Subgroups — C₃×C₅×#1639 #14274673

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₄²	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1639	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	—	2	1	no	—
10	C₂²×C₃×C₅×D₄	—	2	1	no	—
11	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₃×C₅×#127	C₂²	1	1	yes	characteristic
14	C₃×C₅×#121	—	2	1	no	—
15	C₃×C₅×#121	—	2	1	no	—
16	C₃×C₅×#120	—	2	2	no	—
17	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×#103	—	2	1	no	—
23	C₃×C₅×#102	—	2	1	no	—
24	C₃×C₅×#102	—	2	2	no	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×#1639	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄²	C₂×C₃	1	1	yes	characteristic
28	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	1	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	4	2	no	—
41	C₂×C₃×C₅×D₄	—	4	2	no	—
42	C₂×C₃×C₅×D₄	—	4	2	no	—
43	C₂×C₃×C₅×D₄	—	4	2	no	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
46	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₃×C₅×SD₁₆	—	4	2	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₄⋊C₄	—	2	1	no	—
55	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
56	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×D₄²	C₂×C₅	1	1	yes	characteristic
62	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	—	2	1	no	—
69	C₂²×C₅×D₄	—	2	1	no	—
70	C₂×C₅×SD₁₆	—	2	1	no	—
71	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
72	C₅×#127	C₂²×C₃	1	1	yes	characteristic
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#120	—	2	2	no	—
76	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₅×#107	—	2	1	no	—
79	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
80	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
81	C₅×#103	—	2	1	no	—
82	C₅×#102	—	2	1	no	—
83	C₅×#102	—	2	2	no	—
84	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
85	#1639	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂³×C₃×C₅	—	2	1	no	—
88	C₂³×C₃×C₅	—	2	2	no	—
89	C₂³×C₃×C₅	—	4	4	no	—
90	C₂³×C₃×C₅	—	4	4	no	—
91	C₂³×C₃×C₅	—	8	2	no	—
92	C₃×C₅×Q₈	—	4	1	no	—
93	C₃×C₅×Q₈	—	4	1	no	—
94	C₃×C₅×D₄	—	2	1	no	—
95	C₃×C₅×D₄	—	2	1	no	—
96	C₃×C₅×D₄	—	4	2	no	—
97	C₃×C₅×D₄	—	4	4	no	—
98	C₃×C₅×D₄	—	4	4	no	—
99	C₃×C₅×D₄	—	4	1	no	—
100	C₃×C₅×D₄	—	4	1	no	—
101	C₃×C₅×D₄	—	4	1	no	—
102	C₃×C₅×D₄	—	4	1	no	—
103	C₃×C₅×D₄	D₈	1	2	yes	—
104	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
105	C₂×C₃×C₄×C₅	—	2	1	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	4	1	no	—
108	C₂×C₃×C₄×C₅	—	4	1	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	—	4	1	no	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₃×C₅×C₈	—	4	1	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₃×C₅×C₈	—	4	1	no	—
118	C₂²×C₃×D₄	—	2	1	no	—
119	C₂²×C₃×D₄	—	2	1	no	—
120	C₂×C₃×SD₁₆	—	2	1	no	—
121	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
122	C₃×#127	C₂²×C₅	1	1	yes	characteristic
123	C₃×#121	—	2	1	no	—
124	C₃×#121	—	2	1	no	—
125	C₃×#120	—	2	2	no	—
126	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
127	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
128	C₃×#107	—	2	1	no	—
129	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
131	C₃×#103	—	2	1	no	—
132	C₃×#102	—	2	1	no	—
133	C₃×#102	—	2	2	no	—
134	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₂⁴×C₅	—	2	2	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	4	2	no	—
142	C₂×C₅×D₄	—	4	2	no	—
143	C₂×C₅×D₄	—	4	2	no	—
144	C₂×C₅×D₄	—	4	2	no	—
145	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
146	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
147	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₅×SD₁₆	—	4	2	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
157	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
162	D₄²	C₂×C₃×C₅	1	1	yes	characteristic
163	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	#331	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	2	no	—
171	C₂²×C₃×C₅	—	4	1	no	—
172	C₂²×C₃×C₅	—	4	1	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	—	4	1	no	—
