Subgroups — C₃×C₅×#3291 #14276325

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#577	C₂	1	4	yes	maximal, complemented
2	C₃×C₅×#492	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#471	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#456	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#453	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#443	C₂	1	2	yes	maximal, complemented
7	C₅×#3291	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
9	C₃×C₅×H(5,𝔽₂)	C₂²	1	2	yes	complemented
10	C₃×C₅×#137	—	2	4	no	—
11	C₃×C₅×#137	C₂²	1	4	yes	complemented
12	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
13	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	4	yes	—
14	C₃×C₅×#135	—	2	4	no	—
15	C₃×C₅×#135	C₂²	1	2	yes	—
16	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	complemented
18	C₃×C₅×#131	C₂²	1	4	yes	complemented
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#127	C₂²	1	1	yes	characteristic
21	C₃×C₅×#108	C₂²	1	2	yes	complemented
22	C₃×C₅×#104	C₂²	1	4	yes	complemented
23	C₃×C₅×#101	C₂²	1	2	yes	complemented
24	C₃×C₅×#100	C₂²	1	2	yes	complemented
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃×#3291	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#577	C₂×C₃	1	4	yes	complemented
28	C₅×#492	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#471	C₂×C₃	1	4	yes	complemented
30	C₅×#456	C₂×C₃	1	2	yes	complemented
31	C₅×#453	C₂×C₃	1	2	yes	complemented
32	C₅×#443	C₂×C₃	1	2	yes	complemented
33	C₃×C₅×#41	—	2	4	no	—
34	C₃×C₅×#41	—	2	4	no	—
35	C₃×C₅×#41	—	4	2	no	—
36	C₃×C₅×#41	C₂³	1	4	yes	—
37	C₂×C₃×C₅×Q₈	—	2	4	no	—
38	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
39	C₂×C₃×C₅×D₄	—	2	4	no	—
40	C₂×C₃×C₅×D₄	—	4	1	no	—
41	C₂×C₃×C₅×D₄	—	4	2	no	—
42	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
43	C₃×C₅×Q₁₆	—	2	4	no	—
44	C₃×C₅×Q₁₆	D₄	1	2	yes	complemented
45	C₃×C₅×SD₁₆	—	2	4	no	—
46	C₃×C₅×SD₁₆	—	2	4	no	—
47	C₃×C₅×SD₁₆	—	2	4	no	—
48	C₃×C₅×SD₁₆	—	2	4	no	—
49	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
50	C₃×C₅×D₈	—	2	4	no	—
51	C₃×C₅×D₈	D₄	1	2	yes	complemented
52	C₃×C₅×M₁₆	—	2	4	no	—
53	C₃×C₅×M₁₆	C₂³	1	4	yes	—
54	C₂×C₃×C₅×C₈	—	2	4	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	4	1	no	—
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×#577	C₂×C₅	1	4	yes	complemented
59	C₃×#492	C₂×C₅	1	1	yes	characteristic, complemented
60	C₃×#471	C₂×C₅	1	4	yes	complemented
61	C₃×#456	C₂×C₅	1	2	yes	complemented
62	C₃×#453	C₂×C₅	1	2	yes	complemented
63	C₃×#443	C₂×C₅	1	2	yes	complemented
64	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
65	C₅×H(5,𝔽₂)	C₂²×C₃	1	2	yes	complemented
66	C₅×#137	—	2	4	no	—
67	C₅×#137	C₂²×C₃	1	4	yes	complemented
68	C₅×AGL(1,ℤ/8)	—	2	4	no	—
69	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	—
70	C₅×#135	—	2	4	no	—
71	C₅×#135	C₂²×C₃	1	2	yes	—
72	C₂×C₅×SD₁₆	—	2	4	no	—
73	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	complemented
74	C₅×#131	C₂²×C₃	1	4	yes	complemented
75	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
76	C₅×#127	C₂²×C₃	1	1	yes	characteristic
77	C₅×#108	C₂²×C₃	1	2	yes	complemented
78	C₅×#104	C₂²×C₃	1	4	yes	complemented
79	C₅×#101	C₂²×C₃	1	2	yes	complemented
80	C₅×#100	C₂²×C₃	1	2	yes	complemented
81	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
82	#3291	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	—	4	2	no	—
85	C₃×C₅×Q₈	—	2	4	no	—
86	C₃×C₅×Q₈	—	4	2	no	—
87	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
88	C₃×C₅×D₄	—	2	4	no	—
