Subgroups — C₃×C₅×#3022 #14276056

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#456	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#455	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#413	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3022	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
10	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
12	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
13	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	—
14	C₂×C₃×C₅×#41	—	2	4	no	—
15	C₂×C₃×C₅×#41	—	2	2	no	—
16	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₅×#137	—	2	4	no	—
20	C₃×C₅×#137	C₂²	1	8	yes	complemented
21	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
22	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
23	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
24	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#104	C₂²	1	8	yes	complemented
30	C₃×C₅×#101	C₂²	1	2	yes	complemented
31	C₃×C₅×#100	C₂²	1	2	yes	complemented
32	C₃×#3022	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#585	C₂×C₃	1	1	yes	characteristic
34	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
35	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#456	C₂×C₃	1	4	yes	complemented
37	C₅×#455	C₂×C₃	1	4	yes	complemented
38	C₅×#421	C₂×C₃	1	2	yes	complemented
39	C₅×#413	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×C₅×#41	—	2	4	no	—
41	C₃×C₅×#41	—	2	8	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₃×C₅×#41	—	2	4	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₃×C₅×#41	—	2	4	no	—
48	C₃×C₅×#41	—	2	2	no	—
49	C₃×C₅×#41	—	2	2	no	—
50	C₃×C₅×#41	D₄	1	4	yes	—
51	C₃×C₅×#41	C₂³	1	4	yes	—
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	4	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	8	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	4	no	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	2	4	no	—
65	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
66	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
67	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	—	2	4	no	—
69	C₂²×C₃×C₄×C₅	—	2	2	no	—
70	C₂²×C₃×C₄×C₅	—	2	1	no	—
71	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	8	no	—
74	C₃×C₅×SD₁₆	—	2	8	no	—
75	C₃×C₅×M₁₆	—	2	2	no	—
76	C₃×C₅×M₁₆	C₂³	1	4	yes	—
77	C₂×C₃×C₅×C₈	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	—	2	4	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₄²×C₅	C₂³	1	2	yes	—
83	C₃×#585	C₂×C₅	1	1	yes	characteristic
84	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
85	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#456	C₂×C₅	1	4	yes	complemented
87	C₃×#455	C₂×C₅	1	4	yes	complemented
88	C₃×#421	C₂×C₅	1	2	yes	complemented
89	C₃×#413	C₂×C₅	1	1	yes	characteristic, complemented
90	C₅×2₋¹⁺⁴	—	2	2	no	—
91	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
92	C₅×H(5,𝔽₂)	—	2	2	no	—
93	C₅×H(5,𝔽₂)	—	2	2	no	—
94	C₅×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
95	C₂×C₅×#41	—	2	4	no	—
96	C₂×C₅×#41	—	2	2	no	—
97	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
98	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₅×#137	—	2	4	no	—
101	C₅×#137	C₂²×C₃	1	8	yes	complemented
102	C₂×C₅×Q₁₆	—	2	2	no	—
103	C₂×C₅×SD₁₆	—	2	2	no	—
104	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
105	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
106	C₅×#124	C₂²×C₃	1	2	yes	complemented
107	C₅×#123	—	2	2	no	—
108	C₅×C₂²⋊Q₈	—	2	2	no	—
109	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
110	C₅×#104	C₂²×C₃	1	8	yes	complemented
111	C₅×#101	C₂²×C₃	1	2	yes	complemented
112	C₅×#100	C₂²×C₃	1	2	yes	complemented
113	#3022	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₃×C₅	—	2	4	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
117	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
118	C₃×C₅×Q₈	—	2	4	no	—
119	C₃×C₅×Q₈	—	2	2	no	—
120	C₃×C₅×Q₈	—	2	2	no	—
121	C₃×C₅×Q₈	—	2	4	no	—
122	C₃×C₅×Q₈	—	4	1	no	—
123	C₃×C₅×Q₈	—	4	1	no	—
124	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
125	C₃×C₅×D₄	—	2	8	no	—
126	C₃×C₅×D₄	—	2	4	no	—
127	C₃×C₅×D₄	—	2	4	no	—
128	C₃×C₅×D₄	—	2	4	no	—
129	C₃×C₅×D₄	—	2	4	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	4	no	—
