Subgroups — C₃×C₅×#3109 #14276143

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 484 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×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#481	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#476	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#459	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#447	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#442	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3109	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	—	2	1	no	—
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	—	2	1	no	—
13	C₂×C₃×C₅×D₈	C₂²	1	4	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#124	—	2	1	no	—
17	C₃×C₅×#121	—	2	1	no	—
18	C₃×C₅×#121	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	—	2	1	no	—
20	C₃×C₄×C₅×D₄	—	2	1	no	—
21	C₃×C₄×C₅×D₄	—	2	1	no	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#106	C₂²	1	4	yes	complemented
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
30	C₃×C₅×#102	C₂²	1	4	yes	—
31	C₃×C₅×#102	C₂²	1	4	yes	complemented
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	complemented
34	C₃×#3109	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#481	C₂×C₃	1	2	yes	complemented
38	C₅×#476	C₂×C₃	1	2	yes	complemented
39	C₅×#459	C₂×C₃	1	2	yes	complemented
40	C₅×#447	C₂×C₃	1	2	yes	complemented
41	C₅×#442	C₂×C₃	1	4	yes	complemented
42	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₃×C₅×#41	—	4	4	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	1	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	—	4	4	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×D₈	—	2	8	no	—
62	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#481	C₂×C₅	1	2	yes	complemented
78	C₃×#476	C₂×C₅	1	2	yes	complemented
79	C₃×#459	C₂×C₅	1	2	yes	complemented
80	C₃×#447	C₂×C₅	1	2	yes	complemented
81	C₃×#442	C₂×C₅	1	4	yes	complemented
82	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×C₅×#41	—	2	1	no	—
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂³×C₄×C₅	—	2	1	no	—
86	C₂×C₅×D₈	C₂²×C₃	1	4	yes	—
87	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
89	C₅×#124	—	2	1	no	—
90	C₅×#121	—	2	1	no	—
91	C₅×#121	C₂²×C₃	1	2	yes	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
96	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
97	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
101	C₅×#106	C₂²×C₃	1	4	yes	complemented
102	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
103	C₅×#102	C₂²×C₃	1	4	yes	—
104	C₅×#102	C₂²×C₃	1	4	yes	complemented
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	2	yes	complemented
107	#3109	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
108	C₂³×C₃×C₅	—	2	4	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	—	4	2	no	—
113	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₃×C₅×D₄	—	2	4	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	2	4	no	—
118	C₃×C₅×D₄	—	4	2	no	—
119	C₃×C₅×D₄	—	4	4	no	—
120	C₃×C₅×D₄	—	4	2	no	—
121	C₃×C₅×D₄	#41	1	4	yes	complemented
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	4	4	no	—
128	C₂×C₃×C₄×C₅	—	4	4	no	—
129	C₂×C₃×C₄×C₅	—	4	2	no	—
130	C₂×C₃×C₄×C₅	—	4	4	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₃×C₅×C₈	—	2	4	no	—
138	C₂×C₃×#41	—	2	1	no	—
139	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
140	C₂³×C₃×C₄	—	2	1	no	—
141	C₂×C₃×D₈	C₂²×C₅	1	4	yes	—
142	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
143	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
144	C₃×#124	—	2	1	no	—
145	C₃×#121	—	2	1	no	—
