Subgroups — C₃×C₅×#3119 #14276153

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#481	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#480	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×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3119	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#127	C₂²	1	1	yes	characteristic
23	C₃×C₅×#125	C₂²	1	1	yes	characteristic
24	C₃×C₅×#123	—	2	1	no	—
25	C₃×C₅×#123	—	2	1	no	—
26	C₃×C₅×#121	—	2	1	no	—
27	C₃×C₅×#121	—	2	1	no	—
28	C₃×C₅×#121	C₂²	1	1	yes	characteristic
29	C₃×C₅×#121	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×D₄	—	2	1	no	—
33	C₃×C₄×C₅×D₄	—	2	1	no	—
34	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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×#102	C₂²	1	1	yes	characteristic
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	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×#3119	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#481	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#480	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×#460	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
74	C₄×C₅×D₈	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×D₄	—	2	1	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	—	2	1	no	—
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₃×C₅×SD₁₆	—	2	2	no	—
95	C₃×C₅×SD₁₆	—	2	2	no	—
96	C₃×C₅×D₈	—	2	2	no	—
97	C₃×C₅×D₈	—	2	2	no	—
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#540	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#481	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#480	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×#460	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄×D₈	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×SD₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
145	C₅×#127	C₂²×C₃	1	1	yes	characteristic
146	C₅×#125	C₂²×C₃	1	1	yes	characteristic
147	C₅×#123	—	2	1	no	—
148	C₅×#123	—	2	1	no	—
149	C₅×#121	—	2	1	no	—
150	C₅×#121	—	2	1	no	—
151	C₅×#121	C₂²×C₃	1	1	yes	characteristic
152	C₅×#121	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×D₄	—	2	1	no	—
156	C₄×C₅×D₄	—	2	1	no	—
157	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
158	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
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×#102	C₂²×C₃	1	1	yes	characteristic
174	C₅×#102	C₂²×C₃	1	1	yes	characteristic
175	C₅×#102	C₂²×C₃	1	1	yes	characteristic
176	C₅×#102	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	#3119	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₃×C₅	—	2	1	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	—	2	1	no	—
187	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
188	C₃×C₅×Q₈	—	2	1	no	—
189	C₃×C₅×Q₈	#41	1	2	yes	—
190	C₃×C₅×D₄	—	2	4	no	—
191	C₃×C₅×D₄	—	2	1	no	—
192	C₃×C₅×D₄	—	2	1	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	—	8	1	no	—
197	C₃×C₅×D₄	—	8	1	no	—
198	C₃×C₅×D₄	—	8	1	no	—
199	C₃×C₅×D₄	—	8	1	no	—
200	C₃×C₅×D₄	#41	1	2	yes	—
201	C₂×C₃×C₄×C₅	—	2	4	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	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	8	1	no	—
210	C₂×C₃×C₄×C₅	—	8	1	no	—
211	C₂×C₃×C₄×C₅	—	8	1	no	—
212	C₂×C₃×C₄×C₅	—	8	1	no	—
213	C₂×C₃×C₄×C₅	—	8	1	no	—
214	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₃×C₅×C₈	—	2	1	no	—
223	C₃×C₅×C₈	—	2	1	no	—
224	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
