C₅×M₁₆	—	2	4	no	—
159	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
160	C₅×C₄⋊C₄	—	2	2	no	—
161	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	2	2	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	—	2	2	no	—
166	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
167	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
168	C₄²×C₅	C₂³×C₃	1	2	yes	—
169	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
170	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
171	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
172	#460	C₂×C₃×C₅	1	4	yes	complemented
173	#459	C₂×C₃×C₅	1	4	yes	complemented
174	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	#418	C₂×C₃×C₅	1	2	yes	complemented
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	—	4	4	no	—
180	C₂²×C₃×C₅	—	4	8	no	—
181	C₂²×C₃×C₅	—	8	8	no	—
182	C₂²×C₃×C₅	#121	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	4	2	no	—
187	C₃×C₄×C₅	#121	1	2	yes	—
188	C₃×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	complemented
189	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
191	C₂⁴×C₃	—	2	2	no	—
192	C₃×#41	—	2	2	no	—
193	C₃×#41	C₅×D₄	1	4	yes	complemented
194	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	—	2	4	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	2	4	no	—
199	C₂×C₃×D₄	—	2	4	no	—
200	C₂×C₃×D₄	—	2	4	no	—
201	C₂×C₃×D₄	—	4	8	no	—
202	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
203	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	2	no	—
206	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₃×SD₁₆	—	2	8	no	—
209	C₃×D₈	—	2	8	no	—
210	C₃×M₁₆	—	2	4	no	—
211	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
214	C₃×C₂²⋊C₄	—	2	1	no	—
215	C₃×C₂²⋊C₄	—	2	2	no	—
216	C₃×C₄²	—	2	1	no	—
217	C₃×C₄²	—	2	2	no	—
218	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
219	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
220	C₃×C₄²	C₂³×C₅	1	2	yes	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	4	no	—
223	C₂³×C₅	—	4	8	no	—
224	C₂³×C₅	—	4	4	no	—
225	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
226	C₅×Q₈	—	2	1	no	—
227	C₅×Q₈	C₂×C₃×D₄	1	2	yes	complemented
228	C₅×D₄	—	2	4	no	—
229	C₅×D₄	—	2	4	no	—
230	C₅×D₄	—	2	1	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	4	8	no	—
233	C₅×D₄	—	4	4	no	—
234	C₅×D₄	—	4	8	no	—
235	C₅×D₄	C₂×C₃×D₄	1	2	yes	complemented
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	—	2	4	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	4	4	no	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	C₃×#41	1	2	yes	—
246	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
247	C₅×C₈	—	2	4	no	—
248	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
251	AGL(1,ℤ/8)	—	2	8	no	—
252	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	complemented
253	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
254	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
255	#127	—	2	1	no	—
256	#127	—	2	1	no	—
257	#127	C₂²×C₃×C₅	1	4	yes	—
258	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
261	#117	—	2	1	no	—
262	#117	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
266	#102	C₂²×C₃×C₅	1	8	yes	complemented
267	C₂×C₃×C₅	—	2	2	no	—
268	C₂×C₃×C₅	—	4	2	no	—
269	C₂×C₃×C₅	—	8	4	no	—
270	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
272	C₂³×C₃	—	2	1	no	—
273	C₂³×C₃	—	2	4	no	—
274	C₂³×C₃	—	4	8	no	—
275	C₂³×C₃	—	4	4	no	—
276	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
277	C₃×Q₈	—	2	1	no	—
278	C₃×Q₈	C₂×C₅×D₄	1	2	yes	complemented
279	C₃×D₄	—	2	4	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	1	no	—
282	C₃×D₄	—	2	4	no	—
283	C₃×D₄	—	4	8	no	—
284	C₃×D₄	—	4	4	no	—
285	C₃×D₄	—	4	8	no	—
286	C₃×D₄	C₂×C₅×D₄	1	2	yes	complemented
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	4	4	no	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂×C₃×C₄	C₅×#41	1	2	yes	—
297	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
298	C₃×C₈	—	2	4	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	2	2	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	8	no	—
303	C₂²×C₅	—	4	4	no	—
304	C₂²×C₅	—	8	8	no	—
305	C₂²×C₅	C₃×#121	1	2	yes	—
306	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	4	2	no	—
310	C₄×C₅	C₃×#121	1	2	yes	—
311	C₄×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
312	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
313	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
314	C₂⁴	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	C₃×C₅×D₄	1	4	yes	complemented
317	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
326	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
330	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
331	SD₁₆	—	2	8	no	—
332	D₈	—	2	8	no	—
333	M₁₆	—	2	4	no	—
334	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
342	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
343	C₄²	C₂³×C₃×C₅	1	2	yes	—
344	C₃×C₅	#3038	1	1	yes	characteristic, direct product factor, Hall