134	C₂×C₃×C₄×C₅	—	2	8	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	4	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	4	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	4	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₅×C₈	—	2	4	no	—
149	C₃×2₋¹⁺⁴	—	2	2	no	—
150	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
151	C₃×H(5,𝔽₂)	—	2	2	no	—
152	C₃×H(5,𝔽₂)	—	2	2	no	—
153	C₃×H(5,𝔽₂)	C₂²×C₅	1	2	yes	—
154	C₂×C₃×#41	—	2	4	no	—
155	C₂×C₃×#41	—	2	2	no	—
156	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
157	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
158	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₃×#137	—	2	4	no	—
160	C₃×#137	C₂²×C₅	1	8	yes	complemented
161	C₂×C₃×Q₁₆	—	2	2	no	—
162	C₂×C₃×SD₁₆	—	2	2	no	—
163	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
164	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
165	C₃×#124	C₂²×C₅	1	2	yes	complemented
166	C₃×#123	—	2	2	no	—
167	C₃×C₂²⋊Q₈	—	2	2	no	—
168	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₃×#104	C₂²×C₅	1	8	yes	complemented
170	C₃×#101	C₂²×C₅	1	2	yes	complemented
171	C₃×#100	C₂²×C₅	1	2	yes	complemented
172	C₅×#41	—	2	4	no	—
173	C₅×#41	—	2	8	no	—
174	C₅×#41	—	2	4	no	—
175	C₅×#41	—	2	4	no	—
176	C₅×#41	—	2	4	no	—
177	C₅×#41	—	2	2	no	—
178	C₅×#41	—	2	2	no	—
179	C₅×#41	—	2	4	no	—
180	C₅×#41	—	2	2	no	—
181	C₅×#41	—	2	2	no	—
182	C₅×#41	C₃×D₄	1	4	yes	—
183	C₅×#41	C₂³×C₃	1	4	yes	—
184	C₂×C₅×Q₈	—	2	2	no	—
185	C₂×C₅×Q₈	—	2	4	no	—
186	C₂×C₅×Q₈	—	2	1	no	—
187	C₂×C₅×Q₈	—	2	2	no	—
188	C₂×C₅×Q₈	—	2	2	no	—
189	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
190	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
191	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₅×D₄	—	2	8	no	—
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	2	4	no	—
195	C₂×C₅×D₄	—	2	2	no	—
196	C₂×C₅×D₄	—	2	4	no	—
197	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
198	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
199	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	—	2	4	no	—
201	C₂²×C₄×C₅	—	2	2	no	—
202	C₂²×C₄×C₅	—	2	1	no	—
203	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₅×Q₁₆	—	2	8	no	—
206	C₅×SD₁₆	—	2	8	no	—
207	C₅×M₁₆	—	2	2	no	—
208	C₅×M₁₆	C₂³×C₃	1	4	yes	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₄²×C₅	C₂³×C₃	1	2	yes	—
215	#585	C₂×C₃×C₅	1	1	yes	characteristic
216	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
217	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
218	#456	C₂×C₃×C₅	1	4	yes	complemented
219	#455	C₂×C₃×C₅	1	4	yes	complemented
220	#421	C₂×C₃×C₅	1	2	yes	complemented
221	#413	C₂×C₃×C₅	1	1	yes	characteristic, complemented
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	—	2	4	no	—
224	C₂²×C₃×C₅	—	4	1	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	8	2	no	—
227	C₂²×C₃×C₅	—	8	4	no	—
228	C₂²×C₃×C₅	#120	1	2	yes	—
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₃×C₄×C₅	—	2	4	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	#120	1	1	yes	characteristic
235	C₃×C₄×C₅	#120	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
237	C₃×#41	—	2	4	no	—
238	C₃×#41	—	2	8	no	—
239	C₃×#41	—	2	4	no	—
240	C₃×#41	—	2	4	no	—
241	C₃×#41	—	2	4	no	—
242	C₃×#41	—	2	2	no	—
243	C₃×#41	—	2	2	no	—
244	C₃×#41	—	2	4	no	—
245	C₃×#41	—	2	2	no	—
246	C₃×#41	—	2	2	no	—
247	C₃×#41	C₅×D₄	1	4	yes	—
248	C₃×#41	C₂³×C₅	1	4	yes	—
249	C₂×C₃×Q₈	—	2	2	no	—
250	C₂×C₃×Q₈	—	2	4	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	—	2	2	no	—
253	C₂×C₃×Q₈	—	2	2	no	—
254	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
255	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
256	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₃×D₄	—	2	8	no	—
258	C₂×C₃×D₄	—	2	2	no	—
259	C₂×C₃×D₄	—	2	4	no	—
260	C₂×C₃×D₄	—	2	2	no	—
261	C₂×C₃×D₄	—	2	4	no	—
262	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
263	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
264	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
265	C₂²×C₃×C₄	—	2	4	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₃×Q₁₆	—	2	8	no	—
271	C₃×SD₁₆	—	2	8	no	—
272	C₃×M₁₆	—	2	2	no	—
273	C₃×M₁₆	C₂³×C₅	1	4	yes	—
