Subgroups — C₃×C₅×#1872 #14274906

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	2	yes	maximal, complemented
6	C₅×#1872	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	—	2	1	no	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
11	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
12	C₃×C₅×C₂²⋊Q₈	C₄	1	4	yes	complemented
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
19	C₃×C₅×#103	—	2	4	no	—
20	C₃×C₅×C₂²⋊C₈	—	2	2	no	—
21	C₃×#1872	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
25	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
26	C₅×#340	C₂×C₃	1	2	yes	complemented
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	2	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	complemented
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	—	4	2	no	—
39	C₂²×C₃×C₄×C₅	—	4	2	no	—
40	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	—	2	2	no	—
46	C₂×C₃×C₅×C₈	—	2	2	no	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	—	2	4	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	complemented
52	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
53	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
54	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
55	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
56	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
57	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
58	C₃×#340	C₂×C₅	1	2	yes	complemented
59	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₂³×C₄×C₅	—	2	1	no	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
63	C₅×C₂²⋊Q₈	—	2	2	no	—
64	C₅×C₂²⋊Q₈	C₃×C₄	1	4	yes	complemented
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	1	no	—
67	C₂×C₅×C₄⋊C₄	—	2	4	no	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₅×#103	—	2	4	no	—
72	C₅×C₂²⋊C₈	—	2	2	no	—
73	#1872	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₂³×C₃×C₅	—	2	1	no	—
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
79	C₂³×C₃×C₅	SD₁₆	1	2	yes	—
80	C₂³×C₃×C₅	Q₁₆	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₃×C₅×Q₈	—	2	4	no	—
83	C₃×C₅×Q₈	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	4	8	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	1	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	2	yes	—
103	C₃×C₅×C₈	—	4	2	no	—
104	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
108	C₃×C₂²⋊Q₈	—	2	2	no	—
109	C₃×C₂²⋊Q₈	C₄×C₅	1	4	yes	complemented
110	C₂×C₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₃×C₄⋊C₄	—	2	1	no	—
112	C₂×C₃×C₄⋊C₄	—	2	4	no	—
113	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
116	C₃×#103	—	2	4	no	—
117	C₃×C₂²⋊C₈	—	2	2	no	—
118	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	—	2	2	no	—
122	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	complemented
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	4	2	no	—
130	C₂²×C₄×C₅	—	4	2	no	—
131	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
132	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
134	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	4	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	complemented
143	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
144	C₅×C₂²⋊C₄	—	2	4	no	—
145	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
146	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
147	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
148	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
149	#340	C₂×C₃×C₅	1	2	yes	complemented
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	#103	1	4	yes	complemented
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	#120	1	1	yes	characteristic
159	C₂²×C₃×C₅	#123	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
162	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂²×C₃×C₅	#137	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	2	no	—
166	C₃×C₄×C₅	—	4	2	no	—
167	C₃×C₄×C₅	—	4	4	no	—
168	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
169	C₃×C₄×C₅	#121	1	2	yes	—
170	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
171	C₂×C₃×Q₈	—	2	1	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	complemented
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	2	no	—
181	C₂²×C₃×C₄	—	4	2	no	—
182	C₂²×C₃×C₄	—	4	2	no	—
183	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
184	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
186	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂×C₃×C₈	—	2	2	no	—
188	C₂×C₃×C₈	—	2	2	no	—
189	C₂×C₃×C₈	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	4	no	—
192	C₃×C₄⋊C₄	—	2	2	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	complemented
195	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
196	C₃×C₂²⋊C₄	—	2	4	no	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
202	C₂³×C₅	C₃×SD₁₆	1	2	yes	—
203	C₂³×C₅	C₃×Q₁₆	1	2	yes	—
204	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₅×Q₈	—	2	4	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	4	8	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
222	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
225	C₂×C₄×C₅	C₃×#41	1	2	yes	—
226	C₅×C₈	—	4	2	no	—
227	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
231	C₂²⋊Q₈	—	2	2	no	—
232	C₂²⋊Q₈	C₃×C₄×C₅	1	4	yes	complemented
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	#103	—	2	4	no	—
240	C₂²⋊C₈	—	2	2	no	—
241	C₂×C₃×C₅	—	2	4	no	—
242	C₂×C₃×C₅	#386	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
244	C₂×C₃×C₅	#417	1	1	yes	characteristic
245	C₂×C₃×C₅	#450	1	1	yes	characteristic
246	C₂×C₃×C₅	#451	1	1	yes	characteristic
247	C₂×C₃×C₅	#483	1	1	yes	characteristic
248	C₂×C₃×C₅	#484	1	1	yes	characteristic
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
254	C₂³×C₃	C₅×SD₁₆	1	2	yes	—
255	C₂³×C₃	C₅×Q₁₆	1	2	yes	—