175	C₂²×C₃×C₅	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	8	8	no	—
179	C₂²×C₃×C₅	#120	1	1	yes	characteristic
180	C₃×C₄×C₅	—	2	1	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₃×C₄×C₅	—	8	1	no	—
184	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
185	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
186	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
188	C₂⁴×C₃	—	2	2	no	—
189	C₂×C₃×Q₈	—	2	1	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	4	2	no	—
195	C₂×C₃×D₄	—	4	2	no	—
196	C₂×C₃×D₄	—	4	2	no	—
197	C₂×C₃×D₄	—	4	2	no	—
198	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
199	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
200	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₃×SD₁₆	—	4	2	no	—
204	C₂×C₃×C₈	—	2	1	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₃×C₄⋊C₄	—	2	1	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
210	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
211	C₃×C₂²⋊C₄	—	2	2	no	—
212	C₃×C₂²⋊C₄	—	2	1	no	—
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	—	2	1	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	4	4	no	—
219	C₂³×C₅	—	4	4	no	—
220	C₂³×C₅	—	8	2	no	—
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×D₄	—	2	1	no	—
224	C₅×D₄	—	2	1	no	—
225	C₅×D₄	—	4	2	no	—
226	C₅×D₄	—	4	4	no	—
227	C₅×D₄	—	4	4	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	C₃×D₈	1	2	yes	—
233	C₅×D₄	C₃×SD₁₆	1	2	yes	complemented
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	—	4	1	no	—
239	C₂×C₄×C₅	—	4	1	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₅×C₈	—	4	1	no	—
245	C₅×C₈	—	4	1	no	—
246	C₅×C₈	—	4	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂×SD₁₆	—	2	1	no	—
250	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
251	#127	C₂²×C₃×C₅	1	1	yes	characteristic
252	#121	—	2	1	no	—
253	#121	—	2	1	no	—
254	#120	—	2	2	no	—
255	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	#107	—	2	1	no	—
258	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
259	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
260	#103	—	2	1	no	—
261	#102	—	2	1	no	—
262	#102	—	2	2	no	—
263	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
264	C₂×C₃×C₅	—	4	2	no	—
265	C₂×C₃×C₅	—	4	2	no	—
266	C₂×C₃×C₅	—	8	2	no	—
267	C₂×C₃×C₅	#447	1	1	yes	characteristic
268	C₂×C₃×C₅	#450	1	1	yes	characteristic
269	C₂×C₃×C₅	#455	1	1	yes	characteristic
270	C₂³×C₃	—	2	1	no	—
271	C₂³×C₃	—	2	1	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	—	4	4	no	—
274	C₂³×C₃	—	4	4	no	—
275	C₂³×C₃	—	8	2	no	—
276	C₃×Q₈	—	4	1	no	—
277	C₃×Q₈	—	4	1	no	—
278	C₃×D₄	—	2	1	no	—
279	C₃×D₄	—	2	1	no	—
280	C₃×D₄	—	4	2	no	—
281	C₃×D₄	—	4	4	no	—
282	C₃×D₄	—	4	4	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₃×D₄	—	4	1	no	—
286	C₃×D₄	—	4	1	no	—
287	C₃×D₄	C₅×D₈	1	2	yes	—
288	C₃×D₄	C₅×SD₁₆	1	2	yes	complemented
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	—	4	1	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	—	4	1	no	—
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₃×C₈	—	4	1	no	—
300	C₃×C₈	—	4	1	no	—
301	C₃×C₈	—	4	1	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	4	1	no	—
306	C₂²×C₅	—	4	1	no	—
307	C₂²×C₅	—	4	1	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	8	8	no	—
312	C₂²×C₅	C₃×#120	1	1	yes	characteristic
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	—	8	1	no	—
317	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
318	C₄×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
319	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
320	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₂⁴	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
332	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
333	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	SD₁₆	—	4	2	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
343	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
348	C₃×C₅	#1639	1	1	yes	characteristic, direct product factor, Hall