146	C₃×#121	C₂²×C₅	1	2	yes	—
147	C₃×C₄×D₄	—	2	1	no	—
148	C₃×C₄×D₄	—	2	1	no	—
149	C₃×C₄×D₄	—	2	1	no	—
150	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
151	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
152	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
153	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
156	C₃×#106	C₂²×C₅	1	4	yes	complemented
157	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
158	C₃×#102	C₂²×C₅	1	4	yes	—
159	C₃×#102	C₂²×C₅	1	4	yes	complemented
160	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
161	C₃×#97	C₂²×C₅	1	2	yes	complemented
162	C₂⁴×C₅	—	2	1	no	—
163	C₅×#41	—	4	4	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	2	2	no	—
167	C₂×C₅×D₄	—	2	1	no	—
168	C₂×C₅×D₄	—	2	1	no	—
169	C₂×C₅×D₄	—	2	1	no	—
170	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
171	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	2	no	—
174	C₂²×C₄×C₅	—	2	2	no	—
175	C₂²×C₄×C₅	—	2	2	no	—
176	C₂²×C₄×C₅	—	4	4	no	—
177	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
180	C₅×D₈	—	2	8	no	—
181	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
182	C₅×C₄⋊C₄	—	2	1	no	—
183	C₅×C₄⋊C₄	—	2	1	no	—
184	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
185	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
186	C₅×C₂²⋊C₄	—	2	2	no	—
187	C₅×C₂²⋊C₄	—	2	2	no	—
188	C₅×C₂²⋊C₄	—	2	2	no	—
189	C₅×C₂²⋊C₄	—	2	2	no	—
190	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
193	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
194	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
196	#481	C₂×C₃×C₅	1	2	yes	complemented
197	#476	C₂×C₃×C₅	1	2	yes	complemented
198	#459	C₂×C₃×C₅	1	2	yes	complemented
199	#447	C₂×C₃×C₅	1	2	yes	complemented
200	#442	C₂×C₃×C₅	1	4	yes	complemented
201	#432	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	C₂²×C₃×C₅	—	2	1	no	—
203	C₂²×C₃×C₅	—	2	1	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	—	4	8	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	—	4	2	no	—
208	C₂²×C₃×C₅	—	4	2	no	—
209	C₂²×C₃×C₅	—	4	2	no	—
210	C₂²×C₃×C₅	—	4	2	no	—
211	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
212	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	4	2	no	—
218	C₃×C₄×C₅	—	4	2	no	—
219	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
220	C₃×C₄×C₅	C₂×#41	1	2	yes	—
221	C₂⁴×C₃	—	2	1	no	—
222	C₃×#41	—	4	4	no	—
223	C₂×C₃×Q₈	—	2	1	no	—
224	C₂×C₃×D₄	—	2	4	no	—
225	C₂×C₃×D₄	—	2	2	no	—
226	C₂×C₃×D₄	—	2	1	no	—
227	C₂×C₃×D₄	—	2	1	no	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
230	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	2	no	—
233	C₂²×C₃×C₄	—	2	2	no	—
234	C₂²×C₃×C₄	—	2	2	no	—
235	C₂²×C₃×C₄	—	4	4	no	—
236	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
239	C₃×D₈	—	2	8	no	—
240	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	—	2	2	no	—
246	C₃×C₂²⋊C₄	—	2	2	no	—
247	C₃×C₂²⋊C₄	—	2	2	no	—
248	C₃×C₂²⋊C₄	—	2	2	no	—
249	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
250	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
251	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
252	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
253	C₂³×C₅	—	2	4	no	—
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	4	2	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
259	C₅×Q₈	—	4	2	no	—
260	C₅×D₄	—	2	4	no	—
261	C₅×D₄	—	2	2	no	—
262	C₅×D₄	—	2	4	no	—
263	C₅×D₄	—	4	2	no	—
264	C₅×D₄	—	4	4	no	—
265	C₅×D₄	—	4	2	no	—
266	C₅×D₄	C₃×#41	1	4	yes	complemented
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	2	2	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	4	4	no	—
