Subgroups — C₃×#10612754 #14460259

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 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×#65911	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#689	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65155	C₂	1	2	yes	maximal, complemented
7	C₃×#65153	C₂	1	2	yes	maximal, complemented
8	C₃×#65137	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65099	C₂	1	2	yes	maximal, complemented
11	C₃×#65093	C₂	1	2	yes	maximal, complemented
12	#10612754	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×#4093	—	2	1	no	—
17	C₃×Q₈×Dic₅	—	2	1	no	—
18	C₂×C₃×#689	C₂²	1	1	yes	characteristic
19	C₂×C₃×#677	C₂²	1	2	yes	—
20	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
21	C₃×#4044	—	2	2	no	—
22	C₃×#4043	C₂²	1	2	yes	—
23	C₃×#4041	—	2	2	no	—
24	C₃×#4041	C₂²	1	2	yes	—
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×#4020	—	2	1	no	—
27	C₃×#4020	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₂₀	—	2	1	no	—
29	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	1	yes	characteristic
35	C₃×#3953	C₂²	1	2	yes	—
36	C₃×#3952	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	1	yes	characteristic
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3941	C₂²	1	2	yes	—
40	C₃×#3939	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3304	—	5	1	no	maximal, Hall
43	#66066	C₂×C₃	1	1	yes	characteristic, complemented
44	#65911	C₂×C₃	1	1	yes	characteristic
45	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
46	#65377	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#689	C₂×C₃	1	1	yes	characteristic, complemented
48	#65155	C₂×C₃	1	2	yes	complemented
49	#65153	C₂×C₃	1	2	yes	complemented
50	#65137	C₂×C₃	1	1	yes	characteristic, complemented
51	#65123	C₂×C₃	1	1	yes	characteristic, complemented
52	#65099	C₂×C₃	1	2	yes	complemented
53	#65093	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₃×#713	—	2	4	no	—
57	C₃×#713	—	4	2	no	—
58	C₂×C₃×D₂₀	—	2	2	no	—
59	C₂×C₃×D₂₀	—	2	1	no	—
60	C₂×C₃×D₂₀	—	2	2	no	—
61	C₂×C₃×D₂₀	—	2	1	no	—
62	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
63	C₂×C₃×D₂₀	C₂³	1	2	yes	—
64	C₂×C₃×C₄×D₅	—	2	2	no	—
65	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
66	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
72	C₃×C₄²×C₅	—	2	1	no	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#689	—	2	2	no	—
75	C₃×#685	—	2	2	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×#685	—	2	2	no	—
78	C₃×#685	D₄	1	2	yes	—
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×#677	—	4	2	no	—
88	C₃×C₈×D₅	—	4	2	no	—
89	C₃×#556	—	5	1	no	—
90	C₃×#550	—	5	1	no	—
91	C₃×#486	—	5	1	no	—
92	C₃×#482	—	5	2	no	—
93	C₃×#475	D₅	1	1	yes	characteristic, complemented
94	C₃×#465	—	5	2	no	—
95	C₃×#460	—	5	1	no	—
96	C₃×#452	—	5	2	no	—
97	C₃×C₄×Q₁₆	—	5	1	no	—
98	C₃×C₈×D₄	—	5	1	no	—
99	C₃×#416	—	5	2	no	—
100	C₂×#713	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
103	#4093	—	2	1	no	—
104	Q₈×Dic₅	—	2	1	no	—
105	C₂×#689	C₂²×C₃	1	1	yes	characteristic
