Subgroups — C₃×#10613515 #14439532

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4058	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4057	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66049	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65444	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65443	C₂	1	2	yes	maximal, complemented
8	C₃×#65440	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65363	C₂	1	2	yes	maximal, complemented
10	C₃×#64985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64978	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613515	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	2	yes	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×D₈	C₂²	1	2	yes	complemented
18	C₃×C₅×#127	C₂²	1	2	yes	complemented
19	C₃×#4086	C₂²	1	2	yes	complemented
20	C₃×#4085	—	2	4	no	—
21	C₃×#4083	—	2	4	no	—
22	C₃×#4082	C₂²	1	2	yes	complemented
23	C₂×C₃×#687	C₂²	1	2	yes	complemented
24	C₂×C₃×#687	C₂²	1	2	yes	complemented
25	C₂×C₃×#686	C₂²	1	2	yes	—
26	C₂×C₃×#686	C₂²	1	2	yes	complemented
27	C₃×#4058	—	2	4	no	—
28	C₃×#4057	—	2	8	no	—
29	C₃×D₅×D₈	—	2	4	no	—
30	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
32	C₂×C₃×#677	C₂²	1	2	yes	complemented
33	C₂×C₃×#676	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
35	C₃×#4021	C₂²	1	2	yes	complemented
36	C₃×#4018	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3947	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
41	C₃×#3155	—	5	1	no	maximal, Hall
42	C₂×#4058	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#4057	C₂×C₃	1	2	yes	complemented
44	C₂×D₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
45	#66049	C₂×C₃	1	2	yes	complemented
46	C₅×#493	C₂×C₃	1	1	yes	characteristic, complemented
47	#65444	C₂×C₃	1	1	yes	characteristic, complemented
48	#65443	C₂×C₃	1	2	yes	complemented
49	#65440	C₂×C₃	1	1	yes	characteristic, complemented
50	#65363	C₂×C₃	1	2	yes	complemented
51	#64985	C₂×C₃	1	1	yes	characteristic, complemented
52	#64978	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	—	2	2	no	—
54	C₂×C₃×C₅×D₄	—	2	4	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
57	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
60	C₂²×C₃×Dic₅	—	2	2	no	—
61	C₃×#711	—	2	4	no	—
62	C₃×#711	—	2	4	no	—
63	C₃×D₄×D₅	—	2	4	no	—
64	C₃×D₄×D₅	—	2	4	no	—
65	C₂×C₃×D₂₀	C₂³	1	2	yes	—
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
68	C₃×C₅×D₈	—	2	2	no	—
69	C₃×C₅×D₈	—	2	4	no	—
70	C₃×C₅×D₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	4	no	—
75	C₃×#687	—	2	4	no	—
76	C₃×#687	—	2	4	no	—
77	C₃×#686	—	2	4	no	—
78	C₃×#686	—	2	4	no	—
79	C₃×#685	—	2	4	no	—
80	C₃×#685	D₄	1	2	yes	—
81	C₃×#683	D₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₂×C₃×#168	C₂³	1	1	yes	characteristic
85	C₃×Dic₂₀	—	2	2	no	—
86	C₃×D₄₀	—	2	2	no	—
87	C₃×#677	—	2	4	no	—
88	C₃×#676	D₄	1	4	yes	complemented
89	C₃×C₈×D₅	D₄	1	4	yes	complemented
90	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
