Subgroups — C₃×C₅×#1929 #14274963

Order 1920.

448 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1929	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#108	—	2	2	no	—
17	C₃×C₅×#104	—	2	2	no	—
18	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
19	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
20	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
21	C₃×C₅×#102	C₄	1	1	yes	characteristic, complemented
22	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
23	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
24	C₃×C₅×#97	—	2	1	no	—
25	C₃×C₄×C₅×C₈	—	2	1	no	—
26	C₃×#1929	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#104	C₂×C₃	1	1	yes	characteristic
29	C₅×#416	C₂×C₃	1	1	yes	characteristic
30	C₅×#408	C₂×C₃	1	1	yes	characteristic
31	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#339	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	—	2	1	no	—
38	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×M₁₆	—	2	1	no	—
45	C₃×C₅×M₁₆	—	2	1	no	—
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	D₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	—	2	1	no	—
52	C₂×C₃×C₅×C₈	—	2	1	no	—
53	C₂×C₃×C₅×C₈	—	2	1	no	—
54	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
61	C₃×C₄²×C₅	—	2	1	no	—
62	C₃×C₄²×C₅	—	2	1	no	—
63	C₃×C₄²×C₅	—	2	1	no	—
64	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic
66	C₃×#416	C₂×C₅	1	1	yes	characteristic
67	C₃×#408	C₂×C₅	1	1	yes	characteristic
68	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₅×#117	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×#108	—	2	2	no	—
79	C₅×#104	—	2	2	no	—
80	C₅×#103	C₃×C₄	1	1	yes	characteristic, complemented
81	C₅×#103	C₃×C₄	1	1	yes	characteristic, complemented
82	C₅×#102	C₃×C₄	1	1	yes	characteristic, complemented
83	C₅×#102	C₃×C₄	1	1	yes	characteristic, complemented
84	C₅×C₂²⋊C₈	—	2	1	no	—
85	C₅×C₂²⋊C₈	—	2	1	no	—
86	C₅×#97	—	2	1	no	—
87	C₄×C₅×C₈	—	2	1	no	—
88	#1929	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
89	C₂³×C₃×C₅	—	2	1	no	—
90	C₂³×C₃×C₅	#41	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	1	no	—
92	C₃×C₅×Q₈	—	2	1	no	—
93	C₃×C₅×D₄	—	2	1	no	—
94	C₃×C₅×D₄	—	2	1	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₃×C₅×C₈	—	2	1	no	—
112	C₃×C₅×C₈	—	2	1	no	—
113	C₃×C₅×C₈	—	2	2	no	—
114	C₃×C₅×C₈	—	2	1	no	—
115	C₃×C₅×C₈	—	2	1	no	—
116	C₃×C₅×C₈	—	4	1	no	—
117	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
122	C₃×#117	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
124	C₃×#108	—	2	2	no	—
125	C₃×#104	—	2	2	no	—
126	C₃×#103	C₄×C₅	1	1	yes	characteristic, complemented
127	C₃×#103	C₄×C₅	1	1	yes	characteristic, complemented
128	C₃×#102	C₄×C₅	1	1	yes	characteristic, complemented
129	C₃×#102	C₄×C₅	1	1	yes	characteristic, complemented
130	C₃×C₂²⋊C₈	—	2	1	no	—
131	C₃×C₂²⋊C₈	—	2	1	no	—
132	C₃×#97	—	2	1	no	—
133	C₃×C₄×C₈	—	2	1	no	—
134	C₅×#41	—	2	1	no	—
135	C₅×#41	—	2	1	no	—
136	C₅×#41	—	2	1	no	—
137	C₅×#41	—	2	1	no	—
138	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	—	2	1	no	—
146	C₅×M₁₆	—	2	1	no	—
147	C₅×M₁₆	C₃×D₄	1	2	yes	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	2	1	no	—
152	C₂×C₅×C₈	—	2	1	no	—
153	C₂×C₅×C₈	—	2	1	no	—
154	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
157	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
159	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
160	C₅×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	1	no	—
164	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
165	C₂×#104	C₂×C₃×C₅	1	1	yes	characteristic
166	#416	C₂×C₃×C₅	1	1	yes	characteristic
167	#408	C₂×C₃×C₅	1	1	yes	characteristic
168	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	#339	C₂×C₃×C₅	1	1	yes	characteristic, complemented
170	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
171	C₂²×C₃×C₅	—	2	1	no	—
