Subgroups — C₂×C₄×D₃×D₁₅ #13089357

Order 1440.

998 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₃×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#67149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₃×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×D₃×D₁₅	C₂	1	8	yes	maximal, direct product factor
9	C₂²×C₄×D₁₅	—	3	1	no	maximal
10	C₂×C₄×D₃×D₅	—	3	1	no	maximal
11	C₂²×C₃⋊D₁₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×D₁₅	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×D₃×D₁₅	C₄	1	8	yes	direct product factor
15	C₂×D₃×D₁₅	C₂²	1	4	yes	—
16	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃⋊Dic₁₅	C₂²	1	1	yes	characteristic, complemented
18	C₄×C₃⋊D₁₅	C₂²	1	4	yes	complemented
19	C₂×C₃×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄×D₁₅	C₂²	1	4	yes	complemented
21	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₄×C₅×D₃	C₂²	1	4	yes	complemented
23	#67149	C₂²	1	4	yes	complemented
24	D₃×Dic₁₅	C₂²	1	4	yes	complemented
25	Dic₃×D₁₅	C₂²	1	4	yes	complemented
26	C₂×C₄×D₃²	—	5	1	no	maximal, Hall
27	C₂³×D₁₅	—	3	1	no	—
28	C₂²×D₃×D₅	—	3	1	no	—
29	C₂²×C₃×C₄×C₅	—	3	1	no	—
30	C₂²×Dic₁₅	—	3	1	no	—
31	C₂×C₄×D₁₅	—	3	1	no	—
32	C₂×C₄×D₁₅	—	3	1	no	—
33	C₂×C₄×D₁₅	—	3	1	no	—
34	C₂×C₄×D₁₅	—	3	1	no	—
35	C₂×C₄×D₁₅	—	3	8	no	—
36	C₂×C₄×D₁₅	—	6	1	no	—
37	C₂×C₄×D₁₅	D₃	1	1	yes	characteristic, direct product factor
38	C₂×C₄×C₅×D₃	D₃	1	1	yes	characteristic, complemented
39	C₂×C₃×C₄×D₅	—	3	1	no	—
40	C₂×#1200	—	3	1	no	—
41	C₂×D₃×Dic₅	—	3	1	no	—
42	C₂×D₅×Dic₃	—	3	1	no	—
43	C₄×D₃×D₅	—	3	8	no	—
44	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
45	C₂×C₃⋊D₁₅	C₂×C₄	1	4	yes	complemented
46	C₂×C₃⋊D₁₅	C₂³	1	2	yes	—
47	C₂×C₃×D₁₅	C₂×C₄	1	4	yes	complemented
48	C₂×C₃×D₁₅	C₂³	1	2	yes	—
49	C₂×C₃×C₅×D₃	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
51	D₃×D₁₅	C₂×C₄	1	16	yes	direct product factor
52	C₃²×C₄×C₅	C₂³	1	2	yes	complemented
53	C₃⋊Dic₁₅	C₂³	1	2	yes	complemented
54	C₃×Dic₁₅	C₂³	1	2	yes	complemented
55	C₃×C₅×Dic₃	C₂³	1	2	yes	complemented
56	C₂²×C₄×D₅	—	9	1	no	Hall
57	C₂²×D₃²	—	5	1	no	—
58	C₂×C₄×C₃⋊D₃	—	5	1	no	—
59	C₂×C₃×C₄×D₃	—	5	1	no	—
60	C₂×C₃×C₄×D₃	D₅	1	1	yes	characteristic, complemented
61	C₂×#624	—	5	1	no	—
62	C₂×D₃×Dic₃	—	5	1	no	—
63	C₂×D₃×Dic₃	—	5	1	no	—
64	C₄×D₃²	—	5	8	no	—
65	C₂³×C₃×C₅	—	3	1	no	—
66	C₂²×D₁₅	—	3	1	no	—
67	C₂²×D₁₅	—	3	1	no	—
68	C₂²×D₁₅	—	3	8	no	—
