Subgroups — C₃×#10612100 #14471901

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66052	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65452	C₂	1	2	yes	maximal, complemented
5	C₃×SD₁₆×Dic₅	C₂	1	2	yes	maximal, complemented
6	C₃×#65359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65131	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65119	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65050	C₂	1	2	yes	maximal, complemented
11	C₃×#65049	C₂	1	2	yes	maximal, complemented
12	#10612100	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	—	2	1	no	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×#688	C₂²	1	1	yes	characteristic
19	C₃×#4086	C₂²	1	2	yes	—
20	C₃×#4085	—	2	2	no	—
21	C₃×#4084	—	2	1	no	—
22	C₃×D₄×Dic₅	C₂²	1	2	yes	—
23	C₃×#4034	—	2	2	no	—
24	C₃×#4034	C₂²	1	2	yes	—
25	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
26	C₃×#4015	—	2	1	no	—
27	C₃×#4015	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₁₀	—	2	1	no	—
29	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	1	yes	characteristic
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	2	yes	—
35	C₃×#3953	C₂²	1	2	yes	—
36	C₃×#3949	C₂²	1	2	yes	—
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×C₈×Dic₅	C₂²	1	2	yes	—
39	C₃×#3941	C₂²	1	1	yes	characteristic
40	C₃×#3940	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3362	—	5	1	no	maximal, Hall
43	#66052	C₂×C₃	1	1	yes	characteristic
44	Q₈×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
46	#65452	C₂×C₃	1	2	yes	complemented
47	SD₁₆×Dic₅	C₂×C₃	1	2	yes	complemented
48	#65359	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×#688	C₂×C₃	1	1	yes	characteristic, complemented
50	#65131	C₂×C₃	1	1	yes	characteristic, complemented
51	#65119	C₂×C₃	1	1	yes	characteristic, complemented
52	#65050	C₂×C₃	1	2	yes	complemented
53	#65049	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
60	C₂²×C₃×Dic₅	—	2	2	no	—
61	C₃×#711	—	4	4	no	—
62	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	—	2	1	no	—
64	C₂×C₃×Dic₁₀	—	2	1	no	—
65	C₂×C₃×Dic₁₀	—	2	2	no	—
66	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic
67	C₃×C₅×SD₁₆	—	2	4	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₃×C₄²×C₅	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₂²⋊Dic₅	—	2	2	no	—
74	C₃×#688	—	2	2	no	—
75	C₃×#685	—	2	1	no	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	—	2	2	no	—
78	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
79	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
80	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
81	C₃×#683	—	2	2	no	—
82	C₃×#683	D₄	1	2	yes	—
83	C₃×C₄×Dic₅	—	2	2	no	—
84	C₃×C₄×Dic₅	C₂³	1	2	yes	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×Q₈²	—	5	1	no	—
88	C₃×#550	—	5	1	no	—
89	C₃×#486	—	5	1	no	—
90	C₃×#486	—	5	2	no	—
91	C₃×#476	—	5	1	no	—
92	C₃×#476	—	5	2	no	—
93	C₃×#460	—	5	2	no	—
94	C₃×#460	D₅	1	1	yes	characteristic, complemented
95	C₃×C₈×Q₈	—	5	1	no	—
96	C₃×C₄×SD₁₆	—	5	2	no	—
97	C₃×C₄×SD₁₆	—	5	1	no	—
98	C₂×#711	—	2	1	no	—
99	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
100	C₅×#127	C₂²×C₃	1	1	yes	characteristic
