Subgroups — C₃×C₅×#2742 #14275776

Order 1920.

832 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	C₃×C₅×#400	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#388	C₂	1	2	yes	maximal
7	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#380	C₂	1	2	yes	maximal
10	C₅×#2742	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	2	yes	—
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×#2742	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#400	C₂×C₃	1	2	yes	complemented
34	C₅×#399	C₂×C₃	1	1	yes	characteristic
35	C₅×#395	C₂×C₃	1	2	yes	complemented
36	C₅×#393	C₂×C₃	1	1	yes	characteristic
37	C₅×#389	C₂×C₃	1	2	yes	complemented
38	C₅×#388	C₂×C₃	1	2	yes	—
39	C₅×#387	C₂×C₃	1	2	yes	complemented
40	C₅×#385	C₂×C₃	1	1	yes	characteristic
41	C₅×#380	C₂×C₃	1	2	yes	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	—	4	2	no	—
44	C₂×C₃×C₅×Q₈	—	4	1	no	—
45	C₂²×C₃×C₄×C₅	—	2	4	no	—
46	C₂²×C₃×C₄×C₅	—	4	1	no	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₄⋊C₄	—	4	2	no	—
58	C₃×C₅×C₄⋊C₄	—	4	2	no	—
59	C₃×C₅×C₄⋊C₄	—	4	2	no	—
60	C₃×C₅×C₄⋊C₄	—	4	1	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
64	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
65	C₃×C₄²×C₅	—	4	2	no	—
66	C₃×#400	C₂×C₅	1	2	yes	complemented
67	C₃×#399	C₂×C₅	1	1	yes	characteristic
68	C₃×#395	C₂×C₅	1	2	yes	complemented
69	C₃×#393	C₂×C₅	1	1	yes	characteristic
70	C₃×#389	C₂×C₅	1	2	yes	complemented
71	C₃×#388	C₂×C₅	1	2	yes	—
72	C₃×#387	C₂×C₅	1	2	yes	complemented
73	C₃×#385	C₂×C₅	1	1	yes	characteristic
74	C₃×#380	C₂×C₅	1	2	yes	—
75	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
88	C₅×#95	C₂²×C₃	1	2	yes	—
89	C₅×#95	C₂²×C₃	1	2	yes	—
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	1	yes	characteristic
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	C₅×#95	C₂²×C₃	1	2	yes	—
95	C₅×#95	C₂²×C₃	1	1	yes	characteristic
96	#2742	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	1	no	—
100	C₂³×C₃×C₅	—	2	1	no	—
101	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
102	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	1	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
126	C₂×C₃×C₄×C₅	#41	1	4	yes	—
127	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
128	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
137	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	2	yes	—
141	C₃×#95	C₂²×C₅	1	2	yes	—
142	C₃×#95	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	1	yes	characteristic
144	C₃×#95	C₂²×C₅	1	2	yes	—
145	C₃×#95	C₂²×C₅	1	2	yes	—
146	C₃×#95	C₂²×C₅	1	2	yes	—
147	C₃×#95	C₂²×C₅	1	1	yes	characteristic
148	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₅×Q₈	—	4	2	no	—
150	C₂×C₅×Q₈	—	4	1	no	—
151	C₂²×C₄×C₅	—	2	4	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₅×C₄⋊C₄	—	4	2	no	—
164	C₅×C₄⋊C₄	—	4	2	no	—
165	C₅×C₄⋊C₄	—	4	2	no	—
166	C₅×C₄⋊C₄	—	4	1	no	—
167	C₅×C₂²⋊C₄	—	4	2	no	—
168	C₅×C₂²⋊C₄	—	4	2	no	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
171	C₄²×C₅	—	4	2	no	—
172	#400	C₂×C₃×C₅	1	2	yes	complemented
173	#399	C₂×C₃×C₅	1	1	yes	characteristic
174	#395	C₂×C₃×C₅	1	2	yes	complemented
175	#393	C₂×C₃×C₅	1	1	yes	characteristic
176	#389	C₂×C₃×C₅	1	2	yes	complemented
177	#388	C₂×C₃×C₅	1	2	yes	—
178	#387	C₂×C₃×C₅	1	2	yes	complemented
179	#385	C₂×C₃×C₅	1	1	yes	characteristic
180	#380	C₂×C₃×C₅	1	2	yes	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	2	4	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	—	4	1	no	—
186	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
188	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
189	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
191	C₃×C₄×C₅	—	2	4	no	—
192	C₃×C₄×C₅	—	2	4	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	—	4	1	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	—	4	1	no	—
199	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
200	C₂×C₃×Q₈	—	4	2	no	—
201	C₂×C₃×Q₈	—	4	1	no	—
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	—	4	1	no	—
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	4	no	—
214	C₃×C₄⋊C₄	—	4	2	no	—
215	C₃×C₄⋊C₄	—	4	2	no	—
216	C₃×C₄⋊C₄	—	4	2	no	—
217	C₃×C₄⋊C₄	—	4	1	no	—
218	C₃×C₂²⋊C₄	—	4	2	no	—
219	C₃×C₂²⋊C₄	—	4	2	no	—
220	C₃×C₂²⋊C₄	—	4	1	no	—
221	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
222	C₃×C₄²	—	4	2	no	—
223	C₂³×C₅	—	2	2	no	—
224	C₂³×C₅	—	2	2	no	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
228	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
229	C₅×Q₈	—	4	4	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	4	4	no	—
251	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
252	C₂×C₄×C₅	C₃×#41	1	4	yes	—