69	C₂²×D₁₅	—	3	4	no	—
70	C₂²×D₁₅	—	6	1	no	—
71	C₂²×D₁₅	C₂×D₃	1	1	yes	characteristic
72	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₃×D₅	—	3	1	no	—
74	C₂×D₃×D₅	—	3	8	no	—
75	C₂×D₃×D₅	—	3	4	no	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	3	1	no	—
78	C₂×C₃×C₄×C₅	—	3	4	no	—
79	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
80	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
81	C₂×Dic₁₅	—	3	1	no	—
82	C₂×Dic₁₅	—	3	1	no	—
83	C₂×Dic₁₅	—	3	4	no	—
84	C₂×Dic₁₅	—	6	1	no	—
85	C₂×Dic₁₅	C₂×D₃	1	1	yes	characteristic, complemented
86	C₄×D₁₅	—	3	4	no	—
87	C₄×D₁₅	—	3	4	no	—
88	C₄×D₁₅	—	3	4	no	—
89	C₄×D₁₅	—	3	4	no	—
90	C₄×D₁₅	—	6	4	no	—
91	C₄×D₁₅	C₂×D₃	1	4	yes	direct product factor
92	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
93	C₄×C₅×D₃	C₂×D₃	1	4	yes	complemented
94	C₂×C₃×Dic₅	—	3	1	no	—
95	C₃×C₄×D₅	—	3	4	no	—
96	#1200	—	3	4	no	—
97	D₃×Dic₅	—	3	4	no	—
98	D₅×Dic₃	—	3	4	no	—
99	C₂²×C₄×D₃	—	15	1	no	—
100	C₂²×C₄×D₃	—	15	1	no	—
101	C₂×C₃²×C₅	C₂²×C₄	1	2	yes	complemented
102	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
103	C₃⋊D₁₅	C₂²×C₄	1	4	yes	complemented
104	C₃×D₁₅	C₂²×C₄	1	4	yes	complemented
105	C₃×C₅×D₃	C₂²×C₄	1	4	yes	complemented
106	C₂³×D₅	—	9	1	no	—
107	C₂²×C₄×C₅	—	3	1	no	—
108	C₂²×Dic₅	—	9	1	no	—
109	C₂×C₄×D₅	—	3	1	no	—
110	C₂×C₄×D₅	—	9	8	no	—
111	C₂×C₄×D₅	—	9	1	no	—
112	C₂×C₄×D₅	—	9	1	no	—
113	C₂×C₄×D₅	—	9	1	no	—
114	C₂²×C₃⋊D₃	—	5	1	no	—
115	C₂²×C₃×D₃	—	5	1	no	—
116	C₂²×C₃×D₃	C₂×D₅	1	1	yes	characteristic
117	C₂×D₃²	—	5	8	no	—
118	C₂×D₃²	—	5	4	no	—
119	C₂×C₃²×C₄	C₂×D₅	1	1	yes	characteristic, complemented
120	C₂×C₃⋊Dic₃	—	5	1	no	—
121	C₄×C₃⋊D₃	—	5	4	no	—
122	C₂×C₃×Dic₃	—	5	1	no	—
123	C₂×C₃×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
124	C₃×C₄×D₃	—	5	4	no	—
125	C₃×C₄×D₃	C₂×D₅	1	4	yes	complemented
126	#624	—	5	4	no	—
127	D₃×Dic₃	—	5	4	no	—
128	D₃×Dic₃	—	5	4	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	—	3	4	no	—
131	C₂²×C₃×C₅	—	3	2	no	—
132	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₂×D₁₅	—	3	4	no	—
135	C₂×D₁₅	—	3	4	no	—
136	C₂×D₁₅	—	3	2	no	—
137	C₂×D₁₅	—	3	2	no	—
138	C₂×D₁₅	—	3	16	no	—
139	C₂×D₁₅	—	6	4	no	—
140	C₂×D₁₅	—	6	2	no	—
141	C₂×D₁₅	C₄×D₃	1	4	yes	direct product factor
142	C₂×D₁₅	C₂²×D₃	1	2	yes	—
143	C₂×C₅×D₃	C₄×D₃	1	4	yes	complemented
144	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
145	C₂×C₃×D₅	—	3	4	no	—
146	C₂×C₃×D₅	—	3	2	no	—