91	C₂×C₃×#135	—	5	1	no	—
92	C₂²×C₃×D₈	—	5	1	no	—
93	C₃×#535	—	5	2	no	—
94	C₃×#496	—	5	2	no	—
95	C₃×#496	—	5	2	no	—
96	C₃×#495	—	5	1	no	—
97	C₃×#495	—	5	1	no	—
98	C₃×#493	—	5	1	no	—
99	C₃×#493	D₅	1	1	yes	characteristic, complemented
100	C₃×#405	—	5	1	no	—
101	C₂×#711	C₂²×C₃	1	2	yes	—
102	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
103	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×D₈	C₂²×C₃	1	2	yes	complemented
105	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₅×#127	C₂²×C₃	1	2	yes	complemented
107	#4086	C₂²×C₃	1	2	yes	complemented
108	#4085	—	2	4	no	—
109	#4083	—	2	4	no	—
110	#4082	C₂²×C₃	1	2	yes	complemented
111	C₂×#687	C₂²×C₃	1	2	yes	complemented
112	C₂×#687	C₂²×C₃	1	2	yes	complemented
113	C₂×#686	C₂²×C₃	1	2	yes	—
114	C₂×#686	C₂²×C₃	1	2	yes	complemented
115	#4058	—	2	4	no	—
116	#4057	—	2	8	no	—
117	D₅×D₈	—	2	4	no	—
118	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
120	C₂×#677	C₂²×C₃	1	2	yes	complemented
121	C₂×#676	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
123	#4021	C₂²×C₃	1	2	yes	complemented
124	#4018	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3947	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
128	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
129	#3155	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂²×C₃×D₅	—	2	2	no	—
133	C₂²×C₃×D₅	—	4	4	no	—
134	C₂²×C₃×D₅	—	8	4	no	—
135	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
136	C₃×C₅×D₄	—	2	2	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	8	4	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₂²⋊D₅	—	4	4	no	—
144	C₃×C₂²⋊D₅	—	4	4	no	—
145	C₃×C₂²⋊D₅	—	8	4	no	—
146	C₂×C₃×Dic₅	—	2	2	no	—
147	C₂×C₃×Dic₅	—	4	4	no	—
148	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
149	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
150	C₃×D₂₀	—	2	2	no	—
151	C₃×D₂₀	—	2	2	no	—
152	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
153	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	2	2	no	—
156	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₃×#168	C₂×D₄	1	2	yes	—
159	C₃×#168	C₂×D₄	1	2	yes	—
160	C₂×C₃×#41	—	5	2	no	—
161	C₂²×C₃×D₄	—	5	2	no	—
162	C₃×AGL(1,ℤ/8)	—	10	8	no	—
163	C₃×#135	—	10	4	no	—
164	C₂×C₃×Q₁₆	—	5	1	no	—
165	C₂×C₃×SD₁₆	—	5	2	no	—
166	C₂×C₃×SD₁₆	—	5	2	no	—
167	C₂×C₃×SD₁₆	—	5	2	no	—
168	C₂×C₃×D₈	—	5	2	no	—
169	C₂×C₃×D₈	—	5	2	no	—
170	C₂×C₃×D₈	—	5	1	no	—
171	C₂×C₃×D₈	—	10	4	no	—
172	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic
173	C₂×C₃×D₈	C₂×D₅	1	1	yes	characteristic, complemented
174	C₂×C₃×D₈	C₂×D₅	1	2	yes	complemented
175	C₂×C₃×M₁₆	—	5	1	no	—
176	C₂²×C₃×C₈	—	5	1	no	—
177	C₃×#127	—	5	2	no	—
178	C₃×#127	C₂×D₅	1	2	yes	complemented
179	C₃×#124	—	5	2	no	—
180	C₃×#124	—	5	2	no	—
181	C₃×#121	—	10	4	no	—
182	C₃×#120	—	10	4	no	—
183	C₃×#117	—	5	1	no	—
184	C₃×#97	—	5	1	no	—
185	C₃×#97	—	5	1	no	—
186	C₃×C₄×C₈	—	5	1	no	—
187	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
