Subgroups — C₃×#10613576 #14439130

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4060	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4057	C₂	1	2	yes	maximal, complemented
3	C₃×D₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66002	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65464	C₂	1	2	yes	maximal, complemented
7	C₃×#65440	C₂	1	2	yes	maximal, complemented
8	C₃×#65363	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64996	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613576	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	1	yes	characteristic
14	C₂×C₃×#711	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×D₅	—	2	2	no	—
16	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
21	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×#688	C₂²	1	2	yes	complemented
23	C₃×#4086	—	2	2	no	—
24	C₃×#4086	C₂²	1	2	yes	—
25	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#687	C₂²	1	2	yes	complemented
27	C₂×C₃×#686	C₂²	1	2	yes	complemented
28	C₂×C₃×#686	C₂²	1	2	yes	complemented
29	C₃×#4060	—	2	8	no	—
30	C₃×#4057	—	2	8	no	—
31	C₂×C₃×D₄₀	C₂²	1	2	yes	complemented
32	C₂×C₃×#677	C₂²	1	2	yes	complemented
33	C₂×C₃×#676	C₂²	1	2	yes	—
34	C₃×#4030	—	2	2	no	—
35	C₃×#4027	—	2	2	no	—
36	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
37	C₃×#4020	C₂²	1	1	yes	characteristic
38	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
41	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3151	—	5	1	no	maximal, Hall
43	C₂×#4060	C₂×C₃	1	2	yes	complemented
44	C₂×#4057	C₂×C₃	1	2	yes	complemented
45	D₅×#127	C₂×C₃	1	1	yes	characteristic, complemented
46	#66002	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
48	#65464	C₂×C₃	1	2	yes	complemented
49	#65440	C₂×C₃	1	2	yes	complemented
50	#65363	C₂×C₃	1	1	yes	characteristic, complemented
51	#65347	C₂×C₃	1	1	yes	characteristic, complemented
52	#65001	C₂×C₃	1	1	yes	characteristic, complemented
53	#64996	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×C₃×D₅	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
62	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
63	C₂²×C₃×Dic₅	—	2	1	no	—
64	C₃×#713	—	2	4	no	—
65	C₃×#711	—	2	4	no	—
66	C₃×D₄×D₅	—	2	4	no	—
67	C₃×D₄×D₅	—	2	4	no	—
68	C₃×D₄×D₅	—	4	8	no	—
69	C₂×C₃×D₂₀	—	2	1	no	—
70	C₂×C₃×D₂₀	—	2	2	no	—
71	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
72	C₂×C₃×D₂₀	C₂³	1	2	yes	—
73	C₂×C₃×C₄×D₅	—	2	1	no	—
74	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
75	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
76	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
77	C₃×C₅×SD₁₆	—	2	4	no	—
78	C₃×C₅×D₈	—	2	4	no	—
79	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
80	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
