Subgroups — C₃×C₅×#3192 #14276226

Order 1920.

1028 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	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#481	C₂	1	4	yes	maximal, complemented
3	C₃×C₅×#469	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#447	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#3192	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	—	2	2	no	—
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#121	—	2	2	no	—
14	C₃×C₅×#121	C₂²	1	4	yes	—
15	C₃×C₅×#121	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
17	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
18	C₃×C₅×#106	C₂²	1	4	yes	complemented
19	C₃×C₅×#102	C₂²	1	8	yes	complemented
20	C₃×C₅×C₂²⋊C₈	C₂²	1	4	yes	complemented
21	C₃×#3192	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
23	C₅×#481	C₂×C₃	1	4	yes	complemented
24	C₅×#469	C₂×C₃	1	4	yes	complemented
25	C₅×#447	C₂×C₃	1	4	yes	complemented
26	C₅×#407	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂⁴×C₃×C₅	—	2	2	no	—
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₂×C₃×C₅×D₄	—	2	4	no	—
30	C₂×C₃×C₅×D₄	—	2	4	no	—
31	C₂×C₃×C₅×D₄	—	2	2	no	—
32	C₂×C₃×C₅×D₄	—	4	4	no	—
33	C₂×C₃×C₅×D₄	—	4	8	no	—
34	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	—	4	2	no	—
37	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₃×C₅×D₈	—	4	4	no	—
42	C₃×C₅×M₁₆	—	4	2	no	—
43	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
46	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
49	C₃×#481	C₂×C₅	1	4	yes	complemented
50	C₃×#469	C₂×C₅	1	4	yes	complemented
51	C₃×#447	C₂×C₅	1	4	yes	complemented
52	C₃×#407	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂²×C₅×D₄	—	2	2	no	—
54	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
55	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
57	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
58	C₅×#121	—	2	2	no	—
59	C₅×#121	—	2	2	no	—
60	C₅×#121	C₂²×C₃	1	4	yes	—
61	C₅×#121	C₂²×C₃	1	4	yes	complemented
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₅×#106	C₂²×C₃	1	4	yes	complemented
65	C₅×#102	C₂²×C₃	1	8	yes	complemented
66	C₅×C₂²⋊C₈	C₂²×C₃	1	4	yes	complemented
67	#3192	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
68	C₂³×C₃×C₅	—	2	4	no	—
69	C₂³×C₃×C₅	—	2	4	no	—
70	C₂³×C₃×C₅	—	4	1	no	—
71	C₂³×C₃×C₅	—	4	4	no	—
72	C₂³×C₃×C₅	—	4	4	no	—
73	C₂³×C₃×C₅	—	4	4	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
76	C₃×C₅×D₄	—	2	8	no	—
77	C₃×C₅×D₄	—	4	4	no	—
78	C₃×C₅×D₄	—	4	8	no	—
79	C₃×C₅×D₄	—	4	8	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	4	no	—
82	C₂×C₃×C₄×C₅	—	2	4	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	4	1	no	—
85	C₂×C₃×C₄×C₅	—	4	4	no	—
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
89	C₃×C₅×C₈	—	2	4	no	—
90	C₂²×C₃×D₄	—	2	2	no	—
91	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
92	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
94	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
95	C₃×#121	—	2	2	no	—
96	C₃×#121	—	2	2	no	—
97	C₃×#121	C₂²×C₅	1	4	yes	—
98	C₃×#121	C₂²×C₅	1	4	yes	complemented
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
100	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
101	C₃×#106	C₂²×C₅	1	4	yes	complemented
102	C₃×#102	C₂²×C₅	1	8	yes	complemented
103	C₃×C₂²⋊C₈	C₂²×C₅	1	4	yes	complemented
104	C₂⁴×C₅	—	2	2	no	—
105	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
106	C₂×C₅×D₄	—	2	4	no	—
107	C₂×C₅×D₄	—	2	4	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	4	4	no	—
110	C₂×C₅×D₄	—	4	8	no	—
111	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	4	2	no	—
114	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
115	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₅×D₈	—	4	4	no	—
119	C₅×M₁₆	—	4	2	no	—
120	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
123	C₅×C₂²⋊C₄	—	2	4	no	—
124	C₅×C₂²⋊C₄	—	2	4	no	—
125	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
126	#481	C₂×C₃×C₅	1	4	yes	complemented
127	#469	C₂×C₃×C₅	1	4	yes	complemented
128	#447	C₂×C₃×C₅	1	4	yes	complemented
129	#407	C₂×C₃×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₃×C₅	—	2	2	no	—
131	C₂²×C₃×C₅	—	2	2	no	—
132	C₂²×C₃×C₅	—	2	1	no	—
