Subgroups — C₃×C₅×#3312 #14276346

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3312	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
25	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×#126	—	2	1	no	—
27	C₃×C₅×#125	—	2	1	no	—
28	C₃×C₅×#125	C₂²	1	1	yes	characteristic
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	—	2	1	no	—
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₅×#117	—	2	1	no	—
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₄⋊C₄	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×#103	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×#103	C₂²	1	1	yes	characteristic
55	C₃×C₅×#103	C₂²	1	1	yes	characteristic
56	C₃×C₅×#103	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×C₅×#97	C₂²	1	1	yes	characteristic
60	C₃×#3312	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#552	C₂×C₃	1	1	yes	characteristic
62	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
63	C₅×#491	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#483	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#479	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#435	C₂×C₃	1	1	yes	characteristic
74	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×Q₈	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	—	2	2	no	—
79	C₂×C₃×C₅×Q₈	—	2	2	no	—
80	C₂×C₃×C₅×Q₈	—	4	1	no	—
81	C₂×C₃×C₅×Q₈	—	4	1	no	—
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	D₄	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	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₃×C₅×Q₁₆	—	2	2	no	—
93	C₃×C₅×Q₁₆	—	4	1	no	—
94	C₃×C₅×Q₁₆	—	4	1	no	—
95	C₃×C₅×M₁₆	—	4	1	no	—
96	C₂×C₃×C₅×C₈	—	4	1	no	—
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	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	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	—	2	1	no	—
112	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₃×C₄²×C₅	—	2	1	no	—
125	C₃×C₄²×C₅	—	2	1	no	—
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₃×#552	C₂×C₅	1	1	yes	characteristic
129	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic
130	C₃×#491	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#483	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#435	C₂×C₅	1	1	yes	characteristic
141	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₅×C₄⋊Q₈	—	2	1	no	—
151	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×#126	—	2	1	no	—
153	C₅×#125	—	2	1	no	—
154	C₅×#125	C₂²×C₃	1	1	yes	characteristic
155	C₅×#123	—	2	1	no	—
156	C₅×C₂²⋊Q₈	—	2	1	no	—
157	C₅×C₂²⋊Q₈	—	2	1	no	—
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
160	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
161	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
162	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×D₄	—	2	1	no	—
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₅×#117	—	2	1	no	—
167	C₅×#117	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₅×#107	C₂²×C₃	1	1	yes	characteristic
170	C₅×#106	C₂²×C₃	1	1	yes	characteristic
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic
172	C₅×C₄⋊C₈	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×#103	C₂²×C₃	1	1	yes	characteristic
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic
179	C₅×#103	C₂²×C₃	1	1	yes	characteristic
180	C₅×#103	C₂²×C₃	1	1	yes	characteristic
181	C₅×#103	C₂²×C₃	1	1	yes	characteristic
182	C₅×#103	C₂²×C₃	1	1	yes	characteristic
183	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₅×#97	C₂²×C₃	1	1	yes	characteristic
186	#3312	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₃×C₅×Q₈	—	2	1	no	—
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	2	1	no	—
196	C₃×C₅×Q₈	—	4	2	no	—
197	C₃×C₅×Q₈	—	4	2	no	—
198	C₃×C₅×Q₈	#41	1	2	yes	—
199	C₃×C₅×D₄	—	2	2	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	—	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	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	4	2	no	—
213	C₂×C₃×C₄×C₅	—	4	2	no	—
214	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
225	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
231	C₃×C₄⋊Q₈	—	2	1	no	—
232	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
233	C₃×#126	—	2	1	no	—