81	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
82	C₃×#688	—	2	4	no	—
83	C₃×#687	—	2	4	no	—
84	C₃×#686	—	2	4	no	—
85	C₃×#686	—	2	4	no	—
86	C₃×#685	—	2	2	no	—
87	C₃×#683	—	2	2	no	—
88	C₃×C₄×Dic₅	D₄	1	2	yes	—
89	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×#168	C₂³	1	2	yes	—
91	C₃×D₄₀	—	2	4	no	—
92	C₃×#677	—	2	4	no	—
93	C₃×#676	D₄	1	8	yes	complemented
94	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
95	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
96	C₃×#532	—	5	1	no	—
97	C₂×C₃×#127	—	5	1	no	—
98	C₃×#496	—	5	1	no	—
99	C₃×#496	—	5	1	no	—
100	C₃×#496	—	5	1	no	—
101	C₃×#496	D₅	1	1	yes	characteristic, complemented
102	C₃×#493	—	5	2	no	—
103	C₃×#492	—	5	2	no	—
104	C₃×C₄×M₁₆	—	5	1	no	—
105	C₂×#713	C₂²×C₃	1	1	yes	characteristic
106	C₂×#711	C₂²×C₃	1	1	yes	characteristic
107	C₂×D₄×D₅	—	2	2	no	—
108	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
109	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
110	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
111	C₅×#127	C₂²×C₃	1	1	yes	characteristic
112	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
113	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×#688	C₂²×C₃	1	2	yes	complemented
115	#4086	—	2	2	no	—
116	#4086	C₂²×C₃	1	2	yes	—
117	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₂×#687	C₂²×C₃	1	2	yes	complemented
119	C₂×#686	C₂²×C₃	1	2	yes	complemented
120	C₂×#686	C₂²×C₃	1	2	yes	complemented
121	#4060	—	2	8	no	—
122	#4057	—	2	8	no	—
123	C₂×D₄₀	C₂²×C₃	1	2	yes	complemented
124	C₂×#677	C₂²×C₃	1	2	yes	complemented
125	C₂×#676	C₂²×C₃	1	2	yes	—
126	#4030	—	2	2	no	—
127	#4027	—	2	2	no	—
128	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
129	#4020	C₂²×C₃	1	1	yes	characteristic
130	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
131	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
133	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
134	#3151	—	5	1	no	Sylow
135	C₂³×C₃×C₅	—	2	1	no	—
136	C₂³×C₃×C₅	—	2	2	no	—
137	C₂²×C₃×D₅	—	2	1	no	—
138	C₂²×C₃×D₅	—	2	2	no	—
139	C₂²×C₃×D₅	—	4	8	no	—
140	C₂²×C₃×D₅	—	4	4	no	—
141	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	4	4	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
150	C₃×C₂²⋊D₅	—	4	2	no	—
151	C₃×C₂²⋊D₅	—	4	4	no	—
152	C₃×C₂²⋊D₅	—	4	8	no	—
153	C₃×C₂²⋊D₅	—	4	4	no	—
154	C₂×C₃×Dic₅	—	2	1	no	—
155	C₂×C₃×Dic₅	—	4	2	no	—
156	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
158	C₃×D₂₀	—	2	2	no	—
159	C₃×D₂₀	—	2	2	no	—
160	C₃×D₂₀	—	2	2	no	—
161	C₃×D₂₀	—	4	4	no	—
162	C₃×D₂₀	—	4	2	no	—
163	C₃×C₄×D₅	—	2	4	no	—
164	C₃×C₄×D₅	—	4	2	no	—
165	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
166	C₃×Dic₁₀	—	2	2	no	—
167	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