101	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
102	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
103	C₂×#688	C₂²×C₃	1	1	yes	characteristic
104	#4086	C₂²×C₃	1	2	yes	—
105	#4085	—	2	2	no	—
106	#4084	—	2	1	no	—
107	D₄×Dic₅	C₂²×C₃	1	2	yes	—
108	#4034	—	2	2	no	—
109	#4034	C₂²×C₃	1	2	yes	—
110	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
111	#4015	—	2	1	no	—
112	#4015	C₂²×C₃	1	1	yes	characteristic
113	C₄×Dic₁₀	—	2	1	no	—
114	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
115	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
116	C₅×#102	C₂²×C₃	1	2	yes	—
117	#3967	C₂²×C₃	1	1	yes	characteristic
118	#3964	C₂²×C₃	1	2	yes	—
119	#3964	C₂²×C₃	1	2	yes	—
120	#3953	C₂²×C₃	1	2	yes	—
121	#3949	C₂²×C₃	1	2	yes	—
122	#3946	C₂²×C₃	1	2	yes	—
123	C₈×Dic₅	C₂²×C₃	1	2	yes	—
124	#3941	C₂²×C₃	1	1	yes	characteristic
125	#3940	C₂²×C₃	1	1	yes	characteristic
126	C₄×#168	C₂²×C₃	1	1	yes	characteristic
127	#3362	—	5	1	no	Sylow
128	C₂³×C₃×C₅	—	2	2	no	—
129	C₂²×C₃×D₅	—	2	1	no	—
130	C₃×C₅×Q₈	—	2	1	no	—
131	C₃×C₅×Q₈	#41	1	2	yes	complemented
132	C₃×C₅×D₄	—	2	2	no	—
133	C₃×C₅×D₄	—	2	2	no	—
134	C₃×C₅×D₄	—	4	2	no	—
135	C₃×C₅×D₄	—	8	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₂²⋊D₅	—	4	4	no	—
142	C₃×C₂²⋊D₅	—	8	2	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	—	2	1	no	—
145	C₂×C₃×Dic₅	—	4	4	no	—
146	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
148	C₃×D₂₀	—	2	1	no	—
149	C₃×D₂₀	—	2	1	no	—
150	C₃×C₄×D₅	—	4	2	no	—
151	C₃×Dic₁₀	—	8	2	no	—
152	C₃×Dic₁₀	—	8	1	no	—
153	C₃×Dic₁₀	SD₁₆	1	4	yes	complemented
154	C₃×C₅×C₈	—	2	2	no	—
155	C₃×#168	—	2	1	no	—
156	C₃×#168	—	2	1	no	—
157	C₂×C₃×#41	—	10	1	no	—
158	C₂×C₃×SD₁₆	—	5	1	no	—
159	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
160	C₃×C₄⋊Q₈	—	5	2	no	—
161	C₃×C₄⋊Q₈	—	5	1	no	—
162	C₃×C₄⋊Q₈	—	10	1	no	—
163	C₃×C₄⋊Q₈	—	10	2	no	—
164	C₃×#127	—	5	2	no	—
165	C₃×#127	C₂×D₅	1	1	yes	characteristic
166	C₃×#121	—	10	1	no	—
167	C₃×#121	—	10	2	no	—
168	C₃×C₄×Q₈	—	5	1	no	—
169	C₃×C₄×Q₈	—	5	2	no	—
170	C₃×C₄×Q₈	—	10	1	no	—
171	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄×D₄	—	5	2	no	—
173	C₃×C₄×D₄	—	5	1	no	—
174	C₃×#106	—	5	2	no	—
175	C₃×#106	—	5	1	no	—
176	C₃×C₄⋊C₈	—	5	2	no	—
177	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
178	C₃×#103	—	5	1	no	—
179	C₃×#102	—	5	2	no	—
180	C₃×#102	—	5	2	no	—
181	C₃×#102	—	5	2	no	—
182	C₃×#102	—	5	1	no	—
183	C₃×#102	C₂×D₅	1	2	yes	—
184	C₃×C₄×C₈	—	5	2	no	—
185	C₃×C₄×C₈	—	5	1	no	—
186	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
187	C₂×C₅×D₄	—	2	1	no	—
188	C₂×C₅×D₄	—	2	1	no	—
189	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
190	C₂×C₂²⋊D₅	—	2	2	no	—
191	C₂×C₂²⋊D₅	—	2	2	no	—
192	C₂²×Dic₅	—	2	2	no	—
193	#711	—	4	4	no	—
194	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₄×D₅	—	2	1	no	—
196	C₂×Dic₁₀	—	2	1	no	—
197	C₂×Dic₁₀	—	2	2	no	—
198	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic
199	C₅×SD₁₆	—	2	4	no	—
200	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
203	C₄²×C₅	—	2	1	no	—
204	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²⋊Dic₅	—	2	2	no	—
206	#688	—	2	2	no	—