188	C₂³×D₅	—	2	2	no	—
189	C₂×C₅×D₄	—	2	4	no	—
190	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
191	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
192	C₂×C₂²⋊D₅	—	2	2	no	—
193	C₂×C₂²⋊D₅	—	2	2	no	—
194	C₂×C₂²⋊D₅	—	2	4	no	—
195	C₂²×Dic₅	—	2	2	no	—
196	#711	—	2	4	no	—
197	#711	—	2	4	no	—
198	D₄×D₅	—	2	4	no	—
199	D₄×D₅	—	2	4	no	—
200	C₂×D₂₀	C₂³×C₃	1	2	yes	—
201	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
202	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
203	C₅×D₈	—	2	2	no	—
204	C₅×D₈	—	2	4	no	—
205	C₅×D₈	—	2	2	no	—
206	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
208	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂²⋊Dic₅	—	2	4	no	—
210	#687	—	2	4	no	—
211	#687	—	2	4	no	—
212	#686	—	2	4	no	—
213	#686	—	2	4	no	—
214	#685	—	2	4	no	—
215	#685	C₃×D₄	1	2	yes	—
216	#683	C₃×D₄	1	2	yes	—
217	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
218	C₂×#168	C₂³×C₃	1	1	yes	characteristic
219	C₂×#168	C₂³×C₃	1	1	yes	characteristic
220	Dic₂₀	—	2	2	no	—
221	D₄₀	—	2	2	no	—
222	#677	—	2	4	no	—
223	#676	C₃×D₄	1	4	yes	complemented
224	C₈×D₅	C₃×D₄	1	4	yes	complemented
225	C₂×AGL(1,ℤ/8)	—	5	2	no	—
226	C₂×#135	—	5	1	no	—
227	C₂²×D₈	—	5	1	no	—
228	#535	—	5	2	no	—
229	#496	—	5	2	no	—
230	#496	—	5	2	no	—
231	#495	—	5	1	no	—
232	#495	—	5	1	no	—
233	#493	—	5	1	no	—
234	#493	C₃×D₅	1	1	yes	characteristic, complemented
235	#405	—	5	1	no	—
236	C₂²×C₃×C₅	—	4	2	no	—
237	C₂²×C₃×C₅	—	4	2	no	—
238	C₂²×C₃×C₅	—	4	4	no	—
239	C₂²×C₃×C₅	—	4	4	no	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₃×D₅	—	2	2	no	—
242	C₂×C₃×D₅	—	4	2	no	—
243	C₂×C₃×D₅	—	4	4	no	—
244	C₂×C₃×D₅	—	8	8	no	—
245	C₂×C₃×D₅	#127	1	2	yes	—
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
249	C₃×Dic₅	—	2	2	no	—
250	C₃×Dic₅	—	4	2	no	—
251	C₃×Dic₅	#127	1	2	yes	—
252	C₂⁴×C₃	—	10	2	no	—
253	C₃×#41	—	10	4	no	—
254	C₃×#41	—	10	4	no	—
255	C₂×C₃×Q₈	—	5	2	no	—
256	C₂×C₃×D₄	—	2	4	no	—
257	C₂×C₃×D₄	—	5	2	no	—
258	C₂×C₃×D₄	—	10	4	no	—
259	C₂×C₃×D₄	—	10	4	no	—
260	C₂×C₃×D₄	—	10	2	no	—
261	C₂×C₃×D₄	—	10	4	no	—
262	C₂×C₃×D₄	—	10	2	no	—
263	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
264	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
265	C₂²×C₃×C₄	—	5	1	no	—
266	C₂²×C₃×C₄	—	10	2	no	—
267	C₃×Q₁₆	—	10	2	no	—
268	C₃×SD₁₆	—	10	4	no	—
269	C₃×SD₁₆	—	10	4	no	—
270	C₃×SD₁₆	—	10	4	no	—
271	C₃×D₈	—	2	2	no	—
272	C₃×D₈	—	2	2	no	—
273	C₃×D₈	—	2	4	no	—
274	C₃×D₈	—	10	4	no	—
275	C₃×D₈	—	10	4	no	—
276	C₃×D₈	—	10	2	no	—
277	C₃×M₁₆	—	5	4	no	—
278	C₂×C₃×C₈	—	5	1	no	—
279	C₂×C₃×C₈	—	5	1	no	—
280	C₂×C₃×C₈	—	5	4	no	—
281	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
282	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
283	C₃×C₄⋊C₄	—	5	2	no	—
284	C₃×C₂²⋊C₄	—	5	2	no	—
285	C₃×C₂²⋊C₄	—	10	4	no	—
286	C₃×C₂²⋊C₄	—	10	4	no	—
287	C₃×C₄²	—	5	1	no	—
288	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
289	C₂³×C₅	—	2	2	no	—
290	C₂³×C₅	—	2	2	no	—
