Subgroups — C₃×#10615241 #14459950

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×C₅×#547	C₂	1	1	yes	maximal, characteristic
2	C₃×#65876	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65528	C₂	1	2	yes	maximal, complemented
4	C₃×#65522	C₂	1	2	yes	maximal, complemented
5	C₃×#65379	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65340	C₂	1	2	yes	maximal, complemented
8	C₃×#65334	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×#687	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65296	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615241	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#123	—	2	2	no	—
16	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×#121	—	2	1	no	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
21	C₂×C₃×#689	C₂²	1	2	yes	—
22	C₃×#4082	—	2	1	no	—
23	C₂×C₃×#687	C₂²	1	1	yes	characteristic
24	C₃×#4072	C₂²	1	2	yes	—
25	C₃×#4070	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	2	yes	—
27	C₃×#4033	—	2	1	no	—
28	C₃×#4025	—	2	2	no	—
29	C₃×#4015	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
31	C₃×#3967	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3964	C₂²	1	2	yes	—
35	C₃×#3964	C₂²	1	1	yes	characteristic
36	C₃×C₂²⋊#168	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	1	yes	characteristic
38	C₃×#3940	C₂²	1	1	yes	characteristic
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3302	—	5	1	no	maximal, Hall
43	C₅×#547	C₂×C₃	1	1	yes	characteristic
44	#65876	C₂×C₃	1	1	yes	characteristic, complemented
45	#65528	C₂×C₃	1	2	yes	complemented
46	#65522	C₂×C₃	1	2	yes	complemented
47	#65379	C₂×C₃	1	1	yes	characteristic, complemented
48	#65370	C₂×C₃	1	1	yes	characteristic, complemented
49	#65340	C₂×C₃	1	2	yes	complemented
50	#65334	C₂×C₃	1	2	yes	complemented
51	C₄×#687	C₂×C₃	1	1	yes	characteristic, complemented
52	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
53	#65296	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₅×#41	—	2	4	no	—
55	C₃×C₅×#41	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
57	C₂×C₃×C₅×D₄	—	2	2	no	—
58	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	2	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂×C₃×Dic₁₀	—	2	1	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	—	2	1	no	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
69	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	2	no	—
75	C₃×C₂²⋊Dic₅	—	2	2	no	—
76	C₃×#689	—	4	2	no	—
77	C₃×#687	—	2	2	no	—
78	C₃×C₄⋊Dic₅	—	2	1	no	—
79	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×#683	—	2	1	no	—
82	C₃×#683	—	2	2	no	—
83	C₃×C₄×Dic₅	—	2	1	no	—
84	C₃×C₄×Dic₅	—	2	2	no	—
85	C₂×C₃×#168	—	4	2	no	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×#556	—	5	1	no	—
90	C₃×#547	D₅	1	1	yes	characteristic
91	C₃×#487	—	5	1	no	—
92	C₃×#485	—	5	2	no	—
93	C₃×#474	—	5	1	no	—
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×C₅×#41	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×#123	—	2	2	no	—
103	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₅×#121	—	2	1	no	—
105	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	—	2	1	no	—
108	C₂×#689	C₂²×C₃	1	2	yes	—
109	#4082	—	2	1	no	—
110	C₂×#687	C₂²×C₃	1	1	yes	characteristic
111	#4072	C₂²×C₃	1	2	yes	—
112	#4070	C₂²×C₃	1	2	yes	—
113	C₂²×#168	C₂²×C₃	1	2	yes	—
114	#4033	—	2	1	no	—
