Subgroups — C₃×C₅×#3044 #14276078

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#462	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
10	C₅×#3044	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	—	2	4	no	—
15	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₃×C₅×#124	C₂²	1	2	yes	—
23	C₃×C₅×#123	—	2	2	no	—
24	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
25	C₃×C₄×C₅×Q₈	—	2	2	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	—
27	C₃×C₅×#117	—	2	2	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	4	yes	—
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	4	yes	—
33	C₃×C₅×#102	C₂²	1	2	yes	—
34	C₃×#3044	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic
36	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#536	C₂×C₃	1	1	yes	characteristic
38	C₅×#519	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#464	C₂×C₃	1	4	yes	complemented
40	C₅×#462	C₂×C₃	1	4	yes	complemented
41	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
42	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#416	C₂×C₃	1	1	yes	characteristic
44	C₃×C₅×#41	—	2	2	no	—
45	C₃×C₅×#41	—	2	2	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	—	2	1	no	—
48	C₂×C₃×C₅×Q₈	—	2	2	no	—
49	C₂×C₃×C₅×Q₈	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	D₄	1	4	yes	—
52	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×Q₁₆	—	2	8	no	—
62	C₃×C₅×Q₁₆	—	2	4	no	—
63	C₃×C₅×SD₁₆	—	2	4	no	—
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₂×C₃×C₅×C₈	—	2	2	no	—
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	4	no	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
75	C₃×C₄²×C₅	—	2	4	no	—
76	C₃×C₄²×C₅	—	2	1	no	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic
79	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#536	C₂×C₅	1	1	yes	characteristic
81	C₃×#519	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#464	C₂×C₅	1	4	yes	complemented
83	C₃×#462	C₂×C₅	1	4	yes	complemented
84	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
85	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#416	C₂×C₅	1	1	yes	characteristic
87	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
90	C₅×#137	—	2	4	no	—
91	C₂×C₅×Q₁₆	—	2	4	no	—
92	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
93	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
94	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
95	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
96	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
97	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
98	C₅×#124	C₂²×C₃	1	2	yes	—
99	C₅×#123	—	2	2	no	—
100	C₅×C₂²⋊Q₈	—	2	2	no	—
101	C₄×C₅×Q₈	—	2	2	no	—
102	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	—
103	C₅×#117	—	2	2	no	—
104	C₅×#117	C₂²×C₃	1	1	yes	characteristic
105	C₅×#117	C₂²×C₃	1	1	yes	characteristic
106	C₅×C₄⋊C₈	C₂²×C₃	1	4	yes	—
107	C₅×#103	C₂²×C₃	1	2	yes	—
108	C₅×#103	C₂²×C₃	1	4	yes	—
109	C₅×#102	C₂²×C₃	1	2	yes	—
110	#3044	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
111	C₂³×C₃×C₅	—	2	1	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	2	4	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×Q₈	—	2	1	no	—
117	C₃×C₅×Q₈	—	2	2	no	—
118	C₃×C₅×Q₈	—	2	1	no	—
119	C₃×C₅×Q₈	—	4	2	no	—
120	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
121	C₃×C₅×D₄	—	2	1	no	—
122	C₃×C₅×D₄	—	2	1	no	—
123	C₃×C₅×D₄	—	4	2	no	—
124	C₂×C₃×C₄×C₅	—	2	4	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	1	no	—
129	C₂×C₃×C₄×C₅	—	4	2	no	—
130	C₂×C₃×C₄×C₅	—	4	2	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₃×C₅×C₈	—	2	2	no	—
137	C₃×C₅×C₈	—	2	2	no	—
138	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
139	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
140	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
141	C₃×#137	—	2	4	no	—
142	C₂×C₃×Q₁₆	—	2	4	no	—
143	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
144	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
145	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
146	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
147	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
148	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
149	C₃×#124	C₂²×C₅	1	2	yes	—
150	C₃×#123	—	2	2	no	—
151	C₃×C₂²⋊Q₈	—	2	2	no	—
152	C₃×C₄×Q₈	—	2	2	no	—
153	C₃×C₄×Q₈	C₂²×C₅	1	4	yes	—
154	C₃×#117	—	2	2	no	—
155	C₃×#117	C₂²×C₅	1	1	yes	characteristic
156	C₃×#117	C₂²×C₅	1	1	yes	characteristic
157	C₃×C₄⋊C₈	C₂²×C₅	1	4	yes	—
158	C₃×#103	C₂²×C₅	1	2	yes	—
159	C₃×#103	C₂²×C₅	1	4	yes	—
160	C₃×#102	C₂²×C₅	1	2	yes	—