256	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	4	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	2	4	no	—
266	C₂×C₃×C₄	—	4	8	no	—
267	C₂×C₃×C₄	—	4	1	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	2	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	1	no	—
273	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
274	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
277	C₂×C₃×C₄	C₅×#41	1	2	yes	—
278	C₃×C₈	—	4	2	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	C₃×#103	1	4	yes	complemented
286	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₅	C₃×#120	1	1	yes	characteristic
288	C₂²×C₅	C₃×#123	1	1	yes	characteristic
289	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
290	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
291	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂²×C₅	C₃×#137	1	1	yes	characteristic
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	4	4	no	—
297	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
298	C₄×C₅	C₃×#121	1	2	yes	—
299	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	complemented
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₂×C₃×C₄×C₅	1	2	yes	—
313	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
315	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	4	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	complemented
324	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₃×C₅	#1872	1	1	yes	characteristic, direct product factor, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	C₅×#103	1	4	yes	complemented
334	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
335	C₂²×C₃	C₅×#120	1	1	yes	characteristic
336	C₂²×C₃	C₅×#123	1	1	yes	characteristic
337	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
338	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
339	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
340	C₂²×C₃	C₅×#137	1	1	yes	characteristic
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	2	no	—
344	C₃×C₄	—	4	4	no	—
345	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
346	C₃×C₄	C₅×#121	1	2	yes	—
347	C₂×C₅	—	2	4	no	—
348	C₂×C₅	C₃×#386	1	1	yes	characteristic
349	C₂×C₅	C₂×C₃×#103	1	1	yes	characteristic
350	C₂×C₅	C₃×#417	1	1	yes	characteristic
351	C₂×C₅	C₃×#450	1	1	yes	characteristic
352	C₂×C₅	C₃×#451	1	1	yes	characteristic
353	C₂×C₅	C₃×#483	1	1	yes	characteristic
354	C₂×C₅	C₃×#484	1	1	yes	characteristic
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	C₃×C₅×C₂²⋊C₄	1	2	yes	—
360	C₂³	C₃×C₅×SD₁₆	1	2	yes	—
361	C₂³	C₃×C₅×Q₁₆	1	2	yes	—
362	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
380	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
381	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
382	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
383	C₂×C₄	C₃×C₅×#41	1	2	yes	—
384	C₈	—	4	2	no	—
385	C₂×C₃	—	2	4	no	—
386	C₂×C₃	C₅×#386	1	1	yes	characteristic
387	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
388	C₂×C₃	C₅×#417	1	1	yes	characteristic
389	C₂×C₃	C₅×#450	1	1	yes	characteristic
390	C₂×C₃	C₅×#451	1	1	yes	characteristic
391	C₂×C₃	C₅×#483	1	1	yes	characteristic
392	C₂×C₃	C₅×#484	1	1	yes	characteristic
393	C₅	C₃×#1872	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	C₃×C₅×#103	1	4	yes	complemented
401	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
402	C₂²	C₃×C₅×#120	1	1	yes	characteristic
403	C₂²	C₃×C₅×#123	1	1	yes	characteristic
404	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
405	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
406	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂²	C₃×C₅×#137	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	C₃×C₄×C₅×D₄	1	2	yes	—
413	C₄	C₃×C₅×#121	1	2	yes	—
414	C₃	C₅×#1872	1	1	yes	characteristic, direct product factor, Sylow
415	C₂	—	2	4	no	—
416	C₂	C₃×C₅×#386	1	1	yes	characteristic
417	C₂	C₂×C₃×C₅×#103	1	1	yes	characteristic
418	C₂	C₃×C₅×#417	1	1	yes	characteristic
419	C₂	C₃×C₅×#450	1	1	yes	characteristic
420	C₂	C₃×C₅×#451	1	1	yes	characteristic
421	C₂	C₃×C₅×#483	1	1	yes	characteristic
422	C₂	C₃×C₅×#484	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂⁴×C₃×C₅	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×#103	C₂	semidirect
5. C₃×C₅×#340	C₂	semidirect
6. C₅×#1872	C₃	direct (N × H)
12. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
21. C₃×#1872	C₅	direct (N × H)
24. C₂×C₅×#103	C₂×C₃	semidirect
26. C₅×#340	C₂×C₃	semidirect
31. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
51. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
56. C₂×C₃×#103	C₂×C₅	semidirect
58. C₃×#340	C₂×C₅	semidirect
64. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
73. #1872	C₃×C₅	direct (N × H)
109. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
122. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
142. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
147. C₂×#103	C₂×C₃×C₅	semidirect
149. #340	C₂×C₃×C₅	semidirect
156. C₂²×C₃×C₅	#103	semidirect
174. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
194. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
232. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
285. C₂²×C₅	C₃×#103	semidirect
303. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
323. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
326. C₃×C₅	#1872	direct (N × H)
333. C₂²×C₃	C₅×#103	semidirect
393. C₅	C₃×#1872	direct (N × H)
400. C₂²	C₃×C₅×#103	semidirect
414. C₃	C₅×#1872	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×C₂²⋊Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×C₅×#103	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₅×#340	2
C₅×#1872	3
C₃×#1872	5

Subgroups — C3×C5×#1872 #14274906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1872 #14274906