Subgroups — C₃×C₅×#2665 #14275699

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 436 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×#396	C₂	1	2	yes	maximal
3	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#393	C₂	1	2	yes	maximal
5	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₅×#2665	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
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×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₃×C₅×#95	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	1	yes	characteristic
24	C₃×C₅×#95	C₂²	1	2	yes	—
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₃×C₅×#95	C₂²	1	1	yes	characteristic
27	C₃×C₅×#95	C₂²	1	2	yes	—
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	2	yes	—
32	C₃×#2665	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#400	C₂×C₃	1	2	yes	complemented
34	C₅×#396	C₂×C₃	1	2	yes	—
35	C₅×#395	C₂×C₃	1	2	yes	complemented
36	C₅×#393	C₂×C₃	1	2	yes	—
37	C₅×#391	C₂×C₃	1	2	yes	complemented
38	C₅×#387	C₂×C₃	1	2	yes	complemented
39	C₅×#381	C₂×C₃	1	1	yes	characteristic
40	C₅×#380	C₂×C₃	1	1	yes	characteristic
41	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	—	4	2	no	—
45	C₂×C₃×C₅×Q₈	—	4	2	no	—
46	C₂²×C₃×C₄×C₅	—	4	2	no	—
47	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
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×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
64	C₃×C₄²×C₅	—	4	2	no	—
65	C₃×#400	C₂×C₅	1	2	yes	complemented
66	C₃×#396	C₂×C₅	1	2	yes	—
67	C₃×#395	C₂×C₅	1	2	yes	complemented
68	C₃×#393	C₂×C₅	1	2	yes	—
69	C₃×#391	C₂×C₅	1	2	yes	complemented
70	C₃×#387	C₂×C₅	1	2	yes	complemented
71	C₃×#381	C₂×C₅	1	1	yes	characteristic
72	C₃×#380	C₂×C₅	1	1	yes	characteristic
73	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
74	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
75	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
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×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
85	C₅×#95	C₂²×C₃	1	1	yes	characteristic
86	C₅×#95	C₂²×C₃	1	1	yes	characteristic
87	C₅×#95	C₂²×C₃	1	2	yes	—
88	C₅×#95	C₂²×C₃	1	1	yes	characteristic
89	C₅×#95	C₂²×C₃	1	1	yes	characteristic
90	C₅×#95	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	2	yes	—
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	#2665	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	1	no	—
98	C₂³×C₃×C₅	—	2	2	no	—
99	C₂³×C₃×C₅	—	2	1	no	—
100	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
101	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
102	C₃×C₅×Q₈	—	4	8	no	—
103	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	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	—	4	4	no	—
123	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
125	C₂×C₃×C₄×C₅	#41	1	4	yes	—
126	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
127	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
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×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
137	C₃×#95	C₂²×C₅	1	1	yes	characteristic
138	C₃×#95	C₂²×C₅	1	1	yes	characteristic
139	C₃×#95	C₂²×C₅	1	2	yes	—
140	C₃×#95	C₂²×C₅	1	1	yes	characteristic
141	C₃×#95	C₂²×C₅	1	1	yes	characteristic
142	C₃×#95	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
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	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₅×Q₈	—	2	4	no	—
149	C₂×C₅×Q₈	—	4	2	no	—
150	C₂×C₅×Q₈	—	4	2	no	—
151	C₂²×C₄×C₅	—	4	2	no	—
152	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
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	2	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
158	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	4	2	no	—
163	C₅×C₄⋊C₄	—	4	2	no	—
164	C₅×C₄⋊C₄	—	4	2	no	—
165	C₅×C₂²⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	—	4	1	no	—
167	C₅×C₂²⋊C₄	—	4	2	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₄²×C₅	—	4	2	no	—
170	#400	C₂×C₃×C₅	1	2	yes	complemented
171	#396	C₂×C₃×C₅	1	2	yes	—
172	#395	C₂×C₃×C₅	1	2	yes	complemented
173	#393	C₂×C₃×C₅	1	2	yes	—
174	#391	C₂×C₃×C₅	1	2	yes	complemented
175	#387	C₂×C₃×C₅	1	2	yes	complemented
176	#381	C₂×C₃×C₅	1	1	yes	characteristic
177	#380	C₂×C₃×C₅	1	1	yes	characteristic
178	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
186	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
188	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
189	C₃×C₄×C₅	—	2	4	no	—
190	C₃×C₄×C₅	—	2	2	no	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	—	4	2	no	—
193	C₃×C₄×C₅	—	4	2	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	—	4	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
198	C₂×C₃×Q₈	—	2	4	no	—
199	C₂×C₃×Q₈	—	4	2	no	—
200	C₂×C₃×Q₈	—	4	2	no	—
201	C₂²×C₃×C₄	—	4	2	no	—
202	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
203	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₃×C₄⋊C₄	—	2	4	no	—
212	C₃×C₄⋊C₄	—	4	2	no	—
213	C₃×C₄⋊C₄	—	4	2	no	—
214	C₃×C₄⋊C₄	—	4	2	no	—
215	C₃×C₂²⋊C₄	—	2	4	no	—
216	C₃×C₂²⋊C₄	—	4	1	no	—
217	C₃×C₂²⋊C₄	—	4	2	no	—
218	C₃×C₂²⋊C₄	—	4	1	no	—
219	C₃×C₄²	—	4	2	no	—
220	C₂³×C₅	—	2	2	no	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	2	1	no	—
224	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