168	C₃×#168	C₂×D₄	1	4	yes	complemented
169	C₂×C₃×#41	—	5	1	no	—
170	C₂×C₃×#41	—	5	1	no	—
171	C₂²×C₃×D₄	—	5	2	no	—
172	C₂²×C₃×D₄	—	10	2	no	—
173	C₃×AGL(1,ℤ/8)	—	10	8	no	—
174	C₃×AGL(1,ℤ/8)	—	10	8	no	—
175	C₂×C₃×SD₁₆	—	5	2	no	—
176	C₂×C₃×SD₁₆	—	5	2	no	—
177	C₂×C₃×SD₁₆	—	5	2	no	—
178	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	complemented
179	C₂×C₃×D₈	—	5	2	no	—
180	C₂×C₃×D₈	—	5	2	no	—
181	C₂×C₃×D₈	—	5	2	no	—
182	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
183	C₂×C₃×M₁₆	—	5	2	no	—
184	C₃×C₄⋊Q₈	—	5	1	no	—
185	C₃×#127	—	5	2	no	—
186	C₃×#127	—	5	1	no	—
187	C₃×#127	—	5	1	no	—
188	C₃×#127	—	10	2	no	—
189	C₃×#127	C₂×D₅	1	1	yes	characteristic
190	C₃×#124	—	5	1	no	—
191	C₃×#124	C₂×D₅	1	1	yes	characteristic, complemented
192	C₃×#121	—	10	2	no	—
193	C₃×C₄×D₄	—	10	2	no	—
194	C₂×C₃×C₄²	—	5	1	no	—
195	C₃×#97	—	5	1	no	—
196	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
197	C₃×C₄×C₈	—	5	2	no	—
198	C₂³×D₅	—	2	2	no	—
199	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₅×D₄	—	2	2	no	—
201	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
203	C₂×C₂²⋊D₅	—	2	1	no	—
204	C₂×C₂²⋊D₅	—	2	4	no	—
205	C₂×C₂²⋊D₅	—	2	2	no	—
206	C₂×C₂²⋊D₅	—	2	2	no	—
207	C₂²×Dic₅	—	2	1	no	—
208	#713	—	2	4	no	—
209	#711	—	2	4	no	—
210	D₄×D₅	—	2	4	no	—
211	D₄×D₅	—	2	4	no	—
212	D₄×D₅	—	4	8	no	—
213	C₂×D₂₀	—	2	1	no	—
214	C₂×D₂₀	—	2	2	no	—
215	C₂×D₂₀	C₂³×C₃	1	2	yes	—
216	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄×D₅	—	2	1	no	—
218	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
219	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
220	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
221	C₅×SD₁₆	—	2	4	no	—
222	C₅×D₈	—	2	4	no	—
223	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
226	#688	—	2	4	no	—
227	#687	—	2	4	no	—
228	#686	—	2	4	no	—
229	#686	—	2	4	no	—
230	#685	—	2	2	no	—
231	#683	—	2	2	no	—
232	C₄×Dic₅	C₃×D₄	1	2	yes	—
233	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
234	C₂×#168	C₂³×C₃	1	2	yes	—
235	D₄₀	—	2	4	no	—
236	#677	—	2	4	no	—
237	#676	C₃×D₄	1	8	yes	complemented
238	C₂×AGL(1,ℤ/8)	—	5	2	no	—
239	C₂×AGL(1,ℤ/8)	—	5	2	no	—
240	#532	—	5	1	no	—
241	C₂×#127	—	5	1	no	—
242	#496	—	5	1	no	—
243	#496	—	5	1	no	—
244	#496	—	5	1	no	—
245	#496	C₃×D₅	1	1	yes	characteristic, complemented
246	#493	—	5	2	no	—
247	#492	—	5	2	no	—
248	C₄×M₁₆	—	5	1	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	2	no	—
251	C₂²×C₃×C₅	—	4	4	no	—
252	C₂²×C₃×C₅	—	4	2	no	—
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₃×D₅	—	2	2	no	—
255	C₂×C₃×D₅	—	4	1	no	—
256	C₂×C₃×D₅	—	4	2	no	—
257	C₂×C₃×D₅	—	4	4	no	—
258	C₂×C₃×D₅	—	4	2	no	—
259	C₂×C₃×D₅	—	8	8	no	—
260	C₂×C₃×D₅	#127	1	2	yes	—
261	C₃×C₄×C₅	—	2	2	no	—
262	C₃×C₄×C₅	—	4	1	no	—
263	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
