Subgroups — C₃×C₅×#3120 #14276154

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 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×#520	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#484	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3120	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#126	—	2	1	no	—
24	C₃×C₅×#126	—	2	1	no	—
25	C₃×C₅×#125	—	2	1	no	—
26	C₃×C₅×#125	—	2	1	no	—
27	C₃×C₅×#125	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	—	2	1	no	—
35	C₃×C₄×C₅×D₄	—	2	1	no	—
36	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×#117	—	2	1	no	—
39	C₃×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₃×C₅×#107	C₂²	1	1	yes	characteristic
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×#97	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3120	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#520	C₂×C₃	1	1	yes	characteristic
63	C₅×#484	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#479	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#478	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#452	C₂×C₃	1	1	yes	characteristic
70	C₅×#452	C₂×C₃	1	1	yes	characteristic
71	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
74	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	2	2	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	—	2	1	no	—
84	C₂²×C₃×C₄×C₅	—	2	1	no	—
85	C₂²×C₃×C₄×C₅	—	2	1	no	—
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₃×C₅×Q₁₆	—	2	2	no	—
89	C₃×C₅×Q₁₆	—	2	2	no	—
90	C₃×C₅×SD₁₆	—	2	2	no	—
91	C₃×C₅×SD₁₆	—	2	2	no	—
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
96	C₃×C₅×C₄⋊C₄	—	2	1	no	—
97	C₃×C₅×C₄⋊C₄	—	2	1	no	—
98	C₃×C₅×C₄⋊C₄	—	2	1	no	—
99	C₃×C₅×C₄⋊C₄	—	2	1	no	—
100	C₃×C₅×C₄⋊C₄	—	2	1	no	—
101	C₃×C₅×C₄⋊C₄	—	2	1	no	—
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₄⋊C₄	—	2	1	no	—
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
109	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₃×C₄²×C₅	—	2	1	no	—
120	C₃×C₄²×C₅	—	2	1	no	—
121	C₃×C₄²×C₅	—	2	1	no	—
122	C₃×C₄²×C₅	—	2	1	no	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#520	C₂×C₅	1	1	yes	characteristic
127	C₃×#484	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#478	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#452	C₂×C₅	1	1	yes	characteristic
134	C₃×#452	C₂×C₅	1	1	yes	characteristic
135	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
145	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
146	C₅×#126	—	2	1	no	—
147	C₅×#126	—	2	1	no	—
148	C₅×#125	—	2	1	no	—
149	C₅×#125	—	2	1	no	—
150	C₅×#125	C₂²×C₃	1	1	yes	characteristic
151	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
153	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
154	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
155	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
156	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₄×C₅×D₄	—	2	1	no	—
158	C₄×C₅×D₄	—	2	1	no	—
159	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₅×#117	—	2	1	no	—
162	C₅×#117	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₄⋊C₄	—	2	1	no	—
164	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₅×#107	C₂²×C₃	1	1	yes	characteristic
166	C₅×#107	C₂²×C₃	1	1	yes	characteristic
167	C₅×#106	C₂²×C₃	1	1	yes	characteristic
168	C₅×#106	C₂²×C₃	1	1	yes	characteristic
169	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
170	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₅×#103	C₂²×C₃	1	1	yes	characteristic
172	C₅×#103	C₂²×C₃	1	1	yes	characteristic
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic
176	C₅×#103	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic
179	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