234	C₃×#125	—	2	1	no	—
235	C₃×#125	C₂²×C₅	1	1	yes	characteristic
236	C₃×#123	—	2	1	no	—
237	C₃×C₂²⋊Q₈	—	2	1	no	—
238	C₃×C₂²⋊Q₈	—	2	1	no	—
239	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄×D₄	—	2	1	no	—
246	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
247	C₃×#117	—	2	1	no	—
248	C₃×#117	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄⋊C₄	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×#103	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×#103	C₂²×C₅	1	1	yes	characteristic
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic
259	C₃×#103	C₂²×C₅	1	1	yes	characteristic
260	C₃×#103	C₂²×C₅	1	1	yes	characteristic
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic
262	C₃×#103	C₂²×C₅	1	1	yes	characteristic
263	C₃×#103	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₃×#97	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₅×Q₈	—	2	1	no	—
268	C₂×C₅×Q₈	—	2	1	no	—
269	C₂×C₅×Q₈	—	2	2	no	—
270	C₂×C₅×Q₈	—	2	2	no	—
271	C₂×C₅×Q₈	—	4	1	no	—
272	C₂×C₅×Q₈	—	4	1	no	—
273	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₅×D₄	C₃×D₄	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	C₂³×C₃	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₅×Q₁₆	—	2	2	no	—
284	C₅×Q₁₆	—	4	1	no	—
285	C₅×Q₁₆	—	4	1	no	—
286	C₅×M₁₆	—	4	1	no	—
287	C₂×C₅×C₈	—	4	1	no	—
288	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	C₅×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	—	2	1	no	—
303	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
304	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
305	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
307	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
314	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
315	C₄²×C₅	—	2	1	no	—
316	C₄²×C₅	—	2	1	no	—
317	C₄²×C₅	—	2	1	no	—
318	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
319	#552	C₂×C₃×C₅	1	1	yes	characteristic
320	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
321	#491	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#483	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#479	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	#435	C₂×C₃×C₅	1	1	yes	characteristic
332	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	2	1	no	—
336	C₂²×C₃×C₅	—	2	1	no	—
337	C₂²×C₃×C₅	—	2	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	#137	1	2	yes	—
340	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
341	C₃×C₄×C₅	—	2	1	no	—
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	2	no	—
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	—	4	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	C₂×#41	1	1	yes	characteristic
354	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×C₃×Q₈	—	2	1	no	—
356	C₂×C₃×Q₈	—	2	1	no	—
357	C₂×C₃×Q₈	—	2	2	no	—
358	C₂×C₃×Q₈	—	2	2	no	—
359	C₂×C₃×Q₈	—	4	1	no	—
360	C₂×C₃×Q₈	—	4	1	no	—
361	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
366	C₂²×C₃×C₄	—	2	1	no	—
367	C₂²×C₃×C₄	—	2	1	no	—
368	C₂²×C₃×C₄	—	2	1	no	—
369	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
371	C₃×Q₁₆	—	2	2	no	—
372	C₃×Q₁₆	—	4	1	no	—
373	C₃×Q₁₆	—	4	1	no	—
374	C₃×M₁₆	—	4	1	no	—
375	C₂×C₃×C₈	—	4	1	no	—
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₃×C₄⋊C₄	—	2	1	no	—
381	C₃×C₄⋊C₄	—	2	1	no	—
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	—	2	1	no	—
388	C₃×C₄⋊C₄	—	2	1	no	—
389	C₃×C₄⋊C₄	—	2	1	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
392	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
393	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
394	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
400	C₃×C₂²⋊C₄	—	2	1	no	—
401	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
402	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
403	C₃×C₄²	—	2	1	no	—
404	C₃×C₄²	—	2	1	no	—
405	C₃×C₄²	—	2	1	no	—
406	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
407	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
408	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
409	C₅×Q₈	—	2	1	no	—
410	C₅×Q₈	—	2	1	no	—
411	C₅×Q₈	—	2	1	no	—
412	C₅×Q₈	—	2	1	no	—
413	C₅×Q₈	—	2	1	no	—
414	C₅×Q₈	—	2	1	no	—