115	#4025	—	2	2	no	—
116	#4015	C₂²×C₃	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	2	yes	—
119	#3967	C₂²×C₃	1	2	yes	—
120	#3967	C₂²×C₃	1	2	yes	—
121	#3964	C₂²×C₃	1	2	yes	—
122	#3964	C₂²×C₃	1	1	yes	characteristic
123	C₂²⋊#168	C₂²×C₃	1	2	yes	—
124	#3942	C₂²×C₃	1	1	yes	characteristic
125	#3940	C₂²×C₃	1	1	yes	characteristic
126	#3939	C₂²×C₃	1	2	yes	—
127	C₄⋊#168	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	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	—	2	1	no	—
136	C₃×C₅×D₄	—	4	4	no	—
137	C₃×C₅×D₄	#41	1	2	yes	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	4	4	no	—
143	C₂×C₃×C₄×C₅	—	4	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	—	2	2	no	—
151	C₃×Dic₁₀	—	2	1	no	—
152	C₃×Dic₁₀	—	2	1	no	—
153	C₃×Dic₁₀	—	4	2	no	—
154	C₃×#168	—	2	1	no	—
155	C₃×#168	—	2	1	no	—
156	C₃×#168	—	2	2	no	—
157	C₂×C₃×#41	C₂×D₅	1	2	yes	—
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	—	2	2	no	—
166	C₃×C₂²⋊Q₈	—	5	2	no	—
167	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
168	C₃×#121	—	2	1	no	—
169	C₃×C₄×Q₈	—	5	1	no	—
170	C₃×C₄×Q₈	—	10	1	no	—
171	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
173	C₃×#117	—	5	2	no	—
174	C₂×C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×#107	—	5	2	no	—
176	C₃×#106	—	5	1	no	—
177	C₃×C₄⋊C₈	—	5	1	no	—
178	C₃×#103	—	5	2	no	—
179	C₃×#103	—	5	2	no	—
180	C₃×#103	—	5	2	no	—
181	C₃×#103	—	5	1	no	—
182	C₃×#102	—	5	1	no	—
183	C₃×#102	—	5	2	no	—
184	C₃×C₂²⋊C₈	—	5	2	no	—
185	C₃×C₄×C₈	—	5	1	no	—
186	C₅×#41	—	2	4	no	—
187	C₅×#41	—	4	2	no	—
188	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
189	C₂×C₅×D₄	—	2	2	no	—
190	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
191	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₄×C₅	—	2	1	no	—
193	C₂²×C₄×C₅	—	2	2	no	—
194	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
195	C₂×Dic₁₀	—	2	1	no	—
196	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	1	no	—
204	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
205	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂²⋊Dic₅	—	2	2	no	—
207	C₂²⋊Dic₅	—	2	2	no	—
208	#689	—	4	2	no	—
209	#687	—	2	2	no	—
210	C₄⋊Dic₅	—	2	1	no	—
211	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
212	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
213	#683	—	2	1	no	—
214	#683	—	2	2	no	—
215	C₄×Dic₅	—	2	1	no	—
216	C₄×Dic₅	—	2	2	no	—
217	C₂×#168	—	4	2	no	—
218	C₂×#168	C₂³×C₃	1	1	yes	characteristic
219	C₂×#168	C₂³×C₃	1	1	yes	characteristic
220	C₂×#168	C₂³×C₃	1	2	yes	—
221	#556	—	5	1	no	—
222	#547	C₃×D₅	1	1	yes	characteristic
223	#487	—	5	1	no	—
224	#485	—	5	2	no	—
225	#474	—	5	1	no	—
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	—	2	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	4	1	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	1	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₃×C₄×C₅	—	4	1	no	—
243	C₃×C₄×C₅	#135	1	2	yes	—
244	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
245	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₃×Dic₅	—	4	1	no	—
247	C₃×Dic₅	—	4	2	no	—
248	C₃×Dic₅	—	4	1	no	—
249	C₃×#41	—	2	4	no	—
250	C₃×#41	—	4	2	no	—
251	C₂×C₃×Q₈	—	5	1	no	—
252	C₂×C₃×Q₈	—	10	1	no	—
253	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
254	C₂×C₃×D₄	—	2	2	no	—
255	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
