Subgroups — C₃×#10612712 #14459941

Order 1920.

772 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×#66066	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65889	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65177	C₂	1	2	yes	maximal, complemented
7	C₃×#65176	C₂	1	2	yes	maximal, complemented
8	C₃×#65138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65072	C₂	1	2	yes	maximal, complemented
11	C₃×#65061	C₂	1	2	yes	maximal, complemented
12	#10612712	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#711	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₃×#4093	—	2	1	no	—
17	C₃×Q₈×Dic₅	—	2	1	no	—
18	C₂×C₃×#687	C₂²	1	1	yes	characteristic
19	C₃×#4076	—	2	1	no	—
20	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
21	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	C₃×#4044	—	2	2	no	—
24	C₃×#4043	C₂²	1	2	yes	—
25	C₃×#4043	C₂²	1	2	yes	—
26	C₃×#4038	C₂²	1	2	yes	—
27	C₃×#4032	—	2	2	no	—
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
31	C₃×C₅×#107	C₂²	1	2	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#102	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	1	yes	characteristic
35	C₃×#3952	C₂²	1	2	yes	—
36	C₃×#3948	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	1	yes	characteristic
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3942	C₂²	1	2	yes	—
40	C₃×#3940	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3302	—	5	1	no	maximal, Hall
43	#66066	C₂×C₃	1	1	yes	characteristic, complemented
44	#65889	C₂×C₃	1	1	yes	characteristic
45	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
46	#65382	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#687	C₂×C₃	1	1	yes	characteristic, complemented
48	#65177	C₂×C₃	1	2	yes	complemented
49	#65176	C₂×C₃	1	2	yes	complemented
50	#65138	C₂×C₃	1	1	yes	characteristic, complemented
51	#65123	C₂×C₃	1	1	yes	characteristic, complemented
52	#65072	C₂×C₃	1	2	yes	complemented
53	#65061	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
58	C₂²×C₃×Dic₅	—	2	2	no	—
59	C₃×#711	—	2	4	no	—
60	C₃×#711	—	4	2	no	—
61	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
63	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
64	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	—	2	1	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×#687	—	2	2	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×#685	—	2	2	no	—
75	C₃×#685	D₄	1	2	yes	—
76	C₃×C₄⋊Dic₅	—	2	1	no	—
77	C₃×C₄⋊Dic₅	—	2	1	no	—
78	C₃×C₄⋊Dic₅	—	2	2	no	—
79	C₃×C₄⋊Dic₅	—	2	2	no	—
80	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
82	C₃×#683	—	2	1	no	—
83	C₃×C₄×Dic₅	—	2	1	no	—
84	C₃×C₄×Dic₅	—	2	2	no	—
85	C₂×C₃×#168	C₂³	1	1	yes	characteristic
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₃×Dic₂₀	—	4	2	no	—
88	C₃×C₈×D₅	—	4	2	no	—
89	C₃×#556	—	5	1	no	—
90	C₃×#547	—	5	1	no	—
91	C₃×#487	—	5	1	no	—
92	C₃×#485	—	5	2	no	—
93	C₃×#474	D₅	1	1	yes	characteristic, complemented
94	C₃×#467	—	5	2	no	—
95	C₃×#462	—	5	1	no	—
96	C₃×#452	—	5	2	no	—
97	C₃×C₄×SD₁₆	—	5	1	no	—