147	D₃×D₅	—	3	16	no	—
148	C₃×C₄×C₅	—	2	2	no	—
149	C₃×C₄×C₅	—	3	2	no	—
150	C₃×C₄×C₅	C₂²×D₃	1	2	yes	complemented
151	C₃×C₄×C₅	C₂²×D₃	1	2	yes	complemented
152	Dic₁₅	—	3	2	no	—
153	Dic₁₅	—	3	2	no	—
154	Dic₁₅	—	6	2	no	—
155	Dic₁₅	C₂²×D₃	1	2	yes	complemented
156	C₃×Dic₅	—	3	2	no	—
157	C₅×Dic₃	C₂²×D₃	1	2	yes	complemented
158	C₂³×D₃	—	15	1	no	—
159	C₂³×D₃	—	15	1	no	—
160	C₂²×C₃×C₄	—	3	1	no	—
161	C₂²×C₃×C₄	—	15	1	no	—
162	C₂²×Dic₃	—	15	1	no	—
163	C₂²×Dic₃	—	15	1	no	—
164	C₂×C₄×D₃	—	5	1	no	—
165	C₂×C₄×D₃	—	15	8	no	—
166	C₂×C₄×D₃	—	15	1	no	—
167	C₂×C₄×D₃	—	15	1	no	—
168	C₂×C₄×D₃	—	15	1	no	—
169	C₂×C₄×D₃	—	15	1	no	—
170	C₂×C₄×D₃	—	15	1	no	—
171	C₂×C₄×D₃	—	15	1	no	—
172	C₂×C₄×D₃	—	15	8	no	—
173	C₂×C₄×D₃	—	30	1	no	—
174	C₂×C₄×D₃	D₁₅	1	1	yes	characteristic, direct product factor
175	C₃²×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
176	C₂³×C₅	—	3	1	no	—
177	C₂²×D₅	—	3	1	no	—
178	C₂²×D₅	—	9	4	no	—
179	C₂²×D₅	—	9	8	no	—
180	C₂²×D₅	—	9	1	no	—
181	C₂×C₄×C₅	—	3	1	no	—
182	C₂×C₄×C₅	—	3	4	no	—
183	C₂×C₄×C₅	D₃²	1	1	yes	characteristic, complemented
184	C₂×Dic₅	—	3	1	no	—
185	C₂×Dic₅	—	9	4	no	—
186	C₂×Dic₅	—	9	1	no	—
187	C₄×D₅	—	3	4	no	—
188	C₄×D₅	—	9	4	no	—
189	C₄×D₅	—	9	4	no	—
190	C₄×D₅	—	9	4	no	—
191	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
192	C₂×C₃⋊D₃	—	5	4	no	—
193	C₂×C₃⋊D₃	—	5	2	no	—
194	C₂×C₃×D₃	—	5	4	no	—
195	C₂×C₃×D₃	—	5	2	no	—
196	C₂×C₃×D₃	C₄×D₅	1	4	yes	complemented
197	C₂×C₃×D₃	C₂²×D₅	1	2	yes	—
198	D₃²	—	5	16	no	—
199	C₃²×C₄	C₂²×D₅	1	2	yes	complemented
200	C₃⋊Dic₃	—	5	2	no	—
201	C₃×Dic₃	—	5	2	no	—
202	C₃×Dic₃	C₂²×D₅	1	2	yes	complemented
203	C₂³×C₄	—	45	1	no	Sylow
204	C₂×C₃×C₅	—	2	1	no	—
205	C₂×C₃×C₅	—	2	2	no	—
206	C₂×C₃×C₅	—	3	4	no	—
207	C₂×C₃×C₅	C₂×C₄×D₃	1	2	yes	complemented
208	C₂×C₃×C₅	C₂×C₄×D₃	1	2	yes	complemented
209	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
210	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
211	D₁₅	—	3	4	no	—
212	D₁₅	—	3	4	no	—
213	D₁₅	—	6	4	no	—
214	D₁₅	C₂×C₄×D₃	1	4	yes	direct product factor
215	C₃×D₅	—	3	4	no	—
216	C₅×D₃	C₂×C₄×D₃	1	4	yes	complemented
217	C₂³×C₃	—	3	1	no	—
218	C₂³×C₃	—	15	1	no	—
219	C₂²×D₃	—	5	1	no	—
220	C₂²×D₃	—	15	4	no	—
221	C₂²×D₃	—	15	8	no	—
222	C₂²×D₃	—	15	1	no	—
223	C₂²×D₃	—	15	1	no	—
224	C₂²×D₃	—	15	8	no	—
225	C₂²×D₃	—	15	4	no	—
226	C₂²×D₃	—	30	1	no	—
227	C₂²×D₃	C₂×D₁₅	1	1	yes	characteristic
