Subgroups — C₃×C₅×#3179 #14276213

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#465	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×#405	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3179	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#127	C₂²	1	1	yes	characteristic
25	C₃×C₅×#126	—	2	1	no	—
26	C₃×C₅×#125	C₂²	1	1	yes	characteristic
27	C₃×C₅×#124	—	2	1	no	—
28	C₃×C₅×#124	C₂²	1	1	yes	characteristic
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×#123	—	2	1	no	—
31	C₃×C₅×#123	—	2	1	no	—
32	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#121	—	2	1	no	—
35	C₃×C₅×#121	—	2	1	no	—
36	C₃×C₅×#121	C₂²	1	1	yes	characteristic
37	C₃×C₅×#121	C₂²	1	1	yes	characteristic
38	C₃×C₅×#121	C₂²	1	1	yes	characteristic
39	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
40	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
42	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
43	C₃×C₅×#117	C₂²	1	1	yes	characteristic
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic
45	C₃×C₅×#107	C₂²	1	1	yes	characteristic
46	C₃×C₅×#106	C₂²	1	1	yes	characteristic
47	C₃×C₅×#106	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×#97	C₂²	1	1	yes	characteristic
57	C₃×C₅×#97	C₂²	1	1	yes	characteristic
58	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3179	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#501	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#469	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#465	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×#405	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×C₃×C₅×Q₈	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×D₄	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	—	2	1	no	—
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₃×C₅×SD₁₆	—	2	2	no	—
91	C₃×C₅×SD₁₆	—	2	2	no	—
92	C₃×C₅×D₈	—	2	2	no	—
93	C₃×C₅×D₈	—	2	2	no	—
94	C₃×C₅×M₁₆	—	2	2	no	—
95	C₂×C₃×C₅×C₈	—	2	2	no	—
96	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	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	D₄	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#542	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#501	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#469	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#465	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×#405	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
146	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
147	C₅×#127	C₂²×C₃	1	1	yes	characteristic
148	C₅×#126	—	2	1	no	—
149	C₅×#125	C₂²×C₃	1	1	yes	characteristic
150	C₅×#124	—	2	1	no	—
151	C₅×#124	C₂²×C₃	1	1	yes	characteristic
152	C₅×#123	—	2	1	no	—
153	C₅×#123	—	2	1	no	—
154	C₅×#123	—	2	1	no	—
155	C₅×C₂²⋊Q₈	—	2	1	no	—
156	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
157	C₅×#121	—	2	1	no	—
158	C₅×#121	—	2	1	no	—
159	C₅×#121	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	C₂²×C₃	1	1	yes	characteristic
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic
162	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₅×#117	C₂²×C₃	1	1	yes	characteristic
167	C₅×#107	C₂²×C₃	1	1	yes	characteristic
168	C₅×#107	C₂²×C₃	1	1	yes	characteristic
169	C₅×#106	C₂²×C₃	1	1	yes	characteristic
170	C₅×#106	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×#97	C₂²×C₃	1	1	yes	characteristic
180	C₅×#97	C₂²×C₃	1	1	yes	characteristic
181	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
182	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
183	#3179	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	—	2	1	no	—
190	C₃×C₅×Q₈	—	8	1	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	—	2	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	—	8	1	no	—
201	C₃×C₅×D₄	—	8	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	—	8	1	no	—
210	C₂×C₃×C₄×C₅	—	8	1	no	—
211	C₂×C₃×C₄×C₅	—	8	1	no	—
212	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
218	C₃×C₅×C₈	—	2	1	no	—
219	C₃×C₅×C₈	—	2	1	no	—
220	C₃×C₅×C₈	#41	1	2	yes	—
221	C₃×C₅×C₈	#41	1	2	yes	—
222	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
228	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
229	C₃×#127	C₂²×C₅	1	1	yes	characteristic
230	C₃×#126	—	2	1	no	—
231	C₃×#125	C₂²×C₅	1	1	yes	characteristic