207	#685	—	2	1	no	—
208	C₄⋊Dic₅	—	2	1	no	—
209	C₄⋊Dic₅	—	2	2	no	—
210	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
211	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
212	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
213	#683	—	2	2	no	—
214	#683	C₃×D₄	1	2	yes	—
215	C₄×Dic₅	—	2	2	no	—
216	C₄×Dic₅	C₂³×C₃	1	2	yes	—
217	C₂×#168	C₂³×C₃	1	1	yes	characteristic
218	C₂×#168	C₂³×C₃	1	1	yes	characteristic
219	Q₈²	—	5	1	no	—
220	#550	—	5	1	no	—
221	#486	—	5	1	no	—
222	#486	—	5	2	no	—
223	#476	—	5	1	no	—
224	#476	—	5	2	no	—
225	#460	—	5	2	no	—
226	#460	C₃×D₅	1	1	yes	characteristic, complemented
227	C₈×Q₈	—	5	1	no	—
228	C₄×SD₁₆	—	5	2	no	—
229	C₄×SD₁₆	—	5	1	no	—
230	C₂²×C₃×C₅	—	4	2	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₃×D₅	—	4	1	no	—
235	C₂×C₃×D₅	—	4	1	no	—
236	C₂×C₃×D₅	—	4	1	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	—	4	1	no	—
240	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
241	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
242	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
243	C₃×Dic₅	—	2	2	no	—
244	C₃×Dic₅	—	4	1	no	—
245	C₃×Dic₅	—	4	2	no	—
246	C₃×Dic₅	C₂×SD₁₆	1	4	yes	—
247	C₃×#41	—	20	4	no	—
248	C₂×C₃×Q₈	—	5	1	no	—
249	C₂×C₃×Q₈	—	10	2	no	—
250	C₂×C₃×Q₈	—	10	1	no	—
251	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	—	2	1	no	—
254	C₂×C₃×D₄	—	5	1	no	—
255	C₂×C₃×D₄	—	10	2	no	—
256	C₂×C₃×D₄	—	10	2	no	—
257	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
258	C₂²×C₃×C₄	—	10	2	no	—
259	C₂²×C₃×C₄	—	10	1	no	—
260	C₃×SD₁₆	—	2	4	no	—
261	C₃×SD₁₆	—	10	2	no	—
262	C₂×C₃×C₈	—	5	1	no	—
263	C₂×C₃×C₈	—	5	1	no	—
264	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
265	C₃×C₄⋊C₄	—	2	1	no	—
266	C₃×C₄⋊C₄	—	5	2	no	—
267	C₃×C₄⋊C₄	—	5	1	no	—
268	C₃×C₄⋊C₄	—	5	2	no	—
269	C₃×C₄⋊C₄	—	5	1	no	—
270	C₃×C₄⋊C₄	—	10	2	no	—
271	C₃×C₄⋊C₄	—	10	2	no	—
272	C₃×C₄⋊C₄	—	10	1	no	—
273	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
274	C₃×C₂²⋊C₄	—	10	2	no	—
275	C₃×C₂²⋊C₄	—	10	1	no	—
276	C₃×C₄²	—	2	1	no	—
277	C₃×C₄²	—	5	2	no	—
278	C₃×C₄²	—	10	2	no	—
279	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
280	C₂³×C₅	—	2	2	no	—
281	C₂²×D₅	—	2	1	no	—
282	C₅×Q₈	—	2	1	no	—
283	C₅×Q₈	C₃×#41	1	2	yes	complemented
284	C₅×D₄	—	2	2	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	4	2	no	—
287	C₅×D₄	—	8	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₂²⋊D₅	—	4	4	no	—
294	C₂²⋊D₅	—	8	2	no	—
295	C₂×Dic₅	—	2	2	no	—
296	C₂×Dic₅	—	2	1	no	—
297	C₂×Dic₅	—	4	4	no	—
298	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
300	D₂₀	—	2	1	no	—
301	D₂₀	—	2	1	no	—
302	C₄×D₅	—	4	2	no	—
303	Dic₁₀	—	8	2	no	—
304	Dic₁₀	—	8	1	no	—
305	Dic₁₀	C₃×SD₁₆	1	4	yes	complemented
306	C₅×C₈	—	2	2	no	—
307	#168	—	2	1	no	—
308	#168	—	2	1	no	—
309	C₂×#41	—	10	1	no	—
310	C₂×SD₁₆	—	5	1	no	—
311	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
312	C₄⋊Q₈	—	5	2	no	—
313	C₄⋊Q₈	—	5	1	no	—
314	C₄⋊Q₈	—	10	1	no	—
315	C₄⋊Q₈	—	10	2	no	—
316	#127	—	5	2	no	—
317	#127	C₂×C₃×D₅	1	1	yes	characteristic
318	#121	—	10	1	no	—
319	#121	—	10	2	no	—
320	C₄×Q₈	—	5	1	no	—
321	C₄×Q₈	—	5	2	no	—
322	C₄×Q₈	—	10	1	no	—
