Subgroups — C₃×C₅×#1863 #14274897

Order 1920.

596 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#340	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₅×#1863	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄×C₅×Q₈	—	2	2	no	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	—	2	1	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×C₅×#107	—	2	2	no	—
22	C₃×C₅×#103	—	2	2	no	—
23	C₃×C₅×#103	C₄	1	4	yes	complemented
24	C₃×C₅×#95	—	2	1	no	—
25	C₃×#1863	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
27	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic
28	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
29	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
30	C₅×#389	C₂×C₃	1	1	yes	characteristic
31	C₅×#340	C₂×C₃	1	1	yes	characteristic
32	C₅×#336	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	Q₈	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	—	2	1	no	—
47	C₂×C₃×C₅×C₈	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
52	C₃×C₅×C₄⋊C₄	—	2	4	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₄⋊C₄	—	4	2	no	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
60	C₃×C₄²×C₅	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	1	no	—
62	C₃×C₄²×C₅	—	2	1	no	—
63	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
64	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic
65	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
66	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
67	C₃×#389	C₂×C₅	1	1	yes	characteristic
68	C₃×#340	C₂×C₅	1	1	yes	characteristic
69	C₃×#336	C₂×C₅	1	1	yes	characteristic
70	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
71	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₄×C₅×Q₈	—	2	2	no	—
74	C₄×C₅×Q₈	—	2	2	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
82	C₅×#107	—	2	2	no	—
83	C₅×#103	—	2	2	no	—
84	C₅×#103	C₃×C₄	1	4	yes	complemented
85	C₅×#95	—	2	1	no	—
86	#1863	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×Q₈	—	2	2	no	—
89	C₃×C₅×Q₈	—	2	2	no	—
90	C₃×C₅×Q₈	—	2	2	no	—
91	C₃×C₅×Q₈	C₄⋊C₄	1	4	yes	complemented
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	4	1	no	—
108	C₂×C₃×C₄×C₅	—	4	1	no	—
109	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄×Q₈	—	2	2	no	—
122	C₃×C₄×Q₈	—	2	2	no	—
123	C₂×C₃×C₄⋊C₄	—	2	1	no	—
124	C₂×C₃×C₄⋊C₄	—	2	1	no	—
125	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄²	—	2	1	no	—
129	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
130	C₃×#107	—	2	2	no	—
131	C₃×#103	—	2	2	no	—
132	C₃×#103	C₄×C₅	1	4	yes	complemented
133	C₃×#95	—	2	1	no	—
134	C₂×C₅×Q₈	—	2	1	no	—
135	C₂×C₅×Q₈	—	2	1	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
139	C₂×C₅×Q₈	C₃×Q₈	1	2	yes	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	—	2	4	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	1	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	4	2	no	—
159	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
160	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
165	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic
166	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
167	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
168	#389	C₂×C₃×C₅	1	1	yes	characteristic
169	#340	C₂×C₃×C₅	1	1	yes	characteristic
170	#336	C₂×C₃×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	#120	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
175	C₂²×C₃×C₅	#135	1	1	yes	characteristic
176	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂²×C₃×C₅	#137	1	1	yes	characteristic
178	C₃×C₄×C₅	—	2	4	no	—
179	C₃×C₄×C₅	—	2	2	no	—
180	C₃×C₄×C₅	—	4	2	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	—	4	2	no	—
183	C₃×C₄×C₅	—	8	1	no	—
184	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
186	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
187	C₃×C₄×C₅	#123	1	1	yes	characteristic
188	C₂×C₃×Q₈	—	2	1	no	—
189	C₂×C₃×Q₈	—	2	1	no	—
190	C₂×C₃×Q₈	—	2	1	no	—
191	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
192	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
193	C₂×C₃×Q₈	C₅×Q₈	1	2	yes	—
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂²×C₃×C₄	—	2	1	no	—
198	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂×C₃×C₈	—	2	1	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₂×C₃×C₈	—	2	1	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	—	2	1	no	—
211	C₃×C₄⋊C₄	—	2	1	no	—
212	C₃×C₄⋊C₄	—	4	2	no	—
213	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
214	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
215	C₃×C₄²	—	2	4	no	—
216	C₃×C₄²	—	2	1	no	—
217	C₃×C₄²	—	2	1	no	—
218	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₅×Q₈	—	2	2	no	—
220	C₅×Q₈	—	2	2	no	—
221	C₅×Q₈	—	2	2	no	—
222	C₅×Q₈	C₃×C₄⋊C₄	1	4	yes	complemented
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	C₃×Q₁₆	1	2	yes	—
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
245	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
246	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
247	C₅×C₈	—	2	2	no	—
248	C₅×C₈	—	4	1	no	—
249	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₄×Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
261	#107	—	2	2	no	—
262	#103	—	2	2	no	—
263	#103	C₃×C₄×C₅	1	4	yes	complemented
264	#95	—	2	1	no	—
265	C₂×C₃×C₅	#385	1	1	yes	characteristic
266	C₂×C₃×C₅	C₄×Q₁₆	1	1	yes	characteristic
267	C₂×C₃×C₅	#440	1	1	yes	characteristic
