Subgroups — C₃×C₅×#3178 #14276212

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 668 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
2	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#465	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×#405	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3178	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	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×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#126	—	2	1	no	—
26	C₃×C₅×#126	—	2	1	no	—
27	C₃×C₅×#126	—	2	1	no	—
28	C₃×C₅×#125	—	2	1	no	—
29	C₃×C₅×#125	—	2	1	no	—
30	C₃×C₅×#125	C₂²	1	1	yes	characteristic
31	C₃×C₅×#124	—	2	1	no	—
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#123	—	2	1	no	—
34	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₂²⋊Q₈	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×Q₈	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×Q₈	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×#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×#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×#3178	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic
62	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#501	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#470	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic
69	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#465	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×#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×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	—	2	1	no	—
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₅×Q₁₆	—	2	2	no	—
85	C₃×C₅×Q₁₆	—	2	2	no	—
86	C₃×C₅×SD₁₆	—	2	2	no	—
87	C₃×C₅×SD₁₆	—	2	2	no	—
88	C₃×C₅×M₁₆	—	2	2	no	—
89	C₂×C₃×C₅×C₈	—	2	2	no	—
90	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₃×C₅×C₄⋊C₄	—	2	1	no	—
95	C₃×C₅×C₄⋊C₄	—	2	1	no	—
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	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	D₄	1	1	yes	characteristic
119	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
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×#542	C₂×C₅	1	1	yes	characteristic
126	C₃×#541	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#501	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#470	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#468	C₂×C₅	1	1	yes	characteristic
133	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#465	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×#405	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×SD₁₆	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×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
148	C₅×#126	—	2	1	no	—
149	C₅×#126	—	2	1	no	—
150	C₅×#126	—	2	1	no	—
151	C₅×#125	—	2	1	no	—
152	C₅×#125	—	2	1	no	—
153	C₅×#125	C₂²×C₃	1	1	yes	characteristic
154	C₅×#124	—	2	1	no	—
155	C₅×#124	C₂²×C₃	1	1	yes	characteristic
156	C₅×#123	—	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×#121	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×Q₈	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×#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×#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	#3178	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	—	2	1	no	—
192	C₃×C₅×Q₈	—	8	1	no	—
193	C₃×C₅×D₄	—	2	1	no	—
194	C₃×C₅×D₄	—	2	1	no	—
195	C₃×C₅×D₄	—	8	1	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	C₂×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
212	C₃×C₅×C₈	—	2	1	no	—
213	C₃×C₅×C₈	—	2	1	no	—
214	C₃×C₅×C₈	#41	1	2	yes	—
215	C₃×C₅×C₈	#41	1	2	yes	—
216	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
222	C₃×C₄⋊Q₈	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×#126	—	2	1	no	—
227	C₃×#125	—	2	1	no	—
228	C₃×#125	—	2	1	no	—
229	C₃×#125	C₂²×C₅	1	1	yes	characteristic
230	C₃×#124	—	2	1	no	—
231	C₃×#124	C₂²×C₅	1	1	yes	characteristic
232	C₃×#123	—	2	1	no	—
233	C₃×C₂²⋊Q₈	—	2	1	no	—
234	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
235	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
237	C₃×#121	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
239	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