253	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
259	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
266	#95	C₂²×C₃×C₅	1	2	yes	—
267	#95	C₂²×C₃×C₅	1	2	yes	—
268	#95	C₂²×C₃×C₅	1	2	yes	—
269	#95	C₂²×C₃×C₅	1	1	yes	characteristic
270	#95	C₂²×C₃×C₅	1	2	yes	—
271	#95	C₂²×C₃×C₅	1	2	yes	—
272	#95	C₂²×C₃×C₅	1	2	yes	—
273	#95	C₂²×C₃×C₅	1	1	yes	characteristic
274	C₂×C₃×C₅	—	4	2	no	—
275	C₂×C₃×C₅	#542	1	2	yes	—
276	C₂×C₃×C₅	#544	1	1	yes	characteristic
277	C₂×C₃×C₅	#551	1	1	yes	characteristic
278	C₂×C₃×C₅	#554	1	2	yes	—
279	C₂×C₃×C₅	#560	1	1	yes	characteristic
280	C₂³×C₃	—	2	2	no	—
281	C₂³×C₃	—	2	2	no	—
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
285	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
286	C₃×Q₈	—	4	4	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	4	4	no	—
308	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
309	C₂×C₃×C₄	C₅×#41	1	4	yes	—
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	—	2	4	no	—
312	C₂²×C₅	—	4	1	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
316	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
317	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
318	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
320	C₄×C₅	—	2	4	no	—
321	C₄×C₅	—	2	4	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	1	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	4	1	no	—
328	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
335	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
339	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
340	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
351	C₄²	—	4	2	no	—
352	C₃×C₅	#2742	1	1	yes	characteristic, direct product factor, Hall
353	C₂²×C₃	—	2	2	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	1	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
359	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
360	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
361	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
363	C₃×C₄	—	2	4	no	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	4	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	1	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	1	no	—
371	C₂×C₅	—	4	2	no	—
372	C₂×C₅	C₃×#542	1	2	yes	—
373	C₂×C₅	C₃×#544	1	1	yes	characteristic
374	C₂×C₅	C₃×#551	1	1	yes	characteristic
375	C₂×C₅	C₃×#554	1	2	yes	—
376	C₂×C₅	C₃×#560	1	1	yes	characteristic
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
382	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
383	Q₈	—	4	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
406	C₂×C₄	C₃×C₅×#41	1	4	yes	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	C₅×#542	1	2	yes	—
409	C₂×C₃	C₅×#544	1	1	yes	characteristic
410	C₂×C₃	C₅×#551	1	1	yes	characteristic
411	C₂×C₃	C₅×#554	1	2	yes	—
412	C₂×C₃	C₅×#560	1	1	yes	characteristic
413	C₅	C₃×#2742	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
420	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
421	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
422	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
423	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	2	no	—
432	C₃	C₅×#2742	1	1	yes	characteristic, direct product factor, Sylow
433	C₂	—	4	2	no	—
434	C₂	C₃×C₅×#542	1	2	yes	—
435	C₂	C₃×C₅×#544	1	1	yes	characteristic
436	C₂	C₃×C₅×#551	1	1	yes	characteristic
437	C₂	C₃×C₅×#554	1	2	yes	—
438	C₂	C₃×C₅×#560	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#400	C₂	semidirect
3. C₃×C₅×#395	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#387	C₂	semidirect
10. C₅×#2742	C₃	direct (N × H)
32. C₃×#2742	C₅	direct (N × H)
33. C₅×#400	C₂×C₃	semidirect
35. C₅×#395	C₂×C₃	semidirect
37. C₅×#389	C₂×C₃	semidirect
39. C₅×#387	C₂×C₃	semidirect
64. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
66. C₃×#400	C₂×C₅	semidirect
68. C₃×#395	C₂×C₅	semidirect
70. C₃×#389	C₂×C₅	semidirect
72. C₃×#387	C₂×C₅	semidirect
96. #2742	C₃×C₅	direct (N × H)
170. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
172. #400	C₂×C₃×C₅	semidirect
174. #395	C₂×C₃×C₅	semidirect
176. #389	C₂×C₃×C₅	semidirect
178. #387	C₂×C₃×C₅	semidirect
221. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
350. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
352. C₃×C₅	#2742	direct (N × H)
413. C₅	C₃×#2742	direct (N × H)
432. C₃	C₅×#2742	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#400	2
C₃×C₅×#399	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2742	3
C₃×#2742	5

Subgroups — C3×C5×#2742 #14275776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2742 #14275776