264	C₃×Dic₅	—	4	1	no	—
265	C₃×Dic₅	#127	1	2	yes	—
266	C₃×Dic₅	AGL(1,ℤ/8)	1	4	yes	complemented
267	C₂⁴×C₃	—	10	2	no	—
268	C₃×#41	—	10	4	no	—
269	C₃×#41	—	10	4	no	—
270	C₂×C₃×Q₈	—	5	1	no	—
271	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
272	C₂×C₃×D₄	—	2	2	no	—
273	C₂×C₃×D₄	—	5	1	no	—
274	C₂×C₃×D₄	—	5	2	no	—
275	C₂×C₃×D₄	—	10	1	no	—
276	C₂×C₃×D₄	—	10	4	no	—
277	C₂×C₃×D₄	—	10	4	no	—
278	C₂×C₃×D₄	—	10	2	no	—
279	C₂×C₃×D₄	—	10	4	no	—
280	C₂×C₃×D₄	—	10	2	no	—
281	C₂×C₃×D₄	—	10	1	no	—
282	C₂×C₃×D₄	—	10	2	no	—
283	C₂×C₃×D₄	—	20	8	no	—
284	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
285	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
286	C₂²×C₃×C₄	—	5	1	no	—
287	C₂²×C₃×C₄	—	5	2	no	—
288	C₂²×C₃×C₄	—	10	1	no	—
289	C₂²×C₃×C₄	—	10	1	no	—
290	C₃×SD₁₆	—	2	4	no	—
291	C₃×SD₁₆	—	10	4	no	—
292	C₃×SD₁₆	—	10	4	no	—
293	C₃×SD₁₆	—	10	4	no	—
294	C₃×D₈	—	2	4	no	—
295	C₃×D₈	—	10	4	no	—
296	C₃×D₈	—	10	4	no	—
297	C₃×D₈	—	10	4	no	—
298	C₃×M₁₆	—	5	8	no	—
299	C₂×C₃×C₈	—	5	2	no	—
300	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
301	C₃×C₄⋊C₄	—	10	2	no	—
302	C₃×C₂²⋊C₄	—	2	2	no	—
303	C₃×C₂²⋊C₄	—	10	2	no	—
304	C₃×C₄²	—	5	2	no	—
305	C₃×C₄²	—	5	1	no	—
306	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
307	C₂³×C₅	—	2	1	no	—
308	C₂³×C₅	—	2	2	no	—
309	C₂²×D₅	—	2	1	no	—
310	C₂²×D₅	—	2	2	no	—
311	C₂²×D₅	—	4	8	no	—
312	C₂²×D₅	—	4	4	no	—
313	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₅×Q₈	—	2	2	no	—
315	C₅×D₄	—	2	2	no	—
316	C₅×D₄	—	2	2	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	4	4	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
321	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
322	C₂²⋊D₅	—	4	2	no	—
323	C₂²⋊D₅	—	4	4	no	—
324	C₂²⋊D₅	—	4	8	no	—
325	C₂²⋊D₅	—	4	4	no	—
326	C₂×Dic₅	—	2	1	no	—
327	C₂×Dic₅	—	4	2	no	—
328	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
330	D₂₀	—	2	2	no	—
331	D₂₀	—	2	2	no	—
332	D₂₀	—	2	2	no	—
333	D₂₀	—	4	4	no	—
334	D₂₀	—	4	2	no	—
335	C₄×D₅	—	2	4	no	—
336	C₄×D₅	—	4	2	no	—
337	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
338	Dic₁₀	—	2	2	no	—
339	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
340	#168	C₂×C₃×D₄	1	4	yes	complemented
341	C₂×#41	—	5	1	no	—
342	C₂×#41	—	5	1	no	—
343	C₂²×D₄	—	5	2	no	—
344	C₂²×D₄	—	10	2	no	—
345	AGL(1,ℤ/8)	—	10	8	no	—
346	AGL(1,ℤ/8)	—	10	8	no	—
347	C₂×SD₁₆	—	5	2	no	—
348	C₂×SD₁₆	—	5	2	no	—
349	C₂×SD₁₆	—	5	2	no	—
350	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	complemented
351	C₂×D₈	—	5	2	no	—
352	C₂×D₈	—	5	2	no	—
353	C₂×D₈	—	5	2	no	—
354	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
355	C₂×M₁₆	—	5	2	no	—
356	C₄⋊Q₈	—	5	1	no	—
357	#127	—	5	2	no	—
358	#127	—	5	1	no	—
359	#127	—	5	1	no	—
360	#127	—	10	2	no	—