232	C₃×#124	—	2	1	no	—
233	C₃×#124	C₂²×C₅	1	1	yes	characteristic
234	C₃×#123	—	2	1	no	—
235	C₃×#123	—	2	1	no	—
236	C₃×#123	—	2	1	no	—
237	C₃×C₂²⋊Q₈	—	2	1	no	—
238	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×#121	—	2	1	no	—
240	C₃×#121	—	2	1	no	—
241	C₃×#121	C₂²×C₅	1	1	yes	characteristic
242	C₃×#121	C₂²×C₅	1	1	yes	characteristic
243	C₃×#121	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
246	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
247	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
248	C₃×#117	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×#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×#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×#97	C₂²×C₅	1	1	yes	characteristic
262	C₃×#97	C₂²×C₅	1	1	yes	characteristic
263	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₅×Q₈	—	2	1	no	—
266	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₅×D₄	—	2	1	no	—
268	C₂×C₅×D₄	—	2	1	no	—
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
275	C₂²×C₄×C₅	—	2	1	no	—
276	C₂²×C₄×C₅	—	2	1	no	—
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
279	C₅×SD₁₆	—	2	2	no	—
280	C₅×SD₁₆	—	2	2	no	—
281	C₅×D₈	—	2	2	no	—
282	C₅×D₈	—	2	2	no	—
283	C₅×M₁₆	—	2	2	no	—
284	C₂×C₅×C₈	—	2	2	no	—
285	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
293	C₅×C₄⋊C₄	—	2	1	no	—
294	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₃×D₄	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×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
310	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
311	C₄²×C₅	—	2	1	no	—
312	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
313	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
314	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
316	#501	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#469	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	C₂²×C₃×C₅	—	2	1	no	—
330	C₂²×C₃×C₅	—	2	1	no	—
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	4	1	no	—
333	C₂²×C₃×C₅	—	4	1	no	—
334	C₂²×C₃×C₅	—	4	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	C₂²×D₄	1	1	yes	characteristic
342	C₃×C₄×C₅	—	2	1	no	—
343	C₃×C₄×C₅	—	2	1	no	—
344	C₃×C₄×C₅	—	2	1	no	—
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	2	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	C₂×#41	1	1	yes	characteristic
353	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
354	C₂×C₃×Q₈	—	2	1	no	—
355	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
356	C₂×C₃×D₄	—	2	1	no	—
357	C₂×C₃×D₄	—	2	1	no	—
358	C₂×C₃×D₄	—	2	1	no	—
359	C₂×C₃×D₄	—	2	1	no	—
360	C₂×C₃×D₄	—	2	1	no	—
361	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
363	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₃×C₄	—	2	1	no	—
365	C₂²×C₃×C₄	—	2	1	no	—
366	C₂²×C₃×C₄	—	2	1	no	—
367	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
368	C₃×SD₁₆	—	2	2	no	—
369	C₃×SD₁₆	—	2	2	no	—
370	C₃×D₈	—	2	2	no	—
371	C₃×D₈	—	2	2	no	—
372	C₃×M₁₆	—	2	2	no	—
373	C₂×C₃×C₈	—	2	2	no	—
374	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
376	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	—	2	1	no	—
379	C₃×C₄⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
384	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
386	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₃×C₂²⋊C₄	—	2	1	no	—
390	C₃×C₂²⋊C₄	—	2	1	no	—
391	C₃×C₂²⋊C₄	—	2	1	no	—
392	C₃×C₂²⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
399	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
400	C₃×C₄²	—	2	1	no	—
401	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
402	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
403	C₂³×C₅	—	2	1	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
407	C₅×Q₈	—	2	1	no	—
408	C₅×Q₈	—	2	1	no	—
409	C₅×Q₈	—	8	1	no	—
410	C₅×D₄	—	2	1	no	—
411	C₅×D₄	—	2	1	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	—	8	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	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	—	8	1	no	—
429	C₂×C₄×C₅	—	8	1	no	—
430	C₂×C₄×C₅	—	8	1	no	—
431	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
432	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
433	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