242	C₃×#117	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×#103	C₂²×C₅	1	1	yes	characteristic
248	C₃×#103	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×#102	C₂²×C₅	1	1	yes	characteristic
254	C₃×#102	C₂²×C₅	1	1	yes	characteristic
255	C₃×#97	C₂²×C₅	1	1	yes	characteristic
256	C₃×#97	C₂²×C₅	1	1	yes	characteristic
257	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
258	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₅×Q₈	—	2	1	no	—
260	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
262	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₅×D₄	—	2	1	no	—
264	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	—	2	1	no	—
266	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₅×Q₁₆	—	2	2	no	—
268	C₅×Q₁₆	—	2	2	no	—
269	C₅×SD₁₆	—	2	2	no	—
270	C₅×SD₁₆	—	2	2	no	—
271	C₅×M₁₆	—	2	2	no	—
272	C₂×C₅×C₈	—	2	2	no	—
273	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
277	C₅×C₄⋊C₄	—	2	1	no	—
278	C₅×C₄⋊C₄	—	2	1	no	—
279	C₅×C₄⋊C₄	—	2	1	no	—
280	C₅×C₄⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
289	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
290	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
292	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
293	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
294	C₅×C₂²⋊C₄	—	2	1	no	—
295	C₅×C₂²⋊C₄	—	2	1	no	—
296	C₅×C₂²⋊C₄	—	2	1	no	—
297	C₅×C₂²⋊C₄	—	2	1	no	—
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	C₃×D₄	1	1	yes	characteristic
302	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
303	C₄²×C₅	—	2	1	no	—
304	C₄²×C₅	—	2	1	no	—
305	C₄²×C₅	—	2	1	no	—
306	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
307	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
308	#542	C₂×C₃×C₅	1	1	yes	characteristic
309	#541	C₂×C₃×C₅	1	1	yes	characteristic, complemented
310	#501	C₂×C₃×C₅	1	1	yes	characteristic, complemented
311	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
312	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
313	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
314	#470	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	#468	C₂×C₃×C₅	1	1	yes	characteristic
316	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#465	C₂×C₃×C₅	1	1	yes	characteristic
318	#441	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	C₂²×C₃×C₅	—	2	1	no	—
324	C₂²×C₃×C₅	—	2	1	no	—
325	C₂²×C₃×C₅	—	2	1	no	—
326	C₂²×C₃×C₅	—	4	1	no	—
327	C₂²×C₃×C₅	—	4	1	no	—
328	C₂²×C₃×C₅	—	4	1	no	—
329	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₃×C₄×C₅	—	2	1	no	—
331	C₃×C₄×C₅	—	2	1	no	—
332	C₃×C₄×C₅	—	2	1	no	—
333	C₃×C₄×C₅	—	2	1	no	—
334	C₃×C₄×C₅	—	2	1	no	—
335	C₃×C₄×C₅	—	4	1	no	—
336	C₃×C₄×C₅	—	4	1	no	—
337	C₃×C₄×C₅	—	4	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	C₂×#41	1	1	yes	characteristic
343	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
344	C₂×C₃×Q₈	—	2	1	no	—
345	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
346	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
348	C₂×C₃×D₄	—	2	1	no	—
349	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	—	2	1	no	—
351	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
352	C₃×Q₁₆	—	2	2	no	—
353	C₃×Q₁₆	—	2	2	no	—
354	C₃×SD₁₆	—	2	2	no	—
355	C₃×SD₁₆	—	2	2	no	—
356	C₃×M₁₆	—	2	2	no	—
357	C₂×C₃×C₈	—	2	2	no	—
358	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
362	C₃×C₄⋊C₄	—	2	1	no	—
363	C₃×C₄⋊C₄	—	2	1	no	—
364	C₃×C₄⋊C₄	—	2	1	no	—
365	C₃×C₄⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
374	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
375	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
376	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
377	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
378	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
379	C₃×C₂²⋊C₄	—	2	1	no	—
380	C₃×C₂²⋊C₄	—	2	1	no	—
381	C₃×C₂²⋊C₄	—	2	1	no	—
382	C₃×C₂²⋊C₄	—	2	1	no	—
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	C₅×D₄	1	1	yes	characteristic
387	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
388	C₃×C₄²	—	2	1	no	—
389	C₃×C₄²	—	2	1	no	—
390	C₃×C₄²	—	2	1	no	—
391	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
392	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
393	C₂³×C₅	—	2	1	no	—