181	C₅×#97	C₂²×C₃	1	1	yes	characteristic
182	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
183	#3120	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
186	C₃×C₅×Q₈	—	2	1	no	—
187	C₃×C₅×Q₈	—	2	1	no	—
188	C₃×C₅×Q₈	—	2	1	no	—
189	C₃×C₅×Q₈	—	2	1	no	—
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	#41	1	2	yes	—
192	C₃×C₅×D₄	—	2	4	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	#41	1	2	yes	—
195	C₂×C₃×C₄×C₅	—	2	4	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	8	1	no	—
206	C₂×C₃×C₄×C₅	—	8	1	no	—
207	C₂×C₃×C₄×C₅	—	8	1	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₃×C₅×C₈	—	2	1	no	—
215	C₃×C₅×C₈	—	2	1	no	—
216	C₃×C₅×C₈	—	2	1	no	—
217	C₃×C₅×C₈	—	2	1	no	—
218	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
224	C₃×#126	—	2	1	no	—
225	C₃×#126	—	2	1	no	—
226	C₃×#125	—	2	1	no	—
227	C₃×#125	—	2	1	no	—
228	C₃×#125	C₂²×C₅	1	1	yes	characteristic
229	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
230	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
231	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
232	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×C₄×D₄	—	2	1	no	—
236	C₃×C₄×D₄	—	2	1	no	—
237	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
239	C₃×#117	—	2	1	no	—
240	C₃×#117	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₄⋊C₄	—	2	1	no	—
242	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₃×#107	C₂²×C₅	1	1	yes	characteristic
244	C₃×#107	C₂²×C₅	1	1	yes	characteristic
245	C₃×#106	C₂²×C₅	1	1	yes	characteristic
246	C₃×#106	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
248	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
249	C₃×#103	C₂²×C₅	1	1	yes	characteristic
250	C₃×#103	C₂²×C₅	1	1	yes	characteristic
251	C₃×#103	C₂²×C₅	1	1	yes	characteristic
252	C₃×#103	C₂²×C₅	1	1	yes	characteristic
253	C₃×#103	C₂²×C₅	1	1	yes	characteristic
254	C₃×#103	C₂²×C₅	1	1	yes	characteristic
255	C₃×#102	C₂²×C₅	1	1	yes	characteristic
256	C₃×#102	C₂²×C₅	1	1	yes	characteristic
257	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
258	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	C₃×#97	C₂²×C₅	1	1	yes	characteristic
260	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
261	C₅×#41	—	2	2	no	—
262	C₅×#41	—	2	2	no	—
263	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₅×D₄	—	2	1	no	—
267	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	—	2	1	no	—
269	C₂²×C₄×C₅	—	2	1	no	—
270	C₂²×C₄×C₅	—	2	1	no	—
271	C₂²×C₄×C₅	—	2	1	no	—
272	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
273	C₅×Q₁₆	—	2	2	no	—
274	C₅×Q₁₆	—	2	2	no	—
275	C₅×SD₁₆	—	2	2	no	—
276	C₅×SD₁₆	—	2	2	no	—
277	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
280	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
281	C₅×C₄⋊C₄	—	2	1	no	—
282	C₅×C₄⋊C₄	—	2	1	no	—
283	C₅×C₄⋊C₄	—	2	1	no	—
284	C₅×C₄⋊C₄	—	2	1	no	—
285	C₅×C₄⋊C₄	—	2	1	no	—
286	C₅×C₄⋊C₄	—	2	1	no	—
287	C₅×C₄⋊C₄	—	2	1	no	—
288	C₅×C₄⋊C₄	—	2	1	no	—
289	C₅×C₄⋊C₄	—	2	1	no	—
290	C₅×C₄⋊C₄	—	2	1	no	—
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
293	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
294	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
298	C₅×C₂²⋊C₄	—	2	1	no	—
299	C₅×C₂²⋊C₄	—	2	1	no	—
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
303	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
304	C₄²×C₅	—	2	1	no	—
305	C₄²×C₅	—	2	1	no	—
306	C₄²×C₅	—	2	1	no	—
307	C₄²×C₅	—	2	1	no	—
308	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
309	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
310	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
311	#520	C₂×C₃×C₅	1	1	yes	characteristic
