Subgroups — C₃×C₅×#3199 #14276233

Order 1920.

884 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#535	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#482	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#469	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#447	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#3199	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
10	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
11	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×#127	—	2	2	no	—
15	C₃×C₅×#124	—	2	2	no	—
16	C₃×C₅×#121	C₂²	1	4	yes	—
17	C₃×C₅×#121	C₂²	1	4	yes	complemented
18	C₃×C₅×#120	—	2	2	no	—
19	C₃×C₅×#120	—	2	2	no	—
20	C₃×C₅×#117	C₂²	1	2	yes	complemented
21	C₃×C₅×#107	C₂²	1	2	yes	complemented
22	C₃×C₅×#106	C₂²	1	2	yes	complemented
23	C₃×C₅×#102	C₂²	1	4	yes	complemented
24	C₃×C₅×#102	C₂²	1	4	yes	complemented
25	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
26	C₃×#3199	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#535	C₂×C₃	1	2	yes	complemented
28	C₅×#482	C₂×C₃	1	4	yes	complemented
29	C₅×#469	C₂×C₃	1	2	yes	complemented
30	C₅×#466	C₂×C₃	1	2	yes	complemented
31	C₅×#447	C₂×C₃	1	4	yes	complemented
32	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂⁴×C₃×C₅	—	2	2	no	—
34	C₃×C₅×#41	—	4	1	no	—
35	C₃×C₅×#41	—	4	1	no	—
36	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	4	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	—	4	2	no	—
41	C₂×C₃×C₅×D₄	—	4	2	no	—
42	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
44	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₃×C₅×D₈	—	4	2	no	—
48	C₃×C₅×D₈	—	4	2	no	—
49	C₃×C₅×M₁₆	—	4	1	no	—
50	C₂×C₃×C₅×C₈	—	4	1	no	—
51	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
54	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
55	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
56	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
57	C₃×C₄²×C₅	—	2	2	no	—
58	C₃×#535	C₂×C₅	1	2	yes	complemented
59	C₃×#482	C₂×C₅	1	4	yes	complemented
60	C₃×#469	C₂×C₅	1	2	yes	complemented
61	C₃×#466	C₂×C₅	1	2	yes	complemented
62	C₃×#447	C₂×C₅	1	4	yes	complemented
63	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
66	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
67	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
68	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
69	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
70	C₅×#127	—	2	2	no	—
71	C₅×#124	—	2	2	no	—
72	C₅×#121	C₂²×C₃	1	4	yes	—
73	C₅×#121	C₂²×C₃	1	4	yes	complemented
74	C₅×#120	—	2	2	no	—
75	C₅×#120	—	2	2	no	—
76	C₅×#117	C₂²×C₃	1	2	yes	complemented
77	C₅×#107	C₂²×C₃	1	2	yes	complemented
78	C₅×#106	C₂²×C₃	1	2	yes	complemented
79	C₅×#102	C₂²×C₃	1	4	yes	complemented
80	C₅×#102	C₂²×C₃	1	4	yes	complemented
81	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
82	#3199	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	—	2	4	no	—
84	C₂³×C₃×C₅	—	4	4	no	—
85	C₂³×C₃×C₅	—	8	4	no	—
86	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
87	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	2	4	no	—
91	C₃×C₅×D₄	—	4	2	no	—
92	C₃×C₅×D₄	—	4	1	no	—
93	C₃×C₅×D₄	—	4	4	no	—
94	C₃×C₅×D₄	—	8	4	no	—
95	C₃×C₅×D₄	—	8	4	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
104	C₃×C₅×C₈	—	2	2	no	—
105	C₃×C₅×C₈	—	2	2	no	—
106	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
108	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
109	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
110	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
112	C₃×#127	—	2	2	no	—
113	C₃×#124	—	2	2	no	—
114	C₃×#121	C₂²×C₅	1	4	yes	—
115	C₃×#121	C₂²×C₅	1	4	yes	complemented
116	C₃×#120	—	2	2	no	—
117	C₃×#120	—	2	2	no	—
118	C₃×#117	C₂²×C₅	1	2	yes	complemented
119	C₃×#107	C₂²×C₅	1	2	yes	complemented
120	C₃×#106	C₂²×C₅	1	2	yes	complemented
121	C₃×#102	C₂²×C₅	1	4	yes	complemented
122	C₃×#102	C₂²×C₅	1	4	yes	complemented
123	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
124	C₂⁴×C₅	—	2	2	no	—
125	C₅×#41	—	4	1	no	—
126	C₅×#41	—	4	1	no	—
127	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
128	C₂×C₅×D₄	—	2	4	no	—
129	C₂×C₅×D₄	—	2	4	no	—
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	4	2	no	—
132	C₂×C₅×D₄	—	4	2	no	—
133	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
134	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