256	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	2	2	no	—
259	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
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	—	5	2	no	—
265	C₂×C₃×C₈	—	20	2	no	—
266	C₃×C₄⋊C₄	—	2	1	no	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	5	1	no	—
270	C₃×C₄⋊C₄	—	5	2	no	—
271	C₃×C₄⋊C₄	—	10	1	no	—
272	C₃×C₄⋊C₄	—	10	2	no	—
273	C₃×C₄⋊C₄	—	10	1	no	—
274	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	2	1	no	—
278	C₃×C₂²⋊C₄	—	10	2	no	—
279	C₃×C₂²⋊C₄	—	10	2	no	—
280	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
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	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
286	C₅×Q₈	—	2	2	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	4	4	no	—
291	C₅×D₄	C₃×#41	1	2	yes	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	4	4	no	—
297	C₂×C₄×C₅	—	4	2	no	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	2	1	no	—
304	C₂×Dic₅	—	2	2	no	—
305	Dic₁₀	—	2	1	no	—
306	Dic₁₀	—	2	1	no	—
307	Dic₁₀	—	4	2	no	—
308	#168	—	2	1	no	—
309	#168	—	2	1	no	—
310	#168	—	2	2	no	—
311	C₂×#41	C₂×C₃×D₅	1	2	yes	—
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	—	2	2	no	—
320	C₂²⋊Q₈	—	5	2	no	—
321	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
322	#121	—	2	1	no	—
323	C₄×Q₈	—	5	1	no	—
324	C₄×Q₈	—	10	1	no	—
325	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
326	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
327	#117	—	5	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	#107	—	5	2	no	—
330	#106	—	5	1	no	—
331	C₄⋊C₈	—	5	1	no	—
332	#103	—	5	2	no	—
333	#103	—	5	2	no	—
334	#103	—	5	2	no	—
335	#103	—	5	1	no	—
336	#102	—	5	1	no	—
337	#102	—	5	2	no	—
338	C₂²⋊C₈	—	5	2	no	—
339	C₄×C₈	—	5	1	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	—	4	2	no	—
342	C₂×C₃×C₅	#546	1	1	yes	characteristic
343	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
344	C₂×C₃×C₅	#578	1	1	yes	characteristic
345	C₂³×C₃	—	2	1	no	—
346	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	2	2	no	—
349	C₃×Q₈	—	10	1	no	—
350	C₃×Q₈	—	10	1	no	—
351	C₃×Q₈	—	20	2	no	—
352	C₃×D₄	—	2	2	no	—
353	C₃×D₄	—	2	1	no	—
354	C₃×D₄	—	4	4	no	—
355	C₃×D₄	#711	1	2	yes	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	4	4	no	—
361	C₂×C₃×C₄	—	4	2	no	—
362	C₂×C₃×C₄	—	10	1	no	—
363	C₂×C₃×C₄	—	10	2	no	—
364	C₂×C₃×C₄	—	10	1	no	—
365	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
366	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
369	C₃×C₈	—	10	1	no	—
370	C₃×C₈	—	10	1	no	—
371	C₃×C₈	—	10	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
379	C₄×C₅	—	2	1	no	—
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	4	1	no	—
382	C₄×C₅	—	4	2	no	—
383	C₄×C₅	C₃×#135	1	2	yes	—
384	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
385	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
386	Dic₅	—	4	2	no	—
387	Dic₅	—	4	1	no	—
388	Dic₅	—	4	1	no	—
389	#41	—	2	4	no	—
390	#41	—	4	2	no	—
391	C₂×Q₈	—	5	1	no	—
392	C₂×Q₈	—	10	1	no	—
393	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
396	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
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	—	5	2	no	—
405	C₂×C₈	—	20	2	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	5	1	no	—
410	C₄⋊C₄	—	5	2	no	—
411	C₄⋊C₄	—	10	1	no	—