312	#484	C₂×C₃×C₅	1	1	yes	characteristic, complemented
313	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#479	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
316	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#452	C₂×C₃×C₅	1	1	yes	characteristic
319	#452	C₂×C₃×C₅	1	1	yes	characteristic
320	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	C₂²×C₃×C₅	—	2	1	no	—
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	2	1	no	—
328	C₂²×C₃×C₅	—	2	1	no	—
329	C₂²×C₃×C₅	—	4	1	no	—
330	C₂²×C₃×C₅	—	4	1	no	—
331	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
332	C₃×C₄×C₅	—	2	1	no	—
333	C₃×C₄×C₅	—	2	2	no	—
334	C₃×C₄×C₅	—	2	1	no	—
335	C₃×C₄×C₅	—	2	1	no	—
336	C₃×C₄×C₅	—	2	1	no	—
337	C₃×C₄×C₅	—	2	1	no	—
338	C₃×C₄×C₅	—	4	1	no	—
339	C₃×C₄×C₅	—	4	1	no	—
340	C₃×C₄×C₅	—	4	1	no	—
341	C₃×C₄×C₅	—	4	1	no	—
342	C₃×C₄×C₅	—	4	1	no	—
343	C₃×C₄×C₅	—	4	1	no	—
344	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
345	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
346	C₃×#41	—	2	2	no	—
347	C₃×#41	—	2	2	no	—
348	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
349	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
350	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
351	C₂×C₃×D₄	—	2	1	no	—
352	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₃×C₄	—	2	1	no	—
354	C₂²×C₃×C₄	—	2	1	no	—
355	C₂²×C₃×C₄	—	2	1	no	—
356	C₂²×C₃×C₄	—	2	1	no	—
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₃×Q₁₆	—	2	2	no	—
359	C₃×Q₁₆	—	2	2	no	—
360	C₃×SD₁₆	—	2	2	no	—
361	C₃×SD₁₆	—	2	2	no	—
362	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
366	C₃×C₄⋊C₄	—	2	1	no	—
367	C₃×C₄⋊C₄	—	2	1	no	—
368	C₃×C₄⋊C₄	—	2	1	no	—
369	C₃×C₄⋊C₄	—	2	1	no	—
370	C₃×C₄⋊C₄	—	2	1	no	—
371	C₃×C₄⋊C₄	—	2	1	no	—
372	C₃×C₄⋊C₄	—	2	1	no	—
373	C₃×C₄⋊C₄	—	2	1	no	—
374	C₃×C₄⋊C₄	—	2	1	no	—
375	C₃×C₄⋊C₄	—	2	1	no	—
376	C₃×C₄⋊C₄	—	2	1	no	—
377	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
379	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
380	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
381	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
382	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
383	C₃×C₂²⋊C₄	—	2	1	no	—
384	C₃×C₂²⋊C₄	—	2	1	no	—
385	C₃×C₂²⋊C₄	—	2	1	no	—
386	C₃×C₂²⋊C₄	—	2	1	no	—
387	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
388	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
389	C₃×C₄²	—	2	1	no	—
390	C₃×C₄²	—	2	1	no	—
391	C₃×C₄²	—	2	1	no	—
392	C₃×C₄²	—	2	1	no	—
393	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
394	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
395	C₂³×C₅	—	2	1	no	—
396	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
397	C₅×Q₈	—	2	1	no	—
398	C₅×Q₈	—	2	1	no	—
399	C₅×Q₈	—	2	1	no	—
400	C₅×Q₈	—	2	1	no	—
401	C₅×Q₈	—	2	1	no	—
402	C₅×Q₈	C₃×#41	1	2	yes	—
403	C₅×D₄	—	2	4	no	—
404	C₅×D₄	—	2	1	no	—
405	C₅×D₄	C₃×#41	1	2	yes	—
406	C₂×C₄×C₅	—	2	4	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	8	1	no	—
417	C₂×C₄×C₅	—	8	1	no	—
418	C₂×C₄×C₅	—	8	1	no	—
419	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
420	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
421	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
422	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
423	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
425	C₅×C₈	—	2	1	no	—
426	C₅×C₈	—	2	1	no	—
427	C₅×C₈	—	2	1	no	—
428	C₅×C₈	—	2	1	no	—
429	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
435	#126	—	2	1	no	—
436	#126	—	2	1	no	—
437	#125	—	2	1	no	—
438	#125	—	2	1	no	—
439	#125	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
450	#117	—	2	1	no	—
451	#117	C₂²×C₃×C₅	1	1	yes	characteristic