98	C₃×C₈×D₄	—	5	1	no	—
99	C₃×#416	—	5	2	no	—
100	C₂×#711	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
103	#4093	—	2	1	no	—
104	Q₈×Dic₅	—	2	1	no	—
105	C₂×#687	C₂²×C₃	1	1	yes	characteristic
106	#4076	—	2	1	no	—
107	C₂×C₄⋊Dic₅	—	2	1	no	—
108	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
109	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
110	#4044	—	2	2	no	—
111	#4043	C₂²×C₃	1	2	yes	—
112	#4043	C₂²×C₃	1	2	yes	—
113	#4038	C₂²×C₃	1	2	yes	—
114	#4032	—	2	2	no	—
115	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	#4015	C₂²×C₃	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
118	C₅×#107	C₂²×C₃	1	2	yes	—
119	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₅×#102	C₂²×C₃	1	2	yes	—
121	#3964	C₂²×C₃	1	1	yes	characteristic
122	#3952	C₂²×C₃	1	2	yes	—
123	#3948	C₂²×C₃	1	2	yes	—
124	#3942	C₂²×C₃	1	1	yes	characteristic
125	#3942	C₂²×C₃	1	2	yes	—
126	#3942	C₂²×C₃	1	2	yes	—
127	#3940	C₂²×C₃	1	1	yes	characteristic
128	C₄×#168	C₂²×C₃	1	1	yes	characteristic
129	#3302	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	4	2	no	—
133	C₃×C₅×D₄	—	2	1	no	—
134	C₃×C₅×D₄	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	4	2	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	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	1	no	—
144	C₂×C₃×Dic₅	—	2	2	no	—
145	C₂×C₃×Dic₅	—	4	4	no	—
146	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
147	C₃×D₂₀	—	2	2	no	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	—	2	2	no	—
150	C₃×Dic₁₀	—	2	1	no	—
151	C₃×Dic₁₀	—	2	2	no	—
152	C₃×Dic₁₀	—	2	1	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₃×#168	—	2	1	no	—
156	C₃×#168	—	2	1	no	—
157	C₂×C₃×#41	—	5	2	no	—
158	C₂×C₃×Q₁₆	—	5	2	no	—
159	C₂×C₃×SD₁₆	—	5	1	no	—
160	C₂²×C₃×C₈	—	5	2	no	—
161	C₃×C₄⋊Q₈	—	5	1	no	—
162	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
163	C₃×#126	—	10	2	no	—
164	C₃×#124	—	10	1	no	—
165	C₃×#123	—	10	2	no	—
166	C₃×C₂²⋊Q₈	—	5	2	no	—
167	C₃×C₂²⋊Q₈	—	5	2	no	—
168	C₃×#121	—	10	1	no	—
169	C₃×C₄×Q₈	—	5	1	no	—
170	C₃×C₄×Q₈	—	10	1	no	—
171	C₃×C₄×D₄	—	5	1	no	—
172	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
173	C₃×#117	—	5	2	no	—
174	C₂×C₃×C₄⋊C₄	—	10	1	no	—
175	C₃×#107	C₂×D₅	1	2	yes	—
176	C₃×#106	—	5	1	no	—
177	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
178	C₃×#103	—	5	2	no	—
179	C₃×#103	—	5	2	no	—
180	C₃×#103	—	5	1	no	—
181	C₃×#103	—	5	2	no	—
182	C₃×#102	—	5	1	no	—
183	C₃×#102	C₂×D₅	1	2	yes	—
184	C₃×C₂²⋊C₈	—	5	2	no	—
185	C₃×C₄×C₈	—	5	1	no	—
186	C₂×C₅×Q₈	—	2	1	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂×C₂²⋊D₅	—	2	2	no	—
190	C₂²×Dic₅	—	2	2	no	—
191	#711	—	2	4	no	—
192	#711	—	4	2	no	—
193	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
194	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
195	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
196	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
201	C₅×C₂²⋊C₄	—	2	1	no	—
202	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
203	#687	—	2	2	no	—