415	C₅×Q₈	—	2	1	no	—
416	C₅×Q₈	—	4	2	no	—
417	C₅×Q₈	—	4	2	no	—
418	C₅×Q₈	C₃×#41	1	2	yes	—
419	C₅×D₄	—	2	2	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	4	2	no	—
433	C₂×C₄×C₅	—	4	2	no	—
434	C₂×C₄×C₅	—	4	2	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	C₂⁴×C₃	1	1	yes	characteristic
440	C₅×C₈	—	2	1	no	—
441	C₅×C₈	—	2	1	no	—
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₄⋊Q₈	—	2	1	no	—
452	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
453	#126	—	2	1	no	—
454	#125	—	2	1	no	—
455	#125	C₂²×C₃×C₅	1	1	yes	characteristic
456	#123	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
460	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
461	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₄×D₄	—	2	1	no	—
466	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
467	#117	—	2	1	no	—
468	#117	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
470	#107	C₂²×C₃×C₅	1	1	yes	characteristic
471	#106	C₂²×C₃×C₅	1	1	yes	characteristic
472	#106	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
474	#103	C₂²×C₃×C₅	1	1	yes	characteristic
475	#103	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	#103	C₂²×C₃×C₅	1	1	yes	characteristic
479	#103	C₂²×C₃×C₅	1	1	yes	characteristic
480	#103	C₂²×C₃×C₅	1	1	yes	characteristic
481	#103	C₂²×C₃×C₅	1	1	yes	characteristic
482	#103	C₂²×C₃×C₅	1	1	yes	characteristic
483	#103	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	C₂×C₃×C₅	—	2	2	no	—
488	C₂×C₃×C₅	—	4	1	no	—
489	C₂×C₃×C₅	#546	1	1	yes	characteristic
490	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
491	C₂×C₃×C₅	#578	1	1	yes	characteristic
492	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
493	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
494	C₃×Q₈	—	2	1	no	—
495	C₃×Q₈	—	2	1	no	—
496	C₃×Q₈	—	2	1	no	—
497	C₃×Q₈	—	2	1	no	—
498	C₃×Q₈	—	2	1	no	—
499	C₃×Q₈	—	2	1	no	—
500	C₃×Q₈	—	2	1	no	—
501	C₃×Q₈	—	4	2	no	—
502	C₃×Q₈	—	4	2	no	—
503	C₃×Q₈	C₅×#41	1	2	yes	—
504	C₃×D₄	—	2	2	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	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	—	4	2	no	—
518	C₂×C₃×C₄	—	4	2	no	—
519	C₂×C₃×C₄	—	4	2	no	—
520	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
525	C₃×C₈	—	2	1	no	—
526	C₃×C₈	—	2	1	no	—
527	C₃×C₈	—	2	1	no	—
528	C₃×C₈	—	2	1	no	—
529	C₂²×C₅	—	2	1	no	—
530	C₂²×C₅	—	2	1	no	—
531	C₂²×C₅	—	2	1	no	—
532	C₂²×C₅	—	2	1	no	—
533	C₂²×C₅	—	2	1	no	—
534	C₂²×C₅	C₃×#137	1	2	yes	—
535	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
536	C₄×C₅	—	2	1	no	—
537	C₄×C₅	—	2	1	no	—
538	C₄×C₅	—	2	1	no	—
539	C₄×C₅	—	2	1	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	—	4	1	no	—
542	C₄×C₅	—	4	1	no	—
543	C₄×C₅	—	4	1	no	—
544	C₄×C₅	—	4	1	no	—
545	C₄×C₅	—	4	1	no	—
546	C₄×C₅	—	4	1	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
549	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
557	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
558	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
559	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
560	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
566	Q₁₆	—	2	2	no	—
567	Q₁₆	—	4	1	no	—
568	Q₁₆	—	4	1	no	—
569	M₁₆	—	4	1	no	—
570	C₂×C₈	—	4	1	no	—
571	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
572	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
573	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
574	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
587	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
588	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
589	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
590	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
597	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
598	C₄²	—	2	1	no	—
599	C₄²	—	2	1	no	—
600	C₄²	—	2	1	no	—
601	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₃×C₅	#3312	1	1	yes	characteristic, direct product factor, Hall
603	C₂²×C₃	—	2	1	no	—
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	C₅×#137	1	2	yes	—
609	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
610	C₃×C₄	—	2	1	no	—
611	C₃×C₄	—	2	1	no	—
612	C₃×C₄	—	2	2	no	—
613	C₃×C₄	—	2	1	no	—
614	C₃×C₄	—	2	1	no	—