274	C₂×C₃×C₈	—	2	2	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	—	2	4	no	—
277	C₃×C₂²⋊C₄	—	2	1	no	—
278	C₃×C₂²⋊C₄	—	2	4	no	—
279	C₃×C₄²	C₂³×C₅	1	2	yes	—
280	C₂³×C₅	—	2	4	no	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
283	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₅×Q₈	—	2	4	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	2	4	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	4	1	no	—
290	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
291	C₅×D₄	—	2	8	no	—
292	C₅×D₄	—	2	4	no	—
293	C₅×D₄	—	2	4	no	—
294	C₅×D₄	—	2	4	no	—
295	C₅×D₄	—	2	4	no	—
296	C₅×D₄	—	2	2	no	—
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	8	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	4	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	4	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
312	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
314	C₅×C₈	—	2	4	no	—
315	2₋¹⁺⁴	—	2	2	no	—
316	2₋¹⁺⁴	C₂²×C₃×C₅	1	2	yes	—
317	H(5,𝔽₂)	—	2	2	no	—
318	H(5,𝔽₂)	—	2	2	no	—
319	H(5,𝔽₂)	C₂²×C₃×C₅	1	2	yes	—
320	C₂×#41	—	2	4	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
323	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
324	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
325	#137	—	2	4	no	—
326	#137	C₂²×C₃×C₅	1	8	yes	complemented
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×SD₁₆	—	2	2	no	—
329	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
330	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
331	#124	C₂²×C₃×C₅	1	2	yes	complemented
332	#123	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
335	#104	C₂²×C₃×C₅	1	8	yes	complemented
336	#101	C₂²×C₃×C₅	1	2	yes	complemented
337	#100	C₂²×C₃×C₅	1	2	yes	complemented
338	C₂×C₃×C₅	—	2	1	no	—
339	C₂×C₃×C₅	—	2	2	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	—	4	4	no	—
342	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
343	C₂³×C₃	—	2	4	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
346	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
347	C₃×Q₈	—	2	4	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	—	2	2	no	—
350	C₃×Q₈	—	2	4	no	—
351	C₃×Q₈	—	4	1	no	—
352	C₃×Q₈	—	4	1	no	—
353	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
354	C₃×D₄	—	2	8	no	—
355	C₃×D₄	—	2	4	no	—
356	C₃×D₄	—	2	4	no	—
357	C₃×D₄	—	2	4	no	—
358	C₃×D₄	—	2	4	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
362	C₂×C₃×C₄	—	2	4	no	—
363	C₂×C₃×C₄	—	2	8	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	4	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	4	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	4	2	no	—
372	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
376	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
377	C₃×C₈	—	2	4	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	4	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	—	4	2	no	—
382	C₂²×C₅	—	8	2	no	—
383	C₂²×C₅	—	8	4	no	—
384	C₂²×C₅	C₃×#120	1	2	yes	—
385	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
386	C₄×C₅	—	2	4	no	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	—	4	2	no	—
390	C₄×C₅	C₃×#120	1	1	yes	characteristic
391	C₄×C₅	C₃×#120	1	1	yes	characteristic
392	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
393	#41	—	2	4	no	—
394	#41	—	2	8	no	—
395	#41	—	2	4	no	—
396	#41	—	2	4	no	—
397	#41	—	2	4	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	4	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	C₃×C₅×D₄	1	4	yes	—
404	#41	C₂³×C₃×C₅	1	4	yes	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
411	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
412	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
419	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
420	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
425	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
426	Q₁₆	—	2	8	no	—
427	SD₁₆	—	2	8	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	C₂³×C₃×C₅	1	4	yes	—
430	C₂×C₈	—	2	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₄²	C₂³×C₃×C₅	1	2	yes	—
436	C₃×C₅	#3022	1	1	yes	characteristic, direct product factor, Hall
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	4	no	—
439	C₂²×C₃	—	4	1	no	—
440	C₂²×C₃	—	4	2	no	—
