Subgroups — C₃×C₅×#3077 #14276111

Order 1920.

880 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#478	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#476	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#474	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#428	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#418	C₂	1	2	yes	maximal
9	C₅×#3077	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×C₄×C₅	—	2	1	no	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#125	C₂²	1	2	yes	complemented
16	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
18	C₃×C₄×C₅×Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	—	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×C₅×#117	C₂²	1	2	yes	—
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×#107	C₂²	1	4	yes	complemented
29	C₃×C₅×#106	C₂²	1	4	yes	complemented
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	4	yes	—
33	C₃×C₅×#102	C₂²	1	4	yes	—
34	C₃×#3077	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
37	C₅×#478	C₂×C₃	1	4	yes	complemented
38	C₅×#476	C₂×C₃	1	2	yes	complemented
39	C₅×#474	C₂×C₃	1	2	yes	complemented
40	C₅×#428	C₂×C₃	1	2	yes	complemented
41	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#418	C₂×C₃	1	2	yes	—
43	C₂⁴×C₃×C₅	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	Q₈	1	4	yes	complemented
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	—	4	4	no	—
54	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×M₁₆	—	2	4	no	—
58	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₅	—	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×#533	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
77	C₃×#478	C₂×C₅	1	4	yes	complemented
78	C₃×#476	C₂×C₅	1	2	yes	complemented
79	C₃×#474	C₂×C₅	1	2	yes	complemented
80	C₃×#428	C₂×C₅	1	2	yes	complemented
81	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#418	C₂×C₅	1	2	yes	—
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂³×C₄×C₅	—	2	1	no	—
85	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
86	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₅×#125	C₂²×C₃	1	2	yes	complemented
89	C₅×C₂²⋊Q₈	—	2	1	no	—
90	C₅×C₂²⋊Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	—	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	C₅×#117	C₂²×C₃	1	2	yes	—
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×#107	C₂²×C₃	1	4	yes	complemented
102	C₅×#106	C₂²×C₃	1	4	yes	complemented
103	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
104	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
105	C₅×#102	C₂²×C₃	1	4	yes	—
106	C₅×#102	C₂²×C₃	1	4	yes	—
107	#3077	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	—	4	2	no	—
111	C₂³×C₃×C₅	—	4	2	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	4	2	no	—
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	C₂×Q₈	1	4	yes	—
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	1	no	—
123	C₂×C₃×C₄×C₅	—	4	4	no	—
124	C₂×C₃×C₄×C₅	—	4	2	no	—
125	C₂×C₃×C₄×C₅	—	4	4	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
132	C₂×C₃×C₄×C₅	#41	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₃×C₅×C₈	—	2	4	no	—
135	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
136	C₂³×C₃×C₄	—	2	1	no	—
137	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
138	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
140	C₃×#125	C₂²×C₅	1	2	yes	complemented
141	C₃×C₂²⋊Q₈	—	2	1	no	—
142	C₃×C₂²⋊Q₈	—	2	1	no	—
143	C₃×C₄×Q₈	—	2	1	no	—
144	C₃×C₄×Q₈	—	2	1	no	—
145	C₃×C₄×D₄	—	2	1	no	—
146	C₃×C₄×D₄	—	2	1	no	—
147	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
148	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
149	C₃×#117	C₂²×C₅	1	2	yes	—
150	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
153	C₃×#107	C₂²×C₅	1	4	yes	complemented
154	C₃×#106	C₂²×C₅	1	4	yes	complemented
155	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
156	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
157	C₃×#102	C₂²×C₅	1	4	yes	—
158	C₃×#102	C₂²×C₅	1	4	yes	—
159	C₂⁴×C₅	—	2	1	no	—
160	C₂×C₅×Q₈	—	2	1	no	—
161	C₂×C₅×Q₈	—	2	1	no	—
162	C₂×C₅×D₄	—	2	1	no	—
163	C₂×C₅×D₄	—	2	2	no	—
164	C₂×C₅×D₄	C₃×Q₈	1	4	yes	complemented
165	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	4	4	no	—
170	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
173	C₅×M₁₆	—	2	4	no	—
174	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	2	2	no	—
177	C₅×C₄⋊C₄	—	2	2	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
181	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
182	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
183	C₅×C₂²⋊C₄	—	2	2	no	—
184	C₅×C₂²⋊C₄	—	2	2	no	—
185	C₅×C₂²⋊C₄	—	2	2	no	—
186	C₄²×C₅	—	2	2	no	—
