Subgroups — C₃×C₅×#1975 #14275009

Order 1920.

584 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#104	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#408	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1975	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
8	C₃×C₅×#135	—	2	2	no	—
9	C₃×C₅×#135	—	2	2	no	—
10	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
11	C₂×C₃×C₅×SD₁₆	C₄	1	2	yes	complemented
12	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×#108	—	2	2	no	—
18	C₃×C₅×#104	—	2	4	no	—
19	C₃×C₅×C₂²⋊C₈	—	2	4	no	—
20	C₃×C₅×#97	—	2	2	no	—
21	C₃×#1975	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
23	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₅×#104	C₂×C₃	1	2	yes	complemented
25	C₅×#408	C₂×C₃	1	2	yes	complemented
26	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×C₅×#41	—	2	2	no	—
28	C₃×C₅×#41	—	2	2	no	—
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₃×C₅×Q₁₆	—	2	2	no	—
38	C₃×C₅×SD₁₆	—	2	4	no	—
39	C₃×C₅×D₈	—	2	2	no	—
40	C₃×C₅×M₁₆	—	2	2	no	—
41	C₃×C₅×M₁₆	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	2	no	—
45	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	D₄	1	2	yes	—
52	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
53	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×C₃×#104	C₂×C₅	1	2	yes	complemented
55	C₃×#408	C₂×C₅	1	2	yes	complemented
56	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
58	C₅×#135	—	2	2	no	—
59	C₅×#135	—	2	2	no	—
60	C₂×C₅×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
61	C₂×C₅×SD₁₆	C₃×C₄	1	2	yes	complemented
62	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic, complemented
63	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
64	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×#108	—	2	2	no	—
68	C₅×#104	—	2	4	no	—
69	C₅×C₂²⋊C₈	—	2	4	no	—
70	C₅×#97	—	2	2	no	—
71	#1975	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	#41	1	1	yes	characteristic
74	C₃×C₅×Q₈	—	2	2	no	—
75	C₃×C₅×Q₈	—	2	2	no	—
76	C₃×C₅×D₄	—	2	2	no	—
77	C₃×C₅×D₄	—	2	2	no	—
78	C₃×C₅×D₄	—	4	2	no	—
79	C₃×C₅×D₄	—	4	2	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	4	2	no	—
83	C₂×C₃×C₄×C₅	—	4	2	no	—
84	C₂×C₃×C₄×C₅	—	4	2	no	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×C₈	—	2	2	no	—
92	C₃×C₅×C₈	—	4	2	no	—
93	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
94	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
96	C₃×#135	—	2	2	no	—
97	C₃×#135	—	2	2	no	—
98	C₂×C₃×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
99	C₂×C₃×SD₁₆	C₄×C₅	1	2	yes	complemented
100	C₂×C₃×D₈	C₄×C₅	1	1	yes	characteristic, complemented
101	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
102	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	C₃×#108	—	2	2	no	—
106	C₃×#104	—	2	4	no	—
107	C₃×C₂²⋊C₈	—	2	4	no	—
108	C₃×#97	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₅×Q₁₆	—	2	2	no	—
120	C₅×SD₁₆	—	2	4	no	—
121	C₅×D₈	—	2	2	no	—
122	C₅×M₁₆	—	2	2	no	—
123	C₅×M₁₆	—	2	2	no	—
124	C₂×C₅×C₈	—	2	1	no	—
125	C₂×C₅×C₈	—	2	1	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
130	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
131	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
132	C₄²×C₅	—	2	1	no	—
133	C₄²×C₅	C₃×D₄	1	2	yes	—
134	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic
135	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
136	C₂×#104	C₂×C₃×C₅	1	2	yes	complemented
137	#408	C₂×C₃×C₅	1	2	yes	complemented
138	C₂×#97	C₂×C₃×C₅	1	1	yes	characteristic, complemented
139	C₂²×C₃×C₅	—	2	2	no	—
