Subgroups — C₃×C₅×#1621 #14274655

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1621	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
11	C₂×C₃×C₅×D₈	—	2	1	no	—
12	C₂×C₃×C₅×D₈	—	2	2	no	—
13	C₃×C₅×#127	—	2	1	no	—
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₃×C₅×#121	—	2	2	no	—
17	C₃×C₅×#121	—	2	1	no	—
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	—	2	1	no	—
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#102	—	2	1	no	—
24	C₃×C₅×#102	—	2	1	no	—
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×#1621	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#331	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×Q₈⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	4	2	no	—
35	C₃×C₅×#41	—	4	2	no	—
36	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₃×C₅×SD₁₆	—	4	2	no	—
49	C₃×C₅×D₈	—	4	4	no	—
50	C₃×C₅×D₈	—	4	2	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	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×C₄²×C₅	—	2	1	no	—
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
62	C₃×#493	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
64	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
65	C₃×#331	C₂×C₅	1	1	yes	characteristic, complemented
66	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
67	C₃×D₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	2	1	no	—
70	C₂×C₅×D₈	—	2	1	no	—
71	C₂×C₅×D₈	—	2	2	no	—
72	C₅×#127	—	2	1	no	—
73	C₅×#127	C₂²×C₃	1	1	yes	characteristic
74	C₅×#127	C₂²×C₃	1	1	yes	characteristic
75	C₅×#121	—	2	2	no	—
76	C₅×#121	—	2	1	no	—
77	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
81	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
82	C₅×#102	—	2	1	no	—
83	C₅×#102	—	2	1	no	—
84	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
85	#1621	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	—	4	1	no	—
89	C₃×C₅×Q₈	—	2	1	no	—
90	C₃×C₅×Q₈	D₈	1	2	yes	complemented
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	4	4	no	—
94	C₃×C₅×D₄	—	4	2	no	—
95	C₃×C₅×D₄	—	4	2	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₃×C₅×D₄	—	4	1	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	—	4	1	no	—
104	C₃×C₅×D₄	—	8	2	no	—
105	C₂×C₃×C₄×C₅	—	2	1	no	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	1	no	—
108	C₂×C₃×C₄×C₅	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×C₈	—	2	2	no	—
115	C₃×C₅×C₈	—	4	1	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₂×C₃×#41	—	2	1	no	—
118	C₂×C₃×SD₁₆	—	2	1	no	—
119	C₂×C₃×D₈	—	2	1	no	—
120	C₂×C₃×D₈	—	2	2	no	—
121	C₃×#127	—	2	1	no	—
122	C₃×#127	C₂²×C₅	1	1	yes	characteristic
123	C₃×#127	C₂²×C₅	1	1	yes	characteristic
124	C₃×#121	—	2	2	no	—
125	C₃×#121	—	2	1	no	—
126	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
127	C₃×C₄×D₄	—	2	1	no	—
128	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
129	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₃×#102	—	2	1	no	—
132	C₃×#102	—	2	1	no	—
133	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
134	C₅×#41	—	4	2	no	—
135	C₅×#41	—	4	2	no	—
136	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
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	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	—	2	1	no	—
144	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
145	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₅×SD₁₆	—	4	2	no	—
149	C₅×D₈	—	4	4	no	—
150	C₅×D₈	—	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	C₃×D₄	1	1	yes	characteristic
156	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	2	2	no	—
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
161	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
162	#493	C₂×C₃×C₅	1	1	yes	characteristic, complemented
163	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
164	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	#331	C₂×C₃×C₅	1	1	yes	characteristic, complemented
166	Q₈⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
167	D₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	—	8	1	no	—
175	C₂²×C₃×C₅	—	8	1	no	—
176	C₂²×C₃×C₅	—	8	1	no	—
177	C₂²×C₃×C₅	#120	1	1	yes	characteristic
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₃×#41	—	4	2	no	—
187	C₃×#41	—	4	2	no	—
188	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	2	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
197	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	2	1	no	—
200	C₃×SD₁₆	—	4	2	no	—
201	C₃×D₈	—	4	4	no	—
202	C₃×D₈	—	4	2	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₂×C₃×C₈	—	2	1	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
208	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	C₃×C₂²⋊C₄	—	2	1	no	—
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	—	4	1	no	—
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	C₃×D₈	1	2	yes	complemented
218	C₅×D₄	—	2	1	no	—
219	C₅×D₄	—	2	1	no	—
220	C₅×D₄	—	4	2	no	—
221	C₅×D₄	—	4	4	no	—
222	C₅×D₄	—	4	2	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	4	1	no	—
227	C₅×D₄	—	4	1	no	—
228	C₅×D₄	—	4	1	no	—
229	C₅×D₄	—	4	1	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	8	2	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	4	4	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	4	1	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	2	2	no	—
