Subgroups — #14282757

Order 1920.

476 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	#11751033	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751026	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746359	C₂	1	2	yes	maximal, complemented
5	#11746358	C₂	1	2	yes	maximal
6	#10602547	—	3	1	no	maximal, Hall
7	C₃×C₅×#126	—	2	1	no	—
8	C₃×C₅×#125	C₄	1	1	yes	characteristic, complemented
9	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
10	C₃×C₅×#123	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
14	C₃×C₄×C₅×D₄	—	2	1	no	—
15	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic, complemented
16	C₃×C₅×#117	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₄×Dic₁₅	—	2	1	no	—
19	#91115	—	2	1	no	—
20	#91115	C₂²	1	2	yes	—
21	#91114	C₂²	1	2	yes	—
22	C₄⋊(C₃⋊#168)	—	2	1	no	—
23	C₄×C₃⋊#168	—	2	1	no	—
24	#71754	—	5	1	no	maximal, Hall
25	C₅×#529	D₃	1	1	yes	characteristic
26	#65221	—	3	1	no	—
27	#65214	—	3	1	no	—
28	#64758	—	3	2	no	—
29	#64757	—	3	2	no	—
30	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₅	—	2	2	no	—
38	C₃×C₅×C₄⋊C₄	—	2	1	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	—	2	1	no	—
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
54	C₄×Dic₁₅	—	2	4	no	—
55	C₂×C₃⋊#168	—	2	2	no	—
56	C₃×#529	D₅	1	1	yes	characteristic
57	#4932	—	5	1	no	—
58	#4925	—	5	1	no	—
59	#4538	—	5	2	no	—
60	#4537	—	5	2	no	—
61	C₅×#126	—	2	1	no	—
62	C₅×#125	Dic₃	1	1	yes	characteristic, complemented
63	C₅×#124	Dic₃	1	1	yes	characteristic, complemented
64	C₅×#123	—	2	1	no	—
65	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic
66	C₅×#121	C₂×D₃	1	1	yes	characteristic
67	C₄×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
68	C₄×C₅×D₄	—	2	1	no	—
69	C₄×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
70	C₅×#117	—	2	1	no	—
71	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×C₄×Dic₅	—	6	1	no	—
73	#3963	—	3	2	no	—
74	#3963	—	6	1	no	—
75	C₂²⋊#168	—	3	2	no	—
76	C₄⋊#168	—	6	1	no	—
77	C₄×#168	—	6	1	no	—
78	#1500	—	15	1	no	Sylow
79	C₂³×C₃×C₅	—	2	1	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	4	1	no	—
82	C₃×C₅×D₄	—	4	1	no	—
83	C₃×C₅×D₄	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	1	no	—
87	C₂×C₃×C₄×C₅	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×Dic₁₅	—	2	4	no	—
98	C₂×Dic₁₅	—	4	2	no	—
99	C₂×Dic₁₅	—	4	2	no	—
100	C₃⋊#168	—	4	2	no	—
101	C₃×#126	—	2	1	no	—
102	C₃×#125	Dic₅	1	1	yes	characteristic, complemented
103	C₃×#124	Dic₅	1	1	yes	characteristic, complemented
104	C₃×#123	—	2	1	no	—
105	C₃×C₂²⋊Q₈	C₂×D₅	1	1	yes	characteristic
106	C₃×#121	C₂×D₅	1	1	yes	characteristic
107	C₃×C₄×Q₈	Dic₅	1	1	yes	characteristic, complemented
108	C₃×C₄×D₄	—	2	1	no	—
109	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic, complemented
110	C₃×#117	—	2	1	no	—
111	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
112	C₂×C₄×Dic₃	—	10	1	no	—
113	C₃⋊#95	—	5	2	no	—
114	C₃⋊#95	—	10	1	no	—
115	#830	—	5	2	no	—
116	C₄⋊(C₃⋊C₈)	—	10	1	no	—
117	C₄×C₃⋊C₈	—	10	1	no	—
118	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	#67	1	1	yes	characteristic
123	C₂²×C₄×C₅	#67	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₂²×Dic₅	—	6	2	no	—
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	1	no	—
129	C₅×C₄⋊C₄	—	2	1	no	—
130	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
131	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
132	C₅×C₂²⋊C₄	—	2	1	no	—
133	C₅×C₂²⋊C₄	—	2	1	no	—
134	C₅×C₂²⋊C₄	—	2	1	no	—
135	C₅×C₂²⋊C₄	—	2	1	no	—
136	C₅×C₂²⋊C₄	—	2	1	no	—
137	C₄²×C₅	—	2	1	no	—
138	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
139	C₄²×C₅	C₂×Dic₃	1	1	yes	characteristic
140	C₄²×C₅	#67	1	1	yes	characteristic
141	C₄²×C₅	#67	1	1	yes	characteristic
142	C₄×Dic₅	—	6	4	no	—
143	C₂×#168	—	6	2	no	—
144	#529	D₁₅	1	1	yes	characteristic
145	#431	—	15	1	no	—
146	#376	—	15	1	no	—
147	#328	—	15	2	no	—
148	#327	—	15	2	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	4	1	no	—
152	C₂²×C₃×C₅	—	4	1	no	—
153	C₂²×C₃×C₅	—	4	1	no	—
154	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₃×C₅	#135	1	2	yes	—
156	C₃×C₄×C₅	—	2	1	no	—
157	C₃×C₄×C₅	—	2	1	no	—
158	C₃×C₄×C₅	—	2	1	no	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	4	1	no	—
162	C₃×C₄×C₅	—	4	1	no	—
163	C₃×C₄×C₅	—	4	1	no	—
164	C₃×C₄×C₅	#104	1	2	yes	—
165	Dic₁₅	—	4	4	no	—
166	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
167	C₂×C₃×D₄	—	2	1	no	—
168	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
173	C₂²×Dic₃	—	10	2	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	—	2	1	no	—
176	C₃×C₄⋊C₄	—	2	1	no	—
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
180	C₃×C₂²⋊C₄	—	2	1	no	—
181	C₃×C₂²⋊C₄	—	2	1	no	—
182	C₃×C₂²⋊C₄	—	2	1	no	—
183	C₃×C₂²⋊C₄	—	2	1	no	—
184	C₃×C₂²⋊C₄	—	2	1	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
