Subgroups — C₃×C₅×#1803 #14274837

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 380 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×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal
4	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#340	C₂	1	2	yes	maximal
6	C₅×#1803	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
9	C₃×C₄×C₅×Q₈	—	2	2	no	—
10	C₃×C₄×C₅×Q₈	C₄	1	4	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
12	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
13	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊C₈	—	2	2	no	—
19	C₃×C₅×#103	—	2	4	no	—
20	C₃×#1803	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×#103	C₂×C₃	1	2	yes	—
24	C₅×#384	C₂×C₃	1	1	yes	characteristic
25	C₅×#340	C₂×C₃	1	2	yes	—
26	C₂×C₃×C₅×Q₈	—	2	1	no	—
27	C₂×C₃×C₅×Q₈	—	2	1	no	—
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
30	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
31	C₂×C₃×C₅×Q₈	Q₈	1	2	yes	—
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	2	no	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	—	2	2	no	—
39	C₂×C₃×C₅×C₈	—	2	2	no	—
40	C₂×C₃×C₅×C₈	—	2	2	no	—
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	—	4	2	no	—
46	C₃×C₅×C₄⋊C₄	—	4	2	no	—
47	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₃×C₄²×C₅	—	2	4	no	—
49	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
50	C₃×C₄²×C₅	D₄	1	2	yes	—
51	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
52	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
53	C₂×C₃×#103	C₂×C₅	1	2	yes	—
54	C₃×#384	C₂×C₅	1	1	yes	characteristic
55	C₃×#340	C₂×C₅	1	2	yes	—
56	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
58	C₄×C₅×Q₈	—	2	2	no	—
59	C₄×C₅×Q₈	C₃×C₄	1	4	yes	complemented
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₄²×C₅	—	2	1	no	—
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×C₄⋊C₈	—	2	2	no	—
68	C₅×#103	—	2	4	no	—
69	#1803	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
71	C₃×C₅×Q₈	—	2	2	no	—
72	C₃×C₅×Q₈	—	2	2	no	—
73	C₃×C₅×Q₈	—	2	2	no	—
74	C₃×C₅×Q₈	C₄⋊C₄	1	4	yes	complemented
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	4	1	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	—	4	2	no	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
89	C₂×C₃×C₄×C₅	Q₁₆	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
96	C₃×C₅×C₈	—	4	2	no	—
97	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
98	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
99	C₃×C₄×Q₈	—	2	2	no	—
100	C₃×C₄×Q₈	C₄×C₅	1	4	yes	complemented
101	C₂×C₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂×C₃×C₄²	—	2	1	no	—
107	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	2	2	no	—
109	C₃×#103	—	2	4	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
114	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
115	C₂×C₅×Q₈	C₃×Q₈	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	2	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
132	C₄²×C₅	—	2	4	no	—
133	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
134	C₄²×C₅	C₃×D₄	1	2	yes	—
135	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
137	C₂×#103	C₂×C₃×C₅	1	2	yes	—
138	#384	C₂×C₃×C₅	1	1	yes	characteristic
139	#340	C₂×C₃×C₅	1	2	yes	—
140	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₃×C₅	#121	1	1	yes	characteristic
142	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
145	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂²×C₃×C₅	#137	1	1	yes	characteristic
147	C₃×C₄×C₅	—	2	4	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	4	2	no	—
150	C₃×C₄×C₅	—	8	2	no	—
151	C₃×C₄×C₅	#103	1	4	yes	complemented
