Subgroups — C₃×C₅×#3205 #14276239

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#493	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#486	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#459	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#447	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3205	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	—	2	1	no	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂×C₃×C₅×D₈	C₂²	1	8	yes	complemented
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#127	—	2	1	no	—
16	C₃×C₅×#127	—	2	1	no	—
17	C₃×C₅×#127	C₂²	1	2	yes	—
18	C₃×C₅×#127	C₂²	1	2	yes	—
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#124	—	2	1	no	—
21	C₃×C₅×#121	—	2	1	no	—
22	C₃×C₅×#121	C₂²	1	2	yes	—
23	C₃×C₄×C₅×D₄	—	2	1	no	—
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₃×C₅×#102	C₂²	1	8	yes	complemented
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
30	C₃×#3205	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#493	C₂×C₃	1	2	yes	complemented
34	C₅×#486	C₂×C₃	1	2	yes	complemented
35	C₅×#459	C₂×C₃	1	4	yes	complemented
36	C₅×#447	C₂×C₃	1	4	yes	complemented
37	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂⁴×C₃×C₅	—	2	2	no	—
39	C₃×C₅×#41	—	4	4	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	—	4	4	no	—
50	C₂×C₃×C₅×D₄	—	4	4	no	—
51	C₂×C₃×C₅×D₄	—	4	4	no	—
52	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×D₈	—	4	8	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
69	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#493	C₂×C₅	1	2	yes	complemented
71	C₃×#486	C₂×C₅	1	2	yes	complemented
72	C₃×#459	C₂×C₅	1	4	yes	complemented
73	C₃×#447	C₂×C₅	1	4	yes	complemented
74	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₅×#41	—	2	1	no	—
76	C₂²×C₅×D₄	—	2	1	no	—
77	C₂²×C₅×D₄	—	2	1	no	—
78	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×D₈	C₂²×C₃	1	8	yes	complemented
80	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₅×#127	—	2	1	no	—
82	C₅×#127	—	2	1	no	—
83	C₅×#127	C₂²×C₃	1	2	yes	—
84	C₅×#127	C₂²×C₃	1	2	yes	—
85	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
86	C₅×#124	—	2	1	no	—
87	C₅×#121	—	2	1	no	—
88	C₅×#121	C₂²×C₃	1	2	yes	—
89	C₄×C₅×D₄	—	2	1	no	—
90	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
91	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
92	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
93	C₅×#102	C₂²×C₃	1	8	yes	complemented
94	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
95	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
96	#3205	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	2	4	no	—
99	C₂³×C₃×C₅	—	4	4	no	—
100	C₂³×C₃×C₅	—	4	4	no	—
101	C₂³×C₃×C₅	—	4	4	no	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	4	2	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	2	8	no	—
106	C₃×C₅×D₄	—	4	4	no	—
107	C₃×C₅×D₄	—	4	4	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₃×C₅×D₄	—	4	4	no	—
110	C₃×C₅×D₄	—	4	4	no	—
111	C₃×C₅×D₄	—	4	2	no	—
112	C₃×C₅×D₄	—	4	2	no	—
113	C₃×C₅×D₄	—	4	4	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	—	4	4	no	—
118	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₃×C₅×C₈	—	2	4	no	—
126	C₂×C₃×#41	—	2	1	no	—
127	C₂²×C₃×D₄	—	2	1	no	—
128	C₂²×C₃×D₄	—	2	1	no	—
129	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
130	C₂×C₃×D₈	C₂²×C₅	1	8	yes	complemented
131	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
132	C₃×#127	—	2	1	no	—
133	C₃×#127	—	2	1	no	—
134	C₃×#127	C₂²×C₅	1	2	yes	—
135	C₃×#127	C₂²×C₅	1	2	yes	—
136	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₃×#124	—	2	1	no	—
138	C₃×#121	—	2	1	no	—
139	C₃×#121	C₂²×C₅	1	2	yes	—
140	C₃×C₄×D₄	—	2	1	no	—
141	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
142	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
143	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
144	C₃×#102	C₂²×C₅	1	8	yes	complemented
145	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
146	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
147	C₂⁴×C₅	—	2	2	no	—
148	C₅×#41	—	4	4	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	—	2	2	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	4	4	no	—
159	C₂×C₅×D₄	—	4	4	no	—
160	C₂×C₅×D₄	—	4	4	no	—
161	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
162	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
167	C₅×D₈	—	4	8	no	—
168	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
171	C₅×C₂²⋊C₄	—	2	2	no	—
172	C₅×C₂²⋊C₄	—	2	2	no	—
173	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
174	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
