Subgroups — C₃×C₅×#3123 #14276157

Order 1920.

788 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#450	C₂	1	2	yes	maximal
7	C₃×C₅×#440	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3123	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
13	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#126	—	2	2	no	—
16	C₃×C₅×#125	—	2	2	no	—
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
20	C₃×C₄×C₅×D₄	—	2	2	no	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
26	C₃×C₅×#107	C₂²	1	2	yes	complemented
27	C₃×C₅×#106	C₂²	1	2	yes	complemented
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₃×C₅×#103	C₂²	1	2	yes	complemented
30	C₃×C₅×#103	C₂²	1	2	yes	complemented
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×C₅×#102	C₂²	1	2	yes	—
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3123	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#518	C₂×C₃	1	1	yes	characteristic
39	C₅×#485	C₂×C₃	1	2	yes	complemented
40	C₅×#478	C₂×C₃	1	2	yes	complemented
41	C₅×#461	C₂×C₃	1	2	yes	complemented
42	C₅×#450	C₂×C₃	1	2	yes	—
43	C₅×#440	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×SD₁₆	C₂×C₃	1	2	yes	complemented
45	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×SD₁₆	—	2	4	no	—
55	C₃×C₅×SD₁₆	—	2	4	no	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
70	C₃×C₄²×C₅	—	2	1	no	—
71	C₃×C₄²×C₅	—	2	2	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#518	C₂×C₅	1	1	yes	characteristic
76	C₃×#485	C₂×C₅	1	2	yes	complemented
77	C₃×#478	C₂×C₅	1	2	yes	complemented
78	C₃×#461	C₂×C₅	1	2	yes	complemented
79	C₃×#450	C₂×C₅	1	2	yes	—
80	C₃×#440	C₂×C₅	1	2	yes	complemented
81	C₃×C₄×SD₁₆	C₂×C₅	1	2	yes	complemented
82	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
85	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
86	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₅×#126	—	2	2	no	—
88	C₅×#125	—	2	2	no	—
89	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
91	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
94	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
95	C₅×#117	C₂²×C₃	1	1	yes	characteristic
96	C₅×#117	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₅×#107	C₂²×C₃	1	2	yes	complemented
99	C₅×#106	C₂²×C₃	1	2	yes	complemented
100	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
101	C₅×#103	C₂²×C₃	1	2	yes	complemented
102	C₅×#103	C₂²×C₃	1	2	yes	complemented
103	C₅×#102	C₂²×C₃	1	2	yes	—
104	C₅×#102	C₂²×C₃	1	2	yes	—
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
108	#3123	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	8	2	no	—
112	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₅×Q₈	—	2	2	no	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₃×C₅×D₄	—	2	4	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	#41	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	—	8	2	no	—
123	C₂×C₃×C₄×C₅	—	8	2	no	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₃×C₅×C₈	—	2	2	no	—
129	C₃×C₅×C₈	—	2	2	no	—
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
132	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
133	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₃×#126	—	2	2	no	—
135	C₃×#125	—	2	2	no	—
136	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
138	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
139	C₃×C₄×D₄	—	2	2	no	—
140	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
141	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
142	C₃×#117	C₂²×C₅	1	1	yes	characteristic
143	C₃×#117	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
145	C₃×#107	C₂²×C₅	1	2	yes	complemented
146	C₃×#106	C₂²×C₅	1	2	yes	complemented
147	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
148	C₃×#103	C₂²×C₅	1	2	yes	complemented
149	C₃×#103	C₂²×C₅	1	2	yes	complemented
150	C₃×#102	C₂²×C₅	1	2	yes	—
151	C₃×#102	C₂²×C₅	1	2	yes	—
152	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
153	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
154	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₂⁴×C₅	—	2	1	no	—
156	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
157	C₂×C₅×D₄	—	2	4	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₅×SD₁₆	—	2	4	no	—
164	C₅×SD₁₆	—	2	4	no	—
165	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
166	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
172	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₅×C₂²⋊C₄	—	2	2	no	—