187	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
188	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
191	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
193	#478	C₂×C₃×C₅	1	4	yes	complemented
194	#476	C₂×C₃×C₅	1	2	yes	complemented
195	#474	C₂×C₃×C₅	1	2	yes	complemented
196	#428	C₂×C₃×C₅	1	2	yes	complemented
197	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
198	#418	C₂×C₃×C₅	1	2	yes	—
199	C₂²×C₃×C₅	—	2	1	no	—
200	C₂²×C₃×C₅	—	2	1	no	—
201	C₂²×C₃×C₅	—	2	4	no	—
202	C₂²×C₃×C₅	—	4	8	no	—
203	C₂²×C₃×C₅	—	4	2	no	—
204	C₂²×C₃×C₅	—	4	2	no	—
205	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
206	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	—	2	1	no	—
209	C₃×C₄×C₅	—	2	1	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
214	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
215	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₂⁴×C₃	—	2	1	no	—
218	C₂×C₃×Q₈	—	2	1	no	—
219	C₂×C₃×Q₈	—	2	1	no	—
220	C₂×C₃×D₄	—	2	1	no	—
221	C₂×C₃×D₄	—	2	2	no	—
222	C₂×C₃×D₄	C₅×Q₈	1	4	yes	complemented
223	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	—	2	2	no	—
227	C₂²×C₃×C₄	—	4	4	no	—
228	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
231	C₃×M₁₆	—	2	4	no	—
232	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	2	1	no	—
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
239	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
240	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
241	C₃×C₂²⋊C₄	—	2	2	no	—
242	C₃×C₂²⋊C₄	—	2	2	no	—
243	C₃×C₂²⋊C₄	—	2	2	no	—
244	C₃×C₄²	—	2	2	no	—
245	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
246	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
247	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
248	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	4	2	no	—
252	C₂³×C₅	—	4	2	no	—
253	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₅×Q₈	—	4	2	no	—
255	C₅×Q₈	—	4	2	no	—
256	C₅×D₄	—	2	4	no	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	C₂×C₃×Q₈	1	4	yes	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	4	1	no	—
264	C₂×C₄×C₅	—	4	4	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	—	4	4	no	—
267	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
273	C₂×C₄×C₅	C₃×#41	1	2	yes	—
274	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
275	C₅×C₈	—	2	4	no	—
276	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
279	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
280	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
281	#125	C₂²×C₃×C₅	1	2	yes	complemented
282	C₂²⋊Q₈	—	2	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
289	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
290	#117	C₂²×C₃×C₅	1	2	yes	—
291	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
294	#107	C₂²×C₃×C₅	1	4	yes	complemented
295	#106	C₂²×C₃×C₅	1	4	yes	complemented
296	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
297	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
298	#102	C₂²×C₃×C₅	1	4	yes	—
299	#102	C₂²×C₃×C₅	1	4	yes	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	4	4	no	—
302	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂×C₃×C₅	#575	1	1	yes	characteristic
305	C₂³×C₃	—	2	4	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	—	4	2	no	—
308	C₂³×C₃	—	4	2	no	—
309	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
310	C₃×Q₈	—	4	2	no	—
311	C₃×Q₈	—	4	2	no	—
312	C₃×D₄	—	2	4	no	—
313	C₃×D₄	—	2	2	no	—
314	C₃×D₄	C₂×C₅×Q₈	1	4	yes	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	4	1	no	—
320	C₂×C₃×C₄	—	4	4	no	—
321	C₂×C₃×C₄	—	4	2	no	—
322	C₂×C₃×C₄	—	4	4	no	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
329	C₂×C₃×C₄	C₅×#41	1	2	yes	—
330	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
331	C₃×C₈	—	2	4	no	—
332	C₂²×C₅	—	2	1	no	—
333	C₂²×C₅	—	2	1	no	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	4	8	no	—
336	C₂²×C₅	—	4	2	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
339	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
340	C₄×C₅	—	2	1	no	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	1	no	—
343	C₄×C₅	—	4	2	no	—
344	C₄×C₅	—	4	2	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
347	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
348	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
349	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
350	C₂⁴	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₃×C₅×Q₈	1	4	yes	complemented
356	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
363	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
364	M₁₆	—	2	4	no	—
365	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