89	C₃×C₅×D₄	—	2	4	no	—
90	C₃×C₅×D₄	—	4	4	no	—
91	C₃×C₅×D₄	—	4	2	no	—
92	C₃×C₅×D₄	—	8	2	no	—
93	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
98	C₂×C₃×C₄×C₅	—	4	4	no	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
100	C₃×C₅×C₈	—	2	4	no	—
101	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
102	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
103	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
104	C₃×H(5,𝔽₂)	C₂²×C₅	1	2	yes	complemented
105	C₃×#137	—	2	4	no	—
106	C₃×#137	C₂²×C₅	1	4	yes	complemented
107	C₃×AGL(1,ℤ/8)	—	2	4	no	—
108	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	4	yes	—
109	C₃×#135	—	2	4	no	—
110	C₃×#135	C₂²×C₅	1	2	yes	—
111	C₂×C₃×SD₁₆	—	2	4	no	—
112	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	complemented
113	C₃×#131	C₂²×C₅	1	4	yes	complemented
114	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
115	C₃×#127	C₂²×C₅	1	1	yes	characteristic
116	C₃×#108	C₂²×C₅	1	2	yes	complemented
117	C₃×#104	C₂²×C₅	1	4	yes	complemented
118	C₃×#101	C₂²×C₅	1	2	yes	complemented
119	C₃×#100	C₂²×C₅	1	2	yes	complemented
120	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
121	C₅×#41	—	2	4	no	—
122	C₅×#41	—	2	4	no	—
123	C₅×#41	—	4	2	no	—
124	C₅×#41	C₂³×C₃	1	4	yes	—
125	C₂×C₅×Q₈	—	2	4	no	—
126	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
127	C₂×C₅×D₄	—	2	4	no	—
128	C₂×C₅×D₄	—	4	1	no	—
129	C₂×C₅×D₄	—	4	2	no	—
130	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
131	C₅×Q₁₆	—	2	4	no	—
132	C₅×Q₁₆	C₃×D₄	1	2	yes	complemented
133	C₅×SD₁₆	—	2	4	no	—
134	C₅×SD₁₆	—	2	4	no	—
135	C₅×SD₁₆	—	2	4	no	—
136	C₅×SD₁₆	—	2	4	no	—
137	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
138	C₅×D₈	—	2	4	no	—
139	C₅×D₈	C₃×D₄	1	2	yes	complemented
140	C₅×M₁₆	—	2	4	no	—
141	C₅×M₁₆	C₂³×C₃	1	4	yes	—
142	C₂×C₅×C₈	—	2	4	no	—
143	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
144	C₅×C₄⋊C₄	—	4	1	no	—
145	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
146	#577	C₂×C₃×C₅	1	4	yes	complemented
147	#492	C₂×C₃×C₅	1	1	yes	characteristic, complemented
148	#471	C₂×C₃×C₅	1	4	yes	complemented
149	#456	C₂×C₃×C₅	1	2	yes	complemented
150	#453	C₂×C₃×C₅	1	2	yes	complemented
151	#443	C₂×C₃×C₅	1	2	yes	complemented
152	C₂²×C₃×C₅	—	2	4	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	8	2	no	—
155	C₂²×C₃×C₅	—	16	2	no	—
156	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	—	2	4	no	—
159	C₃×C₄×C₅	—	4	2	no	—
160	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
161	C₃×#41	—	2	4	no	—
162	C₃×#41	—	2	4	no	—
163	C₃×#41	—	4	2	no	—
164	C₃×#41	C₂³×C₅	1	4	yes	—
165	C₂×C₃×Q₈	—	2	4	no	—
166	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
167	C₂×C₃×D₄	—	2	4	no	—
168	C₂×C₃×D₄	—	4	1	no	—
169	C₂×C₃×D₄	—	4	2	no	—
170	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
171	C₃×Q₁₆	—	2	4	no	—
172	C₃×Q₁₆	C₅×D₄	1	2	yes	complemented
173	C₃×SD₁₆	—	2	4	no	—
174	C₃×SD₁₆	—	2	4	no	—
175	C₃×SD₁₆	—	2	4	no	—
176	C₃×SD₁₆	—	2	4	no	—
177	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
178	C₃×D₈	—	2	4	no	—
179	C₃×D₈	C₅×D₄	1	2	yes	complemented
180	C₃×M₁₆	—	2	4	no	—
181	C₃×M₁₆	C₂³×C₅	1	4	yes	—
182	C₂×C₃×C₈	—	2	4	no	—
183	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
184	C₃×C₄⋊C₄	—	4	1	no	—
185	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₅×Q₈	—	2	4	no	—
189	C₅×Q₈	—	4	2	no	—
190	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
191	C₅×D₄	—	2	4	no	—
192	C₅×D₄	—	2	4	no	—
193	C₅×D₄	—	4	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	8	2	no	—