106	C₂×#677	C₂²×C₃	1	2	yes	—
107	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
108	#4044	—	2	2	no	—
109	#4043	C₂²×C₃	1	2	yes	—
110	#4041	—	2	2	no	—
111	#4041	C₂²×C₃	1	2	yes	—
112	#4038	C₂²×C₃	1	2	yes	—
113	#4020	—	2	1	no	—
114	#4020	C₂²×C₃	1	1	yes	characteristic
115	C₄×D₂₀	—	2	1	no	—
116	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
118	C₅×#106	C₂²×C₃	1	2	yes	—
119	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
120	C₅×#103	C₂²×C₃	1	2	yes	—
121	#3967	C₂²×C₃	1	1	yes	characteristic
122	#3953	C₂²×C₃	1	2	yes	—
123	#3952	C₂²×C₃	1	2	yes	—
124	#3942	C₂²×C₃	1	1	yes	characteristic
125	#3941	C₂²×C₃	1	2	yes	—
126	#3941	C₂²×C₃	1	2	yes	—
127	#3939	C₂²×C₃	1	1	yes	characteristic
128	C₄×#168	C₂²×C₃	1	1	yes	characteristic
129	#3304	—	5	1	no	Sylow
130	C₂²×C₃×D₅	—	2	2	no	—
131	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	4	2	no	—
134	C₃×C₅×Q₈	#41	1	2	yes	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	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	C₂×C₃×Dic₅	—	2	1	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
144	C₃×D₂₀	—	2	2	no	—
145	C₃×D₂₀	—	2	2	no	—
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	—	4	4	no	—
148	C₃×D₂₀	—	4	2	no	—
149	C₃×D₂₀	—	8	1	no	—
150	C₃×D₂₀	—	8	2	no	—
151	C₃×C₄×D₅	—	2	2	no	—
152	C₃×C₄×D₅	—	2	2	no	—
153	C₃×C₄×D₅	—	4	4	no	—
154	C₃×Dic₁₀	—	2	1	no	—
155	C₃×Dic₁₀	—	2	1	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₃×#168	—	2	1	no	—
158	C₃×#168	—	2	1	no	—
159	C₂×C₃×#41	—	5	2	no	—
160	C₂×C₃×Q₁₆	—	5	1	no	—
161	C₂×C₃×SD₁₆	—	5	2	no	—
162	C₂²×C₃×C₈	—	5	2	no	—
163	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
164	C₃×#127	—	5	1	no	—
165	C₃×#127	—	10	1	no	—
166	C₃×#126	—	10	2	no	—
167	C₃×#124	—	10	1	no	—
168	C₃×C₂²⋊Q₈	—	5	2	no	—
169	C₃×#121	—	5	2	no	—
170	C₃×#121	—	10	2	no	—
171	C₃×C₄×Q₈	—	5	1	no	—
172	C₃×C₄×Q₈	—	10	1	no	—
173	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	5	1	no	—
175	C₃×C₄×D₄	—	10	1	no	—
176	C₃×#117	—	5	2	no	—
177	C₃×#107	—	5	1	no	—
178	C₃×#106	C₂×D₅	1	2	yes	—
179	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
180	C₃×#103	—	5	1	no	—
181	C₃×#103	—	5	1	no	—
182	C₃×#103	C₂×D₅	1	2	yes	—
183	C₃×#102	—	5	2	no	—
184	C₃×#102	—	5	2	no	—
185	C₃×#102	—	5	2	no	—
186	C₃×C₂²⋊C₈	—	5	2	no	—
187	C₃×C₄×C₈	—	5	1	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
190	#713	—	2	4	no	—
191	#713	—	4	2	no	—
192	C₂×D₂₀	—	2	2	no	—
193	C₂×D₂₀	—	2	1	no	—
194	C₂×D₂₀	—	2	2	no	—
195	C₂×D₂₀	—	2	1	no	—
196	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
197	C₂×D₂₀	C₂³×C₃	1	2	yes	—
198	C₂×C₄×D₅	—	2	2	no	—
199	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
200	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
206	C₄²×C₅	—	2	1	no	—
207	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
208	#689	—	2	2	no	—
209	#685	—	2	2	no	—
210	#685	—	2	2	no	—
211	#685	—	2	2	no	—
212	#685	C₃×D₄	1	2	yes	—
213	C₄⋊Dic₅	—	2	2	no	—
214	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