135	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
136	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
138	C₅×D₈	—	4	2	no	—
139	C₅×D₈	—	4	2	no	—
140	C₅×M₁₆	—	4	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
143	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
144	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
145	C₅×C₂²⋊C₄	—	2	2	no	—
146	C₅×C₂²⋊C₄	—	2	4	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₄²×C₅	—	2	2	no	—
149	#535	C₂×C₃×C₅	1	2	yes	complemented
150	#482	C₂×C₃×C₅	1	4	yes	complemented
151	#469	C₂×C₃×C₅	1	2	yes	complemented
152	#466	C₂×C₃×C₅	1	2	yes	complemented
153	#447	C₂×C₃×C₅	1	4	yes	complemented
154	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	2	no	—
158	C₂²×C₃×C₅	—	2	4	no	—
159	C₂²×C₃×C₅	—	4	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	—	4	4	no	—
162	C₂²×C₃×C₅	—	8	8	no	—
163	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	4	no	—
167	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
168	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂⁴×C₃	—	2	2	no	—
170	C₃×#41	—	4	1	no	—
171	C₃×#41	—	4	1	no	—
172	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	4	2	no	—
177	C₂×C₃×D₄	—	4	2	no	—
178	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
179	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
180	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
183	C₃×D₈	—	4	2	no	—
184	C₃×D₈	—	4	2	no	—
185	C₃×M₁₆	—	4	1	no	—
186	C₂×C₃×C₈	—	4	1	no	—
187	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
188	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
189	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	—	2	4	no	—
192	C₃×C₂²⋊C₄	—	2	4	no	—
193	C₃×C₄²	—	2	2	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	4	4	no	—
196	C₂³×C₅	—	8	4	no	—
197	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
198	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
199	C₅×Q₈	—	4	1	no	—
200	C₅×D₄	—	2	4	no	—
201	C₅×D₄	—	2	4	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	1	no	—
204	C₅×D₄	—	4	4	no	—
205	C₅×D₄	—	8	4	no	—
206	C₅×D₄	—	8	4	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
215	C₅×C₈	—	2	2	no	—
216	C₅×C₈	—	2	2	no	—
217	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
219	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
220	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
221	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
222	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
223	#127	—	2	2	no	—
224	#124	—	2	2	no	—
225	#121	C₂²×C₃×C₅	1	4	yes	—
226	#121	C₂²×C₃×C₅	1	4	yes	complemented
227	#120	—	2	2	no	—
228	#120	—	2	2	no	—
229	#117	C₂²×C₃×C₅	1	2	yes	complemented
230	#107	C₂²×C₃×C₅	1	2	yes	complemented
231	#106	C₂²×C₃×C₅	1	2	yes	complemented
232	#102	C₂²×C₃×C₅	1	4	yes	complemented
233	#102	C₂²×C₃×C₅	1	4	yes	complemented
234	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
235	C₂×C₃×C₅	—	4	1	no	—
236	C₂×C₃×C₅	—	4	2	no	—
237	C₂×C₃×C₅	—	8	4	no	—
238	C₂×C₃×C₅	#534	1	1	yes	characteristic
239	C₂×C₃×C₅	#576	1	2	yes	—
240	C₂³×C₃	—	2	4	no	—
241	C₂³×C₃	—	4	4	no	—
242	C₂³×C₃	—	8	4	no	—
243	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
244	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
245	C₃×Q₈	—	4	1	no	—
246	C₃×D₄	—	2	4	no	—
247	C₃×D₄	—	2	4	no	—
248	C₃×D₄	—	4	2	no	—
249	C₃×D₄	—	4	1	no	—
250	C₃×D₄	—	4	4	no	—
251	C₃×D₄	—	8	4	no	—
252	C₃×D₄	—	8	4	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
261	C₃×C₈	—	2	2	no	—
262	C₃×C₈	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	2	no	—
266	C₂²×C₅	—	2	1	no	—
267	C₂²×C₅	—	4	4	no	—
268	C₂²×C₅	—	4	4	no	—
269	C₂²×C₅	—	4	4	no	—
270	C₂²×C₅	—	8	8	no	—
271	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	1	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
276	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
277	C₂⁴	—	2	2	no	—
278	#41	—	4	1	no	—
279	#41	—	4	1	no	—
280	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
287	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
288	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
289	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
290	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
291	D₈	—	4	2	no	—
292	D₈	—	4	2	no	—
293	M₁₆	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
296	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
297	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₄²	—	2	2	no	—