196	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	4	4	no	—
202	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
203	C₅×C₈	—	2	4	no	—
204	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
205	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
206	2₋¹⁺⁴	C₂²×C₃×C₅	1	2	yes	—
207	H(5,𝔽₂)	C₂²×C₃×C₅	1	2	yes	complemented
208	#137	—	2	4	no	—
209	#137	C₂²×C₃×C₅	1	4	yes	complemented
210	AGL(1,ℤ/8)	—	2	4	no	—
211	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	4	yes	—
212	#135	—	2	4	no	—
213	#135	C₂²×C₃×C₅	1	2	yes	—
214	C₂×SD₁₆	—	2	4	no	—
215	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	complemented
216	#131	C₂²×C₃×C₅	1	4	yes	complemented
217	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
218	#127	C₂²×C₃×C₅	1	1	yes	characteristic
219	#108	C₂²×C₃×C₅	1	2	yes	complemented
220	#104	C₂²×C₃×C₅	1	4	yes	complemented
221	#101	C₂²×C₃×C₅	1	2	yes	complemented
222	#100	C₂²×C₃×C₅	1	2	yes	complemented
223	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
224	C₂×C₃×C₅	—	2	1	no	—
225	C₂×C₃×C₅	—	4	4	no	—
226	C₂×C₃×C₅	—	8	2	no	—
227	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	4	2	no	—
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	4	2	no	—
232	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
233	C₃×D₄	—	2	4	no	—
234	C₃×D₄	—	2	4	no	—
235	C₃×D₄	—	4	4	no	—
236	C₃×D₄	—	4	2	no	—
237	C₃×D₄	—	8	2	no	—
238	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	4	2	no	—
243	C₂×C₃×C₄	—	4	4	no	—
244	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
245	C₃×C₈	—	2	4	no	—
246	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
247	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
248	C₂²×C₅	—	2	4	no	—
249	C₂²×C₅	—	4	2	no	—
250	C₂²×C₅	—	8	2	no	—
251	C₂²×C₅	—	16	2	no	—
252	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
253	C₄×C₅	—	2	2	no	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
257	#41	—	2	4	no	—
258	#41	—	2	4	no	—
259	#41	—	4	2	no	—
260	#41	C₂³×C₃×C₅	1	4	yes	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	4	1	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
267	Q₁₆	—	2	4	no	—
268	Q₁₆	C₃×C₅×D₄	1	2	yes	complemented
269	SD₁₆	—	2	4	no	—
270	SD₁₆	—	2	4	no	—
271	SD₁₆	—	2	4	no	—
272	SD₁₆	—	2	4	no	—
273	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
274	D₈	—	2	4	no	—
275	D₈	C₃×C₅×D₄	1	2	yes	complemented
276	M₁₆	—	2	4	no	—
277	M₁₆	C₂³×C₃×C₅	1	4	yes	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
280	C₄⋊C₄	—	4	1	no	—
281	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
282	C₃×C₅	#3291	1	1	yes	characteristic, direct product factor, Hall
283	C₂²×C₃	—	2	4	no	—
284	C₂²×C₃	—	4	2	no	—
285	C₂²×C₃	—	8	2	no	—
286	C₂²×C₃	—	16	2	no	—
287	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	4	2	no	—
291	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
292	C₂×C₅	—	2	1	no	—
293	C₂×C₅	—	4	4	no	—
294	C₂×C₅	—	8	2	no	—
295	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
296	C₂³	—	2	2	no	—
297	C₂³	—	4	2	no	—
298	Q₈	—	2	4	no	—
299	Q₈	—	4	2	no	—
300	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
301	D₄	—	2	4	no	—
302	D₄	—	2	4	no	—
303	D₄	—	4	4	no	—
304	D₄	—	4	2	no	—
305	D₄	—	8	2	no	—
306	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
313	C₈	—	2	4	no	—
314	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
315	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
316	C₂×C₃	—	2	1	no	—
317	C₂×C₃	—	4	4	no	—
318	C₂×C₃	—	8	2	no	—
319	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