361	#127	C₂×C₃×D₅	1	1	yes	characteristic
362	#124	—	5	1	no	—
363	#124	C₂×C₃×D₅	1	1	yes	characteristic, complemented
364	#121	—	10	2	no	—
365	C₄×D₄	—	10	2	no	—
366	C₂×C₄²	—	5	1	no	—
367	#97	—	5	1	no	—
368	#97	C₂×C₃×D₅	1	1	yes	characteristic, complemented
369	C₄×C₈	—	5	2	no	—
370	C₂×C₃×C₅	—	8	2	no	—
371	C₂×C₃×C₅	—	8	1	no	—
372	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
373	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
374	C₃×D₅	—	2	2	no	—
375	C₃×D₅	—	8	1	no	—
376	C₃×D₅	—	8	2	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	5	1	no	—
380	C₂³×C₃	—	10	1	no	—
381	C₂³×C₃	—	10	2	no	—
382	C₂³×C₃	—	20	4	no	—
383	C₂³×C₃	—	20	8	no	—
384	C₃×Q₈	—	2	2	no	—
385	C₃×Q₈	—	10	2	no	—
386	C₃×D₄	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	2	2	no	—
389	C₃×D₄	—	4	4	no	—
390	C₃×D₄	—	10	2	no	—
391	C₃×D₄	—	10	2	no	—
392	C₃×D₄	—	10	2	no	—
393	C₃×D₄	—	20	4	no	—
394	C₃×D₄	—	20	2	no	—
395	C₃×D₄	—	20	4	no	—
396	C₃×D₄	—	20	4	no	—
397	C₃×D₄	—	20	8	no	—
398	C₃×D₄	—	20	2	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	5	2	no	—
401	C₂×C₃×C₄	—	5	1	no	—
402	C₂×C₃×C₄	—	5	4	no	—
403	C₂×C₃×C₄	—	10	4	no	—
404	C₂×C₃×C₄	—	10	1	no	—
405	C₂×C₃×C₄	—	20	2	no	—
406	C₂×C₃×C₄	—	20	2	no	—
407	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
408	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
409	C₃×C₈	—	5	4	no	—
410	C₃×C₈	D₄×D₅	1	4	yes	complemented
411	C₂²×C₅	—	4	4	no	—
412	C₂²×C₅	—	4	2	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	—	4	2	no	—
415	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
416	C₂×D₅	—	2	2	no	—
417	C₂×D₅	—	4	4	no	—
418	C₂×D₅	—	4	2	no	—
419	C₂×D₅	—	4	1	no	—
420	C₂×D₅	—	4	2	no	—
421	C₂×D₅	—	8	8	no	—
422	C₂×D₅	C₃×#127	1	2	yes	—
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	4	1	no	—
425	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
426	Dic₅	—	4	1	no	—
427	Dic₅	C₃×#127	1	2	yes	—
428	Dic₅	C₃×AGL(1,ℤ/8)	1	4	yes	complemented
429	C₂⁴	—	10	2	no	—
430	#41	—	10	4	no	—
431	#41	—	10	4	no	—
432	C₂×Q₈	—	5	1	no	—
433	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	5	1	no	—
436	C₂×D₄	—	5	2	no	—
437	C₂×D₄	—	10	1	no	—
438	C₂×D₄	—	10	4	no	—
439	C₂×D₄	—	10	4	no	—
440	C₂×D₄	—	10	2	no	—
441	C₂×D₄	—	10	4	no	—
442	C₂×D₄	—	10	2	no	—
443	C₂×D₄	—	10	1	no	—
444	C₂×D₄	—	10	2	no	—
445	C₂×D₄	—	20	8	no	—
446	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
447	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
448	C₂²×C₄	—	5	1	no	—
449	C₂²×C₄	—	5	2	no	—
450	C₂²×C₄	—	10	1	no	—
451	C₂²×C₄	—	10	1	no	—
452	SD₁₆	—	2	4	no	—
453	SD₁₆	—	10	4	no	—
454	SD₁₆	—	10	4	no	—
455	SD₁₆	—	10	4	no	—
456	D₈	—	2	4	no	—
457	D₈	—	10	4	no	—
458	D₈	—	10	4	no	—
459	D₈	—	10	4	no	—
460	M₁₆	—	5	8	no	—
461	C₂×C₈	—	5	2	no	—
462	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