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
454	#107	C₂²×C₃×C₅	1	1	yes	characteristic
455	#107	C₂²×C₃×C₅	1	1	yes	characteristic
456	#106	C₂²×C₃×C₅	1	1	yes	characteristic
457	#106	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
460	#103	C₂²×C₃×C₅	1	1	yes	characteristic
461	#103	C₂²×C₃×C₅	1	1	yes	characteristic
462	#103	C₂²×C₃×C₅	1	1	yes	characteristic
463	#103	C₂²×C₃×C₅	1	1	yes	characteristic
464	#103	C₂²×C₃×C₅	1	1	yes	characteristic
465	#103	C₂²×C₃×C₅	1	1	yes	characteristic
466	#102	C₂²×C₃×C₅	1	1	yes	characteristic
467	#102	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
470	#97	C₂²×C₃×C₅	1	1	yes	characteristic
471	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
472	C₂×C₃×C₅	—	4	1	no	—
473	C₂×C₃×C₅	—	4	2	no	—
474	C₂×C₃×C₅	#525	1	1	yes	characteristic
475	C₂×C₃×C₅	#577	1	1	yes	characteristic
476	C₂×C₃×C₅	#578	1	1	yes	characteristic
477	C₂³×C₃	—	2	1	no	—
478	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
479	C₃×Q₈	—	2	1	no	—
480	C₃×Q₈	—	2	1	no	—
481	C₃×Q₈	—	2	1	no	—
482	C₃×Q₈	—	2	1	no	—
483	C₃×Q₈	—	2	1	no	—
484	C₃×Q₈	C₅×#41	1	2	yes	—
485	C₃×D₄	—	2	4	no	—
486	C₃×D₄	—	2	1	no	—
487	C₃×D₄	C₅×#41	1	2	yes	—
488	C₂×C₃×C₄	—	2	4	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	8	1	no	—
499	C₂×C₃×C₄	—	8	1	no	—
500	C₂×C₃×C₄	—	8	1	no	—
501	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
502	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
503	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
505	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
507	C₃×C₈	—	2	1	no	—
508	C₃×C₈	—	2	1	no	—
509	C₃×C₈	—	2	1	no	—
510	C₃×C₈	—	2	1	no	—
511	C₂²×C₅	—	2	1	no	—
512	C₂²×C₅	—	2	1	no	—
513	C₂²×C₅	—	2	1	no	—
514	C₂²×C₅	—	2	2	no	—
515	C₂²×C₅	—	4	1	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
518	C₄×C₅	—	2	1	no	—
519	C₄×C₅	—	2	1	no	—
520	C₄×C₅	—	2	1	no	—
521	C₄×C₅	—	2	1	no	—
522	C₄×C₅	—	2	1	no	—
523	C₄×C₅	—	2	2	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	4	1	no	—
526	C₄×C₅	—	4	1	no	—
527	C₄×C₅	—	4	1	no	—
528	C₄×C₅	—	4	1	no	—
529	C₄×C₅	—	4	1	no	—
530	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
531	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
532	#41	—	2	2	no	—
533	#41	—	2	2	no	—
534	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
535	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
536	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
544	Q₁₆	—	2	2	no	—
545	Q₁₆	—	2	2	no	—
546	SD₁₆	—	2	2	no	—
547	SD₁₆	—	2	2	no	—
548	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
549	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
550	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
551	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	—	2	1	no	—
558	C₄⋊C₄	—	2	1	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
564	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
565	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
566	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
567	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
568	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
574	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
581	C₃×C₅	#3120	1	1	yes	characteristic, direct product factor, Hall
582	C₂²×C₃	—	2	1	no	—
583	C₂²×C₃	—	2	2	no	—
584	C₂²×C₃	—	2	1	no	—
585	C₂²×C₃	—	2	1	no	—
586	C₂²×C₃	—	4	1	no	—
587	C₂²×C₃	—	4	1	no	—
588	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	2	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	1	no	—
593	C₃×C₄	—	2	1	no	—
594	C₃×C₄	—	2	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₃×C₄	—	4	1	no	—
597	C₃×C₄	—	4	1	no	—
598	C₃×C₄	—	4	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	4	1	no	—