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	2	2	no	—
163	C₂×C₅×Q₈	—	2	1	no	—
164	C₂×C₅×Q₈	—	2	1	no	—
165	C₂×C₅×Q₈	—	2	2	no	—
166	C₂×C₅×Q₈	—	2	2	no	—
167	C₂×C₅×Q₈	—	2	2	no	—
168	C₂×C₅×Q₈	C₃×D₄	1	4	yes	—
169	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
170	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	—	2	1	no	—
175	C₂²×C₄×C₅	—	2	1	no	—
176	C₂²×C₄×C₅	—	2	1	no	—
177	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
178	C₅×Q₁₆	—	2	8	no	—
179	C₅×Q₁₆	—	2	4	no	—
180	C₅×SD₁₆	—	2	4	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
184	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	2	4	no	—
187	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
188	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
189	C₅×C₂²⋊C₄	—	2	1	no	—
190	C₅×C₂²⋊C₄	—	2	4	no	—
191	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
192	C₄²×C₅	—	2	4	no	—
193	C₄²×C₅	—	2	1	no	—
194	C₄²×C₅	C₂³×C₃	1	2	yes	—
195	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic
196	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
197	#536	C₂×C₃×C₅	1	1	yes	characteristic
198	#519	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#464	C₂×C₃×C₅	1	4	yes	complemented
200	#462	C₂×C₃×C₅	1	4	yes	complemented
201	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
202	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
203	#416	C₂×C₃×C₅	1	1	yes	characteristic
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	4	1	no	—
206	C₂²×C₃×C₅	—	4	2	no	—
207	C₂²×C₃×C₅	#121	1	2	yes	—
208	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
209	C₃×C₄×C₅	—	2	4	no	—
210	C₃×C₄×C₅	—	2	4	no	—
211	C₃×C₄×C₅	—	4	1	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	#121	1	2	yes	—
215	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₃×#41	—	2	2	no	—
218	C₃×#41	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	1	no	—
220	C₂×C₃×Q₈	—	2	1	no	—
221	C₂×C₃×Q₈	—	2	2	no	—
222	C₂×C₃×Q₈	—	2	2	no	—
223	C₂×C₃×Q₈	—	2	2	no	—
224	C₂×C₃×Q₈	C₅×D₄	1	4	yes	—
225	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
226	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
227	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	—	2	1	no	—
233	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
234	C₃×Q₁₆	—	2	8	no	—
235	C₃×Q₁₆	—	2	4	no	—
236	C₃×SD₁₆	—	2	4	no	—
237	C₃×M₁₆	—	2	2	no	—
238	C₂×C₃×C₈	—	2	2	no	—
239	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
240	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
241	C₃×C₄⋊C₄	—	2	4	no	—
242	C₃×C₄⋊C₄	—	2	4	no	—
243	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
245	C₃×C₂²⋊C₄	—	2	1	no	—
246	C₃×C₂²⋊C₄	—	2	4	no	—
247	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
248	C₃×C₄²	—	2	4	no	—
249	C₃×C₄²	—	2	1	no	—
250	C₃×C₄²	C₂³×C₅	1	2	yes	—
251	C₂³×C₅	—	2	1	no	—
252	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
253	C₅×Q₈	—	2	4	no	—
254	C₅×Q₈	—	2	2	no	—
255	C₅×Q₈	—	2	2	no	—
256	C₅×Q₈	—	2	1	no	—
257	C₅×Q₈	—	2	2	no	—
258	C₅×Q₈	—	2	1	no	—
259	C₅×Q₈	—	4	2	no	—
260	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
261	C₅×D₄	—	2	1	no	—
262	C₅×D₄	—	2	1	no	—
263	C₅×D₄	—	4	2	no	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	2	2	no	—
268	C₂×C₄×C₅	—	2	1	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	—	4	2	no	—
271	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
272	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₃×#41	1	2	yes	—
275	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
276	C₅×C₈	—	2	2	no	—
277	C₅×C₈	—	2	2	no	—
278	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
281	#137	—	2	4	no	—
282	C₂×Q₁₆	—	2	4	no	—
283	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
284	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
285	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
286	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
288	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
289	#124	C₂²×C₃×C₅	1	2	yes	—
290	#123	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	C₂²×C₃×C₅	1	4	yes	—
294	#117	—	2	2	no	—
295	#117	C₂²×C₃×C₅	1	1	yes	characteristic
296	#117	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×C₃×C₅	1	4	yes	—
298	#103	C₂²×C₃×C₅	1	2	yes	—
299	#103	C₂²×C₃×C₅	1	4	yes	—
300	#102	C₂²×C₃×C₅	1	2	yes	—
301	C₂×C₃×C₅	—	2	2	no	—
302	C₂×C₃×C₅	—	8	1	no	—
303	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
304	C₂×C₃×C₅	#578	1	2	yes	—
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
307	C₃×Q₈	—	2	4	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×Q₈	—	2	2	no	—
310	C₃×Q₈	—	2	1	no	—
311	C₃×Q₈	—	2	2	no	—
312	C₃×Q₈	—	2	1	no	—