140	C₂²×C₃×C₅	—	4	2	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	#121	1	1	yes	characteristic
144	C₂²×C₃×C₅	#124	1	1	yes	characteristic
145	C₃×C₄×C₅	—	4	2	no	—
146	C₃×C₄×C₅	—	4	2	no	—
147	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
149	C₃×C₄×C₅	#121	1	1	yes	characteristic
150	C₃×C₄×C₅	#127	1	1	yes	characteristic
151	C₃×#41	—	2	2	no	—
152	C₃×#41	—	2	2	no	—
153	C₃×#41	—	2	2	no	—
154	C₃×#41	—	2	2	no	—
155	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₃×Q₁₆	—	2	2	no	—
162	C₃×SD₁₆	—	2	4	no	—
163	C₃×D₈	—	2	2	no	—
164	C₃×M₁₆	—	2	2	no	—
165	C₃×M₁₆	—	2	2	no	—
166	C₂×C₃×C₈	—	2	1	no	—
167	C₂×C₃×C₈	—	2	1	no	—
168	C₂×C₃×C₈	—	2	2	no	—
169	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
171	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
172	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
173	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
174	C₃×C₄²	—	2	1	no	—
175	C₃×C₄²	C₅×D₄	1	2	yes	—
176	C₂³×C₅	—	2	2	no	—
177	C₂³×C₅	C₃×#41	1	1	yes	characteristic
178	C₅×Q₈	—	2	2	no	—
179	C₅×Q₈	—	2	2	no	—
180	C₅×D₄	—	2	2	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	4	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	4	2	no	—
187	C₂×C₄×C₅	—	4	2	no	—
188	C₂×C₄×C₅	—	4	2	no	—
189	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
195	C₅×C₈	—	2	2	no	—
196	C₅×C₈	—	4	2	no	—
197	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
198	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
199	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
200	#135	—	2	2	no	—
201	#135	—	2	2	no	—
202	C₂×Q₁₆	C₃×C₄×C₅	1	1	yes	characteristic, complemented
203	C₂×SD₁₆	C₃×C₄×C₅	1	2	yes	complemented
204	C₂×D₈	C₃×C₄×C₅	1	1	yes	characteristic, complemented
205	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
206	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
207	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
209	#108	—	2	2	no	—
210	#104	—	2	4	no	—
211	C₂²⋊C₈	—	2	4	no	—
212	#97	—	2	2	no	—
213	C₂×C₃×C₅	—	2	1	no	—
214	C₂×C₃×C₅	—	2	1	no	—
215	C₂×C₃×C₅	—	8	2	no	—
216	C₂×C₃×C₅	#390	1	1	yes	characteristic
217	C₂×C₃×C₅	#444	1	2	yes	—
218	C₂³×C₃	—	2	2	no	—
219	C₂³×C₃	C₅×#41	1	1	yes	characteristic
220	C₃×Q₈	—	2	2	no	—
221	C₃×Q₈	—	2	2	no	—
222	C₃×D₄	—	2	2	no	—
223	C₃×D₄	—	2	2	no	—
224	C₃×D₄	—	4	2	no	—
225	C₃×D₄	—	4	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	4	2	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
237	C₃×C₈	—	2	2	no	—
238	C₃×C₈	—	4	2	no	—
239	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
240	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
241	C₂²×C₅	—	2	2	no	—
242	C₂²×C₅	—	4	2	no	—
243	C₂²×C₅	—	4	4	no	—
244	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₅	C₃×#121	1	1	yes	characteristic
246	C₂²×C₅	C₃×#124	1	1	yes	characteristic
247	C₄×C₅	—	4	2	no	—
248	C₄×C₅	—	4	2	no	—
249	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
250	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
251	C₄×C₅	C₃×#121	1	1	yes	characteristic
252	C₄×C₅	C₃×#127	1	1	yes	characteristic
253	#41	—	2	2	no	—
254	#41	—	2	2	no	—
255	#41	—	2	2	no	—
256	#41	—	2	2	no	—
257	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
263	Q₁₆	—	2	2	no	—
264	SD₁₆	—	2	4	no	—
265	D₈	—	2	2	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	—	2	1	no	—
269	C₂×C₈	—	2	1	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
272	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
273	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
274	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
275	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