215	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
216	#683	—	2	1	no	—
217	C₄×Dic₅	—	2	1	no	—
218	C₄×Dic₅	—	2	2	no	—
219	C₂×#168	C₂³×C₃	1	1	yes	characteristic
220	C₂×#168	C₂³×C₃	1	1	yes	characteristic
221	#677	—	4	2	no	—
222	C₈×D₅	—	4	2	no	—
223	#556	—	5	1	no	—
224	#550	—	5	1	no	—
225	#486	—	5	1	no	—
226	#482	—	5	2	no	—
227	#475	C₃×D₅	1	1	yes	characteristic, complemented
228	#465	—	5	2	no	—
229	#460	—	5	1	no	—
230	#452	—	5	2	no	—
231	C₄×Q₁₆	—	5	1	no	—
232	C₈×D₄	—	5	1	no	—
233	#416	—	5	2	no	—
234	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₃×D₅	—	2	2	no	—
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	—	2	2	no	—
238	C₂×C₃×D₅	—	4	2	no	—
239	C₂×C₃×D₅	—	4	2	no	—
240	C₂×C₃×D₅	—	4	2	no	—
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	—	2	1	no	—
243	C₃×C₄×C₅	—	4	2	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	#135	1	2	yes	—
246	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
247	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₃×Dic₅	—	2	2	no	—
249	C₃×Dic₅	—	4	1	no	—
250	C₃×Dic₅	—	4	1	no	—
251	C₃×#41	—	10	4	no	—
252	C₃×#41	—	20	2	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	—	5	1	no	—
255	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃×D₄	—	5	1	no	—
257	C₂×C₃×D₄	—	5	2	no	—
258	C₂×C₃×D₄	—	10	2	no	—
259	C₂×C₃×D₄	—	10	2	no	—
260	C₂×C₃×D₄	—	10	1	no	—
261	C₂×C₃×D₄	—	10	1	no	—
262	C₂²×C₃×C₄	—	5	2	no	—
263	C₂²×C₃×C₄	—	10	2	no	—
264	C₃×Q₁₆	—	10	2	no	—
265	C₃×SD₁₆	—	20	2	no	—
266	C₂×C₃×C₈	—	5	1	no	—
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	20	2	no	—
269	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	5	1	no	—
273	C₃×C₄⋊C₄	—	5	1	no	—
274	C₃×C₄⋊C₄	—	10	2	no	—
275	C₃×C₄⋊C₄	—	10	1	no	—
276	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
277	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	—	5	2	no	—
279	C₃×C₂²⋊C₄	—	10	2	no	—
280	C₃×C₂²⋊C₄	—	10	2	no	—
281	C₃×C₂²⋊C₄	—	10	2	no	—
282	C₃×C₄²	—	2	1	no	—
283	C₃×C₄²	—	10	2	no	—
284	C₃×C₄²	—	10	1	no	—
285	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
286	C₂²×D₅	—	2	2	no	—
287	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	4	2	no	—
290	C₅×Q₈	C₃×#41	1	2	yes	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	C₂×Dic₅	—	2	1	no	—
298	C₂×Dic₅	—	2	1	no	—
299	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
300	D₂₀	—	2	2	no	—
301	D₂₀	—	2	2	no	—
302	D₂₀	—	2	2	no	—
303	D₂₀	—	4	4	no	—
304	D₂₀	—	4	2	no	—
305	D₂₀	—	8	1	no	—
306	D₂₀	—	8	2	no	—
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	2	2	no	—
309	C₄×D₅	—	4	4	no	—
310	Dic₁₀	—	2	1	no	—
311	Dic₁₀	—	2	1	no	—
312	C₅×C₈	—	2	2	no	—
313	#168	—	2	1	no	—
314	#168	—	2	1	no	—
315	C₂×#41	—	5	2	no	—
316	C₂×Q₁₆	—	5	1	no	—
317	C₂×SD₁₆	—	5	2	no	—
318	C₂²×C₈	—	5	2	no	—
319	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
320	#127	—	5	1	no	—
321	#127	—	10	1	no	—
322	#126	—	10	2	no	—
323	#124	—	10	1	no	—
324	C₂²⋊Q₈	—	5	2	no	—
325	#121	—	5	2	no	—
326	#121	—	10	2	no	—
327	C₄×Q₈	—	5	1	no	—
328	C₄×Q₈	—	10	1	no	—
329	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