229	C₃×#127	C₂²×C₅	1	1	yes	characteristic
230	C₃×#125	C₂²×C₅	1	1	yes	characteristic
231	C₃×#123	—	2	1	no	—
232	C₃×#123	—	2	1	no	—
233	C₃×#121	—	2	1	no	—
234	C₃×#121	—	2	1	no	—
235	C₃×#121	C₂²×C₅	1	1	yes	characteristic
236	C₃×#121	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	—	2	1	no	—
241	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
245	C₃×#117	—	2	1	no	—
246	C₃×#117	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	—	2	1	no	—
248	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₃×#107	C₂²×C₅	1	1	yes	characteristic
250	C₃×#107	C₂²×C₅	1	1	yes	characteristic
251	C₃×#106	C₂²×C₅	1	1	yes	characteristic
252	C₃×#106	C₂²×C₅	1	1	yes	characteristic
253	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
254	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₃×#103	C₂²×C₅	1	1	yes	characteristic
256	C₃×#103	C₂²×C₅	1	1	yes	characteristic
257	C₃×#102	C₂²×C₅	1	1	yes	characteristic
258	C₃×#102	C₂²×C₅	1	1	yes	characteristic
259	C₃×#102	C₂²×C₅	1	1	yes	characteristic
260	C₃×#102	C₂²×C₅	1	1	yes	characteristic
261	C₃×#102	C₂²×C₅	1	1	yes	characteristic
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic
263	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	C₃×#97	C₂²×C₅	1	1	yes	characteristic
266	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
267	C₅×#41	—	2	2	no	—
268	C₅×#41	—	2	2	no	—
269	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	2	1	no	—
274	C₂×C₅×D₄	—	2	1	no	—
275	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
278	C₂²×C₄×C₅	—	2	1	no	—
279	C₂²×C₄×C₅	—	2	1	no	—
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	2	1	no	—
282	C₂²×C₄×C₅	—	2	1	no	—
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
285	C₅×SD₁₆	—	2	2	no	—
286	C₅×SD₁₆	—	2	2	no	—
287	C₅×D₈	—	2	2	no	—
288	C₅×D₈	—	2	2	no	—
289	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
293	C₅×C₄⋊C₄	—	2	1	no	—
294	C₅×C₄⋊C₄	—	2	1	no	—
295	C₅×C₄⋊C₄	—	2	1	no	—
296	C₅×C₄⋊C₄	—	2	1	no	—
297	C₅×C₄⋊C₄	—	2	1	no	—
298	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
300	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
301	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
302	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
303	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
311	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	2	1	no	—
314	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
315	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
316	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#481	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#479	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#478	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	2	no	—
333	C₂²×C₃×C₅	—	2	1	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	4	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	—	4	1	no	—
338	C₂²×C₃×C₅	—	4	1	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	2	no	—
346	C₃×C₄×C₅	—	2	1	no	—
347	C₃×C₄×C₅	—	2	1	no	—
348	C₃×C₄×C₅	—	2	1	no	—
349	C₃×C₄×C₅	—	2	1	no	—
350	C₃×C₄×C₅	—	4	1	no	—
351	C₃×C₄×C₅	—	4	1	no	—
352	C₃×C₄×C₅	—	4	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
355	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₃×#41	—	2	2	no	—
357	C₃×#41	—	2	2	no	—
358	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×D₄	—	2	1	no	—
360	C₂×C₃×D₄	—	2	1	no	—
361	C₂×C₃×D₄	—	2	1	no	—
362	C₂×C₃×D₄	—	2	1	no	—
363	C₂×C₃×D₄	—	2	1	no	—