204	#685	—	2	2	no	—
205	#685	—	2	2	no	—
206	#685	—	2	2	no	—
207	#685	C₃×D₄	1	2	yes	—
208	C₄⋊Dic₅	—	2	1	no	—
209	C₄⋊Dic₅	—	2	1	no	—
210	C₄⋊Dic₅	—	2	2	no	—
211	C₄⋊Dic₅	—	2	2	no	—
212	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
213	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
214	#683	—	2	1	no	—
215	C₄×Dic₅	—	2	1	no	—
216	C₄×Dic₅	—	2	2	no	—
217	C₂×#168	C₂³×C₃	1	1	yes	characteristic
218	C₂×#168	C₂³×C₃	1	1	yes	characteristic
219	Dic₂₀	—	4	2	no	—
220	C₈×D₅	—	4	2	no	—
221	#556	—	5	1	no	—
222	#547	—	5	1	no	—
223	#487	—	5	1	no	—
224	#485	—	5	2	no	—
225	#474	C₃×D₅	1	1	yes	characteristic, complemented
226	#467	—	5	2	no	—
227	#462	—	5	1	no	—
228	#452	—	5	2	no	—
229	C₄×SD₁₆	—	5	1	no	—
230	C₈×D₄	—	5	1	no	—
231	#416	—	5	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	4	1	no	—
234	C₂²×C₃×C₅	—	4	1	no	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	—	2	2	no	—
238	C₂×C₃×D₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	1	no	—
240	C₃×C₄×C₅	—	4	1	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₃×C₄×C₅	#135	1	2	yes	—
243	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
244	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
245	C₃×Dic₅	—	2	2	no	—
246	C₃×Dic₅	—	4	1	no	—
247	C₃×Dic₅	—	4	2	no	—
248	C₃×Dic₅	—	4	1	no	—
249	C₃×#41	—	10	4	no	—
250	C₃×#41	—	20	2	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	—	5	2	no	—
253	C₂×C₃×Q₈	—	5	1	no	—
254	C₂×C₃×D₄	—	5	1	no	—
255	C₂×C₃×D₄	—	10	2	no	—
256	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	5	2	no	—
259	C₂²×C₃×C₄	—	10	2	no	—
260	C₃×Q₁₆	—	20	2	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	—	20	2	no	—
265	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
266	C₃×C₄⋊C₄	—	2	1	no	—
267	C₃×C₄⋊C₄	—	5	1	no	—
268	C₃×C₄⋊C₄	—	5	1	no	—
269	C₃×C₄⋊C₄	—	10	2	no	—
270	C₃×C₄⋊C₄	—	10	2	no	—
271	C₃×C₄⋊C₄	—	10	1	no	—
272	C₃×C₄⋊C₄	—	10	1	no	—
273	C₃×C₄⋊C₄	—	10	1	no	—
274	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
275	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	1	no	—
277	C₃×C₂²⋊C₄	—	5	2	no	—
278	C₃×C₂²⋊C₄	—	10	2	no	—
279	C₃×C₂²⋊C₄	—	10	2	no	—
280	C₃×C₂²⋊C₄	—	10	2	no	—
281	C₃×C₄²	—	10	2	no	—
282	C₃×C₄²	—	10	1	no	—
283	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
284	C₂³×C₅	—	2	1	no	—
285	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
286	C₅×Q₈	—	4	2	no	—
287	C₅×D₄	—	2	1	no	—
288	C₅×D₄	C₃×#41	1	2	yes	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	4	2	no	—
292	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
295	C₂²⋊D₅	—	4	4	no	—
296	C₂×Dic₅	—	2	1	no	—
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	2	no	—
299	C₂×Dic₅	—	4	4	no	—
300	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
301	D₂₀	—	2	2	no	—
302	C₄×D₅	—	2	2	no	—
303	C₄×D₅	—	2	2	no	—
304	Dic₁₀	—	2	1	no	—
305	Dic₁₀	—	2	2	no	—
306	Dic₁₀	—	2	1	no	—
307	Dic₁₀	—	2	2	no	—
308	C₅×C₈	—	2	2	no	—
309	#168	—	2	1	no	—
310	#168	—	2	1	no	—
311	C₂×#41	—	5	2	no	—
312	C₂×Q₁₆	—	5	2	no	—
313	C₂×SD₁₆	—	5	1	no	—
314	C₂²×C₈	—	5	2	no	—