434	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
435	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
436	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
437	C₅×C₈	—	2	1	no	—
438	C₅×C₈	—	2	1	no	—
439	C₅×C₈	C₃×#41	1	2	yes	—
440	C₅×C₈	C₃×#41	1	2	yes	—
441	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
448	#127	C₂²×C₃×C₅	1	1	yes	characteristic
449	#126	—	2	1	no	—
450	#125	C₂²×C₃×C₅	1	1	yes	characteristic
451	#124	—	2	1	no	—
452	#124	C₂²×C₃×C₅	1	1	yes	characteristic
453	#123	—	2	1	no	—
454	#123	—	2	1	no	—
455	#123	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
458	#121	—	2	1	no	—
459	#121	—	2	1	no	—
460	#121	C₂²×C₃×C₅	1	1	yes	characteristic
461	#121	C₂²×C₃×C₅	1	1	yes	characteristic
462	#121	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₄×Q₈	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	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
467	#117	C₂²×C₃×C₅	1	1	yes	characteristic
468	#107	C₂²×C₃×C₅	1	1	yes	characteristic
469	#107	C₂²×C₃×C₅	1	1	yes	characteristic
470	#106	C₂²×C₃×C₅	1	1	yes	characteristic
471	#106	C₂²×C₃×C₅	1	1	yes	characteristic
472	#103	C₂²×C₃×C₅	1	1	yes	characteristic
473	#103	C₂²×C₃×C₅	1	1	yes	characteristic
474	#102	C₂²×C₃×C₅	1	1	yes	characteristic
475	#102	C₂²×C₃×C₅	1	1	yes	characteristic
476	#102	C₂²×C₃×C₅	1	1	yes	characteristic
477	#102	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	#97	C₂²×C₃×C₅	1	1	yes	characteristic
481	#97	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
484	C₂×C₃×C₅	—	4	1	no	—
485	C₂×C₃×C₅	—	8	1	no	—
486	C₂×C₃×C₅	—	8	1	no	—
487	C₂×C₃×C₅	—	8	1	no	—
488	C₂×C₃×C₅	#532	1	1	yes	characteristic
489	C₂×C₃×C₅	#576	1	1	yes	characteristic
490	C₂×C₃×C₅	#577	1	1	yes	characteristic
491	C₂³×C₃	—	2	1	no	—
492	C₂³×C₃	—	2	1	no	—
493	C₂³×C₃	—	2	1	no	—
494	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
495	C₃×Q₈	—	2	1	no	—
496	C₃×Q₈	—	2	1	no	—
497	C₃×Q₈	—	8	1	no	—
498	C₃×D₄	—	2	1	no	—
499	C₃×D₄	—	2	1	no	—
500	C₃×D₄	—	2	1	no	—
501	C₃×D₄	—	2	1	no	—
502	C₃×D₄	—	2	1	no	—
503	C₃×D₄	—	2	1	no	—
504	C₃×D₄	—	8	1	no	—
505	C₃×D₄	—	8	1	no	—
506	C₃×D₄	—	8	1	no	—
507	C₃×D₄	—	8	1	no	—
508	C₃×D₄	—	8	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	—	8	1	no	—
517	C₂×C₃×C₄	—	8	1	no	—
518	C₂×C₃×C₄	—	8	1	no	—
519	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
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	C₅×#41	1	2	yes	—
528	C₃×C₈	C₅×#41	1	2	yes	—
529	C₂²×C₅	—	2	1	no	—
530	C₂²×C₅	—	2	1	no	—
531	C₂²×C₅	—	2	1	no	—
532	C₂²×C₅	—	4	1	no	—
533	C₂²×C₅	—	4	1	no	—
534	C₂²×C₅	—	4	1	no	—
535	C₂²×C₅	—	4	1	no	—
536	C₂²×C₅	—	4	1	no	—
537	C₂²×C₅	—	4	1	no	—
538	C₂²×C₅	—	4	1	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
542	C₄×C₅	—	2	1	no	—
543	C₄×C₅	—	2	1	no	—
544	C₄×C₅	—	2	1	no	—
545	C₄×C₅	—	2	1	no	—
546	C₄×C₅	—	2	1	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	—	4	1	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
553	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
562	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
563	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
568	SD₁₆	—	2	2	no	—
569	SD₁₆	—	2	2	no	—
570	D₈	—	2	2	no	—
571	D₈	—	2	2	no	—
572	M₁₆	—	2	2	no	—
573	C₂×C₈	—	2	2	no	—
574	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
575	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
576	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
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	C₃×C₅×D₄	1	1	yes	characteristic
584	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
585	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₄⋊C₄	C₂³×C₃×C₅	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	C₂²⋊C₄	—	2	1	no	—
590	C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
599	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
600	C₄²	—	2	1	no	—
601	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
602	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
603	C₃×C₅	#3179	1	1	yes	characteristic, direct product factor, Hall
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	4	1	no	—
608	C₂²×C₃	—	4	1	no	—
609	C₂²×C₃	—	4	1	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	—	4	1	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