273	C₂×C₄×C₅	—	4	4	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	—	4	4	no	—
276	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
282	C₅×C₈	—	2	4	no	—
283	C₂×#41	—	2	1	no	—
284	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂×D₈	C₂²×C₃×C₅	1	4	yes	—
287	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
288	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
289	#124	—	2	1	no	—
290	#121	—	2	1	no	—
291	#121	C₂²×C₃×C₅	1	2	yes	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
296	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
297	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
298	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
301	#106	C₂²×C₃×C₅	1	4	yes	complemented
302	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
303	#102	C₂²×C₃×C₅	1	4	yes	—
304	#102	C₂²×C₃×C₅	1	4	yes	complemented
305	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
306	#97	C₂²×C₃×C₅	1	2	yes	complemented
307	C₂×C₃×C₅	—	2	2	no	—
308	C₂×C₃×C₅	—	4	4	no	—
309	C₂×C₃×C₅	—	8	2	no	—
310	C₂×C₃×C₅	#525	1	1	yes	characteristic
311	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
313	C₂³×C₃	—	2	4	no	—
314	C₂³×C₃	—	2	2	no	—
315	C₂³×C₃	—	2	2	no	—
316	C₂³×C₃	—	4	2	no	—
317	C₂³×C₃	—	4	2	no	—
318	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
319	C₃×Q₈	—	4	2	no	—
320	C₃×D₄	—	2	4	no	—
321	C₃×D₄	—	2	2	no	—
322	C₃×D₄	—	2	4	no	—
323	C₃×D₄	—	4	2	no	—
324	C₃×D₄	—	4	4	no	—
325	C₃×D₄	—	4	2	no	—
326	C₃×D₄	C₅×#41	1	4	yes	complemented
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	4	4	no	—
333	C₂×C₃×C₄	—	4	4	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	4	4	no	—
336	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
342	C₃×C₈	—	2	4	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	—	2	1	no	—
345	C₂²×C₅	—	2	4	no	—
346	C₂²×C₅	—	4	8	no	—
347	C₂²×C₅	—	4	2	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	—	4	2	no	—
351	C₂²×C₅	—	4	2	no	—
352	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
353	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	2	1	no	—
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	4	2	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
361	C₄×C₅	C₂×C₃×#41	1	2	yes	—
362	C₂⁴	—	2	1	no	—
363	#41	—	4	4	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
371	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
380	D₈	—	2	8	no	—
381	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
385	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
391	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
392	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
393	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
394	C₃×C₅	#3109	1	1	yes	characteristic, direct product factor, Hall
395	C₂²×C₃	—	2	1	no	—
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	4	no	—
398	C₂²×C₃	—	4	8	no	—
399	C₂²×C₃	—	4	2	no	—
400	C₂²×C₃	—	4	2	no	—
401	C₂²×C₃	—	4	2	no	—
402	C₂²×C₃	—	4	2	no	—
403	C₂²×C₃	—	4	2	no	—
404	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
405	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	4	2	no	—
411	C₃×C₄	—	4	2	no	—
412	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
413	C₃×C₄	C₂×C₅×#41	1	2	yes	—
414	C₂×C₅	—	2	2	no	—
415	C₂×C₅	—	4	4	no	—
416	C₂×C₅	—	8	2	no	—
417	C₂×C₅	C₃×#525	1	1	yes	characteristic
418	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
420	C₂³	—	2	4	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	2	no	—
429	D₄	—	2	4	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	4	no	—
432	D₄	—	4	2	no	—