152	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₃×C₄×C₅	#117	1	1	yes	characteristic
154	C₃×C₄×C₅	#121	1	1	yes	characteristic
155	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₃×Q₈	—	2	1	no	—
157	C₂×C₃×Q₈	—	2	1	no	—
158	C₂×C₃×Q₈	—	2	1	no	—
159	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
160	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
161	C₂×C₃×Q₈	C₅×Q₈	1	2	yes	—
162	C₂²×C₃×C₄	—	2	1	no	—
163	C₂²×C₃×C₄	—	2	1	no	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	—	2	2	no	—
170	C₂×C₃×C₈	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	4	no	—
172	C₃×C₄⋊C₄	—	2	1	no	—
173	C₃×C₄⋊C₄	—	2	2	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	4	2	no	—
176	C₃×C₄⋊C₄	—	4	2	no	—
177	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
180	C₃×C₄²	C₅×D₄	1	2	yes	—
181	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₅×Q₈	—	2	2	no	—
183	C₅×Q₈	—	2	2	no	—
184	C₅×Q₈	—	2	2	no	—
185	C₅×Q₈	C₃×C₄⋊C₄	1	4	yes	complemented
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₅	C₃×SD₁₆	1	2	yes	—
200	C₂×C₄×C₅	C₃×Q₁₆	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
206	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
207	C₅×C₈	—	4	2	no	—
208	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
209	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
210	C₄×Q₈	—	2	2	no	—
211	C₄×Q₈	C₃×C₄×C₅	1	4	yes	complemented
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	2	1	no	—
215	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
216	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
217	C₂×C₄²	—	2	1	no	—
218	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
219	C₄⋊C₈	—	2	2	no	—
220	#103	—	2	4	no	—
221	C₂×C₃×C₅	#380	1	1	yes	characteristic
222	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
223	C₂×C₃×C₅	#417	1	1	yes	characteristic
224	C₂×C₃×C₅	#460	1	1	yes	characteristic
225	C₂×C₃×C₅	#462	1	1	yes	characteristic
226	C₂×C₃×C₅	#475	1	1	yes	characteristic
227	C₂×C₃×C₅	#477	1	1	yes	characteristic
228	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
229	C₃×Q₈	—	2	2	no	—
230	C₃×Q₈	—	2	2	no	—
231	C₃×Q₈	—	2	2	no	—
232	C₃×Q₈	C₅×C₄⋊C₄	1	4	yes	complemented
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	4	1	no	—
240	C₂×C₃×C₄	—	4	1	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
245	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
246	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
247	C₂×C₃×C₄	C₅×Q₁₆	1	2	yes	—
248	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
252	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
253	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
254	C₃×C₈	—	4	2	no	—
255	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₅	C₃×#121	1	1	yes	characteristic
257	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
258	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
259	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
260	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
261	C₂²×C₅	C₃×#137	1	1	yes	characteristic
262	C₄×C₅	—	2	4	no	—
263	C₄×C₅	—	2	2	no	—
264	C₄×C₅	—	4	2	no	—
265	C₄×C₅	—	8	2	no	—
266	C₄×C₅	C₃×#103	1	4	yes	complemented
267	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₅	C₃×#117	1	1	yes	characteristic
269	C₄×C₅	C₃×#121	1	1	yes	characteristic
270	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
275	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
276	C₂×Q₈	C₃×C₅×Q₈	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	C₂×C₃×C₄×C₅	1	2	yes	—
293	C₄²	—	2	4	no	—
294	C₄²	C₂×C₃×C₄×C₅	1	2	yes	—
295	C₄²	C₃×C₅×D₄	1	2	yes	—
296	C₃×C₅	#1803	1	1	yes	characteristic, direct product factor, Hall
297	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