617	C₃×C₄	—	2	1	no	—
618	C₃×C₄	—	2	1	no	—
619	C₃×C₄	—	2	1	no	—
620	C₃×C₄	—	2	1	no	—
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	4	1	no	—
623	C₃×C₄	—	4	1	no	—
624	C₃×C₄	—	4	1	no	—
625	C₃×C₄	—	4	1	no	—
626	C₃×C₄	—	4	1	no	—
627	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
628	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
629	C₂×C₅	—	4	1	no	—
630	C₂×C₅	—	8	1	no	—
631	C₂×C₅	—	8	1	no	—
632	C₂×C₅	—	8	1	no	—
633	C₂×C₅	C₃×#532	1	1	yes	characteristic
634	C₂×C₅	C₃×#576	1	1	yes	characteristic
635	C₂×C₅	C₃×#577	1	1	yes	characteristic
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
640	Q₈	—	2	1	no	—
641	Q₈	—	2	1	no	—
642	Q₈	—	8	1	no	—
643	D₄	—	2	1	no	—
644	D₄	—	2	1	no	—
645	D₄	—	2	1	no	—
646	D₄	—	2	1	no	—
647	D₄	—	2	1	no	—
648	D₄	—	2	1	no	—
649	D₄	—	8	1	no	—
650	D₄	—	8	1	no	—
651	D₄	—	8	1	no	—
652	D₄	—	8	1	no	—
653	D₄	—	8	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	8	1	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
665	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
666	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
667	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
668	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
669	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
670	C₈	—	2	1	no	—
671	C₈	—	2	1	no	—
672	C₈	C₃×C₅×#41	1	2	yes	—
673	C₈	C₃×C₅×#41	1	2	yes	—
674	C₂×C₃	—	4	1	no	—
675	C₂×C₃	—	8	1	no	—
676	C₂×C₃	—	8	1	no	—
677	C₂×C₃	—	8	1	no	—
678	C₂×C₃	C₅×#532	1	1	yes	characteristic
679	C₂×C₃	C₅×#576	1	1	yes	characteristic
680	C₂×C₃	C₅×#577	1	1	yes	characteristic
681	C₅	C₃×#3179	1	1	yes	characteristic, direct product factor, Sylow
682	C₂²	—	2	1	no	—
683	C₂²	—	2	1	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
706	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
707	C₃	C₅×#3179	1	1	yes	characteristic, direct product factor, Sylow
708	C₂	—	4	1	no	—
709	C₂	—	8	1	no	—
710	C₂	—	8	1	no	—
711	C₂	—	8	1	no	—
712	C₂	C₃×C₅×#532	1	1	yes	characteristic
713	C₂	C₃×C₅×#576	1	1	yes	characteristic
714	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×#542	C₂	semidirect
2. C₃×C₅×#540	C₂	semidirect
3. C₃×C₅×#501	C₂	semidirect
4. C₃×C₅×#496	C₂	semidirect
5. C₃×C₅×#488	C₂	semidirect
6. C₃×C₅×#486	C₂	semidirect
7. C₃×C₅×#469	C₂	semidirect
8. C₃×C₅×#468	C₂	semidirect
9. C₃×C₅×#466	C₂	semidirect
10. C₃×C₅×#465	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×#405	C₂	semidirect
16. C₅×#3179	C₃	direct (N × H)
60. C₃×#3179	C₅	direct (N × H)
61. C₅×#542	C₂×C₃	semidirect
62. C₅×#540	C₂×C₃	semidirect
63. C₅×#501	C₂×C₃	semidirect
64. C₅×#496	C₂×C₃	semidirect
65. C₅×#488	C₂×C₃	semidirect
66. C₅×#486	C₂×C₃	semidirect
67. C₅×#469	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#466	C₂×C₃	semidirect
70. C₅×#465	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×#405	C₂×C₃	semidirect
125. C₃×#542	C₂×C₅	semidirect
126. C₃×#540	C₂×C₅	semidirect
127. C₃×#501	C₂×C₅	semidirect
128. C₃×#496	C₂×C₅	semidirect
129. C₃×#488	C₂×C₅	semidirect
130. C₃×#486	C₂×C₅	semidirect
131. C₃×#469	C₂×C₅	semidirect
132. C₃×#468	C₂×C₅	semidirect
133. C₃×#466	C₂×C₅	semidirect
134. C₃×#465	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×#405	C₂×C₅	semidirect
183. #3179	C₃×C₅	direct (N × H)
314. #542	C₂×C₃×C₅	semidirect
315. #540	C₂×C₃×C₅	semidirect
316. #501	C₂×C₃×C₅	semidirect
317. #496	C₂×C₃×C₅	semidirect
318. #488	C₂×C₃×C₅	semidirect
319. #486	C₂×C₃×C₅	semidirect
320. #469	C₂×C₃×C₅	semidirect
321. #468	C₂×C₃×C₅	semidirect
322. #466	C₂×C₃×C₅	semidirect
323. #465	C₂×C₃×C₅	semidirect
324. #442	C₂×C₃×C₅	semidirect
325. #440	C₂×C₃×C₅	semidirect
326. C₄×SD₁₆	C₂×C₃×C₅	semidirect
327. C₄×D₈	C₂×C₃×C₅	semidirect
328. #405	C₂×C₃×C₅	semidirect
603. C₃×C₅	#3179	direct (N × H)
681. C₅	C₃×#3179	direct (N × H)
707. C₃	C₅×#3179	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×#542	2
C₃×C₅×#540	2
C₃×C₅×#501	2
C₃×C₅×#496	2
C₃×C₅×#488	2
C₃×C₅×#486	2
C₃×C₅×#469	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#465	2
C₃×C₅×#442	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#405	2
C₅×#3179	3
C₃×#3179	5

Subgroups — C3×C5×#3179 #14276213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3179 #14276213