463	C₄⋊C₄	—	10	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	10	2	no	—
466	C₄²	—	5	2	no	—
467	C₄²	—	5	1	no	—
468	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₃×C₅	#3151	1	1	yes	characteristic, complemented, Hall
470	C₂²×C₃	—	4	1	no	—
471	C₂²×C₃	—	4	2	no	—
472	C₂²×C₃	—	4	4	no	—
473	C₂²×C₃	—	4	2	no	—
474	C₂²×C₃	—	5	2	no	—
475	C₂²×C₃	—	10	2	no	—
476	C₂²×C₃	—	20	1	no	—
477	C₂²×C₃	—	20	2	no	—
478	C₂²×C₃	—	20	4	no	—
479	C₂²×C₃	—	20	2	no	—
480	C₂²×C₃	—	40	8	no	—
481	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	4	1	no	—
484	C₃×C₄	—	5	2	no	—
485	C₃×C₄	—	5	4	no	—
486	C₃×C₄	—	20	1	no	—
487	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
488	C₂×C₅	—	8	2	no	—
489	C₂×C₅	—	8	1	no	—
490	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
491	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
492	D₅	—	2	2	no	—
493	D₅	—	8	2	no	—
494	D₅	—	8	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	5	1	no	—
498	C₂³	—	10	1	no	—
499	C₂³	—	10	2	no	—
500	C₂³	—	20	4	no	—
501	C₂³	—	20	8	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	10	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	4	no	—
508	D₄	—	10	2	no	—
509	D₄	—	10	2	no	—
510	D₄	—	10	2	no	—
511	D₄	—	20	4	no	—
512	D₄	—	20	2	no	—
513	D₄	—	20	4	no	—
514	D₄	—	20	8	no	—
515	D₄	—	20	4	no	—
516	D₄	—	20	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	5	2	no	—
519	C₂×C₄	—	5	1	no	—
520	C₂×C₄	—	5	4	no	—
521	C₂×C₄	—	10	4	no	—
522	C₂×C₄	—	10	1	no	—
523	C₂×C₄	—	20	2	no	—
524	C₂×C₄	—	20	2	no	—
525	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
526	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
527	C₈	—	5	4	no	—
528	C₈	C₃×D₄×D₅	1	4	yes	complemented
529	C₂×C₃	—	8	2	no	—
530	C₂×C₃	—	8	1	no	—
531	C₂×C₃	—	10	2	no	—
532	C₂×C₃	—	40	2	no	—
533	C₂×C₃	—	40	1	no	—
534	C₂×C₃	D₅×#127	1	1	yes	characteristic
535	C₂×C₃	D₅×AGL(1,ℤ/8)	1	2	yes	—
536	C₅	C₃×#3151	1	1	yes	characteristic, complemented, Sylow
537	C₂²	—	4	4	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	1	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	5	2	no	—
542	C₂²	—	10	2	no	—
543	C₂²	—	20	4	no	—
544	C₂²	—	20	2	no	—
545	C₂²	—	20	1	no	—
546	C₂²	—	20	2	no	—
547	C₂²	—	40	8	no	—
548	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	4	1	no	—
551	C₄	—	5	4	no	—
552	C₄	—	5	2	no	—
553	C₄	—	20	1	no	—
554	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
555	C₃	#10613576	1	1	yes	characteristic, direct product factor, Sylow
556	C₂	—	8	2	no	—
557	C₂	—	8	1	no	—
558	C₂	—	10	2	no	—
559	C₂	—	40	2	no	—
560	C₂	—	40	1	no	—
561	C₂	C₃×D₅×#127	1	1	yes	characteristic
562	C₂	C₃×D₅×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#496	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#496	D₅
hypocenter	C₅	C₃×#3151