323	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
324	C₄×D₄	—	5	2	no	—
325	C₄×D₄	—	5	1	no	—
326	#106	—	5	2	no	—
327	#106	—	5	1	no	—
328	C₄⋊C₈	—	5	2	no	—
329	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
330	#103	—	5	1	no	—
331	#102	—	5	2	no	—
332	#102	—	5	2	no	—
333	#102	—	5	2	no	—
334	#102	—	5	1	no	—
335	#102	C₂×C₃×D₅	1	2	yes	—
336	C₄×C₈	—	5	2	no	—
337	C₄×C₈	—	5	1	no	—
338	C₂×C₃×C₅	—	8	2	no	—
339	C₂×C₃×C₅	#548	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	#576	1	1	yes	characteristic
342	C₃×D₅	—	8	1	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂³×C₃	—	10	1	no	—
345	C₃×Q₈	—	2	1	no	—
346	C₃×Q₈	—	5	4	no	—
347	C₃×Q₈	—	40	1	no	—
348	C₃×Q₈	—	40	2	no	—
349	C₃×Q₈	#711	1	2	yes	complemented
350	C₃×D₄	—	2	2	no	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	4	2	no	—
353	C₃×D₄	—	8	1	no	—
354	C₃×D₄	—	10	1	no	—
355	C₃×D₄	—	10	1	no	—
356	C₃×D₄	—	20	4	no	—
357	C₃×D₄	—	40	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	5	2	no	—
361	C₂×C₃×C₄	—	5	2	no	—
362	C₂×C₃×C₄	—	10	2	no	—
363	C₂×C₃×C₄	—	10	1	no	—
364	C₂×C₃×C₄	—	20	4	no	—
365	C₂×C₃×C₄	—	20	2	no	—
366	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
367	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
369	C₃×C₈	—	2	2	no	—
370	C₃×C₈	—	10	1	no	—
371	C₃×C₈	—	10	1	no	—
372	C₂²×C₅	—	4	2	no	—
373	C₂²×C₅	—	4	2	no	—
374	C₂²×C₅	—	4	2	no	—
375	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
376	C₂×D₅	—	4	1	no	—
377	C₂×D₅	—	4	1	no	—
378	C₂×D₅	—	4	1	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
383	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
384	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
385	Dic₅	—	2	2	no	—
386	Dic₅	—	4	1	no	—
387	Dic₅	—	4	2	no	—
388	Dic₅	C₂×C₃×SD₁₆	1	4	yes	—
389	#41	—	20	4	no	—
390	C₂×Q₈	—	5	1	no	—
391	C₂×Q₈	—	10	2	no	—
392	C₂×Q₈	—	10	1	no	—
393	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	5	1	no	—
397	C₂×D₄	—	10	2	no	—
398	C₂×D₄	—	10	2	no	—
399	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
400	C₂²×C₄	—	10	2	no	—
401	C₂²×C₄	—	10	1	no	—
402	SD₁₆	—	2	4	no	—
403	SD₁₆	—	10	2	no	—
404	C₂×C₈	—	5	1	no	—
405	C₂×C₈	—	5	1	no	—
406	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	5	2	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	5	2	no	—
411	C₄⋊C₄	—	5	1	no	—
412	C₄⋊C₄	—	10	2	no	—
413	C₄⋊C₄	—	10	2	no	—
414	C₄⋊C₄	—	10	1	no	—
415	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
416	C₂²⋊C₄	—	10	2	no	—
417	C₂²⋊C₄	—	10	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	5	2	no	—
420	C₄²	—	10	2	no	—
421	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₃×C₅	#3362	1	1	yes	characteristic, complemented, Hall
423	C₂²×C₃	—	4	2	no	—
424	C₂²×C₃	—	4	2	no	—
425	C₂²×C₃	—	4	2	no	—
426	C₂²×C₃	—	20	1	no	—
427	C₂²×C₃	—	20	1	no	—
428	C₂²×C₃	—	20	1	no	—
429	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	4	1	no	—
433	C₃×C₄	—	5	4	no	—
434	C₃×C₄	—	10	2	no	—
435	C₃×C₄	—	20	1	no	—
436	C₃×C₄	—	20	2	no	—
437	C₃×C₄	D₅×SD₁₆	1	2	yes	—
438	C₃×C₄	C₂×#711	1	1	yes	characteristic
439	C₃×C₄	#4150	1	1	yes	characteristic
440	C₂×C₅	—	8	2	no	—
441	C₂×C₅	C₃×#548	1	1	yes	characteristic