187	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
188	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
189	C₃×C₄²	C₂²⋊D₅	1	1	yes	characteristic
190	C₄×Dic₃	—	10	4	no	—
191	C₂×C₃⋊C₈	—	10	2	no	—
192	C₂³×C₅	—	2	1	no	—
193	C₂³×C₅	C₂×#67	1	1	yes	characteristic
194	C₅×Q₈	—	4	1	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	1	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	#217	1	1	yes	characteristic
205	C₂×C₄×C₅	#217	1	1	yes	characteristic
206	C₂×C₄×C₅	#217	1	1	yes	characteristic
207	C₂×C₄×C₅	#217	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
210	C₂×Dic₅	—	6	4	no	—
211	C₂×Dic₅	—	12	2	no	—
212	C₂×Dic₅	—	12	2	no	—
213	#168	—	12	2	no	—
214	#126	—	2	1	no	—
215	#125	Dic₁₅	1	1	yes	characteristic, complemented
216	#124	Dic₁₅	1	1	yes	characteristic, complemented
217	#123	—	2	1	no	—
218	C₂²⋊Q₈	C₂×D₁₅	1	1	yes	characteristic
219	#121	C₂×D₁₅	1	1	yes	characteristic
220	C₄×Q₈	Dic₁₅	1	1	yes	characteristic, complemented
221	C₄×D₄	—	2	1	no	—
222	C₄×D₄	Dic₁₅	1	1	yes	characteristic, complemented
223	#117	—	2	1	no	—
224	C₂×C₄²	—	30	1	no	—
225	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
226	C₄⋊C₈	—	30	1	no	—
227	C₂²⋊C₈	—	15	2	no	—
228	C₄×C₈	—	30	1	no	—
229	#95	—	15	2	no	—
230	#95	—	30	1	no	—
231	C₂×C₃×C₅	—	2	2	no	—
232	C₂×C₃×C₅	—	8	1	no	—
233	C₂×C₃×C₅	#410	1	1	yes	characteristic
234	C₂×C₃×C₅	#416	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
236	C₂³×C₃	—	2	1	no	—
237	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
238	C₃×Q₈	—	4	1	no	—
239	C₃×D₄	—	4	1	no	—
240	C₃×D₄	—	4	2	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	4	2	no	—
248	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
254	C₂×Dic₃	—	10	4	no	—
255	C₂×Dic₃	—	20	2	no	—
256	C₂×Dic₃	—	20	2	no	—
257	C₃⋊C₈	—	20	2	no	—
258	C₂²×C₅	—	2	1	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	4	1	no	—
261	C₂²×C₅	—	4	1	no	—
262	C₂²×C₅	—	4	1	no	—
263	C₂²×C₅	#950	1	2	yes	—
264	C₂²×C₅	C₂×#217	1	1	yes	characteristic
265	C₄×C₅	—	2	1	no	—
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	2	1	no	—
270	C₄×C₅	—	4	1	no	—
271	C₄×C₅	—	4	1	no	—
272	C₄×C₅	—	4	1	no	—
273	C₄×C₅	#837	1	2	yes	—
274	Dic₅	—	12	4	no	—
275	C₂×Q₈	C₂×Dic₁₅	1	1	yes	characteristic
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₂×Dic₁₅	1	1	yes	characteristic
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	30	2	no	—
280	C₂²×C₄	#1220	1	1	yes	characteristic
281	C₂²×C₄	#1220	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
283	C₂×C₈	—	30	2	no	—
284	C₄⋊C₄	—	2	1	no	—
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	2	1	no	—
288	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
289	C₄⋊C₄	C₂×Dic₁₅	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	30	4	no	—
297	C₄²	C₂×Dic₁₅	1	1	yes	characteristic
298	C₄²	C₂×Dic₁₅	1	1	yes	characteristic
299	C₄²	#1220	1	1	yes	characteristic
300	C₄²	#1220	1	1	yes	characteristic
301	C₃×C₅	#1500	1	1	yes	characteristic, complemented, Hall
302	C₂²×C₃	—	2	1	no	—
303	C₂²×C₃	—	2	1	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	4	1	no	—
307	C₂²×C₃	#4096	1	2	yes	—
308	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	#3969	1	2	yes	—
318	Dic₃	—	20	4	no	—
319	C₂×C₅	—	2	2	no	—
320	C₂×C₅	—	8	1	no	—
321	C₂×C₅	#5233	1	1	yes	characteristic
322	C₂×C₅	C₂×#837	1	1	yes	characteristic
323	C₂×C₅	#5240	1	1	yes	characteristic
324	C₂³	—	2	1	no	—
325	C₂³	C₂×#1220	1	1	yes	characteristic
326	Q₈	—	4	1	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	30	4	no	—
337	C₂×C₄	—	60	2	no	—
338	C₂×C₄	—	60	2	no	—
339	C₂×C₄	#6719	1	1	yes	characteristic
340	C₂×C₄	#6719	1	1	yes	characteristic
341	C₂×C₄	#6719	1	1	yes	characteristic
342	C₂×C₄	#6719	1	1	yes	characteristic
343	C₂×C₄	C₂²×Dic₁₅	1	1	yes	characteristic
344	C₂×C₄	C₂×#1220	1	1	yes	characteristic
345	C₈	—	60	2	no	—
346	C₂×C₃	—	2	2	no	—
347	C₂×C₃	—	8	1	no	—
348	C₂×C₃	#65522	1	1	yes	characteristic
349	C₂×C₃	C₂×#3969	1	1	yes	characteristic
350	C₂×C₃	#65529	1	1	yes	characteristic
351	C₅	#71754	1	1	yes	characteristic, complemented, Sylow
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	#91839	1	2	yes	—
358	C₂²	C₂×#6719	1	1	yes	characteristic
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	60	4	no	—
368	C₄	#91121	1	2	yes	—
369	C₃	#10602547	1	1	yes	characteristic, complemented, Sylow
370	C₂	—	2	2	no	—
371	C₂	—	8	1	no	—
372	C₂	#11751334	1	1	yes	characteristic
373	C₂	C₂×#91121	1	1	yes	characteristic
374	C₂	#11751341	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6719
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₅
Fitting	C₃×C₅×#529	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₃×C₅×#121	C₂²
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	#529	D₁₅
hypocenter	C₃×C₅	#1500
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #529