433	D₄	C₃×C₅×#41	1	4	yes	complemented
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
444	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
445	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
449	C₈	—	2	4	no	—
450	C₂×C₃	—	2	2	no	—
451	C₂×C₃	—	4	4	no	—
452	C₂×C₃	—	8	2	no	—
453	C₂×C₃	C₅×#525	1	1	yes	characteristic
454	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
455	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
456	C₅	C₃×#3109	1	1	yes	characteristic, direct product factor, Sylow
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	4	8	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
467	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
475	C₄	C₂×C₃×C₅×#41	1	2	yes	—
476	C₃	C₅×#3109	1	1	yes	characteristic, direct product factor, Sylow
477	C₂	—	2	2	no	—
478	C₂	—	4	4	no	—
479	C₂	—	8	2	no	—
480	C₂	C₃×C₅×#525	1	1	yes	characteristic
481	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
482	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×C₄×C₅×D₄	C₂	semidirect
3. C₃×C₅×#481	C₂	semidirect
4. C₃×C₅×#476	C₂	semidirect
5. C₃×C₅×#459	C₂	semidirect
6. C₃×C₅×#447	C₂	semidirect
7. C₃×C₅×#442	C₂	semidirect
8. C₃×C₅×#432	C₂	semidirect
9. C₅×#3109	C₃	direct (N × H)
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
15. C₃×C₅×#127	C₂²	semidirect
24. C₃×C₄×C₅×D₄	C₂²	semidirect
28. C₃×C₅×#106	C₂²	semidirect
29. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
33. C₃×C₅×#97	C₂²	semidirect
34. C₃×#3109	C₅	direct (N × H)
35. C₅×#532	C₂×C₃	semidirect
36. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
37. C₅×#481	C₂×C₃	semidirect
38. C₅×#476	C₂×C₃	semidirect
39. C₅×#459	C₂×C₃	semidirect
40. C₅×#447	C₂×C₃	semidirect
41. C₅×#442	C₂×C₃	semidirect
42. C₅×#432	C₂×C₃	semidirect
75. C₃×#532	C₂×C₅	semidirect
76. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
77. C₃×#481	C₂×C₅	semidirect
78. C₃×#476	C₂×C₅	semidirect
79. C₃×#459	C₂×C₅	semidirect
80. C₃×#447	C₂×C₅	semidirect
81. C₃×#442	C₂×C₅	semidirect
82. C₃×#432	C₂×C₅	semidirect
87. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
88. C₅×#127	C₂²×C₃	semidirect
97. C₄×C₅×D₄	C₂²×C₃	semidirect
101. C₅×#106	C₂²×C₃	semidirect
102. C₅×C₄⋊C₈	C₂²×C₃	semidirect
104. C₅×#102	C₂²×C₃	semidirect
106. C₅×#97	C₂²×C₃	semidirect
107. #3109	C₃×C₅	direct (N × H)
121. C₃×C₅×D₄	#41	semidirect
142. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
143. C₃×#127	C₂²×C₅	semidirect
152. C₃×C₄×D₄	C₂²×C₅	semidirect
156. C₃×#106	C₂²×C₅	semidirect
157. C₃×C₄⋊C₈	C₂²×C₅	semidirect
159. C₃×#102	C₂²×C₅	semidirect
161. C₃×#97	C₂²×C₅	semidirect
194. #532	C₂×C₃×C₅	semidirect
195. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
196. #481	C₂×C₃×C₅	semidirect
197. #476	C₂×C₃×C₅	semidirect
198. #459	C₂×C₃×C₅	semidirect
199. #447	C₂×C₃×C₅	semidirect
200. #442	C₂×C₃×C₅	semidirect
201. #432	C₂×C₃×C₅	semidirect
266. C₅×D₄	C₃×#41	semidirect
287. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
288. #127	C₂²×C₃×C₅	semidirect
297. C₄×D₄	C₂²×C₃×C₅	semidirect
301. #106	C₂²×C₃×C₅	semidirect
302. C₄⋊C₈	C₂²×C₃×C₅	semidirect
304. #102	C₂²×C₃×C₅	semidirect
306. #97	C₂²×C₃×C₅	semidirect
326. C₃×D₄	C₅×#41	semidirect
394. C₃×C₅	#3109	direct (N × H)
433. D₄	C₃×C₅×#41	semidirect
456. C₅	C₃×#3109	direct (N × H)
476. C₃	C₅×#3109	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×C₄×C₅×D₄	2
C₃×C₅×#481	2
C₃×C₅×#476	2
C₃×C₅×#459	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₅×#432	2
C₅×#3109	3
C₃×#3109	5

Subgroups — C3×C5×#3109 #14276143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3109 #14276143