394	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
395	C₅×Q₈	—	2	1	no	—
396	C₅×Q₈	—	2	1	no	—
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	—	8	1	no	—
402	C₅×D₄	—	2	1	no	—
403	C₅×D₄	—	2	1	no	—
404	C₅×D₄	—	8	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	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	—	8	1	no	—
415	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
416	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
417	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
419	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
420	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
421	C₅×C₈	—	2	1	no	—
422	C₅×C₈	—	2	1	no	—
423	C₅×C₈	C₃×#41	1	2	yes	—
424	C₅×C₈	C₃×#41	1	2	yes	—
425	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
426	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
427	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
428	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
429	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
431	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
433	#126	—	2	1	no	—
434	#126	—	2	1	no	—
435	#126	—	2	1	no	—
436	#125	—	2	1	no	—
437	#125	—	2	1	no	—
438	#125	C₂²×C₃×C₅	1	1	yes	characteristic
439	#124	—	2	1	no	—
440	#124	C₂²×C₃×C₅	1	1	yes	characteristic
441	#123	—	2	1	no	—
442	C₂²⋊Q₈	—	2	1	no	—
443	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
446	#121	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
451	#117	C₂²×C₃×C₅	1	1	yes	characteristic
452	#107	C₂²×C₃×C₅	1	1	yes	characteristic
453	#107	C₂²×C₃×C₅	1	1	yes	characteristic
454	#106	C₂²×C₃×C₅	1	1	yes	characteristic
455	#106	C₂²×C₃×C₅	1	1	yes	characteristic
456	#103	C₂²×C₃×C₅	1	1	yes	characteristic
457	#103	C₂²×C₃×C₅	1	1	yes	characteristic
458	#103	C₂²×C₃×C₅	1	1	yes	characteristic
459	#103	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	#102	C₂²×C₃×C₅	1	1	yes	characteristic
463	#102	C₂²×C₃×C₅	1	1	yes	characteristic
464	#97	C₂²×C₃×C₅	1	1	yes	characteristic
465	#97	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₂×C₃×C₅	—	4	1	no	—
469	C₂×C₃×C₅	—	8	1	no	—
470	C₂×C₃×C₅	#532	1	1	yes	characteristic
471	C₂×C₃×C₅	#577	1	1	yes	characteristic
472	C₂×C₃×C₅	#578	1	1	yes	characteristic
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
475	C₃×Q₈	—	2	1	no	—
476	C₃×Q₈	—	2	1	no	—
477	C₃×Q₈	—	2	1	no	—
478	C₃×Q₈	—	2	1	no	—
479	C₃×Q₈	—	2	1	no	—
480	C₃×Q₈	—	2	1	no	—
481	C₃×Q₈	—	8	1	no	—
482	C₃×D₄	—	2	1	no	—
483	C₃×D₄	—	2	1	no	—
484	C₃×D₄	—	8	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	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	—	8	1	no	—
495	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
498	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
500	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
501	C₃×C₈	—	2	1	no	—
502	C₃×C₈	—	2	1	no	—
503	C₃×C₈	C₅×#41	1	2	yes	—
504	C₃×C₈	C₅×#41	1	2	yes	—
505	C₂²×C₅	—	2	1	no	—
506	C₂²×C₅	—	2	1	no	—
507	C₂²×C₅	—	2	1	no	—
508	C₂²×C₅	—	4	1	no	—
509	C₂²×C₅	—	4	1	no	—
510	C₂²×C₅	—	4	1	no	—
511	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
512	C₄×C₅	—	2	1	no	—
513	C₄×C₅	—	2	1	no	—
514	C₄×C₅	—	2	1	no	—
515	C₄×C₅	—	2	1	no	—
516	C₄×C₅	—	2	1	no	—
517	C₄×C₅	—	4	1	no	—
518	C₄×C₅	—	4	1	no	—
519	C₄×C₅	—	4	1	no	—
520	C₄×C₅	—	4	1	no	—
521	C₄×C₅	—	4	1	no	—
522	C₄×C₅	—	4	1	no	—
523	C₄×C₅	—	4	1	no	—
524	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
525	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
528	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
529	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
534	Q₁₆	—	2	2	no	—
535	Q₁₆	—	2	2	no	—
536	SD₁₆	—	2	2	no	—
537	SD₁₆	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	C₂×C₈	—	2	2	no	—
540	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
541	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
542	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
543	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
556	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
557	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
558	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
559	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
560	C₄⋊C₄	C₂³×C₃×C₅	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	—	2	1	no	—