330	C₄×D₄	—	5	1	no	—
331	C₄×D₄	—	10	1	no	—
332	#117	—	5	2	no	—
333	#107	—	5	1	no	—
334	#106	C₂×C₃×D₅	1	2	yes	—
335	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
336	#103	—	5	1	no	—
337	#103	—	5	1	no	—
338	#103	C₂×C₃×D₅	1	2	yes	—
339	#102	—	5	2	no	—
340	#102	—	5	2	no	—
341	#102	—	5	2	no	—
342	C₂²⋊C₈	—	5	2	no	—
343	C₄×C₈	—	5	1	no	—
344	C₂×C₃×C₅	#546	1	1	yes	characteristic
345	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
346	C₂×C₃×C₅	#577	1	1	yes	characteristic
347	C₃×D₅	—	4	2	no	—
348	C₃×D₅	—	8	2	no	—
349	C₂³×C₃	—	5	2	no	—
350	C₂³×C₃	—	10	2	no	—
351	C₃×Q₈	—	2	1	no	—
352	C₃×Q₈	—	4	2	no	—
353	C₃×Q₈	—	10	1	no	—
354	C₃×Q₈	—	10	1	no	—
355	C₃×Q₈	#713	1	2	yes	—
356	C₃×D₄	—	10	2	no	—
357	C₃×D₄	—	10	2	no	—
358	C₃×D₄	—	10	2	no	—
359	C₃×D₄	—	20	4	no	—
360	C₃×D₄	—	20	2	no	—
361	C₃×D₄	—	40	1	no	—
362	C₃×D₄	—	40	2	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	5	2	no	—
367	C₂×C₃×C₄	—	10	2	no	—
368	C₂×C₃×C₄	—	10	2	no	—
369	C₂×C₃×C₄	—	10	1	no	—
370	C₂×C₃×C₄	—	10	1	no	—
371	C₂×C₃×C₄	—	20	4	no	—
372	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
373	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
375	C₃×C₈	—	2	2	no	—
376	C₃×C₈	—	10	1	no	—
377	C₃×C₈	—	10	1	no	—
378	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₂×D₅	—	2	2	no	—
380	C₂×D₅	—	2	2	no	—
381	C₂×D₅	—	2	2	no	—
382	C₂×D₅	—	4	2	no	—
383	C₂×D₅	—	4	2	no	—
384	C₂×D₅	—	4	2	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	C₃×#135	1	2	yes	—
390	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
391	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
392	Dic₅	—	2	2	no	—
393	Dic₅	—	4	1	no	—
394	Dic₅	—	4	1	no	—
395	#41	—	10	4	no	—
396	#41	—	20	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	5	1	no	—
399	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₂×D₄	—	5	1	no	—
401	C₂×D₄	—	5	2	no	—
402	C₂×D₄	—	10	2	no	—
403	C₂×D₄	—	10	2	no	—
404	C₂×D₄	—	10	1	no	—
405	C₂×D₄	—	10	1	no	—
406	C₂²×C₄	—	5	2	no	—
407	C₂²×C₄	—	10	2	no	—
408	Q₁₆	—	10	2	no	—
409	SD₁₆	—	20	2	no	—
410	C₂×C₈	—	5	1	no	—
411	C₂×C₈	—	5	1	no	—
412	C₂×C₈	—	20	2	no	—
413	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	5	1	no	—
417	C₄⋊C₄	—	5	1	no	—
418	C₄⋊C₄	—	10	2	no	—
419	C₄⋊C₄	—	10	1	no	—
420	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
421	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂²⋊C₄	—	5	2	no	—
423	C₂²⋊C₄	—	10	2	no	—
424	C₂²⋊C₄	—	10	2	no	—
425	C₂²⋊C₄	—	10	2	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	10	2	no	—
428	C₄²	—	10	1	no	—
429	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
430	C₃×C₅	#3304	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	10	2	no	—
432	C₂²×C₃	—	10	2	no	—
433	C₂²×C₃	—	10	2	no	—
434	C₂²×C₃	—	20	2	no	—
435	C₂²×C₃	—	20	2	no	—
436	C₂²×C₃	—	20	2	no	—
437	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	10	2	no	—
443	C₃×C₄	—	20	1	no	—
444	C₃×C₄	—	20	1	no	—
445	C₃×C₄	#4062	1	2	yes	—
446	C₃×C₄	C₂×#713	1	1	yes	characteristic
447	C₃×C₄	#4149	1	1	yes	characteristic