302	C₃×C₅	#3199	1	1	yes	characteristic, direct product factor, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	—	2	1	no	—
305	C₂²×C₃	—	2	2	no	—
306	C₂²×C₃	—	2	4	no	—
307	C₂²×C₃	—	4	4	no	—
308	C₂²×C₃	—	4	4	no	—
309	C₂²×C₃	—	4	4	no	—
310	C₂²×C₃	—	8	8	no	—
311	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
312	C₃×C₄	—	2	2	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	4	no	—
315	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
316	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₅	—	4	2	no	—
318	C₂×C₅	—	4	1	no	—
319	C₂×C₅	—	8	4	no	—
320	C₂×C₅	C₃×#534	1	1	yes	characteristic
321	C₂×C₅	C₃×#576	1	2	yes	—
322	C₂³	—	2	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	8	4	no	—
325	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
326	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
327	Q₈	—	4	1	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	4	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
341	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₂×C₃	—	4	2	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	—	8	4	no	—
348	C₂×C₃	C₅×#534	1	1	yes	characteristic
349	C₂×C₃	C₅×#576	1	2	yes	—
350	C₅	C₃×#3199	1	1	yes	characteristic, direct product factor, Sylow
351	C₂²	—	2	2	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	8	8	no	—
359	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	1	no	—
362	C₄	—	4	4	no	—
363	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
364	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
365	C₃	C₅×#3199	1	1	yes	characteristic, direct product factor, Sylow
366	C₂	—	4	2	no	—
367	C₂	—	4	1	no	—
368	C₂	—	8	4	no	—
369	C₂	C₃×C₅×#534	1	1	yes	characteristic
370	C₂	C₃×C₅×#576	1	2	yes	—

	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 ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#535	C₂	semidirect
2. C₃×C₅×#482	C₂	semidirect
3. C₃×C₅×#469	C₂	semidirect
4. C₃×C₅×#466	C₂	semidirect
5. C₃×C₅×#447	C₂	semidirect
6. C₃×C₅×#408	C₂	semidirect
7. C₅×#3199	C₃	direct (N × H)
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
12. C₂×C₃×C₅×M₁₆	C₂²	semidirect
13. C₂²×C₃×C₅×C₈	C₂²	semidirect
17. C₃×C₅×#121	C₂²	semidirect
20. C₃×C₅×#117	C₂²	semidirect
21. C₃×C₅×#107	C₂²	semidirect
22. C₃×C₅×#106	C₂²	semidirect
23. C₃×C₅×#102	C₂²	semidirect
24. C₃×C₅×#102	C₂²	semidirect
25. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
26. C₃×#3199	C₅	direct (N × H)
27. C₅×#535	C₂×C₃	semidirect
28. C₅×#482	C₂×C₃	semidirect
29. C₅×#469	C₂×C₃	semidirect
30. C₅×#466	C₂×C₃	semidirect
31. C₅×#447	C₂×C₃	semidirect
32. C₅×#408	C₂×C₃	semidirect
58. C₃×#535	C₂×C₅	semidirect
59. C₃×#482	C₂×C₅	semidirect
60. C₃×#469	C₂×C₅	semidirect
61. C₃×#466	C₂×C₅	semidirect
62. C₃×#447	C₂×C₅	semidirect
63. C₃×#408	C₂×C₅	semidirect
65. C₂²×C₅×D₄	C₂²×C₃	semidirect
68. C₂×C₅×M₁₆	C₂²×C₃	semidirect
69. C₂²×C₅×C₈	C₂²×C₃	semidirect
73. C₅×#121	C₂²×C₃	semidirect
76. C₅×#117	C₂²×C₃	semidirect
77. C₅×#107	C₂²×C₃	semidirect
78. C₅×#106	C₂²×C₃	semidirect
79. C₅×#102	C₂²×C₃	semidirect
80. C₅×#102	C₂²×C₃	semidirect
81. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
82. #3199	C₃×C₅	direct (N × H)
107. C₂²×C₃×D₄	C₂²×C₅	semidirect
110. C₂×C₃×M₁₆	C₂²×C₅	semidirect
111. C₂²×C₃×C₈	C₂²×C₅	semidirect
115. C₃×#121	C₂²×C₅	semidirect
118. C₃×#117	C₂²×C₅	semidirect
119. C₃×#107	C₂²×C₅	semidirect
120. C₃×#106	C₂²×C₅	semidirect
121. C₃×#102	C₂²×C₅	semidirect
122. C₃×#102	C₂²×C₅	semidirect
123. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
149. #535	C₂×C₃×C₅	semidirect
150. #482	C₂×C₃×C₅	semidirect
151. #469	C₂×C₃×C₅	semidirect
152. #466	C₂×C₃×C₅	semidirect
153. #447	C₂×C₃×C₅	semidirect
154. #408	C₂×C₃×C₅	semidirect
218. C₂²×D₄	C₂²×C₃×C₅	semidirect
221. C₂×M₁₆	C₂²×C₃×C₅	semidirect
222. C₂²×C₈	C₂²×C₃×C₅	semidirect
226. #121	C₂²×C₃×C₅	semidirect
229. #117	C₂²×C₃×C₅	semidirect
230. #107	C₂²×C₃×C₅	semidirect
231. #106	C₂²×C₃×C₅	semidirect
232. #102	C₂²×C₃×C₅	semidirect
233. #102	C₂²×C₃×C₅	semidirect
234. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
302. C₃×C₅	#3199	direct (N × H)
350. C₅	C₃×#3199	direct (N × H)
365. C₃	C₅×#3199	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×#535	2
C₃×C₅×#482	2
C₃×C₅×#469	2
C₃×C₅×#466	2
C₃×C₅×#447	2
C₃×C₅×#408	2
C₅×#3199	3
C₃×#3199	5

Subgroups — C3×C5×#3199 #14276233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3199 #14276233