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	—	4	4	no	—
349	C₂²×C₃	—	4	8	no	—
350	C₂²×C₃	—	8	8	no	—
351	C₂²×C₃	C₅×#121	1	2	yes	—
352	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	4	2	no	—
356	C₃×C₄	C₅×#121	1	2	yes	—
357	C₃×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
358	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
360	C₂×C₅	—	2	2	no	—
361	C₂×C₅	—	4	2	no	—
362	C₂×C₅	—	8	4	no	—
363	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
364	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	4	8	no	—
368	C₂³	—	4	4	no	—
369	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	Q₈	—	2	1	no	—
371	Q₈	C₂×C₃×C₅×D₄	1	2	yes	complemented
372	D₄	—	2	4	no	—
373	D₄	—	2	4	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	4	no	—
376	D₄	—	4	8	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	8	no	—
379	D₄	C₂×C₃×C₅×D₄	1	2	yes	complemented
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
386	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
387	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
389	C₂×C₄	C₃×C₅×#41	1	2	yes	—
390	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	—	8	4	no	—
395	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
396	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
397	C₅	C₃×#3038	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	8	no	—
403	C₂²	—	8	8	no	—
404	C₂²	C₃×C₅×#121	1	2	yes	—
405	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	C₃×C₅×#121	1	2	yes	—
410	C₄	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	complemented
411	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
412	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
413	C₃	C₅×#3038	1	1	yes	characteristic, direct product factor, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	4	2	no	—
416	C₂	—	8	4	no	—
417	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
418	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—

	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 ◁ 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×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₃×C₄×C₅×#41	C₂	semidirect
4. C₃×C₅×#460	C₂	semidirect
5. C₃×C₅×#459	C₂	semidirect
6. C₃×C₅×#423	C₂	semidirect
7. C₃×C₅×#418	C₂	semidirect
8. C₅×#3038	C₃	direct (N × H)
13. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
14. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₃×C₄×C₅×Q₈	C₂²	semidirect
21. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×C₅×C₄⋊C₈	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
28. C₃×#3038	C₅	direct (N × H)
29. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
30. C₂×C₅×#127	C₂×C₃	semidirect
31. C₄×C₅×#41	C₂×C₃	semidirect
32. C₅×#460	C₂×C₃	semidirect
33. C₅×#459	C₂×C₃	semidirect
34. C₅×#423	C₂×C₃	semidirect
35. C₅×#418	C₂×C₃	semidirect
38. C₃×C₅×#41	D₄	semidirect
66. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
67. C₂×C₃×#127	C₂×C₅	semidirect
68. C₃×C₄×#41	C₂×C₅	semidirect
69. C₃×#460	C₂×C₅	semidirect
70. C₃×#459	C₂×C₅	semidirect
71. C₃×#423	C₂×C₅	semidirect
72. C₃×#418	C₂×C₅	semidirect
77. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
78. C₂×C₅×D₈	C₂²×C₃	semidirect
83. C₄×C₅×Q₈	C₂²×C₃	semidirect
85. C₄×C₅×D₄	C₂²×C₃	semidirect
90. C₅×C₄⋊C₈	C₂²×C₃	semidirect
91. C₅×#102	C₂²×C₃	semidirect
92. #3038	C₃×C₅	direct (N × H)
99. C₃×C₅×Q₈	C₂×D₄	semidirect
107. C₃×C₅×D₄	C₂×D₄	semidirect
124. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
125. C₂×C₃×D₈	C₂²×C₅	semidirect
130. C₃×C₄×Q₈	C₂²×C₅	semidirect
132. C₃×C₄×D₄	C₂²×C₅	semidirect
137. C₃×C₄⋊C₈	C₂²×C₅	semidirect
138. C₃×#102	C₂²×C₅	semidirect
141. C₅×#41	C₃×D₄	semidirect
169. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
170. C₂×#127	C₂×C₃×C₅	semidirect
171. C₄×#41	C₂×C₃×C₅	semidirect
172. #460	C₂×C₃×C₅	semidirect
173. #459	C₂×C₃×C₅	semidirect
174. #423	C₂×C₃×C₅	semidirect
175. #418	C₂×C₃×C₅	semidirect
188. C₃×C₄×C₅	AGL(1,ℤ/8)	semidirect
193. C₃×#41	C₅×D₄	semidirect
227. C₅×Q₈	C₂×C₃×D₄	semidirect
235. C₅×D₄	C₂×C₃×D₄	semidirect
252. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
253. C₂×D₈	C₂²×C₃×C₅	semidirect
258. C₄×Q₈	C₂²×C₃×C₅	semidirect
260. C₄×D₄	C₂²×C₃×C₅	semidirect
265. C₄⋊C₈	C₂²×C₃×C₅	semidirect
266. #102	C₂²×C₃×C₅	semidirect
278. C₃×Q₈	C₂×C₅×D₄	semidirect
286. C₃×D₄	C₂×C₅×D₄	semidirect
311. C₄×C₅	C₃×AGL(1,ℤ/8)	semidirect
316. #41	C₃×C₅×D₄	semidirect
344. C₃×C₅	#3038	direct (N × H)
357. C₃×C₄	C₅×AGL(1,ℤ/8)	semidirect
371. Q₈	C₂×C₃×C₅×D₄	semidirect
379. D₄	C₂×C₃×C₅×D₄	semidirect
397. C₅	C₃×#3038	direct (N × H)
410. C₄	C₃×C₅×AGL(1,ℤ/8)	semidirect
413. C₃	C₅×#3038	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×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#127	2
C₃×C₄×C₅×#41	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#423	2
C₃×C₅×#418	2
C₅×#3038	3
C₃×#3038	5

Subgroups — C3×C5×#3038 #14276072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3038 #14276072