133	C₂²×C₃×C₅	—	2	2	no	—
134	C₂²×C₃×C₅	—	4	4	no	—
135	C₂²×C₃×C₅	—	4	4	no	—
136	C₂²×C₃×C₅	—	4	4	no	—
137	C₂²×C₃×C₅	—	4	4	no	—
138	C₂²×C₃×C₅	—	8	8	no	—
139	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
140	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	2	2	no	—
143	C₃×C₄×C₅	—	4	4	no	—
144	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
145	C₂⁴×C₃	—	2	2	no	—
146	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
147	C₂×C₃×D₄	—	2	4	no	—
148	C₂×C₃×D₄	—	2	4	no	—
149	C₂×C₃×D₄	—	2	2	no	—
150	C₂×C₃×D₄	—	4	4	no	—
151	C₂×C₃×D₄	—	4	8	no	—
152	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
153	C₂²×C₃×C₄	—	2	2	no	—
154	C₂²×C₃×C₄	—	4	2	no	—
155	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
156	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
158	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
159	C₃×D₈	—	4	4	no	—
160	C₃×M₁₆	—	4	2	no	—
161	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
162	C₃×C₄⋊C₄	—	2	2	no	—
163	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
164	C₃×C₂²⋊C₄	—	2	4	no	—
165	C₃×C₂²⋊C₄	—	2	4	no	—
166	C₂³×C₅	—	2	4	no	—
167	C₂³×C₅	—	2	4	no	—
168	C₂³×C₅	—	4	1	no	—
169	C₂³×C₅	—	4	4	no	—
170	C₂³×C₅	—	4	4	no	—
171	C₂³×C₅	—	4	4	no	—
172	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
173	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
174	C₅×D₄	—	2	8	no	—
175	C₅×D₄	—	4	4	no	—
176	C₅×D₄	—	4	8	no	—
177	C₅×D₄	—	4	8	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	4	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	4	no	—
184	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
186	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
187	C₅×C₈	—	2	4	no	—
188	C₂²×D₄	—	2	2	no	—
189	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
190	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
191	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
192	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	complemented
193	#121	—	2	2	no	—
194	#121	—	2	2	no	—
195	#121	C₂²×C₃×C₅	1	4	yes	—
196	#121	C₂²×C₃×C₅	1	4	yes	complemented
197	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
198	C₂×C₂²⋊C₄	—	2	2	no	—
199	#106	C₂²×C₃×C₅	1	4	yes	complemented
200	#102	C₂²×C₃×C₅	1	8	yes	complemented
201	C₂²⋊C₈	C₂²×C₃×C₅	1	4	yes	complemented
202	C₂×C₃×C₅	—	2	4	no	—
203	C₂×C₃×C₅	—	4	1	no	—
204	C₂×C₃×C₅	—	8	4	no	—
205	C₂×C₃×C₅	#534	1	1	yes	characteristic
206	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
207	C₂³×C₃	—	2	4	no	—
208	C₂³×C₃	—	2	4	no	—
209	C₂³×C₃	—	4	1	no	—
210	C₂³×C₃	—	4	4	no	—
211	C₂³×C₃	—	4	4	no	—
212	C₂³×C₃	—	4	4	no	—
213	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
214	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
215	C₃×D₄	—	2	8	no	—
216	C₃×D₄	—	4	4	no	—
217	C₃×D₄	—	4	8	no	—
218	C₃×D₄	—	4	8	no	—
219	C₂×C₃×C₄	—	2	2	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	4	no	—
222	C₂×C₃×C₄	—	4	2	no	—
223	C₂×C₃×C₄	—	4	1	no	—
224	C₂×C₃×C₄	—	4	4	no	—
225	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
227	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
228	C₃×C₈	—	2	4	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	4	4	no	—
234	C₂²×C₅	—	4	4	no	—
235	C₂²×C₅	—	4	4	no	—
236	C₂²×C₅	—	4	4	no	—
237	C₂²×C₅	—	8	8	no	—
238	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
239	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	2	no	—
242	C₄×C₅	—	4	4	no	—
243	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
244	C₂⁴	—	2	2	no	—
245	C₂⁴	C₃×C₅×D₄	1	1	yes	characteristic
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	4	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	4	4	no	—
250	C₂×D₄	—	4	8	no	—
251	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
255	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
256	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
257	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
258	D₈	—	4	4	no	—
259	M₁₆	—	4	2	no	—
260	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
261	C₄⋊C₄	—	2	2	no	—
262	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
263	C₂²⋊C₄	—	2	4	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₃×C₅	#3192	1	1	yes	characteristic, direct product factor, Hall