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	3	1	no	—
230	C₂×C₃×C₄	—	3	4	no	—
231	C₂×C₃×C₄	—	15	1	no	—
232	C₂×C₃×C₄	—	15	4	no	—
233	C₂×C₃×C₄	D₃×D₅	1	1	yes	characteristic, complemented
234	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
235	C₂×Dic₃	—	5	1	no	—
236	C₂×Dic₃	—	15	4	no	—
237	C₂×Dic₃	—	15	1	no	—
238	C₂×Dic₃	—	15	1	no	—
239	C₂×Dic₃	—	15	4	no	—
240	C₂×Dic₃	—	30	1	no	—
241	C₂×Dic₃	C₂×D₁₅	1	1	yes	characteristic, complemented
242	C₄×D₃	—	5	4	no	—
243	C₄×D₃	—	15	4	no	—
244	C₄×D₃	—	15	4	no	—
245	C₄×D₃	—	15	4	no	—
246	C₄×D₃	—	15	4	no	—
247	C₄×D₃	—	15	4	no	—
248	C₄×D₃	—	15	4	no	—
249	C₄×D₃	—	30	4	no	—
250	C₄×D₃	C₂×D₁₅	1	4	yes	direct product factor
251	C₂²×C₅	—	3	2	no	—
252	C₂²×C₅	—	3	4	no	—
253	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
254	C₂×D₅	—	3	2	no	—
255	C₂×D₅	—	3	4	no	—
256	C₂×D₅	—	9	16	no	—
257	C₂×D₅	—	9	2	no	—
258	C₂×D₅	—	9	4	no	—
259	C₄×C₅	—	3	2	no	—
260	C₄×C₅	C₂×D₃²	1	2	yes	complemented
261	Dic₅	—	3	2	no	—
262	Dic₅	—	9	2	no	—
263	C₂×C₃²	C₂×C₄×D₅	1	2	yes	complemented
264	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
265	C₃⋊D₃	—	5	4	no	—
266	C₃×D₃	—	5	4	no	—
267	C₃×D₃	C₂×C₄×D₅	1	4	yes	complemented
268	C₂⁴	—	45	1	no	—
269	C₂²×C₄	—	3	1	no	—
270	C₂²×C₄	—	15	1	no	—
271	C₂²×C₄	—	45	1	no	—
272	C₂²×C₄	—	45	8	no	—
273	C₂²×C₄	—	45	1	no	—
274	C₂²×C₄	—	45	1	no	—
275	C₂²×C₄	—	45	1	no	—
276	C₃×C₅	—	2	1	no	—
277	C₃×C₅	C₂²×C₄×D₃	1	1	yes	characteristic, complemented
278	C₃×C₅	C₂²×C₄×D₃	1	1	yes	characteristic, complemented
279	C₂²×C₃	—	2	1	no	—
280	C₂²×C₃	—	3	4	no	—
281	C₂²×C₃	—	3	2	no	—
282	C₂²×C₃	—	15	4	no	—
283	C₂²×C₃	—	15	2	no	—
284	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
285	C₂²×C₃	C₂²×D₁₅	1	1	yes	characteristic
286	C₂×D₃	—	5	4	no	—
287	C₂×D₃	—	5	2	no	—
288	C₂×D₃	—	15	16	no	—
289	C₂×D₃	—	15	4	no	—
290	C₂×D₃	—	15	4	no	—
291	C₂×D₃	—	15	2	no	—
292	C₂×D₃	—	15	2	no	—
293	C₂×D₃	—	15	16	no	—
294	C₂×D₃	—	30	2	no	—
295	C₂×D₃	—	30	4	no	—
296	C₂×D₃	C₄×D₁₅	1	4	yes	direct product factor
297	C₂×D₃	C₂²×D₁₅	1	2	yes	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	3	2	no	—
300	C₃×C₄	—	15	2	no	—
301	C₃×C₄	C₂×D₃×D₅	1	2	yes	complemented
302	C₃×C₄	C₂²×D₁₅	1	2	yes	complemented
303	Dic₃	—	5	2	no	—
304	Dic₃	—	15	2	no	—
305	Dic₃	—	15	2	no	—
306	Dic₃	—	30	2	no	—
307	Dic₃	C₂²×D₁₅	1	2	yes	complemented
308	C₂×C₅	—	3	4	no	—
309	C₂×C₅	C₄×D₃²	1	2	yes	complemented