291	C₂²×D₅	—	2	2	no	—
292	C₂²×D₅	—	4	4	no	—
293	C₂²×D₅	—	8	4	no	—
294	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	2	no	—
297	C₅×D₄	—	2	2	no	—
298	C₅×D₄	—	2	2	no	—
299	C₅×D₄	—	8	4	no	—
300	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
301	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
302	C₂²⋊D₅	—	4	4	no	—
303	C₂²⋊D₅	—	4	4	no	—
304	C₂²⋊D₅	—	8	4	no	—
305	C₂×Dic₅	—	2	2	no	—
306	C₂×Dic₅	—	4	4	no	—
307	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
308	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
309	D₂₀	—	2	2	no	—
310	D₂₀	—	2	2	no	—
311	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
312	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
313	Dic₁₀	—	2	2	no	—
314	Dic₁₀	—	2	2	no	—
315	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
316	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
317	#168	C₂×C₃×D₄	1	2	yes	—
318	#168	C₂×C₃×D₄	1	2	yes	—
319	C₂×#41	—	5	2	no	—
320	C₂²×D₄	—	5	2	no	—
321	AGL(1,ℤ/8)	—	10	8	no	—
322	#135	—	10	4	no	—
323	C₂×Q₁₆	—	5	1	no	—
324	C₂×SD₁₆	—	5	2	no	—
325	C₂×SD₁₆	—	5	2	no	—
326	C₂×SD₁₆	—	5	2	no	—
327	C₂×D₈	—	5	2	no	—
328	C₂×D₈	—	5	2	no	—
329	C₂×D₈	—	5	1	no	—
330	C₂×D₈	—	10	4	no	—
331	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic
332	C₂×D₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
333	C₂×D₈	C₂×C₃×D₅	1	2	yes	complemented
334	C₂×M₁₆	—	5	1	no	—
335	C₂²×C₈	—	5	1	no	—
336	#127	—	5	2	no	—
337	#127	C₂×C₃×D₅	1	2	yes	complemented
338	#124	—	5	2	no	—
339	#124	—	5	2	no	—
340	#121	—	10	4	no	—
341	#120	—	10	4	no	—
342	#117	—	5	1	no	—
343	#97	—	5	1	no	—
344	#97	—	5	1	no	—
345	C₄×C₈	—	5	1	no	—
346	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
347	C₂×C₃×C₅	—	8	2	no	—
348	C₂×C₃×C₅	—	8	2	no	—
349	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
350	C₂×C₃×C₅	#576	1	2	yes	—
351	C₃×D₅	—	2	2	no	—
352	C₃×D₅	—	8	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	—	2	2	no	—
355	C₂³×C₃	—	5	1	no	—
356	C₂³×C₃	—	10	2	no	—
357	C₂³×C₃	—	20	4	no	—
358	C₂³×C₃	—	40	4	no	—
359	C₃×Q₈	—	10	2	no	—
360	C₃×Q₈	—	10	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	2	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	2	2	no	—
365	C₃×D₄	—	8	4	no	—
366	C₃×D₄	—	10	2	no	—
367	C₃×D₄	—	10	2	no	—
368	C₃×D₄	—	20	4	no	—
369	C₃×D₄	—	20	4	no	—
370	C₃×D₄	—	40	4	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	2	no	—
373	C₂×C₃×C₄	—	5	2	no	—
374	C₂×C₃×C₄	—	5	2	no	—
375	C₂×C₃×C₄	—	10	2	no	—
376	C₂×C₃×C₄	—	20	4	no	—
377	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
378	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
379	C₃×C₈	—	5	2	no	—
380	C₃×C₈	—	5	2	no	—
381	C₃×C₈	D₄×D₅	1	2	yes	—
382	C₃×C₈	D₄×D₅	1	2	yes	—
383	C₂²×C₅	—	4	4	no	—
384	C₂²×C₅	—	4	4	no	—
385	C₂²×C₅	—	4	2	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
388	C₂×D₅	—	2	2	no	—
389	C₂×D₅	—	4	4	no	—
390	C₂×D₅	—	4	2	no	—
391	C₂×D₅	—	8	8	no	—
392	C₂×D₅	C₃×#127	1	2	yes	—
393	C₄×C₅	—	2	2	no	—