276	C₄²	—	2	1	no	—
277	C₄²	C₃×C₅×D₄	1	2	yes	—
278	C₃×C₅	#1975	1	1	yes	characteristic, direct product factor, Hall
279	C₂²×C₃	—	2	2	no	—
280	C₂²×C₃	—	4	2	no	—
281	C₂²×C₃	—	4	4	no	—
282	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
283	C₂²×C₃	C₅×#121	1	1	yes	characteristic
284	C₂²×C₃	C₅×#124	1	1	yes	characteristic
285	C₃×C₄	—	4	2	no	—
286	C₃×C₄	—	4	2	no	—
287	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
288	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
289	C₃×C₄	C₅×#121	1	1	yes	characteristic
290	C₃×C₄	C₅×#127	1	1	yes	characteristic
291	C₂×C₅	—	2	1	no	—
292	C₂×C₅	—	2	1	no	—
293	C₂×C₅	—	8	2	no	—
294	C₂×C₅	C₃×#390	1	1	yes	characteristic
295	C₂×C₅	C₃×#444	1	2	yes	—
296	C₂³	—	2	2	no	—
297	C₂³	C₃×C₅×#41	1	1	yes	characteristic
298	Q₈	—	2	2	no	—
299	Q₈	—	2	2	no	—
300	D₄	—	2	2	no	—
301	D₄	—	2	2	no	—
302	D₄	—	4	2	no	—
303	D₄	—	4	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
310	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
311	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
312	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
313	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
314	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	—	4	2	no	—
317	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
318	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	8	2	no	—
322	C₂×C₃	C₅×#390	1	1	yes	characteristic
323	C₂×C₃	C₅×#444	1	2	yes	—
324	C₅	C₃×#1975	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²	—	2	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	4	no	—
328	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
329	C₂²	C₃×C₅×#121	1	1	yes	characteristic
330	C₂²	C₃×C₅×#124	1	1	yes	characteristic
331	C₄	—	4	2	no	—
332	C₄	—	4	2	no	—
333	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
335	C₄	C₃×C₅×#121	1	1	yes	characteristic
336	C₄	C₃×C₅×#127	1	1	yes	characteristic
337	C₃	C₅×#1975	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	2	1	no	—
339	C₂	—	2	1	no	—
340	C₂	—	8	2	no	—
341	C₂	C₃×C₅×#390	1	1	yes	characteristic
342	C₂	C₃×C₅×#444	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×C₅×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂²×C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
3. C₂×C₃×C₅×#104	C₂	semidirect
4. C₃×C₅×#408	C₂	semidirect
5. C₂×C₃×C₅×#97	C₂	semidirect
6. C₅×#1975	C₃	direct (N × H)
10. C₂×C₃×C₅×Q₁₆	C₄	semidirect
11. C₂×C₃×C₅×SD₁₆	C₄	semidirect
12. C₂×C₃×C₅×D₈	C₄	semidirect
21. C₃×#1975	C₅	direct (N × H)
23. C₂×C₅×#108	C₂×C₃	semidirect
24. C₂×C₅×#104	C₂×C₃	semidirect
25. C₅×#408	C₂×C₃	semidirect
26. C₂×C₅×#97	C₂×C₃	semidirect
53. C₂×C₃×#108	C₂×C₅	semidirect
54. C₂×C₃×#104	C₂×C₅	semidirect
55. C₃×#408	C₂×C₅	semidirect
56. C₂×C₃×#97	C₂×C₅	semidirect
60. C₂×C₅×Q₁₆	C₃×C₄	semidirect
61. C₂×C₅×SD₁₆	C₃×C₄	semidirect
62. C₂×C₅×D₈	C₃×C₄	semidirect
71. #1975	C₃×C₅	direct (N × H)
98. C₂×C₃×Q₁₆	C₄×C₅	semidirect
99. C₂×C₃×SD₁₆	C₄×C₅	semidirect
100. C₂×C₃×D₈	C₄×C₅	semidirect
135. C₂×#108	C₂×C₃×C₅	semidirect
136. C₂×#104	C₂×C₃×C₅	semidirect
137. #408	C₂×C₃×C₅	semidirect
138. C₂×#97	C₂×C₃×C₅	semidirect
202. C₂×Q₁₆	C₃×C₄×C₅	semidirect
203. C₂×SD₁₆	C₃×C₄×C₅	semidirect
204. C₂×D₈	C₃×C₄×C₅	semidirect
278. C₃×C₅	#1975	direct (N × H)
324. C₅	C₃×#1975	direct (N × H)
337. C₃	C₅×#1975	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×#135	2
C₂×C₃×C₅×#108	2
C₂×C₃×C₅×#104	2
C₃×C₅×#408	2
C₂×C₃×C₅×#97	2
C₅×#1975	3
C₃×#1975	5

Subgroups — C3×C5×#1975 #14275009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1975 #14275009