310	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
311	D₅	—	3	4	no	—
312	D₅	—	9	4	no	—
313	C₃²	C₂²×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
314	C₂³	—	3	1	no	—
315	C₂³	—	15	1	no	—
316	C₂³	—	45	4	no	—
317	C₂³	—	45	8	no	—
318	C₂³	—	45	1	no	—
319	C₂×C₄	—	3	1	no	—
320	C₂×C₄	—	3	4	no	—
321	C₂×C₄	—	15	1	no	—
322	C₂×C₄	—	15	4	no	—
323	C₂×C₄	—	45	4	no	—
324	C₂×C₄	—	45	4	no	—
325	C₂×C₄	—	45	4	no	—
326	C₂×C₄	—	45	1	no	—
327	C₂×C₄	—	45	4	no	—
328	C₂×C₄	D₃×D₁₅	1	1	yes	characteristic, direct product factor
329	C₂×C₃	—	2	1	no	—
330	C₂×C₃	—	2	2	no	—
331	C₂×C₃	—	3	4	no	—
332	C₂×C₃	—	15	4	no	—
333	C₂×C₃	C₄×D₃×D₅	1	2	yes	complemented
334	C₂×C₃	C₂×C₄×D₁₅	1	2	yes	complemented
335	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
336	C₂×C₃	C₂³×D₁₅	1	1	yes	characteristic
337	D₃	—	5	4	no	—
338	D₃	—	15	4	no	—
339	D₃	—	15	4	no	—
340	D₃	—	30	4	no	—
341	D₃	C₂×C₄×D₁₅	1	4	yes	direct product factor
342	C₅	C₂×C₄×D₃²	1	1	yes	characteristic, complemented, Sylow
343	C₂²	—	3	2	no	—
344	C₂²	—	3	4	no	—
345	C₂²	—	15	2	no	—
346	C₂²	—	15	4	no	—
347	C₂²	—	45	16	no	—
348	C₂²	—	45	2	no	—
349	C₂²	—	45	4	no	—
350	C₂²	C₂×D₃×D₁₅	1	1	yes	characteristic
351	C₄	—	3	2	no	—
352	C₄	—	15	2	no	—
353	C₄	—	45	2	no	—
354	C₄	C₂×D₃×D₁₅	1	2	yes	direct product factor
355	C₃	—	2	1	no	—
356	C₃	C₂×C₄×D₃×D₅	1	1	yes	characteristic, complemented
357	C₃	C₂²×C₄×D₁₅	1	1	yes	characteristic, complemented
358	C₂	—	3	4	no	—
359	C₂	—	15	4	no	—
360	C₂	—	45	4	no	—
361	C₂	C₄×D₃×D₁₅	1	2	yes	direct product factor
362	C₂	C₂²×D₃×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃×D₁₅
commutator, hypocenter	C₃²×C₅	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₁₅
Fitting	C₂×C₃²×C₄×C₅	C₂²
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂²×D₃×D₁₅	C₂
cosocle	C₂×C₃²×C₅	C₂⁴
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₃⋊D₁₅	C₂	semidirect
3. C₂×C₃×C₄×D₁₅	C₂	semidirect
4. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
5. C₂×#67149	C₂	semidirect
6. C₂×D₃×Dic₁₅	C₂	semidirect
7. C₂×Dic₃×D₁₅	C₂	semidirect
8. C₄×D₃×D₁₅	C₂	direct (N × H)
14. C₂×D₃×D₁₅	C₄	direct (N × H)
16. C₂×C₃²×C₄×C₅	C₂²	semidirect
17. C₂×C₃⋊Dic₁₅	C₂²	semidirect
18. C₄×C₃⋊D₁₅	C₂²	semidirect
19. C₂×C₃×Dic₁₅	C₂²	semidirect
20. C₃×C₄×D₁₅	C₂²	semidirect
21. C₂×C₃×C₅×Dic₃	C₂²	semidirect
22. C₃×C₄×C₅×D₃	C₂²	semidirect
23. #67149	C₂²	semidirect
24. D₃×Dic₁₅	C₂²	semidirect
25. Dic₃×D₁₅	C₂²	semidirect