268	C₂×C₃×C₅	#449	1	1	yes	characteristic
269	C₂×C₃×C₅	#451	1	1	yes	characteristic
270	C₂×C₃×C₅	#477	1	1	yes	characteristic
271	C₂×C₃×C₅	#479	1	1	yes	characteristic
272	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
273	C₃×Q₈	—	2	2	no	—
274	C₃×Q₈	—	2	2	no	—
275	C₃×Q₈	—	2	2	no	—
276	C₃×Q₈	C₅×C₄⋊C₄	1	4	yes	complemented
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	4	1	no	—
288	C₂×C₃×C₄	—	4	1	no	—
289	C₂×C₃×C₄	—	4	1	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	—	4	1	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	C₅×Q₁₆	1	2	yes	—
295	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
299	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
300	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
301	C₃×C₈	—	2	2	no	—
302	C₃×C₈	—	4	1	no	—
303	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₅	C₃×#120	1	1	yes	characteristic
305	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
306	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
307	C₂²×C₅	C₃×#135	1	1	yes	characteristic
308	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
309	C₂²×C₅	C₃×#137	1	1	yes	characteristic
310	C₄×C₅	—	2	4	no	—
311	C₄×C₅	—	2	2	no	—
312	C₄×C₅	—	4	2	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	8	1	no	—
316	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
317	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
318	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
319	C₄×C₅	C₃×#123	1	1	yes	characteristic
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
324	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
325	C₂×Q₈	C₃×C₅×Q₈	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
346	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₃×C₅	#1863	1	1	yes	characteristic, direct product factor, Hall
351	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
352	C₂²×C₃	C₅×#120	1	1	yes	characteristic
353	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
355	C₂²×C₃	C₅×#135	1	1	yes	characteristic
356	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
357	C₂²×C₃	C₅×#137	1	1	yes	characteristic
358	C₃×C₄	—	2	4	no	—
359	C₃×C₄	—	2	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	—	4	1	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	8	1	no	—
364	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
365	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
366	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
367	C₃×C₄	C₅×#123	1	1	yes	characteristic
368	C₂×C₅	C₃×#385	1	1	yes	characteristic
369	C₂×C₅	C₃×C₄×Q₁₆	1	1	yes	characteristic
370	C₂×C₅	C₃×#440	1	1	yes	characteristic
371	C₂×C₅	C₃×#449	1	1	yes	characteristic
372	C₂×C₅	C₃×#451	1	1	yes	characteristic
373	C₂×C₅	C₃×#477	1	1	yes	characteristic
374	C₂×C₅	C₃×#479	1	1	yes	characteristic
375	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	2	2	no	—
379	Q₈	C₃×C₅×C₄⋊C₄	1	4	yes	complemented
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	C₃×C₅×Q₁₆	1	2	yes	—
398	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
399	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
400	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
402	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
403	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
404	C₈	—	2	2	no	—
405	C₈	—	4	1	no	—
406	C₂×C₃	C₅×#385	1	1	yes	characteristic
407	C₂×C₃	C₄×C₅×Q₁₆	1	1	yes	characteristic
408	C₂×C₃	C₅×#440	1	1	yes	characteristic
409	C₂×C₃	C₅×#449	1	1	yes	characteristic
410	C₂×C₃	C₅×#451	1	1	yes	characteristic
411	C₂×C₃	C₅×#477	1	1	yes	characteristic
412	C₂×C₃	C₅×#479	1	1	yes	characteristic
413	C₅	C₃×#1863	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
415	C₂²	C₃×C₅×#120	1	1	yes	characteristic
416	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
417	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
418	C₂²	C₃×C₅×#135	1	1	yes	characteristic
419	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂²	C₃×C₅×#137	1	1	yes	characteristic
421	C₄	—	2	2	no	—
422	C₄	—	2	4	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	8	1	no	—
427	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
428	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
429	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
430	C₄	C₃×C₅×#123	1	1	yes	characteristic
431	C₃	C₅×#1863	1	1	yes	characteristic, direct product factor, Sylow
432	C₂	C₃×C₅×#385	1	1	yes	characteristic
433	C₂	C₃×C₄×C₅×Q₁₆	1	1	yes	characteristic
434	C₂	C₃×C₅×#440	1	1	yes	characteristic
435	C₂	C₃×C₅×#449	1	1	yes	characteristic
436	C₂	C₃×C₅×#451	1	1	yes	characteristic
437	C₂	C₃×C₅×#477	1	1	yes	characteristic
438	C₂	C₃×C₅×#479	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#1863	C₃	direct (N × H)
23. C₃×C₅×#103	C₄	semidirect
25. C₃×#1863	C₅	direct (N × H)
84. C₅×#103	C₃×C₄	semidirect
86. #1863	C₃×C₅	direct (N × H)
91. C₃×C₅×Q₈	C₄⋊C₄	semidirect
132. C₃×#103	C₄×C₅	semidirect
222. C₅×Q₈	C₃×C₄⋊C₄	semidirect
263. #103	C₃×C₄×C₅	semidirect
276. C₃×Q₈	C₅×C₄⋊C₄	semidirect
350. C₃×C₅	#1863	direct (N × H)
379. Q₈	C₃×C₅×C₄⋊C₄	semidirect
413. C₅	C₃×#1863	direct (N × H)
431. C₃	C₅×#1863	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×C₄×C₅×Q₈	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#103	2
C₃×C₅×#389	2
C₃×C₅×#340	2
C₃×C₅×#336	2
C₅×#1863	3
C₃×#1863	5

Subgroups — C3×C5×#1863 #14274897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1863 #14274897