320	C₅	C₃×#3291	1	1	yes	characteristic, direct product factor, Sylow
321	C₂²	—	2	4	no	—
322	C₂²	—	4	2	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	16	2	no	—
325	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	4	no	—
328	C₄	—	4	2	no	—
329	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
330	C₃	C₅×#3291	1	1	yes	characteristic, direct product factor, Sylow
331	C₂	—	2	1	no	—
332	C₂	—	4	4	no	—
333	C₂	—	8	2	no	—
334	C₂	C₃×C₅×D₄²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#577	C₂	semidirect
2. C₃×C₅×#492	C₂	semidirect
3. C₃×C₅×#471	C₂	semidirect
4. C₃×C₅×#456	C₂	semidirect
5. C₃×C₅×#453	C₂	semidirect
6. C₃×C₅×#443	C₂	semidirect
7. C₅×#3291	C₃	direct (N × H)
9. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
11. C₃×C₅×#137	C₂²	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₃×C₅×#131	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#108	C₂²	semidirect
22. C₃×C₅×#104	C₂²	semidirect
23. C₃×C₅×#101	C₂²	semidirect
24. C₃×C₅×#100	C₂²	semidirect
25. C₃×C₄×C₅×C₈	C₂²	semidirect
26. C₃×#3291	C₅	direct (N × H)
27. C₅×#577	C₂×C₃	semidirect
28. C₅×#492	C₂×C₃	semidirect
29. C₅×#471	C₂×C₃	semidirect
30. C₅×#456	C₂×C₃	semidirect
31. C₅×#453	C₂×C₃	semidirect
32. C₅×#443	C₂×C₃	semidirect
44. C₃×C₅×Q₁₆	D₄	semidirect
49. C₃×C₅×SD₁₆	D₄	semidirect
51. C₃×C₅×D₈	D₄	semidirect
58. C₃×#577	C₂×C₅	semidirect
59. C₃×#492	C₂×C₅	semidirect
60. C₃×#471	C₂×C₅	semidirect
61. C₃×#456	C₂×C₅	semidirect
62. C₃×#453	C₂×C₅	semidirect
63. C₃×#443	C₂×C₅	semidirect
65. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
67. C₅×#137	C₂²×C₃	semidirect
73. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
74. C₅×#131	C₂²×C₃	semidirect
75. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
77. C₅×#108	C₂²×C₃	semidirect
78. C₅×#104	C₂²×C₃	semidirect
79. C₅×#101	C₂²×C₃	semidirect
80. C₅×#100	C₂²×C₃	semidirect
81. C₄×C₅×C₈	C₂²×C₃	semidirect
82. #3291	C₃×C₅	direct (N × H)
104. C₃×H(5,𝔽₂)	C₂²×C₅	semidirect
106. C₃×#137	C₂²×C₅	semidirect
112. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
113. C₃×#131	C₂²×C₅	semidirect
114. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
116. C₃×#108	C₂²×C₅	semidirect
117. C₃×#104	C₂²×C₅	semidirect
118. C₃×#101	C₂²×C₅	semidirect
119. C₃×#100	C₂²×C₅	semidirect
120. C₃×C₄×C₈	C₂²×C₅	semidirect
132. C₅×Q₁₆	C₃×D₄	semidirect
137. C₅×SD₁₆	C₃×D₄	semidirect
139. C₅×D₈	C₃×D₄	semidirect
146. #577	C₂×C₃×C₅	semidirect
147. #492	C₂×C₃×C₅	semidirect
148. #471	C₂×C₃×C₅	semidirect
149. #456	C₂×C₃×C₅	semidirect
150. #453	C₂×C₃×C₅	semidirect
151. #443	C₂×C₃×C₅	semidirect
172. C₃×Q₁₆	C₅×D₄	semidirect
177. C₃×SD₁₆	C₅×D₄	semidirect
179. C₃×D₈	C₅×D₄	semidirect
207. H(5,𝔽₂)	C₂²×C₃×C₅	semidirect
209. #137	C₂²×C₃×C₅	semidirect
215. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
216. #131	C₂²×C₃×C₅	semidirect
217. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
219. #108	C₂²×C₃×C₅	semidirect
220. #104	C₂²×C₃×C₅	semidirect
221. #101	C₂²×C₃×C₅	semidirect
222. #100	C₂²×C₃×C₅	semidirect
223. C₄×C₈	C₂²×C₃×C₅	semidirect
268. Q₁₆	C₃×C₅×D₄	semidirect
273. SD₁₆	C₃×C₅×D₄	semidirect
275. D₈	C₃×C₅×D₄	semidirect
282. C₃×C₅	#3291	direct (N × H)
320. C₅	C₃×#3291	direct (N × H)
330. C₃	C₅×#3291	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×#577	2
C₃×C₅×#492	2
C₃×C₅×#471	2
C₃×C₅×#456	2
C₃×C₅×#453	2
C₃×C₅×#443	2
C₅×#3291	3
C₃×#3291	5

Subgroups — C3×C5×#3291 #14276325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3291 #14276325