175	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
176	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
177	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic, complemented
179	#493	C₂×C₃×C₅	1	2	yes	complemented
180	#486	C₂×C₃×C₅	1	2	yes	complemented
181	#459	C₂×C₃×C₅	1	4	yes	complemented
182	#447	C₂×C₃×C₅	1	4	yes	complemented
183	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	—	2	1	no	—
186	C₂²×C₃×C₅	—	4	4	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	2	no	—
189	C₂²×C₃×C₅	—	4	4	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	8	8	no	—
193	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
194	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	2	1	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
199	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
200	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
201	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
202	C₂⁴×C₃	—	2	2	no	—
203	C₃×#41	—	4	4	no	—
204	C₂×C₃×Q₈	—	2	1	no	—
205	C₂×C₃×D₄	—	2	2	no	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	2	2	no	—
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	—	2	2	no	—
212	C₂×C₃×D₄	—	2	2	no	—
213	C₂×C₃×D₄	—	4	4	no	—
214	C₂×C₃×D₄	—	4	4	no	—
215	C₂×C₃×D₄	—	4	4	no	—
216	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
217	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	—	2	2	no	—
219	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₃×D₈	—	4	8	no	—
223	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
224	C₃×C₄⋊C₄	—	2	1	no	—
225	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
226	C₃×C₂²⋊C₄	—	2	2	no	—
227	C₃×C₂²⋊C₄	—	2	2	no	—
228	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
229	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
230	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
231	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	2	4	no	—
234	C₂³×C₅	—	4	4	no	—
235	C₂³×C₅	—	4	4	no	—
236	C₂³×C₅	—	4	4	no	—
237	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
238	C₅×Q₈	—	4	2	no	—
239	C₅×D₄	—	2	4	no	—
240	C₅×D₄	—	2	8	no	—
241	C₅×D₄	—	4	4	no	—
242	C₅×D₄	—	4	4	no	—
243	C₅×D₄	—	4	4	no	—
244	C₅×D₄	—	4	4	no	—
245	C₅×D₄	—	4	4	no	—
246	C₅×D₄	—	4	2	no	—
247	C₅×D₄	—	4	2	no	—
248	C₅×D₄	—	4	4	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	4	4	no	—
253	C₂×C₄×C₅	C₃×D₈	1	4	yes	complemented
254	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
260	C₅×C₈	—	2	4	no	—
261	C₂×#41	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
265	C₂×D₈	C₂²×C₃×C₅	1	8	yes	complemented
266	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	C₂²×C₃×C₅	1	2	yes	—
270	#127	C₂²×C₃×C₅	1	2	yes	—
271	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
272	#124	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	C₂²×C₃×C₅	1	2	yes	—
275	C₄×D₄	—	2	1	no	—
276	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
277	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
279	#102	C₂²×C₃×C₅	1	8	yes	complemented
280	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
281	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
282	C₂×C₃×C₅	—	2	2	no	—
283	C₂×C₃×C₅	—	8	2	no	—
284	C₂×C₃×C₅	—	8	4	no	—
285	C₂×C₃×C₅	#535	1	1	yes	characteristic
286	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
287	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
288	C₂³×C₃	—	2	2	no	—
289	C₂³×C₃	—	2	4	no	—
290	C₂³×C₃	—	4	4	no	—
291	C₂³×C₃	—	4	4	no	—
292	C₂³×C₃	—	4	4	no	—
293	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
294	C₃×Q₈	—	4	2	no	—
295	C₃×D₄	—	2	4	no	—
296	C₃×D₄	—	2	8	no	—
297	C₃×D₄	—	4	4	no	—
298	C₃×D₄	—	4	4	no	—
299	C₃×D₄	—	4	4	no	—
300	C₃×D₄	—	4	4	no	—
301	C₃×D₄	—	4	4	no	—
302	C₃×D₄	—	4	2	no	—
303	C₃×D₄	—	4	2	no	—
304	C₃×D₄	—	4	4	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	4	4	no	—
309	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
310	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
316	C₃×C₈	—	2	4	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	4	2	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	4	4	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	8	8	no	—
326	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
327	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
328	C₄×C₅	—	2	1	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	C₂×C₃×D₈	1	2	yes	—
332	C₄×C₅	C₂×C₃×D₈	1	2	yes	—
333	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
334	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
335	C₂⁴	—	2	2	no	—
336	#41	—	4	4	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
350	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