441	C₂²×C₃	—	8	2	no	—
442	C₂²×C₃	—	8	4	no	—
443	C₂²×C₃	C₅×#120	1	2	yes	—
444	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
445	C₃×C₄	—	2	4	no	—
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	—	4	2	no	—
449	C₃×C₄	C₅×#120	1	1	yes	characteristic
450	C₃×C₄	C₅×#120	1	1	yes	characteristic
451	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	2	no	—
454	C₂×C₅	—	4	2	no	—
455	C₂×C₅	—	4	4	no	—
456	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
457	C₂³	—	2	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
460	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
461	Q₈	—	2	4	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	2	2	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	4	1	no	—
467	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
468	D₄	—	2	8	no	—
469	D₄	—	2	4	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
487	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
488	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
489	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
490	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
491	C₈	—	2	4	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	2	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	—	4	4	no	—
496	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
497	C₅	C₃×#3022	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	2	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	4	no	—
504	C₂²	C₃×C₅×#120	1	2	yes	—
505	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	C₃×C₅×#120	1	1	yes	characteristic
511	C₄	C₃×C₅×#120	1	1	yes	characteristic
512	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
513	C₃	C₅×#3022	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	2	no	—
517	C₂	—	4	4	no	—
518	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#137	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₃×C₅×#456	C₂	semidirect
5. C₃×C₅×#455	C₂	semidirect
6. C₃×C₅×#421	C₂	semidirect
7. C₃×C₅×#413	C₂	semidirect
8. C₅×#3022	C₃	direct (N × H)
18. C₂²×C₃×C₅×Q₈	C₂²	semidirect
20. C₃×C₅×#137	C₂²	semidirect
23. C₂×C₃×C₅×M₁₆	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
28. C₃×C₅×#117	C₂²	semidirect
29. C₃×C₅×#104	C₂²	semidirect
30. C₃×C₅×#101	C₂²	semidirect
31. C₃×C₅×#100	C₂²	semidirect
32. C₃×#3022	C₅	direct (N × H)
34. C₂×C₅×#137	C₂×C₃	semidirect
35. C₅×#536	C₂×C₃	semidirect
36. C₅×#456	C₂×C₃	semidirect
37. C₅×#455	C₂×C₃	semidirect
38. C₅×#421	C₂×C₃	semidirect
39. C₅×#413	C₂×C₃	semidirect
84. C₂×C₃×#137	C₂×C₅	semidirect
85. C₃×#536	C₂×C₅	semidirect
86. C₃×#456	C₂×C₅	semidirect
87. C₃×#455	C₂×C₅	semidirect
88. C₃×#421	C₂×C₅	semidirect
89. C₃×#413	C₂×C₅	semidirect
99. C₂²×C₅×Q₈	C₂²×C₃	semidirect
101. C₅×#137	C₂²×C₃	semidirect
104. C₂×C₅×M₁₆	C₂²×C₃	semidirect
105. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
106. C₅×#124	C₂²×C₃	semidirect
109. C₅×#117	C₂²×C₃	semidirect
110. C₅×#104	C₂²×C₃	semidirect
111. C₅×#101	C₂²×C₃	semidirect
112. C₅×#100	C₂²×C₃	semidirect
113. #3022	C₃×C₅	direct (N × H)
158. C₂²×C₃×Q₈	C₂²×C₅	semidirect
160. C₃×#137	C₂²×C₅	semidirect
163. C₂×C₃×M₁₆	C₂²×C₅	semidirect
164. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
165. C₃×#124	C₂²×C₅	semidirect
168. C₃×#117	C₂²×C₅	semidirect
169. C₃×#104	C₂²×C₅	semidirect
170. C₃×#101	C₂²×C₅	semidirect
171. C₃×#100	C₂²×C₅	semidirect
216. C₂×#137	C₂×C₃×C₅	semidirect
217. #536	C₂×C₃×C₅	semidirect
218. #456	C₂×C₃×C₅	semidirect
219. #455	C₂×C₃×C₅	semidirect
220. #421	C₂×C₃×C₅	semidirect
221. #413	C₂×C₃×C₅	semidirect
324. C₂²×Q₈	C₂²×C₃×C₅	semidirect
326. #137	C₂²×C₃×C₅	semidirect
329. C₂×M₁₆	C₂²×C₃×C₅	semidirect
330. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
331. #124	C₂²×C₃×C₅	semidirect
334. #117	C₂²×C₃×C₅	semidirect
335. #104	C₂²×C₃×C₅	semidirect
336. #101	C₂²×C₃×C₅	semidirect
337. #100	C₂²×C₃×C₅	semidirect
436. C₃×C₅	#3022	direct (N × H)
497. C₅	C₃×#3022	direct (N × H)
513. C₃	C₅×#3022	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×#585	2
C₂×C₃×C₅×#137	2
C₃×C₅×#536	2
C₃×C₅×#456	2
C₃×C₅×#455	2
C₃×C₅×#421	2
C₃×C₅×#413	2
C₅×#3022	3
C₃×#3022	5

Subgroups — C3×C5×#3022 #14276056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3022 #14276056