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	4	4	no	—
271	C₂²×C₃	—	4	4	no	—
272	C₂²×C₃	—	4	4	no	—
273	C₂²×C₃	—	4	4	no	—
274	C₂²×C₃	—	8	8	no	—
275	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
276	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	4	4	no	—
280	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
281	C₂×C₅	—	2	4	no	—
282	C₂×C₅	—	4	1	no	—
283	C₂×C₅	—	8	4	no	—
284	C₂×C₅	C₃×#534	1	1	yes	characteristic
285	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	4	1	no	—
289	C₂³	—	4	4	no	—
290	C₂³	—	4	4	no	—
291	C₂³	—	4	4	no	—
292	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
293	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
294	D₄	—	2	8	no	—
295	D₄	—	4	4	no	—
296	D₄	—	4	8	no	—
297	D₄	—	4	8	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	4	1	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
305	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
306	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
307	C₈	—	2	4	no	—
308	C₂×C₃	—	2	4	no	—
309	C₂×C₃	—	4	1	no	—
310	C₂×C₃	—	8	4	no	—
311	C₂×C₃	C₅×#534	1	1	yes	characteristic
312	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
313	C₅	C₃×#3192	1	1	yes	characteristic, direct product factor, Sylow
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	4	4	no	—
319	C₂²	—	4	4	no	—
320	C₂²	—	4	4	no	—
321	C₂²	—	4	4	no	—
322	C₂²	—	8	8	no	—
323	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	—
324	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	4	4	no	—
328	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
329	C₃	C₅×#3192	1	1	yes	characteristic, direct product factor, Sylow
330	C₂	—	2	4	no	—
331	C₂	—	4	1	no	—
332	C₂	—	8	4	no	—
333	C₂	C₃×C₅×#534	1	1	yes	characteristic
334	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	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 ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₃×C₅×#481	C₂	semidirect
3. C₃×C₅×#469	C₂	semidirect
4. C₃×C₅×#447	C₂	semidirect
5. C₃×C₅×#407	C₂	semidirect
6. C₅×#3192	C₃	direct (N × H)
8. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂×C₃×C₅×D₈	C₂²	semidirect
11. C₂×C₃×C₅×M₁₆	C₂²	semidirect
15. C₃×C₅×#121	C₂²	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₃×C₅×#106	C₂²	semidirect
19. C₃×C₅×#102	C₂²	semidirect
20. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
21. C₃×#3192	C₅	direct (N × H)
22. C₂×C₅×#121	C₂×C₃	semidirect
23. C₅×#481	C₂×C₃	semidirect
24. C₅×#469	C₂×C₃	semidirect
25. C₅×#447	C₂×C₃	semidirect
26. C₅×#407	C₂×C₃	semidirect
48. C₂×C₃×#121	C₂×C₅	semidirect
49. C₃×#481	C₂×C₅	semidirect
50. C₃×#469	C₂×C₅	semidirect
51. C₃×#447	C₂×C₅	semidirect
52. C₃×#407	C₂×C₅	semidirect
54. C₂²×C₅×D₄	C₂²×C₃	semidirect
56. C₂×C₅×D₈	C₂²×C₃	semidirect
57. C₂×C₅×M₁₆	C₂²×C₃	semidirect
61. C₅×#121	C₂²×C₃	semidirect
62. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
64. C₅×#106	C₂²×C₃	semidirect
65. C₅×#102	C₂²×C₃	semidirect
66. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
67. #3192	C₃×C₅	direct (N × H)
91. C₂²×C₃×D₄	C₂²×C₅	semidirect
93. C₂×C₃×D₈	C₂²×C₅	semidirect
94. C₂×C₃×M₁₆	C₂²×C₅	semidirect
98. C₃×#121	C₂²×C₅	semidirect
99. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
101. C₃×#106	C₂²×C₅	semidirect
102. C₃×#102	C₂²×C₅	semidirect
103. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
125. C₂×#121	C₂×C₃×C₅	semidirect
126. #481	C₂×C₃×C₅	semidirect
127. #469	C₂×C₃×C₅	semidirect
128. #447	C₂×C₃×C₅	semidirect
129. #407	C₂×C₃×C₅	semidirect
189. C₂²×D₄	C₂²×C₃×C₅	semidirect
191. C₂×D₈	C₂²×C₃×C₅	semidirect
192. C₂×M₁₆	C₂²×C₃×C₅	semidirect
196. #121	C₂²×C₃×C₅	semidirect
197. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
199. #106	C₂²×C₃×C₅	semidirect
200. #102	C₂²×C₃×C₅	semidirect
201. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
265. C₃×C₅	#3192	direct (N × H)
313. C₅	C₃×#3192	direct (N × H)
329. C₃	C₅×#3192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#121	2
C₃×C₅×#481	2
C₃×C₅×#469	2
C₃×C₅×#447	2
C₃×C₅×#407	2
C₅×#3192	3
C₃×#3192	5

Subgroups — C3×C5×#3192 #14276226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3192 #14276226