313	C₃×Q₈	—	4	2	no	—
314	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
315	C₃×D₄	—	2	1	no	—
316	C₃×D₄	—	2	1	no	—
317	C₃×D₄	—	4	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	4	2	no	—
324	C₂×C₃×C₄	—	4	2	no	—
325	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
326	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
328	C₂×C₃×C₄	C₅×#41	1	2	yes	—
329	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
330	C₃×C₈	—	2	2	no	—
331	C₃×C₈	—	2	2	no	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	—	4	2	no	—
334	C₂²×C₅	—	4	1	no	—
335	C₂²×C₅	C₃×#121	1	2	yes	—
336	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
337	C₄×C₅	—	2	4	no	—
338	C₄×C₅	—	2	4	no	—
339	C₄×C₅	—	4	2	no	—
340	C₄×C₅	—	4	1	no	—
341	C₄×C₅	—	4	2	no	—
342	C₄×C₅	C₃×#121	1	2	yes	—
343	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
345	#41	—	2	2	no	—
346	#41	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	C₃×C₅×D₄	1	4	yes	—
353	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
354	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
355	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
362	Q₁₆	—	2	8	no	—
363	Q₁₆	—	2	4	no	—
364	SD₁₆	—	2	4	no	—
365	M₁₆	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
368	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
372	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
376	C₄²	—	2	4	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂³×C₃×C₅	1	2	yes	—
379	C₃×C₅	#3044	1	1	yes	characteristic, direct product factor, Hall
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	4	1	no	—
382	C₂²×C₃	—	4	2	no	—
383	C₂²×C₃	C₅×#121	1	2	yes	—
384	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	—	2	4	no	—
387	C₃×C₄	—	4	1	no	—
388	C₃×C₄	—	4	2	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	C₅×#121	1	2	yes	—
391	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
392	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
393	C₂×C₅	—	2	2	no	—
394	C₂×C₅	—	8	1	no	—
395	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
396	C₂×C₅	C₃×#578	1	2	yes	—
397	C₂³	—	2	1	no	—
398	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
399	Q₈	—	2	4	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	1	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	2	1	no	—
405	Q₈	—	4	2	no	—
406	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	4	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
418	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
419	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
420	C₂×C₄	C₃×C₅×#41	1	2	yes	—
421	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	2	2	no	—
424	C₂×C₃	—	2	2	no	—
425	C₂×C₃	—	8	1	no	—
426	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
427	C₂×C₃	C₅×#578	1	2	yes	—
428	C₅	C₃×#3044	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	2	2	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	C₃×C₅×#121	1	2	yes	—
433	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	C₃×C₅×#121	1	2	yes	—
440	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
441	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
442	C₃	C₅×#3044	1	1	yes	characteristic, direct product factor, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	8	1	no	—
445	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
446	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#519	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#424	C₂	semidirect
8. C₃×C₅×#419	C₂	semidirect
10. C₅×#3044	C₃	direct (N × H)
34. C₃×#3044	C₅	direct (N × H)
36. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
38. C₅×#519	C₂×C₃	semidirect
39. C₅×#464	C₂×C₃	semidirect
40. C₅×#462	C₂×C₃	semidirect
41. C₅×#424	C₂×C₃	semidirect
42. C₅×#419	C₂×C₃	semidirect
79. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
81. C₃×#519	C₂×C₅	semidirect
82. C₃×#464	C₂×C₅	semidirect
83. C₃×#462	C₂×C₅	semidirect
84. C₃×#424	C₂×C₅	semidirect
85. C₃×#419	C₂×C₅	semidirect
110. #3044	C₃×C₅	direct (N × H)
196. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
198. #519	C₂×C₃×C₅	semidirect
199. #464	C₂×C₃×C₅	semidirect
200. #462	C₂×C₃×C₅	semidirect
201. #424	C₂×C₃×C₅	semidirect
202. #419	C₂×C₃×C₅	semidirect
379. C₃×C₅	#3044	direct (N × H)
428. C₅	C₃×#3044	direct (N × H)
442. C₃	C₅×#3044	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#137	2
C₂²×C₃×C₅×Q₁₆	2
C₃×C₅×#536	2
C₃×C₅×#519	2
C₃×C₅×#464	2
C₃×C₅×#462	2
C₃×C₅×#424	2
C₃×C₅×#419	2
C₃×C₅×#416	2
C₅×#3044	3
C₃×#3044	5

Subgroups — C3×C5×#3044 #14276078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3044 #14276078