442	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
443	C₂×C₅	C₃×#576	1	1	yes	characteristic
444	D₅	—	8	1	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	10	1	no	—
447	Q₈	—	2	1	no	—
448	Q₈	—	5	4	no	—
449	Q₈	—	40	1	no	—
450	Q₈	—	40	2	no	—
451	Q₈	C₃×#711	1	2	yes	complemented
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	8	1	no	—
456	D₄	—	10	1	no	—
457	D₄	—	10	1	no	—
458	D₄	—	20	4	no	—
459	D₄	—	40	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	5	2	no	—
463	C₂×C₄	—	5	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	1	no	—
466	C₂×C₄	—	20	4	no	—
467	C₂×C₄	—	20	2	no	—
468	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
469	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
471	C₈	—	2	2	no	—
472	C₈	—	10	1	no	—
473	C₈	—	10	1	no	—
474	C₂×C₃	—	8	2	no	—
475	C₂×C₃	—	40	1	no	—
476	C₂×C₃	#65932	1	1	yes	characteristic
477	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
478	C₂×C₃	#66108	1	1	yes	characteristic
479	C₅	C₃×#3362	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	20	1	no	—
484	C₂²	—	20	1	no	—
485	C₂²	—	20	1	no	—
486	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	5	4	no	—
491	C₄	—	10	2	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	1	no	—
494	C₄	C₃×D₅×SD₁₆	1	2	yes	—
495	C₄	C₂×C₃×#711	1	1	yes	characteristic
496	C₄	C₃×#4150	1	1	yes	characteristic
497	C₃	#10612100	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	8	2	no	—
499	C₂	—	40	1	no	—
500	C₂	C₃×#65932	1	1	yes	characteristic
501	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
502	C₂	C₃×#66108	1	1	yes	characteristic

	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×#460	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66052	C₂
hypercenter	C₃×#460	D₅
hypocenter	C₅	C₃×#3362
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#460

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×Dic₁₀	C₂	semidirect
3. C₃×C₅×#460	C₂	semidirect
4. C₃×#65452	C₂	semidirect
5. C₃×SD₁₆×Dic₅	C₂	semidirect
6. C₃×#65359	C₂	semidirect
7. C₃×C₄×#688	C₂	semidirect
8. C₃×#65131	C₂	semidirect
9. C₃×#65119	C₂	semidirect
10. C₃×#65050	C₂	semidirect
11. C₃×#65049	C₂	semidirect
12. #10612100	C₃	direct (N × H)
44. Q₈×Dic₁₀	C₂×C₃	semidirect
45. C₅×#460	C₂×C₃	semidirect
46. #65452	C₂×C₃	semidirect
47. SD₁₆×Dic₅	C₂×C₃	semidirect
48. #65359	C₂×C₃	semidirect
49. C₄×#688	C₂×C₃	semidirect
50. #65131	C₂×C₃	semidirect
51. #65119	C₂×C₃	semidirect
52. #65050	C₂×C₃	semidirect
53. #65049	C₂×C₃	semidirect
94. C₃×#460	D₅	semidirect
131. C₃×C₅×Q₈	#41	semidirect
153. C₃×Dic₁₀	SD₁₆	semidirect
226. #460	C₃×D₅	semidirect
283. C₅×Q₈	C₃×#41	semidirect
305. Dic₁₀	C₃×SD₁₆	semidirect
349. C₃×Q₈	#711	semidirect
422. C₃×C₅	#3362	semidirect
451. Q₈	C₃×#711	semidirect
479. C₅	C₃×#3362	semidirect
497. C₃	#10612100	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#66052	2
C₃×Q₈×Dic₁₀	2
C₃×C₅×#460	2
C₃×#65452	2
C₃×SD₁₆×Dic₅	2
C₃×#65359	2
C₃×C₄×#688	2
C₃×#65131	2
C₃×#65119	2
C₃×#65050	2
C₃×#65049	2
#10612100	3
C₃×#3362	5

Subgroups — C3×#10612100 #14471901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612100 #14471901