448	C₂×C₅	C₃×#546	1	1	yes	characteristic
449	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
450	C₂×C₅	C₃×#577	1	1	yes	characteristic
451	D₅	—	4	2	no	—
452	D₅	—	8	2	no	—
453	C₂³	—	5	2	no	—
454	C₂³	—	10	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	10	1	no	—
458	Q₈	—	10	1	no	—
459	Q₈	C₃×#713	1	2	yes	—
460	D₄	—	10	2	no	—
461	D₄	—	10	2	no	—
462	D₄	—	10	2	no	—
463	D₄	—	20	4	no	—
464	D₄	—	20	2	no	—
465	D₄	—	40	1	no	—
466	D₄	—	40	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	5	2	no	—
471	C₂×C₄	—	10	2	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	10	1	no	—
474	C₂×C₄	—	10	1	no	—
475	C₂×C₄	—	20	4	no	—
476	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
477	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
478	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	10	1	no	—
481	C₈	—	10	1	no	—
482	C₂×C₃	—	20	2	no	—
483	C₂×C₃	—	40	2	no	—
484	C₂×C₃	#65964	1	1	yes	characteristic
485	C₂×C₃	C₂×#4062	1	1	yes	characteristic
486	C₂×C₃	#66112	1	1	yes	characteristic
487	C₅	C₃×#3304	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	10	2	no	—
489	C₂²	—	10	2	no	—
490	C₂²	—	10	2	no	—
491	C₂²	—	20	2	no	—
492	C₂²	—	20	2	no	—
493	C₂²	—	20	2	no	—
494	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	4	2	no	—
499	C₄	—	10	2	no	—
500	C₄	—	20	1	no	—
501	C₄	—	20	1	no	—
502	C₄	C₃×#4062	1	2	yes	—
503	C₄	C₂×C₃×#713	1	1	yes	characteristic
504	C₄	C₃×#4149	1	1	yes	characteristic
505	C₃	#10612754	1	1	yes	characteristic, direct product factor, Sylow
506	C₂	—	20	2	no	—
507	C₂	—	40	2	no	—
508	C₂	C₃×#65964	1	1	yes	characteristic
509	C₂	C₂×C₃×#4062	1	1	yes	characteristic
510	C₂	C₃×#66112	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×#475	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65911	C₂
hypercenter	C₃×#475	D₅
hypocenter	C₅	C₃×#3304
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#475

Complements

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

N	H ≅ G/N	type
1. C₃×#66066	C₂	semidirect
3. C₃×C₅×#475	C₂	semidirect
4. C₃×#65377	C₂	semidirect
5. C₃×C₄×#689	C₂	semidirect
6. C₃×#65155	C₂	semidirect
7. C₃×#65153	C₂	semidirect
8. C₃×#65137	C₂	semidirect
9. C₃×#65123	C₂	semidirect
10. C₃×#65099	C₂	semidirect
11. C₃×#65093	C₂	semidirect
12. #10612754	C₃	direct (N × H)
43. #66066	C₂×C₃	semidirect
45. C₅×#475	C₂×C₃	semidirect
46. #65377	C₂×C₃	semidirect
47. C₄×#689	C₂×C₃	semidirect
48. #65155	C₂×C₃	semidirect
49. #65153	C₂×C₃	semidirect
50. #65137	C₂×C₃	semidirect
51. #65123	C₂×C₃	semidirect
52. #65099	C₂×C₃	semidirect
53. #65093	C₂×C₃	semidirect
93. C₃×#475	D₅	semidirect
227. #475	C₃×D₅	semidirect
430. C₃×C₅	#3304	semidirect
487. C₅	C₃×#3304	semidirect
505. C₃	#10612754	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×#65911	2
C₃×C₅×#475	2
C₃×#65377	2
C₃×C₄×#689	2
C₃×#65155	2
C₃×#65153	2
C₃×#65137	2
C₃×#65123	2
C₃×#65099	2
C₃×#65093	2
#10612754	3
C₃×#3304	5

Subgroups — C3×#10612754 #14460259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612754 #14460259