176	C₅×C₂²⋊C₄	—	2	2	no	—
177	C₅×C₂²⋊C₄	—	2	2	no	—
178	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
179	C₄²×C₅	—	2	1	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
182	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
183	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	#518	C₂×C₃×C₅	1	1	yes	characteristic
185	#485	C₂×C₃×C₅	1	2	yes	complemented
186	#478	C₂×C₃×C₅	1	2	yes	complemented
187	#461	C₂×C₃×C₅	1	2	yes	complemented
188	#450	C₂×C₃×C₅	1	2	yes	—
189	#440	C₂×C₃×C₅	1	2	yes	complemented
190	C₄×SD₁₆	C₂×C₃×C₅	1	2	yes	complemented
191	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₂²×C₃×C₅	—	2	1	no	—
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	2	2	no	—
195	C₂²×C₃×C₅	—	4	2	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	8	4	no	—
198	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₃×C₄×C₅	—	2	1	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	2	2	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	—	4	2	no	—
204	C₃×C₄×C₅	—	4	2	no	—
205	C₃×C₄×C₅	C₂×#41	1	2	yes	—
206	C₂⁴×C₃	—	2	1	no	—
207	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
208	C₂×C₃×D₄	—	2	4	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₃×SD₁₆	—	2	4	no	—
215	C₃×SD₁₆	—	2	4	no	—
216	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
217	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
218	C₃×C₄⋊C₄	—	2	2	no	—
219	C₃×C₄⋊C₄	—	2	2	no	—
220	C₃×C₄⋊C₄	—	2	2	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
223	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
224	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
225	C₃×C₂²⋊C₄	—	2	1	no	—
226	C₃×C₂²⋊C₄	—	2	2	no	—
227	C₃×C₂²⋊C₄	—	2	2	no	—
228	C₃×C₂²⋊C₄	—	2	2	no	—
229	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
230	C₃×C₄²	—	2	1	no	—
231	C₃×C₄²	—	2	2	no	—
232	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
233	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
234	C₂³×C₅	—	2	4	no	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	8	2	no	—
237	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
238	C₅×Q₈	—	2	2	no	—
239	C₅×Q₈	—	2	2	no	—
240	C₅×D₄	—	2	4	no	—
241	C₅×D₄	—	2	2	no	—
242	C₅×D₄	C₃×#41	1	4	yes	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	8	2	no	—
248	C₂×C₄×C₅	—	8	2	no	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
253	C₅×C₈	—	2	2	no	—
254	C₅×C₈	—	2	2	no	—
255	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
257	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
258	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
259	#126	—	2	2	no	—
260	#125	—	2	2	no	—
261	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
262	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
263	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
266	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
267	#117	C₂²×C₃×C₅	1	1	yes	characteristic
268	#117	C₂²×C₃×C₅	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	#107	C₂²×C₃×C₅	1	2	yes	complemented
271	#106	C₂²×C₃×C₅	1	2	yes	complemented
272	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
273	#103	C₂²×C₃×C₅	1	2	yes	complemented
274	#103	C₂²×C₃×C₅	1	2	yes	complemented
275	#102	C₂²×C₃×C₅	1	2	yes	—
276	#102	C₂²×C₃×C₅	1	2	yes	—
277	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
278	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
279	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
280	C₂×C₃×C₅	—	4	1	no	—
281	C₂×C₃×C₅	—	4	4	no	—
282	C₂×C₃×C₅	#525	1	1	yes	characteristic
283	C₂×C₃×C₅	#577	1	2	yes	—
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	8	2	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₃×Q₈	—	2	2	no	—
289	C₃×Q₈	—	2	2	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	C₅×#41	1	4	yes	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	8	2	no	—
298	C₂×C₃×C₄	—	8	2	no	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
303	C₃×C₈	—	2	2	no	—
304	C₃×C₈	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	2	4	no	—
308	C₂²×C₅	—	4	2	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	8	4	no	—
311	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
312	C₄×C₅	—	2	2	no	—
313	C₄×C₅	—	2	2	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	C₂×C₃×#41	1	2	yes	—
319	C₂⁴	—	2	1	no	—
320	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
327	SD₁₆	—	2	4	no	—
328	SD₁₆	—	2	4	no	—
329	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