601	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
602	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
603	C₂×C₅	—	4	1	no	—
604	C₂×C₅	—	4	2	no	—
605	C₂×C₅	C₃×#525	1	1	yes	characteristic
606	C₂×C₅	C₃×#577	1	1	yes	characteristic
607	C₂×C₅	C₃×#578	1	1	yes	characteristic
608	C₂³	—	2	1	no	—
609	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
610	Q₈	—	2	1	no	—
611	Q₈	—	2	1	no	—
612	Q₈	—	2	1	no	—
613	Q₈	—	2	1	no	—
614	Q₈	—	2	1	no	—
615	Q₈	C₃×C₅×#41	1	2	yes	—
616	D₄	—	2	4	no	—
617	D₄	—	2	1	no	—
618	D₄	C₃×C₅×#41	1	2	yes	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	8	1	no	—
630	C₂×C₄	—	8	1	no	—
631	C₂×C₄	—	8	1	no	—
632	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
633	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
634	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
635	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
636	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
637	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₂×C₃	—	4	1	no	—
643	C₂×C₃	—	4	2	no	—
644	C₂×C₃	C₅×#525	1	1	yes	characteristic
645	C₂×C₃	C₅×#577	1	1	yes	characteristic
646	C₂×C₃	C₅×#578	1	1	yes	characteristic
647	C₅	C₃×#3120	1	1	yes	characteristic, direct product factor, Sylow
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
668	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
669	C₃	C₅×#3120	1	1	yes	characteristic, direct product factor, Sylow
670	C₂	—	4	1	no	—
671	C₂	—	4	2	no	—
672	C₂	C₃×C₅×#525	1	1	yes	characteristic
673	C₂	C₃×C₅×#577	1	1	yes	characteristic
674	C₂	C₃×C₅×#578	1	1	yes	characteristic

	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
1. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#484	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#479	C₂	semidirect
6. C₃×C₅×#478	C₂	semidirect
7. C₃×C₅×#462	C₂	semidirect
8. C₃×C₅×#461	C₂	semidirect
11. C₃×C₅×#441	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₄×C₅×Q₁₆	C₂	semidirect
14. C₃×C₄×C₅×SD₁₆	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3120	C₃	direct (N × H)
60. C₃×#3120	C₅	direct (N × H)
61. C₅×#541	C₂×C₃	semidirect
63. C₅×#484	C₂×C₃	semidirect
64. C₅×#483	C₂×C₃	semidirect
65. C₅×#479	C₂×C₃	semidirect
66. C₅×#478	C₂×C₃	semidirect
67. C₅×#462	C₂×C₃	semidirect
68. C₅×#461	C₂×C₃	semidirect
71. C₅×#441	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₄×C₅×Q₁₆	C₂×C₃	semidirect
74. C₄×C₅×SD₁₆	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
125. C₃×#541	C₂×C₅	semidirect
127. C₃×#484	C₂×C₅	semidirect
128. C₃×#483	C₂×C₅	semidirect
129. C₃×#479	C₂×C₅	semidirect
130. C₃×#478	C₂×C₅	semidirect
131. C₃×#462	C₂×C₅	semidirect
132. C₃×#461	C₂×C₅	semidirect
135. C₃×#441	C₂×C₅	semidirect
136. C₃×#440	C₂×C₅	semidirect
137. C₃×C₄×Q₁₆	C₂×C₅	semidirect
138. C₃×C₄×SD₁₆	C₂×C₅	semidirect
139. C₃×#433	C₂×C₅	semidirect
183. #3120	C₃×C₅	direct (N × H)
310. #541	C₂×C₃×C₅	semidirect
312. #484	C₂×C₃×C₅	semidirect
313. #483	C₂×C₃×C₅	semidirect
314. #479	C₂×C₃×C₅	semidirect
315. #478	C₂×C₃×C₅	semidirect
316. #462	C₂×C₃×C₅	semidirect
317. #461	C₂×C₃×C₅	semidirect
320. #441	C₂×C₃×C₅	semidirect
321. #440	C₂×C₃×C₅	semidirect
322. C₄×Q₁₆	C₂×C₃×C₅	semidirect
323. C₄×SD₁₆	C₂×C₃×C₅	semidirect
324. #433	C₂×C₃×C₅	semidirect
581. C₃×C₅	#3120	direct (N × H)
647. C₅	C₃×#3120	direct (N × H)
669. C₃	C₅×#3120	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×#520	2
C₃×C₅×#484	2
C₃×C₅×#483	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₅×#441	2
C₃×C₅×#440	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#433	2
C₅×#3120	3
C₃×#3120	5

Subgroups — C3×C5×#3120 #14276154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3120 #14276154