298	C₂²×C₃	C₅×#121	1	1	yes	characteristic
299	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
301	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
302	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
303	C₂²×C₃	C₅×#137	1	1	yes	characteristic
304	C₃×C₄	—	2	4	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	—	8	2	no	—
308	C₃×C₄	C₅×#103	1	4	yes	complemented
309	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
310	C₃×C₄	C₅×#117	1	1	yes	characteristic
311	C₃×C₄	C₅×#121	1	1	yes	characteristic
312	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
313	C₂×C₅	C₃×#380	1	1	yes	characteristic
314	C₂×C₅	C₂×C₃×#103	1	1	yes	characteristic
315	C₂×C₅	C₃×#417	1	1	yes	characteristic
316	C₂×C₅	C₃×#460	1	1	yes	characteristic
317	C₂×C₅	C₃×#462	1	1	yes	characteristic
318	C₂×C₅	C₃×#475	1	1	yes	characteristic
319	C₂×C₅	C₃×#477	1	1	yes	characteristic
320	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
321	Q₈	—	2	2	no	—
322	Q₈	—	2	2	no	—
323	Q₈	—	2	2	no	—
324	Q₈	C₃×C₅×C₄⋊C₄	1	4	yes	complemented
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
337	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	2	yes	—
338	C₂×C₄	C₃×C₅×SD₁₆	1	2	yes	—
339	C₂×C₄	C₃×C₅×Q₁₆	1	2	yes	—
340	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
344	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
345	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
346	C₈	—	4	2	no	—
347	C₂×C₃	C₅×#380	1	1	yes	characteristic
348	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
349	C₂×C₃	C₅×#417	1	1	yes	characteristic
350	C₂×C₃	C₅×#460	1	1	yes	characteristic
351	C₂×C₃	C₅×#462	1	1	yes	characteristic
352	C₂×C₃	C₅×#475	1	1	yes	characteristic
353	C₂×C₃	C₅×#477	1	1	yes	characteristic
354	C₅	C₃×#1803	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
356	C₂²	C₃×C₅×#121	1	1	yes	characteristic
357	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
358	C₂²	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
359	C₂²	C₂×C₃×C₅×Q₁₆	1	1	yes	characteristic
360	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₂²	C₃×C₅×#137	1	1	yes	characteristic
362	C₄	—	2	4	no	—
363	C₄	—	2	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	8	2	no	—
366	C₄	C₃×C₅×#103	1	4	yes	complemented
367	C₄	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
368	C₄	C₃×C₅×#117	1	1	yes	characteristic
369	C₄	C₃×C₅×#121	1	1	yes	characteristic
370	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
371	C₃	C₅×#1803	1	1	yes	characteristic, direct product factor, Sylow
372	C₂	C₃×C₅×#380	1	1	yes	characteristic
373	C₂	C₂×C₃×C₅×#103	1	1	yes	characteristic
374	C₂	C₃×C₅×#417	1	1	yes	characteristic
375	C₂	C₃×C₅×#460	1	1	yes	characteristic
376	C₂	C₃×C₅×#462	1	1	yes	characteristic
377	C₂	C₃×C₅×#475	1	1	yes	characteristic
378	C₂	C₃×C₅×#477	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
6. C₅×#1803	C₃	direct (N × H)
10. C₃×C₄×C₅×Q₈	C₄	semidirect
20. C₃×#1803	C₅	direct (N × H)
59. C₄×C₅×Q₈	C₃×C₄	semidirect
69. #1803	C₃×C₅	direct (N × H)
74. C₃×C₅×Q₈	C₄⋊C₄	semidirect
100. C₃×C₄×Q₈	C₄×C₅	semidirect
151. C₃×C₄×C₅	#103	semidirect
185. C₅×Q₈	C₃×C₄⋊C₄	semidirect
211. C₄×Q₈	C₃×C₄×C₅	semidirect
232. C₃×Q₈	C₅×C₄⋊C₄	semidirect
266. C₄×C₅	C₃×#103	semidirect
296. C₃×C₅	#1803	direct (N × H)
308. C₃×C₄	C₅×#103	semidirect
324. Q₈	C₃×C₅×C₄⋊C₄	semidirect
354. C₅	C₃×#1803	direct (N × H)
366. C₄	C₃×C₅×#103	semidirect
371. C₃	C₅×#1803	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×C₄⋊C₈	2
C₂×C₃×C₅×#103	2
C₃×C₅×#384	2
C₃×C₅×#340	2
C₅×#1803	3
C₃×#1803	5

Subgroups — C3×C5×#1803 #14274837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1803 #14274837