330	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
336	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
346	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
347	C₃×C₅	#3123	1	1	yes	characteristic, direct product factor, Hall
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	4	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	2	no	—
353	C₂²×C₃	—	8	4	no	—
354	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	2	2	no	—
358	C₃×C₄	—	4	2	no	—
359	C₃×C₄	—	4	2	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	C₂×C₅×#41	1	2	yes	—
362	C₂×C₅	—	4	1	no	—
363	C₂×C₅	—	4	4	no	—
364	C₂×C₅	C₃×#525	1	1	yes	characteristic
365	C₂×C₅	C₃×#577	1	2	yes	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	8	2	no	—
369	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	D₄	—	2	4	no	—
373	D₄	—	2	2	no	—
374	D₄	C₃×C₅×#41	1	4	yes	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	—	8	2	no	—
381	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
382	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
384	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₂×C₃	—	4	1	no	—
388	C₂×C₃	—	4	4	no	—
389	C₂×C₃	C₅×#525	1	1	yes	characteristic
390	C₂×C₃	C₅×#577	1	2	yes	—
391	C₅	C₃×#3123	1	1	yes	characteristic, direct product factor, Sylow
392	C₂²	—	2	1	no	—
393	C₂²	—	2	4	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	8	4	no	—
398	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	C₂×C₃×C₅×#41	1	2	yes	—
406	C₃	C₅×#3123	1	1	yes	characteristic, direct product factor, Sylow
407	C₂	—	4	1	no	—
408	C₂	—	4	4	no	—
409	C₂	C₃×C₅×#525	1	1	yes	characteristic
410	C₂	C₃×C₅×#577	1	2	yes	—

	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 ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#461	C₂	semidirect
7. C₃×C₅×#440	C₂	semidirect
8. C₃×C₄×C₅×SD₁₆	C₂	semidirect
9. C₃×C₅×#433	C₂	semidirect
10. C₅×#3123	C₃	direct (N × H)
14. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
17. C₃×C₅×#125	C₂²	semidirect
19. C₃×C₄×C₅×Q₈	C₂²	semidirect
26. C₃×C₅×#107	C₂²	semidirect
27. C₃×C₅×#106	C₂²	semidirect
28. C₃×C₅×C₄⋊C₈	C₂²	semidirect
29. C₃×C₅×#103	C₂²	semidirect
30. C₃×C₅×#103	C₂²	semidirect
34. C₃×C₅×#97	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₃×#3123	C₅	direct (N × H)
37. C₅×#541	C₂×C₃	semidirect
39. C₅×#485	C₂×C₃	semidirect
40. C₅×#478	C₂×C₃	semidirect
41. C₅×#461	C₂×C₃	semidirect
43. C₅×#440	C₂×C₃	semidirect
44. C₄×C₅×SD₁₆	C₂×C₃	semidirect
45. C₅×#433	C₂×C₃	semidirect
74. C₃×#541	C₂×C₅	semidirect
76. C₃×#485	C₂×C₅	semidirect
77. C₃×#478	C₂×C₅	semidirect
78. C₃×#461	C₂×C₅	semidirect
80. C₃×#440	C₂×C₅	semidirect
81. C₃×C₄×SD₁₆	C₂×C₅	semidirect
82. C₃×#433	C₂×C₅	semidirect
86. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
89. C₅×#125	C₂²×C₃	semidirect
91. C₄×C₅×Q₈	C₂²×C₃	semidirect
98. C₅×#107	C₂²×C₃	semidirect
99. C₅×#106	C₂²×C₃	semidirect
100. C₅×C₄⋊C₈	C₂²×C₃	semidirect
101. C₅×#103	C₂²×C₃	semidirect
102. C₅×#103	C₂²×C₃	semidirect
106. C₅×#97	C₂²×C₃	semidirect
107. C₄×C₅×C₈	C₂²×C₃	semidirect
108. #3123	C₃×C₅	direct (N × H)
133. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
136. C₃×#125	C₂²×C₅	semidirect
138. C₃×C₄×Q₈	C₂²×C₅	semidirect
145. C₃×#107	C₂²×C₅	semidirect
146. C₃×#106	C₂²×C₅	semidirect
147. C₃×C₄⋊C₈	C₂²×C₅	semidirect
148. C₃×#103	C₂²×C₅	semidirect
149. C₃×#103	C₂²×C₅	semidirect
153. C₃×#97	C₂²×C₅	semidirect
154. C₃×C₄×C₈	C₂²×C₅	semidirect
183. #541	C₂×C₃×C₅	semidirect
185. #485	C₂×C₃×C₅	semidirect
186. #478	C₂×C₃×C₅	semidirect
187. #461	C₂×C₃×C₅	semidirect
189. #440	C₂×C₃×C₅	semidirect
190. C₄×SD₁₆	C₂×C₃×C₅	semidirect
191. #433	C₂×C₃×C₅	semidirect
258. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
261. #125	C₂²×C₃×C₅	semidirect
263. C₄×Q₈	C₂²×C₃×C₅	semidirect
270. #107	C₂²×C₃×C₅	semidirect
271. #106	C₂²×C₃×C₅	semidirect
272. C₄⋊C₈	C₂²×C₃×C₅	semidirect
273. #103	C₂²×C₃×C₅	semidirect
274. #103	C₂²×C₃×C₅	semidirect
278. #97	C₂²×C₃×C₅	semidirect
279. C₄×C₈	C₂²×C₃×C₅	semidirect
347. C₃×C₅	#3123	direct (N × H)
391. C₅	C₃×#3123	direct (N × H)
406. C₃	C₅×#3123	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×#541	2
C₃×C₅×#518	2
C₃×C₅×#485	2
C₃×C₅×#478	2
C₃×C₅×#461	2
C₃×C₅×#450	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#433	2
C₅×#3123	3
C₃×#3123	5

Subgroups — C3×C5×#3123 #14276157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3123 #14276157