172	C₂²×C₃×C₅	—	2	1	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	—	4	1	no	—
175	C₂²×C₃×C₅	—	4	1	no	—
176	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	#124	1	1	yes	characteristic
178	C₂²×C₃×C₅	#126	1	1	yes	characteristic
179	C₃×C₄×C₅	—	4	2	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	—	4	1	no	—
183	C₃×C₄×C₅	#117	1	1	yes	characteristic
184	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
185	C₃×C₄×C₅	#121	1	1	yes	characteristic
186	C₃×C₄×C₅	#123	1	1	yes	characteristic
187	C₃×#41	—	2	1	no	—
188	C₃×#41	—	2	1	no	—
189	C₃×#41	—	2	1	no	—
190	C₃×#41	—	2	1	no	—
191	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
194	C₂²×C₃×C₄	—	2	1	no	—
195	C₂²×C₃×C₄	—	2	1	no	—
196	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
197	C₃×M₁₆	—	2	1	no	—
198	C₃×M₁₆	—	2	1	no	—
199	C₃×M₁₆	—	2	1	no	—
200	C₃×M₁₆	C₅×D₄	1	2	yes	—
201	C₂×C₃×C₈	—	2	1	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₂×C₃×C₈	—	2	1	no	—
205	C₂×C₃×C₈	—	2	1	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
210	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
211	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	—	2	1	no	—
214	C₃×C₄²	—	2	1	no	—
215	C₃×C₄²	—	2	1	no	—
216	C₃×C₄²	—	2	1	no	—
217	C₂³×C₅	—	2	1	no	—
218	C₂³×C₅	C₃×#41	1	1	yes	characteristic
219	C₅×Q₈	—	2	1	no	—
220	C₅×Q₈	—	2	1	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	2	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
237	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
239	C₅×C₈	—	2	1	no	—
240	C₅×C₈	—	2	1	no	—
241	C₅×C₈	—	2	2	no	—
242	C₅×C₈	—	2	1	no	—
243	C₅×C₈	—	2	1	no	—
244	C₅×C₈	—	4	1	no	—
245	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
246	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
247	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
250	#117	C₂²×C₃×C₅	1	1	yes	characteristic
251	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
252	#108	—	2	2	no	—
253	#104	—	2	2	no	—
254	#103	C₃×C₄×C₅	1	1	yes	characteristic, complemented
255	#103	C₃×C₄×C₅	1	1	yes	characteristic, complemented
256	#102	C₃×C₄×C₅	1	1	yes	characteristic, complemented
257	#102	C₃×C₄×C₅	1	1	yes	characteristic, complemented
258	C₂²⋊C₈	—	2	1	no	—
259	C₂²⋊C₈	—	2	1	no	—
260	#97	—	2	1	no	—
261	C₄×C₈	—	2	1	no	—
262	C₂×C₃×C₅	—	2	1	no	—
263	C₂×C₃×C₅	—	2	1	no	—
264	C₂×C₃×C₅	—	8	1	no	—
265	C₂×C₃×C₅	#388	1	1	yes	characteristic
266	C₂×C₃×C₅	#443	1	1	yes	characteristic
267	C₂×C₃×C₅	#444	1	1	yes	characteristic
268	C₂³×C₃	—	2	1	no	—
269	C₂³×C₃	C₅×#41	1	1	yes	characteristic
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	—	2	1	no	—
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	1	no	—
274	C₃×D₄	—	4	1	no	—
275	C₃×D₄	—	4	1	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	4	1	no	—
284	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
288	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
289	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
290	C₃×C₈	—	2	1	no	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	—	2	1	no	—
294	C₃×C₈	—	2	1	no	—
295	C₃×C₈	—	4	1	no	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	1	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	4	1	no	—
301	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₅	C₃×#124	1	1	yes	characteristic
303	C₂²×C₅	C₃×#126	1	1	yes	characteristic
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	4	1	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	C₃×#117	1	1	yes	characteristic
309	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
310	C₄×C₅	C₃×#121	1	1	yes	characteristic
311	C₄×C₅	C₃×#123	1	1	yes	characteristic
312	#41	—	2	1	no	—
313	#41	—	2	1	no	—
314	#41	—	2	1	no	—
315	#41	—	2	1	no	—
316	C₂×Q₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	C₃×C₅×D₄	1	2	yes	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
333	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