355	D₈	—	4	8	no	—
356	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
362	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
363	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
364	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
365	C₃×C₅	#3205	1	1	yes	characteristic, direct product factor, Hall
366	C₂²×C₃	—	2	1	no	—
367	C₂²×C₃	—	2	1	no	—
368	C₂²×C₃	—	4	4	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	—	4	4	no	—
372	C₂²×C₃	—	4	4	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	8	8	no	—
375	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
376	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	4	2	no	—
380	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
381	C₃×C₄	C₂×C₅×D₈	1	2	yes	—
382	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
383	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
384	C₂×C₅	—	2	2	no	—
385	C₂×C₅	—	8	4	no	—
386	C₂×C₅	—	8	2	no	—
387	C₂×C₅	C₃×#535	1	1	yes	characteristic
388	C₂×C₅	C₂²×C₃×D₈	1	1	yes	characteristic
389	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
396	Q₈	—	4	2	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	8	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	C₃×C₅×D₈	1	4	yes	complemented
412	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
414	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
415	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
417	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	8	4	no	—
421	C₂×C₃	—	8	2	no	—
422	C₂×C₃	C₅×#535	1	1	yes	characteristic
423	C₂×C₃	C₂²×C₅×D₈	1	1	yes	characteristic
424	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₅	C₃×#3205	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	8	8	no	—
435	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
436	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	C₂×C₃×C₅×D₈	1	2	yes	—
441	C₄	C₂×C₃×C₅×D₈	1	2	yes	—
442	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
443	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
444	C₃	C₅×#3205	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	2	2	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₃×C₅×#535	1	1	yes	characteristic
449	C₂	C₂²×C₃×C₅×D₈	1	1	yes	characteristic
450	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₃×C₅×#493	C₂	semidirect
4. C₃×C₅×#486	C₂	semidirect
5. C₃×C₅×#459	C₂	semidirect
6. C₃×C₅×#447	C₂	semidirect
7. C₃×C₅×#431	C₂	semidirect
8. C₅×#3205	C₃	direct (N × H)
13. C₂×C₃×C₅×D₈	C₂²	semidirect
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#127	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×C₅×C₄⋊C₈	C₂²	semidirect
27. C₃×C₅×#102	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
30. C₃×#3205	C₅	direct (N × H)
31. C₅×#532	C₂×C₃	semidirect
32. C₂×C₅×#127	C₂×C₃	semidirect
33. C₅×#493	C₂×C₃	semidirect
34. C₅×#486	C₂×C₃	semidirect
35. C₅×#459	C₂×C₃	semidirect
36. C₅×#447	C₂×C₃	semidirect
37. C₅×#431	C₂×C₃	semidirect
68. C₃×#532	C₂×C₅	semidirect
69. C₂×C₃×#127	C₂×C₅	semidirect
70. C₃×#493	C₂×C₅	semidirect
71. C₃×#486	C₂×C₅	semidirect
72. C₃×#459	C₂×C₅	semidirect
73. C₃×#447	C₂×C₅	semidirect
74. C₃×#431	C₂×C₅	semidirect
79. C₂×C₅×D₈	C₂²×C₃	semidirect
80. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
85. C₅×#127	C₂²×C₃	semidirect
90. C₄×C₅×D₄	C₂²×C₃	semidirect
92. C₅×C₄⋊C₈	C₂²×C₃	semidirect
93. C₅×#102	C₂²×C₃	semidirect
95. C₄×C₅×C₈	C₂²×C₃	semidirect
96. #3205	C₃×C₅	direct (N × H)
118. C₂×C₃×C₄×C₅	D₈	semidirect
130. C₂×C₃×D₈	C₂²×C₅	semidirect
131. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
136. C₃×#127	C₂²×C₅	semidirect
141. C₃×C₄×D₄	C₂²×C₅	semidirect
143. C₃×C₄⋊C₈	C₂²×C₅	semidirect
144. C₃×#102	C₂²×C₅	semidirect
146. C₃×C₄×C₈	C₂²×C₅	semidirect
177. #532	C₂×C₃×C₅	semidirect
178. C₂×#127	C₂×C₃×C₅	semidirect
179. #493	C₂×C₃×C₅	semidirect
180. #486	C₂×C₃×C₅	semidirect
181. #459	C₂×C₃×C₅	semidirect
182. #447	C₂×C₃×C₅	semidirect
183. #431	C₂×C₃×C₅	semidirect
253. C₂×C₄×C₅	C₃×D₈	semidirect
265. C₂×D₈	C₂²×C₃×C₅	semidirect
266. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
271. #127	C₂²×C₃×C₅	semidirect
276. C₄×D₄	C₂²×C₃×C₅	semidirect
278. C₄⋊C₈	C₂²×C₃×C₅	semidirect
279. #102	C₂²×C₃×C₅	semidirect
281. C₄×C₈	C₂²×C₃×C₅	semidirect
309. C₂×C₃×C₄	C₅×D₈	semidirect
365. C₃×C₅	#3205	direct (N × H)
411. C₂×C₄	C₃×C₅×D₈	semidirect
425. C₅	C₃×#3205	direct (N × H)
444. C₃	C₅×#3205	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×#532	2
C₂×C₃×C₅×#127	2
C₃×C₅×#493	2
C₃×C₅×#486	2
C₃×C₅×#459	2
C₃×C₅×#447	2
C₃×C₅×#431	2
C₅×#3205	3
C₃×#3205	5

Subgroups — C3×C5×#3205 #14276239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3205 #14276239