364	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
367	C₂²×C₃×C₄	—	2	1	no	—
368	C₂²×C₃×C₄	—	2	1	no	—
369	C₂²×C₃×C₄	—	2	1	no	—
370	C₂²×C₃×C₄	—	2	1	no	—
371	C₂²×C₃×C₄	—	2	1	no	—
372	C₂²×C₃×C₄	—	2	1	no	—
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₃×SD₁₆	—	2	2	no	—
375	C₃×SD₁₆	—	2	2	no	—
376	C₃×D₈	—	2	2	no	—
377	C₃×D₈	—	2	2	no	—
378	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
382	C₃×C₄⋊C₄	—	2	1	no	—
383	C₃×C₄⋊C₄	—	2	1	no	—
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
389	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
391	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
392	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
393	C₃×C₂²⋊C₄	—	2	1	no	—
394	C₃×C₂²⋊C₄	—	2	1	no	—
395	C₃×C₂²⋊C₄	—	2	1	no	—
396	C₃×C₂²⋊C₄	—	2	1	no	—
397	C₃×C₂²⋊C₄	—	2	1	no	—
398	C₃×C₂²⋊C₄	—	2	1	no	—
399	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
400	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
401	C₃×C₄²	—	2	1	no	—
402	C₃×C₄²	—	2	1	no	—
403	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
404	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
409	C₅×Q₈	—	2	1	no	—
410	C₅×Q₈	C₃×#41	1	2	yes	—
411	C₅×D₄	—	2	4	no	—
412	C₅×D₄	—	2	1	no	—
413	C₅×D₄	—	2	1	no	—
414	C₅×D₄	—	2	1	no	—
415	C₅×D₄	—	2	1	no	—
416	C₅×D₄	—	2	1	no	—
417	C₅×D₄	—	8	1	no	—
418	C₅×D₄	—	8	1	no	—
419	C₅×D₄	—	8	1	no	—
420	C₅×D₄	—	8	1	no	—
421	C₅×D₄	C₃×#41	1	2	yes	—
422	C₂×C₄×C₅	—	2	4	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	8	1	no	—
431	C₂×C₄×C₅	—	8	1	no	—
432	C₂×C₄×C₅	—	8	1	no	—
433	C₂×C₄×C₅	—	8	1	no	—
434	C₂×C₄×C₅	—	8	1	no	—
435	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
436	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
437	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
441	C₅×C₈	—	2	1	no	—
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₅×C₈	—	2	1	no	—
445	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
450	#127	C₂²×C₃×C₅	1	1	yes	characteristic
451	#125	C₂²×C₃×C₅	1	1	yes	characteristic
452	#123	—	2	1	no	—
453	#123	—	2	1	no	—
454	#121	—	2	1	no	—
455	#121	—	2	1	no	—
456	#121	C₂²×C₃×C₅	1	1	yes	characteristic
457	#121	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
466	#117	—	2	1	no	—
467	#117	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂×C₄⋊C₄	—	2	1	no	—
469	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
470	#107	C₂²×C₃×C₅	1	1	yes	characteristic
471	#107	C₂²×C₃×C₅	1	1	yes	characteristic
472	#106	C₂²×C₃×C₅	1	1	yes	characteristic
473	#106	C₂²×C₃×C₅	1	1	yes	characteristic
474	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
475	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
476	#103	C₂²×C₃×C₅	1	1	yes	characteristic
477	#103	C₂²×C₃×C₅	1	1	yes	characteristic
478	#102	C₂²×C₃×C₅	1	1	yes	characteristic
479	#102	C₂²×C₃×C₅	1	1	yes	characteristic
480	#102	C₂²×C₃×C₅	1	1	yes	characteristic
481	#102	C₂²×C₃×C₅	1	1	yes	characteristic
482	#102	C₂²×C₃×C₅	1	1	yes	characteristic
483	#102	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
485	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
486	#97	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂×C₃×C₅	—	4	1	no	—
489	C₂×C₃×C₅	—	4	2	no	—
490	C₂×C₃×C₅	—	8	1	no	—
491	C₂×C₃×C₅	—	8	1	no	—
492	C₂×C₃×C₅	#525	1	1	yes	characteristic
493	C₂×C₃×C₅	#576	1	1	yes	characteristic
494	C₂×C₃×C₅	#577	1	1	yes	characteristic
495	C₂³×C₃	—	2	1	no	—
496	C₂³×C₃	—	2	1	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₃×Q₈	—	2	1	no	—