315	C₄⋊Q₈	—	5	1	no	—
316	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
317	#126	—	10	2	no	—
318	#124	—	10	1	no	—
319	#123	—	10	2	no	—
320	C₂²⋊Q₈	—	5	2	no	—
321	C₂²⋊Q₈	—	5	2	no	—
322	#121	—	10	1	no	—
323	C₄×Q₈	—	5	1	no	—
324	C₄×Q₈	—	10	1	no	—
325	C₄×D₄	—	5	1	no	—
326	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
327	#117	—	5	2	no	—
328	C₂×C₄⋊C₄	—	10	1	no	—
329	#107	C₂×C₃×D₅	1	2	yes	—
330	#106	—	5	1	no	—
331	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
332	#103	—	5	2	no	—
333	#103	—	5	2	no	—
334	#103	—	5	1	no	—
335	#103	—	5	2	no	—
336	#102	—	5	1	no	—
337	#102	C₂×C₃×D₅	1	2	yes	—
338	C₂²⋊C₈	—	5	2	no	—
339	C₄×C₈	—	5	1	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	#546	1	1	yes	characteristic
342	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
343	C₂×C₃×C₅	#578	1	1	yes	characteristic
344	C₃×D₅	—	4	2	no	—
345	C₂³×C₃	—	2	1	no	—
346	C₂³×C₃	—	5	2	no	—
347	C₃×Q₈	—	4	2	no	—
348	C₃×Q₈	—	10	1	no	—
349	C₃×Q₈	—	10	2	no	—
350	C₃×Q₈	—	10	1	no	—
351	C₃×Q₈	—	10	2	no	—
352	C₃×D₄	—	2	1	no	—
353	C₃×D₄	—	10	2	no	—
354	C₃×D₄	—	20	4	no	—
355	C₃×D₄	#713	1	2	yes	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	4	2	no	—
359	C₂×C₃×C₄	—	5	2	no	—
360	C₂×C₃×C₄	—	10	2	no	—
361	C₂×C₃×C₄	—	10	2	no	—
362	C₂×C₃×C₄	—	10	1	no	—
363	C₂×C₃×C₄	—	10	1	no	—
364	C₂×C₃×C₄	—	10	2	no	—
365	C₂×C₃×C₄	—	20	4	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	—	2	2	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
376	C₂×D₅	—	2	2	no	—
377	C₂×D₅	—	2	2	no	—
378	C₂×D₅	—	2	2	no	—
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	—	4	2	no	—
382	C₄×C₅	C₃×#135	1	2	yes	—
383	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
384	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
385	Dic₅	—	2	2	no	—
386	Dic₅	—	4	1	no	—
387	Dic₅	—	4	1	no	—
388	Dic₅	—	4	2	no	—
389	#41	—	10	4	no	—
390	#41	—	20	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	5	2	no	—
393	C₂×Q₈	—	5	1	no	—
394	C₂×D₄	—	5	1	no	—
395	C₂×D₄	—	10	2	no	—
396	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	5	2	no	—
399	C₂²×C₄	—	10	2	no	—
400	Q₁₆	—	20	2	no	—
401	SD₁₆	—	10	2	no	—
402	C₂×C₈	—	5	1	no	—
403	C₂×C₈	—	5	1	no	—
404	C₂×C₈	—	20	2	no	—
405	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	5	1	no	—
408	C₄⋊C₄	—	5	1	no	—
409	C₄⋊C₄	—	10	2	no	—
410	C₄⋊C₄	—	10	2	no	—
411	C₄⋊C₄	—	10	1	no	—
412	C₄⋊C₄	—	10	1	no	—
413	C₄⋊C₄	—	10	1	no	—
414	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
415	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	5	2	no	—
418	C₂²⋊C₄	—	10	2	no	—
419	C₂²⋊C₄	—	10	2	no	—
420	C₂²⋊C₄	—	10	2	no	—
421	C₄²	—	10	2	no	—
422	C₄²	—	10	1	no	—
423	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
424	C₃×C₅	#3302	1	1	yes	characteristic, complemented, Hall
425	C₂²×C₃	—	2	2	no	—
426	C₂²×C₃	—	4	1	no	—
427	C₂²×C₃	—	4	1	no	—
428	C₂²×C₃	—	10	2	no	—
429	C₂²×C₃	—	10	2	no	—
430	C₂²×C₃	—	10	2	no	—
431	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
432	C₃×C₄	—	2	1	no	—
433	C₃×C₄	—	4	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	10	2	no	—