225	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
226	C₅×Q₈	—	4	8	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	2	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	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	4	4	no	—
247	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
248	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
249	C₂×C₄×C₅	C₃×#41	1	4	yes	—
250	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
251	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
253	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
254	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
261	#95	C₂²×C₃×C₅	1	1	yes	characteristic
262	#95	C₂²×C₃×C₅	1	1	yes	characteristic
263	#95	C₂²×C₃×C₅	1	2	yes	—
264	#95	C₂²×C₃×C₅	1	1	yes	characteristic
265	#95	C₂²×C₃×C₅	1	1	yes	characteristic
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	2	yes	—
270	#95	C₂²×C₃×C₅	1	2	yes	—
271	C₂×C₃×C₅	—	4	2	no	—
272	C₂×C₃×C₅	#533	1	1	yes	characteristic
273	C₂×C₃×C₅	#538	1	2	yes	—
274	C₂×C₃×C₅	#542	1	2	yes	—
275	C₂×C₃×C₅	#543	1	1	yes	characteristic
276	C₂×C₃×C₅	#544	1	1	yes	characteristic
277	C₂³×C₃	—	2	2	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	—	2	1	no	—
281	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
282	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
283	C₃×Q₈	—	4	8	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	2	no	—
286	C₂×C₃×C₄	—	2	2	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	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	4	4	no	—
304	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
306	C₂×C₃×C₄	C₅×#41	1	4	yes	—
307	C₂²×C₅	—	2	2	no	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	2	no	—
312	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
313	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
314	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
316	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
317	C₄×C₅	—	2	4	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	4	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	—	4	2	no	—
325	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
331	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
332	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
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	2	yes	—
336	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
337	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	4	2	no	—
348	C₃×C₅	#2665	1	1	yes	characteristic, direct product factor, Hall
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
355	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
356	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
358	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₂×C₅	—	4	2	no	—
368	C₂×C₅	C₃×#533	1	1	yes	characteristic
369	C₂×C₅	C₃×#538	1	2	yes	—
370	C₂×C₅	C₃×#542	1	2	yes	—
371	C₂×C₅	C₃×#543	1	1	yes	characteristic
372	C₂×C₅	C₃×#544	1	1	yes	characteristic
373	C₂³	—	2	2	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	1	no	—
377	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
378	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
379	Q₈	—	4	8	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	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	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
401	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
402	C₂×C₄	C₃×C₅×#41	1	4	yes	—
403	C₂×C₃	—	4	2	no	—
404	C₂×C₃	C₅×#533	1	1	yes	characteristic
405	C₂×C₃	C₅×#538	1	2	yes	—
406	C₂×C₃	C₅×#542	1	2	yes	—
407	C₂×C₃	C₅×#543	1	1	yes	characteristic
408	C₂×C₃	C₅×#544	1	1	yes	characteristic
409	C₅	C₃×#2665	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
416	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
417	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
418	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
419	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₃	C₅×#2665	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	4	2	no	—
430	C₂	C₃×C₅×#533	1	1	yes	characteristic
431	C₂	C₃×C₅×#538	1	2	yes	—
432	C₂	C₃×C₅×#542	1	2	yes	—
433	C₂	C₃×C₅×#543	1	1	yes	characteristic
434	C₂	C₃×C₅×#544	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×#391	C₂	semidirect
6. C₃×C₅×#387	C₂	semidirect
10. C₅×#2665	C₃	direct (N × H)
32. C₃×#2665	C₅	direct (N × H)
33. C₅×#400	C₂×C₃	semidirect
35. C₅×#395	C₂×C₃	semidirect
37. C₅×#391	C₂×C₃	semidirect
38. C₅×#387	C₂×C₃	semidirect
47. C₂²×C₃×C₄×C₅	Q₈	semidirect
65. C₃×#400	C₂×C₅	semidirect
67. C₃×#395	C₂×C₅	semidirect
69. C₃×#391	C₂×C₅	semidirect
70. C₃×#387	C₂×C₅	semidirect
95. #2665	C₃×C₅	direct (N × H)
152. C₂²×C₄×C₅	C₃×Q₈	semidirect
170. #400	C₂×C₃×C₅	semidirect
172. #395	C₂×C₃×C₅	semidirect
174. #391	C₂×C₃×C₅	semidirect
175. #387	C₂×C₃×C₅	semidirect
202. C₂²×C₃×C₄	C₅×Q₈	semidirect
330. C₂²×C₄	C₃×C₅×Q₈	semidirect
348. C₃×C₅	#2665	direct (N × H)
409. C₅	C₃×#2665	direct (N × H)
428. C₃	C₅×#2665	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×#396	2
C₃×C₅×#395	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#387	2
C₃×C₅×#381	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2665	3
C₃×#2665	5

Subgroups — C3×C5×#2665 #14275699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2665 #14275699