37. C₂×C₄×D₁₅	D₃	direct (N × H)
38. C₂×C₄×C₅×D₃	D₃	semidirect
45. C₂×C₃⋊D₁₅	C₂×C₄	semidirect
47. C₂×C₃×D₁₅	C₂×C₄	semidirect
49. C₂×C₃×C₅×D₃	C₂×C₄	semidirect
51. D₃×D₁₅	C₂×C₄	direct (N × H)
52. C₃²×C₄×C₅	C₂³	semidirect
53. C₃⋊Dic₁₅	C₂³	semidirect
54. C₃×Dic₁₅	C₂³	semidirect
55. C₃×C₅×Dic₃	C₂³	semidirect
60. C₂×C₃×C₄×D₃	D₅	semidirect
79. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
80. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
85. C₂×Dic₁₅	C₂×D₃	semidirect
91. C₄×D₁₅	C₂×D₃	direct (N × H)
92. C₂×C₅×Dic₃	C₂×D₃	semidirect
93. C₄×C₅×D₃	C₂×D₃	semidirect
101. C₂×C₃²×C₅	C₂²×C₄	semidirect
103. C₃⋊D₁₅	C₂²×C₄	semidirect
104. C₃×D₁₅	C₂²×C₄	semidirect
105. C₃×C₅×D₃	C₂²×C₄	semidirect
119. C₂×C₃²×C₄	C₂×D₅	semidirect
123. C₂×C₃×Dic₃	C₂×D₅	semidirect
125. C₃×C₄×D₃	C₂×D₅	semidirect
141. C₂×D₁₅	C₄×D₃	direct (N × H)
143. C₂×C₅×D₃	C₄×D₃	semidirect
150. C₃×C₄×C₅	C₂²×D₃	semidirect
151. C₃×C₄×C₅	C₂²×D₃	semidirect
155. Dic₁₅	C₂²×D₃	semidirect
157. C₅×Dic₃	C₂²×D₃	semidirect
174. C₂×C₄×D₃	D₁₅	direct (N × H)
175. C₃²×C₅	C₂³×C₄	semidirect
183. C₂×C₄×C₅	D₃²	semidirect
196. C₂×C₃×D₃	C₄×D₅	semidirect
199. C₃²×C₄	C₂²×D₅	semidirect
202. C₃×Dic₃	C₂²×D₅	semidirect
207. C₂×C₃×C₅	C₂×C₄×D₃	semidirect
208. C₂×C₃×C₅	C₂×C₄×D₃	semidirect
214. D₁₅	C₂×C₄×D₃	direct (N × H)
216. C₅×D₃	C₂×C₄×D₃	semidirect
233. C₂×C₃×C₄	D₃×D₅	semidirect
234. C₂×C₃×C₄	C₂×D₁₅	semidirect
241. C₂×Dic₃	C₂×D₁₅	semidirect
250. C₄×D₃	C₂×D₁₅	direct (N × H)
260. C₄×C₅	C₂×D₃²	semidirect
263. C₂×C₃²	C₂×C₄×D₅	semidirect
267. C₃×D₃	C₂×C₄×D₅	semidirect
277. C₃×C₅	C₂²×C₄×D₃	semidirect
278. C₃×C₅	C₂²×C₄×D₃	semidirect
296. C₂×D₃	C₄×D₁₅	direct (N × H)
301. C₃×C₄	C₂×D₃×D₅	semidirect
302. C₃×C₄	C₂²×D₁₅	semidirect
307. Dic₃	C₂²×D₁₅	semidirect
309. C₂×C₅	C₄×D₃²	semidirect
313. C₃²	C₂²×C₄×D₅	semidirect
328. C₂×C₄	D₃×D₁₅	direct (N × H)
333. C₂×C₃	C₄×D₃×D₅	semidirect
334. C₂×C₃	C₂×C₄×D₁₅	semidirect
341. D₃	C₂×C₄×D₁₅	direct (N × H)
342. C₅	C₂×C₄×D₃²	semidirect
354. C₄	C₂×D₃×D₁₅	direct (N × H)
356. C₃	C₂×C₄×D₃×D₅	semidirect
357. C₃	C₂²×C₄×D₁₅	semidirect
361. C₂	C₄×D₃×D₁₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×D₃×D₁₅	2
C₂×C₄×C₃⋊D₁₅	2
C₂×C₃×C₄×D₁₅	2
C₂×C₃×C₄×C₅×D₃	2
C₂×#67149	2
C₂×D₃×Dic₁₅	2
C₂×Dic₃×D₁₅	2
C₄×D₃×D₁₅	2
C₂²×C₄×D₁₅	3
C₂×C₄×D₃×D₅	3
C₂×C₄×D₃²	5

Subgroups — C2×C4×D3×D15 #13089357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₃×D₁₅ #13089357