436	C₃×C₄	—	20	1	no	—
437	C₃×C₄	—	20	2	no	—
438	C₃×C₄	—	20	1	no	—
439	C₃×C₄	#4058	1	2	yes	—
440	C₃×C₄	C₂×#713	1	1	yes	characteristic
441	C₃×C₄	#4149	1	1	yes	characteristic
442	C₂×C₅	—	4	2	no	—
443	C₂×C₅	C₃×#546	1	1	yes	characteristic
444	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
445	C₂×C₅	C₃×#578	1	1	yes	characteristic
446	D₅	—	4	2	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	5	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	10	1	no	—
451	Q₈	—	10	2	no	—
452	Q₈	—	10	1	no	—
453	Q₈	—	10	2	no	—
454	D₄	—	2	1	no	—
455	D₄	—	10	2	no	—
456	D₄	—	20	4	no	—
457	D₄	C₃×#713	1	2	yes	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	5	2	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	1	no	—
465	C₂×C₄	—	10	1	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	20	4	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	—	4	2	no	—
475	C₂×C₃	—	20	2	no	—
476	C₂×C₃	#65964	1	1	yes	characteristic
477	C₂×C₃	C₂×#4058	1	1	yes	characteristic
478	C₂×C₃	#66113	1	1	yes	characteristic
479	C₅	C₃×#3302	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	10	2	no	—
484	C₂²	—	10	2	no	—
485	C₂²	—	10	2	no	—
486	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	10	2	no	—
491	C₄	—	20	1	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	1	no	—
494	C₄	C₃×#4058	1	2	yes	—
495	C₄	C₂×C₃×#713	1	1	yes	characteristic
496	C₄	C₃×#4149	1	1	yes	characteristic
497	C₃	#10612712	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	4	2	no	—
499	C₂	—	20	2	no	—
500	C₂	C₃×#65964	1	1	yes	characteristic
501	C₂	C₂×C₃×#4058	1	1	yes	characteristic
502	C₂	C₃×#66113	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×#474	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65889	C₂
hypercenter	C₃×#474	D₅
hypocenter	C₅	C₃×#3302
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#474

Complements

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

N	H ≅ G/N	type
1. C₃×#66066	C₂	semidirect
3. C₃×C₅×#474	C₂	semidirect
4. C₃×#65382	C₂	semidirect
5. C₃×C₄×#687	C₂	semidirect
6. C₃×#65177	C₂	semidirect
7. C₃×#65176	C₂	semidirect
8. C₃×#65138	C₂	semidirect
9. C₃×#65123	C₂	semidirect
10. C₃×#65072	C₂	semidirect
11. C₃×#65061	C₂	semidirect
12. #10612712	C₃	direct (N × H)
43. #66066	C₂×C₃	semidirect
45. C₅×#474	C₂×C₃	semidirect
46. #65382	C₂×C₃	semidirect
47. C₄×#687	C₂×C₃	semidirect
48. #65177	C₂×C₃	semidirect
49. #65176	C₂×C₃	semidirect
50. #65138	C₂×C₃	semidirect
51. #65123	C₂×C₃	semidirect
52. #65072	C₂×C₃	semidirect
53. #65061	C₂×C₃	semidirect
93. C₃×#474	D₅	semidirect
225. #474	C₃×D₅	semidirect
424. C₃×C₅	#3302	semidirect
479. C₅	C₃×#3302	semidirect
497. C₃	#10612712	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×#66066	2
C₃×#65889	2
C₃×C₅×#474	2
C₃×#65382	2
C₃×C₄×#687	2
C₃×#65177	2
C₃×#65176	2
C₃×#65138	2
C₃×#65123	2
C₃×#65072	2
C₃×#65061	2
#10612712	3
C₃×#3302	5

Subgroups — C3×#10612712 #14459941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612712 #14459941