372	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
373	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
379	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
380	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
381	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
382	C₃×C₅	#3077	1	1	yes	characteristic, direct product factor, Hall
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	2	1	no	—
385	C₂²×C₃	—	2	4	no	—
386	C₂²×C₃	—	4	8	no	—
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
390	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₃×C₄	—	2	1	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	4	2	no	—
395	C₃×C₄	—	4	2	no	—
396	C₃×C₄	—	4	2	no	—
397	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
398	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
399	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
400	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	4	4	no	—
403	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
405	C₂×C₅	C₃×#575	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	—	2	4	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	C₂×C₃×C₅×Q₈	1	4	yes	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
425	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
427	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
430	C₂×C₄	C₃×C₅×#41	1	2	yes	—
431	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	4	4	no	—
435	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
436	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂×C₃	C₅×#575	1	1	yes	characteristic
438	C₅	C₃×#3077	1	1	yes	characteristic, direct product factor, Sylow
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	4	8	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
446	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
454	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
455	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
456	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
457	C₃	C₅×#3077	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	2	2	no	—
459	C₂	—	4	4	no	—
460	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
461	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
462	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
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×#533	C₂	semidirect
3. C₃×C₅×#478	C₂	semidirect
4. C₃×C₅×#476	C₂	semidirect
5. C₃×C₅×#474	C₂	semidirect
6. C₃×C₅×#428	C₂	semidirect
7. C₃×C₅×#423	C₂	semidirect
9. C₅×#3077	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
15. C₃×C₅×#125	C₂²	semidirect
28. C₃×C₅×#107	C₂²	semidirect
29. C₃×C₅×#106	C₂²	semidirect
30. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×C₄⋊C₈	C₂²	semidirect
34. C₃×#3077	C₅	direct (N × H)
35. C₅×#533	C₂×C₃	semidirect
37. C₅×#478	C₂×C₃	semidirect
38. C₅×#476	C₂×C₃	semidirect
39. C₅×#474	C₂×C₃	semidirect
40. C₅×#428	C₂×C₃	semidirect
41. C₅×#423	C₂×C₃	semidirect
48. C₂×C₃×C₅×D₄	Q₈	semidirect
75. C₃×#533	C₂×C₅	semidirect
77. C₃×#478	C₂×C₅	semidirect
78. C₃×#476	C₂×C₅	semidirect
79. C₃×#474	C₂×C₅	semidirect
80. C₃×#428	C₂×C₅	semidirect
81. C₃×#423	C₂×C₅	semidirect
86. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
87. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
88. C₅×#125	C₂²×C₃	semidirect
101. C₅×#107	C₂²×C₃	semidirect
102. C₅×#106	C₂²×C₃	semidirect
103. C₅×C₄⋊C₈	C₂²×C₃	semidirect
104. C₅×C₄⋊C₈	C₂²×C₃	semidirect
107. #3077	C₃×C₅	direct (N × H)
138. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
139. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
140. C₃×#125	C₂²×C₅	semidirect
153. C₃×#107	C₂²×C₅	semidirect
154. C₃×#106	C₂²×C₅	semidirect
155. C₃×C₄⋊C₈	C₂²×C₅	semidirect
156. C₃×C₄⋊C₈	C₂²×C₅	semidirect
164. C₂×C₅×D₄	C₃×Q₈	semidirect
191. #533	C₂×C₃×C₅	semidirect
193. #478	C₂×C₃×C₅	semidirect
194. #476	C₂×C₃×C₅	semidirect
195. #474	C₂×C₃×C₅	semidirect
196. #428	C₂×C₃×C₅	semidirect
197. #423	C₂×C₃×C₅	semidirect
222. C₂×C₃×D₄	C₅×Q₈	semidirect
279. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
280. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
281. #125	C₂²×C₃×C₅	semidirect
294. #107	C₂²×C₃×C₅	semidirect
295. #106	C₂²×C₃×C₅	semidirect
296. C₄⋊C₈	C₂²×C₃×C₅	semidirect
297. C₄⋊C₈	C₂²×C₃×C₅	semidirect
355. C₂×D₄	C₃×C₅×Q₈	semidirect
382. C₃×C₅	#3077	direct (N × H)
438. C₅	C₃×#3077	direct (N × H)
457. C₃	C₅×#3077	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×#533	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#478	2
C₃×C₅×#476	2
C₃×C₅×#474	2
C₃×C₅×#428	2
C₃×C₅×#423	2
C₃×C₅×#418	2
C₅×#3077	3
C₃×#3077	5

Subgroups — C3×C5×#3077 #14276111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3077 #14276111