615	C₃×C₄	—	4	1	no	—
616	C₃×C₄	—	4	1	no	—
617	C₃×C₄	—	4	1	no	—
618	C₃×C₄	—	4	1	no	—
619	C₃×C₄	—	4	1	no	—
620	C₃×C₄	—	4	1	no	—
621	C₃×C₄	—	4	1	no	—
622	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
623	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂×C₅	—	2	2	no	—
625	C₂×C₅	—	4	1	no	—
626	C₂×C₅	C₃×#546	1	1	yes	characteristic
627	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
628	C₂×C₅	C₃×#578	1	1	yes	characteristic
629	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
630	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
631	Q₈	—	2	1	no	—
632	Q₈	—	2	1	no	—
633	Q₈	—	2	1	no	—
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	2	1	no	—
637	Q₈	—	2	1	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	4	2	no	—
640	Q₈	C₃×C₅×#41	1	2	yes	—
641	D₄	—	2	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	4	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
658	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
659	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
660	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
661	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
662	C₈	—	2	1	no	—
663	C₈	—	2	1	no	—
664	C₈	—	2	1	no	—
665	C₈	—	2	1	no	—
666	C₂×C₃	—	2	2	no	—
667	C₂×C₃	—	4	1	no	—
668	C₂×C₃	C₅×#546	1	1	yes	characteristic
669	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
670	C₂×C₃	C₅×#578	1	1	yes	characteristic
671	C₅	C₃×#3312	1	1	yes	characteristic, direct product factor, Sylow
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	C₃×C₅×#137	1	2	yes	—
678	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	4	1	no	—
685	C₄	—	4	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	1	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
692	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
693	C₃	C₅×#3312	1	1	yes	characteristic, direct product factor, Sylow
694	C₂	—	2	2	no	—
695	C₂	—	4	1	no	—
696	C₂	C₃×C₅×#546	1	1	yes	characteristic
697	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
698	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×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#491	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#483	C₂	semidirect
6. C₃×C₅×#479	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
8. C₃×C₅×#467	C₂	semidirect
9. C₃×C₅×#462	C₂	semidirect
10. C₃×C₅×#451	C₂	semidirect
11. C₃×C₅×#451	C₂	semidirect
12. C₃×C₅×#441	C₂	semidirect
14. C₃×C₅×#419	C₂	semidirect
15. C₂×C₃×C₅×#103	C₂	semidirect
16. C₅×#3312	C₃	direct (N × H)
60. C₃×#3312	C₅	direct (N × H)
63. C₅×#491	C₂×C₃	semidirect
64. C₅×#485	C₂×C₃	semidirect
65. C₅×#483	C₂×C₃	semidirect
66. C₅×#479	C₂×C₃	semidirect
67. C₅×#470	C₂×C₃	semidirect
68. C₅×#467	C₂×C₃	semidirect
69. C₅×#462	C₂×C₃	semidirect
70. C₅×#451	C₂×C₃	semidirect
71. C₅×#451	C₂×C₃	semidirect
72. C₅×#441	C₂×C₃	semidirect
74. C₅×#419	C₂×C₃	semidirect
75. C₂×C₅×#103	C₂×C₃	semidirect
130. C₃×#491	C₂×C₅	semidirect
131. C₃×#485	C₂×C₅	semidirect
132. C₃×#483	C₂×C₅	semidirect
133. C₃×#479	C₂×C₅	semidirect
134. C₃×#470	C₂×C₅	semidirect
135. C₃×#467	C₂×C₅	semidirect
136. C₃×#462	C₂×C₅	semidirect
137. C₃×#451	C₂×C₅	semidirect
138. C₃×#451	C₂×C₅	semidirect
139. C₃×#441	C₂×C₅	semidirect
141. C₃×#419	C₂×C₅	semidirect
142. C₂×C₃×#103	C₂×C₅	semidirect
186. #3312	C₃×C₅	direct (N × H)
321. #491	C₂×C₃×C₅	semidirect
322. #485	C₂×C₃×C₅	semidirect
323. #483	C₂×C₃×C₅	semidirect
324. #479	C₂×C₃×C₅	semidirect
325. #470	C₂×C₃×C₅	semidirect
326. #467	C₂×C₃×C₅	semidirect
327. #462	C₂×C₃×C₅	semidirect
328. #451	C₂×C₃×C₅	semidirect
329. #451	C₂×C₃×C₅	semidirect
330. #441	C₂×C₃×C₅	semidirect
332. #419	C₂×C₃×C₅	semidirect
333. C₂×#103	C₂×C₃×C₅	semidirect
602. C₃×C₅	#3312	direct (N × H)
671. C₅	C₃×#3312	direct (N × H)
693. C₃	C₅×#3312	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×#552	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#491	2
C₃×C₅×#485	2
C₃×C₅×#483	2
C₃×C₅×#479	2
C₃×C₅×#470	2
C₃×C₅×#467	2
C₃×C₅×#462	2
C₃×C₅×#451	2
C₃×C₅×#441	2
C₃×C₅×#435	2
C₃×C₅×#419	2
C₂×C₃×C₅×#103	2
C₅×#3312	3
C₃×#3312	5

Subgroups — C3×C5×#3312 #14276346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3312 #14276346