Subgroups — C₃×C₅×#1977 #14275011

Order 1920.

592 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#418	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1977	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
12	C₂×C₃×C₅×SD₁₆	—	2	1	no	—
13	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
14	C₂×C₃×C₅×SD₁₆	C₄	1	4	yes	complemented
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#117	C₂²	1	1	yes	characteristic
20	C₃×C₅×#108	—	2	2	no	—
21	C₃×C₅×#103	—	2	2	no	—
22	C₃×C₅×#102	—	2	2	no	—
23	C₃×C₅×#101	—	2	2	no	—
24	C₃×C₅×#100	—	2	2	no	—
25	C₃×C₅×#97	—	2	1	no	—
26	C₃×C₄×C₅×C₈	—	2	1	no	—
27	C₃×#1977	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic
29	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
30	C₅×#419	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#418	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×#101	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#100	C₂×C₃	1	1	yes	characteristic
34	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₅	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	—	2	1	no	—
38	C₂×C₃×C₅×Q₈	—	2	1	no	—
39	C₂×C₃×C₅×Q₈	—	2	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	1	no	—
41	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	—	2	4	no	—
51	C₃×C₅×SD₁₆	—	2	4	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	1	no	—
56	C₃×C₅×M₁₆	—	2	1	no	—
57	C₃×C₅×M₁₆	D₄	1	2	yes	—
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₂×C₃×C₅×C₈	—	2	1	no	—
61	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
62	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
67	C₃×C₄²×C₅	—	2	1	no	—
68	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic
69	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
70	C₃×#419	C₂×C₅	1	1	yes	characteristic, complemented
71	C₃×#418	C₂×C₅	1	1	yes	characteristic
72	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic
74	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×SD₁₆	—	2	1	no	—
79	C₂×C₅×SD₁₆	—	2	2	no	—
80	C₂×C₅×SD₁₆	C₃×C₄	1	4	yes	complemented
81	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
85	C₅×#117	C₂²×C₃	1	1	yes	characteristic
86	C₅×#108	—	2	2	no	—
87	C₅×#103	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×#101	—	2	2	no	—
90	C₅×#100	—	2	2	no	—
91	C₅×#97	—	2	1	no	—
92	C₄×C₅×C₈	—	2	1	no	—
93	#1977	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	4	1	no	—
96	C₂³×C₃×C₅	—	4	1	no	—
97	C₂³×C₃×C₅	—	8	2	no	—
98	C₂³×C₃×C₅	#41	1	1	yes	characteristic
99	C₃×C₅×Q₈	—	2	2	no	—
100	C₃×C₅×Q₈	—	2	2	no	—
101	C₃×C₅×Q₈	—	4	1	no	—
102	C₃×C₅×Q₈	—	4	1	no	—
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	—	2	2	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₃×C₅×D₄	—	4	1	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	4	1	no	—
110	C₂×C₃×C₄×C₅	—	4	1	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
117	C₃×C₅×C₈	—	2	2	no	—
118	C₃×C₅×C₈	—	4	1	no	—
119	C₃×C₅×C₈	—	4	1	no	—
120	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
121	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	—
122	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
123	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×SD₁₆	—	2	1	no	—
125	C₂×C₃×SD₁₆	—	2	1	no	—
126	C₂×C₃×SD₁₆	—	2	2	no	—
127	C₂×C₃×SD₁₆	C₄×C₅	1	4	yes	complemented
128	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
131	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#117	C₂²×C₅	1	1	yes	characteristic
133	C₃×#108	—	2	2	no	—
134	C₃×#103	—	2	2	no	—
135	C₃×#102	—	2	2	no	—
136	C₃×#101	—	2	2	no	—
137	C₃×#100	—	2	2	no	—
138	C₃×#97	—	2	1	no	—
139	C₃×C₄×C₈	—	2	1	no	—
140	C₂⁴×C₅	—	2	1	no	—
141	C₂×C₅×Q₈	—	2	1	no	—
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	—	2	1	no	—
146	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₅×SD₁₆	—	2	4	no	—
156	C₅×SD₁₆	—	2	4	no	—