500	C₃×Q₈	C₅×#41	1	2	yes	—
501	C₃×D₄	—	2	4	no	—
502	C₃×D₄	—	2	1	no	—
503	C₃×D₄	—	2	1	no	—
504	C₃×D₄	—	2	1	no	—
505	C₃×D₄	—	2	1	no	—
506	C₃×D₄	—	2	1	no	—
507	C₃×D₄	—	8	1	no	—
508	C₃×D₄	—	8	1	no	—
509	C₃×D₄	—	8	1	no	—
510	C₃×D₄	—	8	1	no	—
511	C₃×D₄	C₅×#41	1	2	yes	—
512	C₂×C₃×C₄	—	2	4	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	8	1	no	—
521	C₂×C₃×C₄	—	8	1	no	—
522	C₂×C₃×C₄	—	8	1	no	—
523	C₂×C₃×C₄	—	8	1	no	—
524	C₂×C₃×C₄	—	8	1	no	—
525	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
531	C₃×C₈	—	2	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃×C₈	—	2	1	no	—
535	C₂²×C₅	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	4	1	no	—
544	C₂²×C₅	—	4	1	no	—
545	C₂²×C₅	—	4	1	no	—
546	C₂²×C₅	—	4	1	no	—
547	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
548	C₄×C₅	—	2	1	no	—
549	C₄×C₅	—	2	1	no	—
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	2	1	no	—
552	C₄×C₅	—	2	1	no	—
553	C₄×C₅	—	2	2	no	—
554	C₄×C₅	—	4	1	no	—
555	C₄×C₅	—	4	1	no	—
556	C₄×C₅	—	4	1	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
559	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
560	#41	—	2	2	no	—
561	#41	—	2	2	no	—
562	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
569	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
570	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
578	SD₁₆	—	2	2	no	—
579	SD₁₆	—	2	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	2	2	no	—
582	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
583	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
592	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
593	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
594	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
595	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
596	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
604	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
605	C₄²	—	2	1	no	—
606	C₄²	—	2	1	no	—
607	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
609	C₃×C₅	#3119	1	1	yes	characteristic, direct product factor, Hall
610	C₂²×C₃	—	2	1	no	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
623	C₃×C₄	—	2	1	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	—	4	1	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	—	4	1	no	—
633	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
634	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
635	C₂×C₅	—	4	1	no	—
636	C₂×C₅	—	4	2	no	—
637	C₂×C₅	—	8	1	no	—
638	C₂×C₅	—	8	1	no	—
639	C₂×C₅	C₃×#525	1	1	yes	characteristic
640	C₂×C₅	C₃×#576	1	1	yes	characteristic
641	C₂×C₅	C₃×#577	1	1	yes	characteristic
642	C₂³	—	2	1	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	2	1	no	—
645	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
646	Q₈	—	2	1	no	—
647	Q₈	C₃×C₅×#41	1	2	yes	—
648	D₄	—	2	4	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	1	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	2	1	no	—
654	D₄	—	8	1	no	—
655	D₄	—	8	1	no	—
656	D₄	—	8	1	no	—
657	D₄	—	8	1	no	—
658	D₄	C₃×C₅×#41	1	2	yes	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	8	1	no	—
668	C₂×C₄	—	8	1	no	—
669	C₂×C₄	—	8	1	no	—
670	C₂×C₄	—	8	1	no	—
671	C₂×C₄	—	8	1	no	—
672	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
674	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
675	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
676	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