394	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
395	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
396	Dic₅	—	2	2	no	—
397	Dic₅	—	4	2	no	—
398	Dic₅	C₃×#127	1	2	yes	—
399	C₂⁴	—	10	2	no	—
400	#41	—	10	4	no	—
401	#41	—	10	4	no	—
402	C₂×Q₈	—	5	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	5	2	no	—
405	C₂×D₄	—	10	4	no	—
406	C₂×D₄	—	10	4	no	—
407	C₂×D₄	—	10	2	no	—
408	C₂×D₄	—	10	4	no	—
409	C₂×D₄	—	10	2	no	—
410	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
411	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
412	C₂²×C₄	—	5	1	no	—
413	C₂²×C₄	—	10	2	no	—
414	Q₁₆	—	10	2	no	—
415	SD₁₆	—	10	4	no	—
416	SD₁₆	—	10	4	no	—
417	SD₁₆	—	10	4	no	—
418	D₈	—	2	2	no	—
419	D₈	—	2	2	no	—
420	D₈	—	2	4	no	—
421	D₈	—	10	4	no	—
422	D₈	—	10	4	no	—
423	D₈	—	10	2	no	—
424	M₁₆	—	5	4	no	—
425	C₂×C₈	—	5	1	no	—
426	C₂×C₈	—	5	1	no	—
427	C₂×C₈	—	5	4	no	—
428	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
429	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
430	C₄⋊C₄	—	5	2	no	—
431	C₂²⋊C₄	—	5	2	no	—
432	C₂²⋊C₄	—	10	4	no	—
433	C₂²⋊C₄	—	10	4	no	—
434	C₄²	—	5	1	no	—
435	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
436	C₃×C₅	#3155	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	—	4	4	no	—
440	C₂²×C₃	—	4	4	no	—
441	C₂²×C₃	—	5	2	no	—
442	C₂²×C₃	—	10	2	no	—
443	C₂²×C₃	—	20	2	no	—
444	C₂²×C₃	—	20	4	no	—
445	C₂²×C₃	—	40	8	no	—
446	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	5	2	no	—
449	C₃×C₄	—	10	2	no	—
450	C₃×C₄	—	20	2	no	—
451	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
452	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
453	C₂×C₅	—	8	2	no	—
454	C₂×C₅	—	8	2	no	—
455	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
456	C₂×C₅	C₃×#576	1	2	yes	—
457	D₅	—	2	2	no	—
458	D₅	—	8	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	5	1	no	—
462	C₂³	—	10	2	no	—
463	C₂³	—	20	4	no	—
464	C₂³	—	40	4	no	—
465	Q₈	—	10	2	no	—
466	Q₈	—	10	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	8	4	no	—
472	D₄	—	10	2	no	—
473	D₄	—	10	2	no	—
474	D₄	—	20	4	no	—
475	D₄	—	20	4	no	—
476	D₄	—	40	4	no	—
477	C₂×C₄	—	5	1	no	—
478	C₂×C₄	—	5	2	no	—
479	C₂×C₄	—	5	2	no	—
480	C₂×C₄	—	5	2	no	—
481	C₂×C₄	—	10	2	no	—
482	C₂×C₄	—	20	4	no	—
483	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
484	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
485	C₈	—	5	2	no	—
486	C₈	—	5	2	no	—
487	C₈	C₃×D₄×D₅	1	2	yes	—
488	C₈	C₃×D₄×D₅	1	2	yes	—
489	C₂×C₃	—	8	2	no	—
490	C₂×C₃	—	8	2	no	—
491	C₂×C₃	—	10	2	no	—
492	C₂×C₃	—	40	2	no	—
493	C₂×C₃	D₅×#127	1	1	yes	characteristic
494	C₂×C₃	#66091	1	2	yes	—
495	C₅	C₃×#3155	1	1	yes	characteristic, complemented, Sylow
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	5	2	no	—
501	C₂²	—	10	2	no	—
502	C₂²	—	20	2	no	—
503	C₂²	—	20	4	no	—
504	C₂²	—	40	8	no	—
505	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	5	2	no	—
508	C₄	—	10	2	no	—
509	C₄	—	20	2	no	—
510	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