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	4	1	no	—
352	C₂²×C₃	—	4	1	no	—
353	C₂²×C₃	—	4	1	no	—
354	C₂²×C₃	—	4	1	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	8	8	no	—
359	C₂²×C₃	C₅×#120	1	1	yes	characteristic
360	C₃×C₄	—	2	1	no	—
361	C₃×C₄	—	4	1	no	—
362	C₃×C₄	—	4	1	no	—
363	C₃×C₄	—	8	1	no	—
364	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
365	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
366	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
367	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
368	C₂×C₅	—	4	2	no	—
369	C₂×C₅	—	4	2	no	—
370	C₂×C₅	—	8	2	no	—
371	C₂×C₅	C₃×#447	1	1	yes	characteristic
372	C₂×C₅	C₃×#450	1	1	yes	characteristic
373	C₂×C₅	C₃×#455	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	8	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	1	no	—
389	D₄	—	4	1	no	—
390	D₄	—	4	1	no	—
391	D₄	C₃×C₅×D₈	1	2	yes	—
392	D₄	C₃×C₅×SD₁₆	1	2	yes	complemented
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
402	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
403	C₈	—	4	1	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₂×C₃	—	4	2	no	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	—	8	2	no	—
409	C₂×C₃	C₅×#447	1	1	yes	characteristic
410	C₂×C₃	C₅×#450	1	1	yes	characteristic
411	C₂×C₃	C₅×#455	1	1	yes	characteristic
412	C₅	C₃×#1639	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	8	no	—
423	C₂²	C₃×C₅×#120	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	1	no	—
428	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
429	C₄	C₂×C₃×C₅×SD₁₆	1	1	yes	characteristic
430	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
431	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₃	C₅×#1639	1	1	yes	characteristic, direct product factor, Sylow
433	C₂	—	4	2	no	—
434	C₂	—	4	2	no	—
435	C₂	—	8	2	no	—
436	C₂	C₃×C₅×#447	1	1	yes	characteristic
437	C₂	C₃×C₅×#450	1	1	yes	characteristic
438	C₂	C₃×C₅×#455	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
prime radical	C₃×C₅×D₄²	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#486	C₂	semidirect
3. C₃×C₅×#474	C₂	semidirect
4. C₃×C₅×#461	C₂	semidirect
5. C₃×C₅×#331	C₂	semidirect
6. C₃×C₅×D₄⋊C₈	C₂	semidirect
7. C₃×C₅×D₄⋊C₈	C₂	semidirect
8. C₅×#1639	C₃	direct (N × H)
12. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
21. C₃×C₅×C₄⋊C₈	C₂²	semidirect
25. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₃×#1639	C₅	direct (N × H)
28. C₅×#486	C₂×C₃	semidirect
29. C₅×#474	C₂×C₃	semidirect
30. C₅×#461	C₂×C₃	semidirect
31. C₅×#331	C₂×C₃	semidirect
32. C₅×D₄⋊C₈	C₂×C₃	semidirect
33. C₅×D₄⋊C₈	C₂×C₃	semidirect
62. C₃×#486	C₂×C₅	semidirect
63. C₃×#474	C₂×C₅	semidirect
64. C₃×#461	C₂×C₅	semidirect
65. C₃×#331	C₂×C₅	semidirect
66. C₃×D₄⋊C₈	C₂×C₅	semidirect
67. C₃×D₄⋊C₈	C₂×C₅	semidirect
71. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
79. C₅×C₄⋊C₈	C₂²×C₃	semidirect
80. C₅×C₄⋊C₈	C₂²×C₃	semidirect
84. C₄×C₅×C₈	C₂²×C₃	semidirect
85. #1639	C₃×C₅	direct (N × H)
104. C₃×C₅×D₄	SD₁₆	semidirect
121. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
129. C₃×C₄⋊C₈	C₂²×C₅	semidirect
130. C₃×C₄⋊C₈	C₂²×C₅	semidirect
134. C₃×C₄×C₈	C₂²×C₅	semidirect
163. #486	C₂×C₃×C₅	semidirect
164. #474	C₂×C₃×C₅	semidirect
165. #461	C₂×C₃×C₅	semidirect
166. #331	C₂×C₃×C₅	semidirect
167. D₄⋊C₈	C₂×C₃×C₅	semidirect
168. D₄⋊C₈	C₂×C₃×C₅	semidirect
233. C₅×D₄	C₃×SD₁₆	semidirect
250. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
258. C₄⋊C₈	C₂²×C₃×C₅	semidirect
259. C₄⋊C₈	C₂²×C₃×C₅	semidirect
263. C₄×C₈	C₂²×C₃×C₅	semidirect
288. C₃×D₄	C₅×SD₁₆	semidirect
348. C₃×C₅	#1639	direct (N × H)
392. D₄	C₃×C₅×SD₁₆	semidirect
412. C₅	C₃×#1639	direct (N × H)
432. C₃	C₅×#1639	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×D₄²	2
C₃×C₅×#486	2
C₃×C₅×#474	2
C₃×C₅×#461	2
C₃×C₅×#331	2
C₃×C₅×D₄⋊C₈	2
C₅×#1639	3
C₃×#1639	5

Subgroups — C3×C5×#1639 #14274673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1639 #14274673