Complements

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

N	H ≅ G/N	type
2. #11751033	C₂	semidirect
3. #11751026	C₂	semidirect
4. #11746359	C₂	semidirect
8. C₃×C₅×#125	C₄	semidirect
9. C₃×C₅×#124	C₄	semidirect
13. C₃×C₄×C₅×Q₈	C₄	semidirect
15. C₃×C₄×C₅×D₄	C₄	semidirect
62. C₅×#125	Dic₃	semidirect
63. C₅×#124	Dic₃	semidirect
67. C₄×C₅×Q₈	Dic₃	semidirect
69. C₄×C₅×D₄	Dic₃	semidirect
102. C₃×#125	Dic₅	semidirect
103. C₃×#124	Dic₅	semidirect
107. C₃×C₄×Q₈	Dic₅	semidirect
109. C₃×C₄×D₄	Dic₅	semidirect
215. #125	Dic₁₅	semidirect
216. #124	Dic₁₅	semidirect
220. C₄×Q₈	Dic₁₅	semidirect
222. C₄×D₄	Dic₁₅	semidirect
301. C₃×C₅	#1500	semidirect
351. C₅	#71754	semidirect
369. C₃	#10602547	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#529	2
#11751033	2
#11751026	2
#11746359	2
#11746358	2
#10602547	3
#71754	5