565	C₂²⋊C₄	—	2	1	no	—
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
569	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
570	C₄²	—	2	1	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
574	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
575	C₃×C₅	#3178	1	1	yes	characteristic, direct product factor, Hall
576	C₂²×C₃	—	2	1	no	—
577	C₂²×C₃	—	2	1	no	—
578	C₂²×C₃	—	2	1	no	—
579	C₂²×C₃	—	4	1	no	—
580	C₂²×C₃	—	4	1	no	—
581	C₂²×C₃	—	4	1	no	—
582	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	1	no	—
586	C₃×C₄	—	2	1	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	4	1	no	—
589	C₃×C₄	—	4	1	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	1	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
596	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
597	C₂×C₅	—	4	1	no	—
598	C₂×C₅	—	8	1	no	—
599	C₂×C₅	C₃×#532	1	1	yes	characteristic
600	C₂×C₅	C₃×#577	1	1	yes	characteristic
601	C₂×C₅	C₃×#578	1	1	yes	characteristic
602	C₂³	—	2	1	no	—
603	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
604	Q₈	—	2	1	no	—
605	Q₈	—	2	1	no	—
606	Q₈	—	2	1	no	—
607	Q₈	—	2	1	no	—
608	Q₈	—	2	1	no	—
609	Q₈	—	2	1	no	—
610	Q₈	—	8	1	no	—
611	D₄	—	2	1	no	—
612	D₄	—	2	1	no	—
613	D₄	—	8	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	8	1	no	—
624	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
625	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
626	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
627	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
628	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
629	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
630	C₈	—	2	1	no	—
631	C₈	—	2	1	no	—
632	C₈	C₃×C₅×#41	1	2	yes	—
633	C₈	C₃×C₅×#41	1	2	yes	—
634	C₂×C₃	—	4	1	no	—
635	C₂×C₃	—	8	1	no	—
636	C₂×C₃	C₅×#532	1	1	yes	characteristic
637	C₂×C₃	C₅×#577	1	1	yes	characteristic
638	C₂×C₃	C₅×#578	1	1	yes	characteristic
639	C₅	C₃×#3178	1	1	yes	characteristic, direct product factor, Sylow
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	1	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
660	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
661	C₃	C₅×#3178	1	1	yes	characteristic, direct product factor, Sylow
662	C₂	—	4	1	no	—
663	C₂	—	8	1	no	—
664	C₂	C₃×C₅×#532	1	1	yes	characteristic
665	C₂	C₃×C₅×#577	1	1	yes	characteristic
666	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	C₃×C₅×#121	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
2. C₃×C₅×#541	C₂	semidirect
3. C₃×C₅×#501	C₂	semidirect
4. C₃×C₅×#497	C₂	semidirect
5. C₃×C₅×#488	C₂	semidirect
6. C₃×C₅×#487	C₂	semidirect
7. C₃×C₅×#470	C₂	semidirect
9. C₃×C₅×#467	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×#405	C₂	semidirect
16. C₅×#3178	C₃	direct (N × H)
60. C₃×#3178	C₅	direct (N × H)
62. C₅×#541	C₂×C₃	semidirect
63. C₅×#501	C₂×C₃	semidirect
64. C₅×#497	C₂×C₃	semidirect
65. C₅×#488	C₂×C₃	semidirect
66. C₅×#487	C₂×C₃	semidirect
67. C₅×#470	C₂×C₃	semidirect
69. C₅×#467	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×#405	C₂×C₃	semidirect
126. C₃×#541	C₂×C₅	semidirect
127. C₃×#501	C₂×C₅	semidirect
128. C₃×#497	C₂×C₅	semidirect
129. C₃×#488	C₂×C₅	semidirect
130. C₃×#487	C₂×C₅	semidirect
131. C₃×#470	C₂×C₅	semidirect
133. C₃×#467	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×#405	C₂×C₅	semidirect
183. #3178	C₃×C₅	direct (N × H)
309. #541	C₂×C₃×C₅	semidirect
310. #501	C₂×C₃×C₅	semidirect
311. #497	C₂×C₃×C₅	semidirect
312. #488	C₂×C₃×C₅	semidirect
313. #487	C₂×C₃×C₅	semidirect
314. #470	C₂×C₃×C₅	semidirect
316. #467	C₂×C₃×C₅	semidirect
318. #441	C₂×C₃×C₅	semidirect
319. #440	C₂×C₃×C₅	semidirect
320. C₄×Q₁₆	C₂×C₃×C₅	semidirect
321. C₄×SD₁₆	C₂×C₃×C₅	semidirect
322. #405	C₂×C₃×C₅	semidirect
575. C₃×C₅	#3178	direct (N × H)
639. C₅	C₃×#3178	direct (N × H)
661. C₃	C₅×#3178	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×#541	2
C₃×C₅×#501	2
C₃×C₅×#497	2
C₃×C₅×#488	2
C₃×C₅×#487	2
C₃×C₅×#470	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#441	2
C₃×C₅×#440	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#405	2
C₅×#3178	3
C₃×#3178	5

Subgroups — C3×C5×#3178 #14276212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3178 #14276212