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	2	1	no	—
159	C₅×M₁₆	—	2	1	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	C₃×D₄	1	2	yes	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
167	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
168	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
170	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic
174	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	#419	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	#418	C₂×C₃×C₅	1	1	yes	characteristic
177	C₂×#101	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂×#100	C₂×C₃×C₅	1	1	yes	characteristic
179	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	4	2	no	—
182	C₂²×C₃×C₅	—	8	2	no	—
183	C₂²×C₃×C₅	—	8	2	no	—
184	C₂²×C₃×C₅	—	8	2	no	—
185	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	#121	1	1	yes	characteristic
187	C₂²×C₃×C₅	#124	1	1	yes	characteristic
188	C₃×C₄×C₅	—	4	2	no	—
189	C₃×C₄×C₅	—	4	2	no	—
190	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	#121	1	1	yes	characteristic
193	C₃×C₄×C₅	#127	1	1	yes	characteristic
194	C₂⁴×C₃	—	2	1	no	—
195	C₂×C₃×Q₈	—	2	1	no	—
196	C₂×C₃×Q₈	—	2	1	no	—
197	C₂×C₃×Q₈	—	2	1	no	—
198	C₂×C₃×Q₈	—	2	1	no	—
199	C₂×C₃×Q₈	—	2	1	no	—
200	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
201	C₂×C₃×D₄	—	2	1	no	—
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	—	2	1	no	—
204	C₂×C₃×D₄	—	2	1	no	—
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₃×SD₁₆	—	2	4	no	—
210	C₃×SD₁₆	—	2	4	no	—
211	C₃×M₁₆	—	2	1	no	—
212	C₃×M₁₆	—	2	1	no	—
213	C₃×M₁₆	—	2	1	no	—
214	C₃×M₁₆	—	2	1	no	—
215	C₃×M₁₆	—	2	1	no	—
216	C₃×M₁₆	C₅×D₄	1	2	yes	—
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
222	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
223	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
224	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
225	C₃×C₂²⋊C₄	—	2	1	no	—
226	C₃×C₄²	—	2	1	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	4	1	no	—
229	C₂³×C₅	—	4	1	no	—
230	C₂³×C₅	—	8	2	no	—
231	C₂³×C₅	C₃×#41	1	1	yes	characteristic
232	C₅×Q₈	—	2	2	no	—
233	C₅×Q₈	—	2	2	no	—
234	C₅×Q₈	—	4	1	no	—
235	C₅×Q₈	—	4	1	no	—
236	C₅×D₄	—	2	2	no	—
237	C₅×D₄	—	2	2	no	—
238	C₅×D₄	—	4	1	no	—
239	C₅×D₄	—	4	1	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	4	1	no	—
243	C₂×C₄×C₅	—	4	1	no	—
244	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
249	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	4	1	no	—
252	C₅×C₈	—	4	1	no	—
253	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
254	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	—
255	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
256	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×SD₁₆	—	2	1	no	—
258	C₂×SD₁₆	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	C₃×C₄×C₅	1	4	yes	complemented
261	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
262	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	#117	C₂²×C₃×C₅	1	1	yes	characteristic
266	#108	—	2	2	no	—
267	#103	—	2	2	no	—
268	#102	—	2	2	no	—
269	#101	—	2	2	no	—
270	#100	—	2	2	no	—
271	#97	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₂×C₃×C₅	—	2	1	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	8	2	no	—
276	C₂×C₃×C₅	#390	1	1	yes	characteristic
277	C₂×C₃×C₅	#471	1	2	yes	—
278	C₂³×C₃	—	2	2	no	—
279	C₂³×C₃	—	4	1	no	—
280	C₂³×C₃	—	4	1	no	—
281	C₂³×C₃	—	8	2	no	—
282	C₂³×C₃	C₅×#41	1	1	yes	characteristic
283	C₃×Q₈	—	2	2	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	—	4	1	no	—
286	C₃×Q₈	—	4	1	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	4	1	no	—
290	C₃×D₄	—	4	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
301	C₃×C₈	—	2	2	no	—
302	C₃×C₈	—	4	1	no	—
303	C₃×C₈	—	4	1	no	—
304	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