511	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
512	C₃	#10613515	1	1	yes	characteristic, direct product factor, Sylow
513	C₂	—	8	2	no	—
514	C₂	—	8	2	no	—
515	C₂	—	10	2	no	—
516	C₂	—	40	2	no	—
517	C₂	C₃×D₅×#127	1	1	yes	characteristic
518	C₂	C₃×#66091	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×#493	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#493	D₅
hypocenter	C₅	C₃×#3155
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#493

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4058	C₂	semidirect
2. C₂×C₃×#4057	C₂	semidirect
3. C₂×C₃×D₅×D₈	C₂	semidirect
4. C₃×#66049	C₂	semidirect
5. C₃×C₅×#493	C₂	semidirect
6. C₃×#65444	C₂	semidirect
7. C₃×#65443	C₂	semidirect
8. C₃×#65440	C₂	semidirect
9. C₃×#65363	C₂	semidirect
10. C₃×#64985	C₂	semidirect
11. C₃×#64978	C₂	semidirect
12. #10613515	C₃	direct (N × H)
16. C₂×C₃×C₅×D₈	C₂²	semidirect
17. C₂×C₃×C₅×D₈	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₃×#4086	C₂²	semidirect
22. C₃×#4082	C₂²	semidirect
23. C₂×C₃×#687	C₂²	semidirect
24. C₂×C₃×#687	C₂²	semidirect
26. C₂×C₃×#686	C₂²	semidirect
30. C₂×C₃×Dic₂₀	C₂²	semidirect
32. C₂×C₃×#677	C₂²	semidirect
35. C₃×#4021	C₂²	semidirect
37. C₃×C₄×C₅×C₈	C₂²	semidirect
38. C₃×#3947	C₂²	semidirect
39. C₃×C₈×Dic₅	C₂²	semidirect
40. C₃×#3935	C₂²	semidirect
42. C₂×#4058	C₂×C₃	semidirect
43. C₂×#4057	C₂×C₃	semidirect
44. C₂×D₅×D₈	C₂×C₃	semidirect
45. #66049	C₂×C₃	semidirect
46. C₅×#493	C₂×C₃	semidirect
47. #65444	C₂×C₃	semidirect
48. #65443	C₂×C₃	semidirect
49. #65440	C₂×C₃	semidirect
50. #65363	C₂×C₃	semidirect
51. #64985	C₂×C₃	semidirect
52. #64978	C₂×C₃	semidirect
88. C₃×#676	D₄	semidirect
89. C₃×C₈×D₅	D₄	semidirect
99. C₃×#493	D₅	semidirect
104. C₂×C₅×D₈	C₂²×C₃	semidirect
105. C₂×C₅×D₈	C₂²×C₃	semidirect
106. C₅×#127	C₂²×C₃	semidirect
107. #4086	C₂²×C₃	semidirect
110. #4082	C₂²×C₃	semidirect
111. C₂×#687	C₂²×C₃	semidirect
112. C₂×#687	C₂²×C₃	semidirect
114. C₂×#686	C₂²×C₃	semidirect
118. C₂×Dic₂₀	C₂²×C₃	semidirect
120. C₂×#677	C₂²×C₃	semidirect
123. #4021	C₂²×C₃	semidirect
125. C₄×C₅×C₈	C₂²×C₃	semidirect
126. #3947	C₂²×C₃	semidirect
127. C₈×Dic₅	C₂²×C₃	semidirect
128. #3935	C₂²×C₃	semidirect
173. C₂×C₃×D₈	C₂×D₅	semidirect
174. C₂×C₃×D₈	C₂×D₅	semidirect
178. C₃×#127	C₂×D₅	semidirect
187. C₃×C₄×C₈	C₂×D₅	semidirect
223. #676	C₃×D₄	semidirect
224. C₈×D₅	C₃×D₄	semidirect
234. #493	C₃×D₅	semidirect
332. C₂×D₈	C₂×C₃×D₅	semidirect
333. C₂×D₈	C₂×C₃×D₅	semidirect
337. #127	C₂×C₃×D₅	semidirect
346. C₄×C₈	C₂×C₃×D₅	semidirect
436. C₃×C₅	#3155	semidirect
495. C₅	C₃×#3155	semidirect
512. C₃	#10613515	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×#4058	2
C₂×C₃×#4057	2
C₂×C₃×D₅×D₈	2
C₃×#66049	2
C₃×C₅×#493	2
C₃×#65444	2
C₃×#65443	2
C₃×#65440	2
C₃×#65363	2
C₃×#64985	2
C₃×#64978	2
#10613515	3
C₃×#3155	5

Subgroups — C3×#10613515 #14439532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613515 #14439532