248	#127	—	2	1	no	—
249	#127	C₂²×C₃×C₅	1	1	yes	characteristic
250	#127	C₂²×C₃×C₅	1	1	yes	characteristic
251	#121	—	2	2	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
258	#102	—	2	1	no	—
259	#102	—	2	1	no	—
260	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂×C₃×C₅	—	8	1	no	—
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	—	16	1	no	—
264	C₂×C₃×C₅	#447	1	1	yes	characteristic
265	C₂×C₃×C₅	#449	1	1	yes	characteristic
266	C₂×C₃×C₅	#453	1	1	yes	characteristic
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	4	1	no	—
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	C₅×D₈	1	2	yes	complemented
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	1	no	—
274	C₃×D₄	—	4	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₃×D₄	—	4	2	no	—
277	C₃×D₄	—	4	1	no	—
278	C₃×D₄	—	4	1	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	4	1	no	—
281	C₃×D₄	—	4	1	no	—
282	C₃×D₄	—	4	1	no	—
283	C₃×D₄	—	4	1	no	—
284	C₃×D₄	—	4	1	no	—
285	C₃×D₄	—	8	2	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	4	4	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	4	1	no	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	4	1	no	—
297	C₃×C₈	—	4	1	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	4	1	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	8	1	no	—
305	C₂²×C₅	—	8	1	no	—
306	C₂²×C₅	—	8	1	no	—
307	C₂²×C₅	C₃×#120	1	1	yes	characteristic
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	4	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	C₂×C₃×D₈	1	1	yes	characteristic
313	C₄×C₅	C₃×#135	1	1	yes	characteristic
314	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
315	C₄×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
327	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	SD₁₆	—	4	2	no	—
331	D₈	—	4	4	no	—
332	D₈	—	4	2	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
338	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
343	C₃×C₅	#1621	1	1	yes	characteristic, direct product factor, Hall
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	8	1	no	—
351	C₂²×C₃	—	8	1	no	—
352	C₂²×C₃	—	8	1	no	—
353	C₂²×C₃	C₅×#120	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	—	4	1	no	—
358	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
359	C₃×C₄	C₅×#135	1	1	yes	characteristic
360	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂×C₅	—	8	1	no	—
363	C₂×C₅	—	8	2	no	—
364	C₂×C₅	—	16	1	no	—
365	C₂×C₅	C₃×#447	1	1	yes	characteristic
366	C₂×C₅	C₃×#449	1	1	yes	characteristic
367	C₂×C₅	C₃×#453	1	1	yes	characteristic
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	Q₈	—	2	1	no	—
372	Q₈	C₃×C₅×D₈	1	2	yes	complemented
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	8	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₂×C₃	—	8	1	no	—
400	C₂×C₃	—	8	2	no	—
401	C₂×C₃	—	16	1	no	—
402	C₂×C₃	C₅×#447	1	1	yes	characteristic
403	C₂×C₃	C₅×#449	1	1	yes	characteristic
404	C₂×C₃	C₅×#453	1	1	yes	characteristic
405	C₅	C₃×#1621	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	4	1	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	C₃×C₅×#120	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	C₂×C₃×C₅×D₈	1	1	yes	characteristic
421	C₄	C₃×C₅×#135	1	1	yes	characteristic
422	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₄	C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
424	C₃	C₅×#1621	1	1	yes	characteristic, direct product factor, Sylow
425	C₂	—	8	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	16	1	no	—
428	C₂	C₃×C₅×#447	1	1	yes	characteristic
429	C₂	C₃×C₅×#449	1	1	yes	characteristic
430	C₂	C₃×C₅×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₃×C₅
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
1. C₃×C₅×#550	C₂	semidirect
2. C₃×C₅×#493	C₂	semidirect
3. C₃×C₅×#460	C₂	semidirect
4. C₃×C₅×#459	C₂	semidirect
5. C₃×C₅×#331	C₂	semidirect
6. C₃×C₅×Q₈⋊C₈	C₂	semidirect
7. C₃×C₅×D₄⋊C₈	C₂	semidirect
8. C₅×#1621	C₃	direct (N × H)
26. C₃×#1621	C₅	direct (N × H)
27. C₅×#550	C₂×C₃	semidirect
28. C₅×#493	C₂×C₃	semidirect
29. C₅×#460	C₂×C₃	semidirect
30. C₅×#459	C₂×C₃	semidirect
31. C₅×#331	C₂×C₃	semidirect
32. C₅×Q₈⋊C₈	C₂×C₃	semidirect
33. C₅×D₄⋊C₈	C₂×C₃	semidirect
61. C₃×#550	C₂×C₅	semidirect
62. C₃×#493	C₂×C₅	semidirect
63. C₃×#460	C₂×C₅	semidirect
64. C₃×#459	C₂×C₅	semidirect
65. C₃×#331	C₂×C₅	semidirect
66. C₃×Q₈⋊C₈	C₂×C₅	semidirect
67. C₃×D₄⋊C₈	C₂×C₅	semidirect
85. #1621	C₃×C₅	direct (N × H)
90. C₃×C₅×Q₈	D₈	semidirect
161. #550	C₂×C₃×C₅	semidirect
162. #493	C₂×C₃×C₅	semidirect
163. #460	C₂×C₃×C₅	semidirect
164. #459	C₂×C₃×C₅	semidirect
165. #331	C₂×C₃×C₅	semidirect
166. Q₈⋊C₈	C₂×C₃×C₅	semidirect
167. D₄⋊C₈	C₂×C₃×C₅	semidirect
217. C₅×Q₈	C₃×D₈	semidirect
271. C₃×Q₈	C₅×D₈	semidirect
343. C₃×C₅	#1621	direct (N × H)
372. Q₈	C₃×C₅×D₈	semidirect
405. C₅	C₃×#1621	direct (N × H)
424. C₃	C₅×#1621	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×#550	2
C₃×C₅×#493	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#331	2
C₃×C₅×Q₈⋊C₈	2
C₃×C₅×D₄⋊C₈	2
C₅×#1621	3
C₃×#1621	5

Subgroups — C3×C5×#1621 #14274655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1621 #14274655