305	C₃×C₈	C₅×C₂²⋊C₄	1	2	yes	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	4	2	no	—
308	C₂²×C₅	—	8	2	no	—
309	C₂²×C₅	—	8	2	no	—
310	C₂²×C₅	—	8	2	no	—
311	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
312	C₂²×C₅	C₃×#121	1	1	yes	characteristic
313	C₂²×C₅	C₃×#124	1	1	yes	characteristic
314	C₄×C₅	—	4	2	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
317	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
318	C₄×C₅	C₃×#121	1	1	yes	characteristic
319	C₄×C₅	C₃×#127	1	1	yes	characteristic
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
335	SD₁₆	—	2	4	no	—
336	SD₁₆	—	2	4	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	2	1	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	—	2	1	no	—
341	M₁₆	—	2	1	no	—
342	M₁₆	C₃×C₅×D₄	1	2	yes	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
347	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
348	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
349	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
350	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₃×C₅	#1977	1	1	yes	characteristic, direct product factor, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	4	2	no	—
356	C₂²×C₃	—	8	2	no	—
357	C₂²×C₃	—	8	2	no	—
358	C₂²×C₃	—	8	2	no	—
359	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₃	C₅×#121	1	1	yes	characteristic
361	C₂²×C₃	C₅×#124	1	1	yes	characteristic
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	2	no	—
364	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
365	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
366	C₃×C₄	C₅×#121	1	1	yes	characteristic
367	C₃×C₄	C₅×#127	1	1	yes	characteristic
368	C₂×C₅	—	2	1	no	—
369	C₂×C₅	—	2	1	no	—
370	C₂×C₅	—	8	2	no	—
371	C₂×C₅	C₃×#390	1	1	yes	characteristic
372	C₂×C₅	C₃×#471	1	2	yes	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	8	2	no	—
377	C₂³	C₃×C₅×#41	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
391	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
392	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
400	C₈	C₃×C₅×C₂²⋊C₄	1	2	yes	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	8	2	no	—
404	C₂×C₃	C₅×#390	1	1	yes	characteristic
405	C₂×C₃	C₅×#471	1	2	yes	—
406	C₅	C₃×#1977	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	8	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
413	C₂²	C₃×C₅×#121	1	1	yes	characteristic
414	C₂²	C₃×C₅×#124	1	1	yes	characteristic
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
419	C₄	C₃×C₅×#121	1	1	yes	characteristic
420	C₄	C₃×C₅×#127	1	1	yes	characteristic
421	C₃	C₅×#1977	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	C₃×C₅×#390	1	1	yes	characteristic
426	C₂	C₃×C₅×#471	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ 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. C₃×C₅×#419	C₂	semidirect
5. C₂×C₃×C₅×#101	C₂	semidirect
7. C₃×C₅×#405	C₂	semidirect
8. C₅×#1977	C₃	direct (N × H)
14. C₂×C₃×C₅×SD₁₆	C₄	semidirect
27. C₃×#1977	C₅	direct (N × H)
29. C₂×C₅×#108	C₂×C₃	semidirect
30. C₅×#419	C₂×C₃	semidirect
32. C₂×C₅×#101	C₂×C₃	semidirect
34. C₅×#405	C₂×C₃	semidirect
69. C₂×C₃×#108	C₂×C₅	semidirect
70. C₃×#419	C₂×C₅	semidirect
72. C₂×C₃×#101	C₂×C₅	semidirect
74. C₃×#405	C₂×C₅	semidirect
80. C₂×C₅×SD₁₆	C₃×C₄	semidirect
93. #1977	C₃×C₅	direct (N × H)
127. C₂×C₃×SD₁₆	C₄×C₅	semidirect
174. C₂×#108	C₂×C₃×C₅	semidirect
175. #419	C₂×C₃×C₅	semidirect
177. C₂×#101	C₂×C₃×C₅	semidirect
179. #405	C₂×C₃×C₅	semidirect
260. C₂×SD₁₆	C₃×C₄×C₅	semidirect
353. C₃×C₅	#1977	direct (N × H)
406. C₅	C₃×#1977	direct (N × H)
421. C₃	C₅×#1977	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×C₃×C₅×SD₁₆	2
C₂×C₃×C₅×#108	2
C₃×C₅×#419	2
C₃×C₅×#418	2
C₂×C₃×C₅×#101	2
C₂×C₃×C₅×#100	2
C₃×C₅×#405	2
C₅×#1977	3
C₃×#1977	5

Subgroups — C3×C5×#1977 #14275011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1977 #14275011