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#496

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4060	C₂	semidirect
2. C₂×C₃×#4057	C₂	semidirect
3. C₃×D₅×#127	C₂	semidirect
4. C₃×#66002	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₃×#65464	C₂	semidirect
7. C₃×#65440	C₂	semidirect
8. C₃×#65363	C₂	semidirect
9. C₃×#65347	C₂	semidirect
10. C₃×#65001	C₂	semidirect
11. C₃×#64996	C₂	semidirect
12. #10613576	C₃	direct (N × H)
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×D₈	C₂²	semidirect
20. C₃×C₅×#124	C₂²	semidirect
21. C₃×#4090	C₂²	semidirect
22. C₂×C₃×#688	C₂²	semidirect
25. C₃×#4086	C₂²	semidirect
26. C₂×C₃×#687	C₂²	semidirect
27. C₂×C₃×#686	C₂²	semidirect
28. C₂×C₃×#686	C₂²	semidirect
31. C₂×C₃×D₄₀	C₂²	semidirect
32. C₂×C₃×#677	C₂²	semidirect
36. C₃×#4021	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₃×C₈×Dic₅	C₂²	semidirect
41. C₃×#3935	C₂²	semidirect
43. C₂×#4060	C₂×C₃	semidirect
44. C₂×#4057	C₂×C₃	semidirect
45. D₅×#127	C₂×C₃	semidirect
46. #66002	C₂×C₃	semidirect
47. C₅×#496	C₂×C₃	semidirect
48. #65464	C₂×C₃	semidirect
49. #65440	C₂×C₃	semidirect
50. #65363	C₂×C₃	semidirect
51. #65347	C₂×C₃	semidirect
52. #65001	C₂×C₃	semidirect
53. #64996	C₂×C₃	semidirect
93. C₃×#676	D₄	semidirect
101. C₃×#496	D₅	semidirect
109. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
110. C₂×C₅×D₈	C₂²×C₃	semidirect
112. C₅×#124	C₂²×C₃	semidirect
113. #4090	C₂²×C₃	semidirect
114. C₂×#688	C₂²×C₃	semidirect
117. #4086	C₂²×C₃	semidirect
118. C₂×#687	C₂²×C₃	semidirect
119. C₂×#686	C₂²×C₃	semidirect
120. C₂×#686	C₂²×C₃	semidirect
123. C₂×D₄₀	C₂²×C₃	semidirect
124. C₂×#677	C₂²×C₃	semidirect
128. #4021	C₂²×C₃	semidirect
131. C₅×#97	C₂²×C₃	semidirect
132. C₈×Dic₅	C₂²×C₃	semidirect
133. #3935	C₂²×C₃	semidirect
167. C₃×C₅×C₈	C₂×D₄	semidirect
168. C₃×#168	C₂×D₄	semidirect
178. C₂×C₃×SD₁₆	C₂×D₅	semidirect
182. C₂×C₃×D₈	C₂×D₅	semidirect
191. C₃×#124	C₂×D₅	semidirect
196. C₃×#97	C₂×D₅	semidirect
237. #676	C₃×D₄	semidirect
245. #496	C₃×D₅	semidirect
266. C₃×Dic₅	AGL(1,ℤ/8)	semidirect
339. C₅×C₈	C₂×C₃×D₄	semidirect
340. #168	C₂×C₃×D₄	semidirect
350. C₂×SD₁₆	C₂×C₃×D₅	semidirect
354. C₂×D₈	C₂×C₃×D₅	semidirect
363. #124	C₂×C₃×D₅	semidirect
368. #97	C₂×C₃×D₅	semidirect
410. C₃×C₈	D₄×D₅	semidirect
428. Dic₅	C₃×AGL(1,ℤ/8)	semidirect
469. C₃×C₅	#3151	semidirect
528. C₈	C₃×D₄×D₅	semidirect
536. C₅	C₃×#3151	semidirect
555. C₃	#10613576	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×#4060	2
C₂×C₃×#4057	2
C₃×D₅×#127	2
C₃×#66002	2
C₃×C₅×#496	2
C₃×#65464	2
C₃×#65440	2
C₃×#65363	2
C₃×#65347	2
C₃×#65001	2
C₃×#64996	2
#10613576	3
C₃×#3151	5

Subgroups — C3×#10613576 #14439130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613576 #14439130