334	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
335	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
336	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
338	C₂²⋊C₄	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₃×C₅	#1929	1	1	yes	characteristic, direct product factor, Hall
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
349	C₂²×C₃	C₅×#124	1	1	yes	characteristic
350	C₂²×C₃	C₅×#126	1	1	yes	characteristic
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	1	no	—
353	C₃×C₄	—	4	1	no	—
354	C₃×C₄	—	4	1	no	—
355	C₃×C₄	C₅×#117	1	1	yes	characteristic
356	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
357	C₃×C₄	C₅×#121	1	1	yes	characteristic
358	C₃×C₄	C₅×#123	1	1	yes	characteristic
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	2	1	no	—
361	C₂×C₅	—	8	1	no	—
362	C₂×C₅	C₃×#388	1	1	yes	characteristic
363	C₂×C₅	C₃×#443	1	1	yes	characteristic
364	C₂×C₅	C₃×#444	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	C₃×C₅×#41	1	1	yes	characteristic
367	Q₈	—	2	1	no	—
368	Q₈	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
382	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
384	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
385	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
386	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	2	1	no	—
389	C₈	—	2	2	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	1	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	8	1	no	—
396	C₂×C₃	C₅×#388	1	1	yes	characteristic
397	C₂×C₃	C₅×#443	1	1	yes	characteristic
398	C₂×C₃	C₅×#444	1	1	yes	characteristic
399	C₅	C₃×#1929	1	1	yes	characteristic, direct product factor, Sylow
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
406	C₂²	C₃×C₅×#124	1	1	yes	characteristic
407	C₂²	C₃×C₅×#126	1	1	yes	characteristic
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	C₃×C₅×#117	1	1	yes	characteristic
413	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
414	C₄	C₃×C₅×#121	1	1	yes	characteristic
415	C₄	C₃×C₅×#123	1	1	yes	characteristic
416	C₃	C₅×#1929	1	1	yes	characteristic, direct product factor, Sylow
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	1	no	—
420	C₂	C₃×C₅×#388	1	1	yes	characteristic
421	C₂	C₃×C₅×#443	1	1	yes	characteristic
422	C₂	C₃×C₅×#444	1	1	yes	characteristic

	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×#41	C₂²
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
1. C₂×C₃×C₅×#108	C₂	semidirect
5. C₃×C₅×#405	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₃×C₅×#336	C₂	semidirect
8. C₅×#1929	C₃	direct (N × H)
18. C₃×C₅×#103	C₄	semidirect
19. C₃×C₅×#103	C₄	semidirect
20. C₃×C₅×#102	C₄	semidirect
21. C₃×C₅×#102	C₄	semidirect
26. C₃×#1929	C₅	direct (N × H)
27. C₂×C₅×#108	C₂×C₃	semidirect
31. C₅×#405	C₂×C₃	semidirect
32. C₅×#339	C₂×C₃	semidirect
33. C₅×#336	C₂×C₃	semidirect
64. C₂×C₃×#108	C₂×C₅	semidirect
68. C₃×#405	C₂×C₅	semidirect
69. C₃×#339	C₂×C₅	semidirect
70. C₃×#336	C₂×C₅	semidirect
80. C₅×#103	C₃×C₄	semidirect
81. C₅×#103	C₃×C₄	semidirect
82. C₅×#102	C₃×C₄	semidirect
83. C₅×#102	C₃×C₄	semidirect
88. #1929	C₃×C₅	direct (N × H)
126. C₃×#103	C₄×C₅	semidirect
127. C₃×#103	C₄×C₅	semidirect
128. C₃×#102	C₄×C₅	semidirect
129. C₃×#102	C₄×C₅	semidirect
164. C₂×#108	C₂×C₃×C₅	semidirect
168. #405	C₂×C₃×C₅	semidirect
169. #339	C₂×C₃×C₅	semidirect
170. #336	C₂×C₃×C₅	semidirect
254. #103	C₃×C₄×C₅	semidirect
255. #103	C₃×C₄×C₅	semidirect
256. #102	C₃×C₄×C₅	semidirect
257. #102	C₃×C₄×C₅	semidirect
342. C₃×C₅	#1929	direct (N × H)
399. C₅	C₃×#1929	direct (N × H)
416. C₃	C₅×#1929	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×#108	2
C₂×C₃×C₅×#104	2
C₃×C₅×#416	2
C₃×C₅×#408	2
C₃×C₅×#405	2
C₃×C₅×#339	2
C₃×C₅×#336	2
C₅×#1929	3
C₃×#1929	5

Subgroups — C3×C5×#1929 #14274963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1929 #14274963