677	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
678	C₈	—	2	1	no	—
679	C₈	—	2	1	no	—
680	C₈	—	2	1	no	—
681	C₈	—	2	1	no	—
682	C₂×C₃	—	4	1	no	—
683	C₂×C₃	—	4	2	no	—
684	C₂×C₃	—	8	1	no	—
685	C₂×C₃	—	8	1	no	—
686	C₂×C₃	C₅×#525	1	1	yes	characteristic
687	C₂×C₃	C₅×#576	1	1	yes	characteristic
688	C₂×C₃	C₅×#577	1	1	yes	characteristic
689	C₅	C₃×#3119	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	2	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	1	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
703	C₄	—	2	1	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	1	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
714	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
715	C₃	C₅×#3119	1	1	yes	characteristic, direct product factor, Sylow
716	C₂	—	4	1	no	—
717	C₂	—	4	2	no	—
718	C₂	—	8	1	no	—
719	C₂	—	8	1	no	—
720	C₂	C₃×C₅×#525	1	1	yes	characteristic
721	C₂	C₃×C₅×#576	1	1	yes	characteristic
722	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
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×#540	C₂	semidirect
2. C₃×C₅×#520	C₂	semidirect
3. C₃×C₅×#481	C₂	semidirect
4. C₃×C₅×#480	C₂	semidirect
5. C₃×C₅×#479	C₂	semidirect
6. C₃×C₅×#478	C₂	semidirect
7. C₃×C₅×#460	C₂	semidirect
8. C₃×C₅×#459	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₅×#449	C₂	semidirect
11. C₃×C₅×#442	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₄×C₅×SD₁₆	C₂	semidirect
14. C₃×C₄×C₅×D₈	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3119	C₃	direct (N × H)
60. C₃×#3119	C₅	direct (N × H)
61. C₅×#540	C₂×C₃	semidirect
62. C₅×#520	C₂×C₃	semidirect
63. C₅×#481	C₂×C₃	semidirect
64. C₅×#480	C₂×C₃	semidirect
65. C₅×#479	C₂×C₃	semidirect
66. C₅×#478	C₂×C₃	semidirect
67. C₅×#460	C₂×C₃	semidirect
68. C₅×#459	C₂×C₃	semidirect
69. C₅×#449	C₂×C₃	semidirect
70. C₅×#449	C₂×C₃	semidirect
71. C₅×#442	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₄×C₅×SD₁₆	C₂×C₃	semidirect
74. C₄×C₅×D₈	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
125. C₃×#540	C₂×C₅	semidirect
126. C₃×#520	C₂×C₅	semidirect
127. C₃×#481	C₂×C₅	semidirect
128. C₃×#480	C₂×C₅	semidirect
129. C₃×#479	C₂×C₅	semidirect
130. C₃×#478	C₂×C₅	semidirect
131. C₃×#460	C₂×C₅	semidirect
132. C₃×#459	C₂×C₅	semidirect
133. C₃×#449	C₂×C₅	semidirect
134. C₃×#449	C₂×C₅	semidirect
135. C₃×#442	C₂×C₅	semidirect
136. C₃×#440	C₂×C₅	semidirect
137. C₃×C₄×SD₁₆	C₂×C₅	semidirect
138. C₃×C₄×D₈	C₂×C₅	semidirect
139. C₃×#433	C₂×C₅	semidirect
183. #3119	C₃×C₅	direct (N × H)
316. #540	C₂×C₃×C₅	semidirect
317. #520	C₂×C₃×C₅	semidirect
318. #481	C₂×C₃×C₅	semidirect
319. #480	C₂×C₃×C₅	semidirect
320. #479	C₂×C₃×C₅	semidirect
321. #478	C₂×C₃×C₅	semidirect
322. #460	C₂×C₃×C₅	semidirect
323. #459	C₂×C₃×C₅	semidirect
324. #449	C₂×C₃×C₅	semidirect
325. #449	C₂×C₃×C₅	semidirect
326. #442	C₂×C₃×C₅	semidirect
327. #440	C₂×C₃×C₅	semidirect
328. C₄×SD₁₆	C₂×C₃×C₅	semidirect
329. C₄×D₈	C₂×C₃×C₅	semidirect
330. #433	C₂×C₃×C₅	semidirect
609. C₃×C₅	#3119	direct (N × H)
689. C₅	C₃×#3119	direct (N × H)
715. C₃	C₅×#3119	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×#540	2
C₃×C₅×#520	2
C₃×C₅×#481	2
C₃×C₅×#480	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#449	2
C₃×C₅×#442	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#433	2
C₅×#3119	3
C₃×#3119	5

Subgroups — C3×C5×#3119 #14276153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3119 #14276153