412	C₄⋊C₄	—	10	2	no	—
413	C₄⋊C₄	—	10	1	no	—
414	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
415	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	10	2	no	—
419	C₂²⋊C₄	—	10	2	no	—
420	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
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	—	2	2	no	—
427	C₂²×C₃	—	2	2	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	1	no	—
431	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	2	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	20	1	no	—
437	C₃×C₄	—	20	2	no	—
438	C₃×C₄	—	20	1	no	—
439	C₃×C₄	#4096	1	2	yes	—
440	C₃×C₄	C₂×#711	1	1	yes	characteristic
441	C₃×C₄	#4144	1	1	yes	characteristic
442	C₂×C₅	—	4	2	no	—
443	C₂×C₅	—	4	2	no	—
444	C₂×C₅	C₃×#546	1	1	yes	characteristic
445	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
446	C₂×C₅	C₃×#578	1	1	yes	characteristic
447	C₂³	—	2	1	no	—
448	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
449	Q₈	—	2	2	no	—
450	Q₈	—	2	2	no	—
451	Q₈	—	10	1	no	—
452	Q₈	—	10	1	no	—
453	Q₈	—	20	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	1	no	—
456	D₄	—	4	4	no	—
457	D₄	C₃×#711	1	2	yes	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	10	1	no	—
465	C₂×C₄	—	10	2	no	—
466	C₂×C₄	—	10	1	no	—
467	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
468	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
469	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
470	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
471	C₈	—	10	1	no	—
472	C₈	—	10	1	no	—
473	C₈	—	10	2	no	—
474	C₂×C₃	—	4	2	no	—
475	C₂×C₃	—	4	2	no	—
476	C₂×C₃	#66140	1	1	yes	characteristic
477	C₂×C₃	C₂×#4096	1	1	yes	characteristic
478	C₂×C₃	#66172	1	1	yes	characteristic
479	C₅	C₃×#3302	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	20	1	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	1	no	—
494	C₄	C₃×#4096	1	2	yes	—
495	C₄	C₂×C₃×#711	1	1	yes	characteristic
496	C₄	C₃×#4144	1	1	yes	characteristic
497	C₃	#10615241	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	4	2	no	—
499	C₂	—	4	2	no	—
500	C₂	C₃×#66140	1	1	yes	characteristic
501	C₂	C₂×C₃×#4096	1	1	yes	characteristic
502	C₂	C₃×#66172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₃×C₅×#547	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#547	D₅
hypocenter	C₅	C₃×#3302
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×#547

Complements

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

N	H ≅ G/N	type
2. C₃×#65876	C₂	semidirect
3. C₃×#65528	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65379	C₂	semidirect
6. C₃×#65370	C₂	semidirect
7. C₃×#65340	C₂	semidirect
8. C₃×#65334	C₂	semidirect
9. C₃×C₄×#687	C₂	semidirect
10. C₃×D₄×#168	C₂	semidirect
11. C₃×#65296	C₂	semidirect
12. #10615241	C₃	direct (N × H)
44. #65876	C₂×C₃	semidirect
45. #65528	C₂×C₃	semidirect
46. #65522	C₂×C₃	semidirect
47. #65379	C₂×C₃	semidirect
48. #65370	C₂×C₃	semidirect
49. #65340	C₂×C₃	semidirect
50. #65334	C₂×C₃	semidirect
51. C₄×#687	C₂×C₃	semidirect
52. D₄×#168	C₂×C₃	semidirect
53. #65296	C₂×C₃	semidirect
424. C₃×C₅	#3302	semidirect
479. C₅	C₃×#3302	semidirect
497. C₃	#10615241	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×C₅×#547	2
C₃×#65876	2
C₃×#65528	2
C₃×#65522	2
C₃×#65379	2
C₃×#65370	2
C₃×#65340	2
C₃×#65334	2
C₃×C₄×#687	2
C₃×D₄×#168	2
C₃×#65296	2
#10615241	3
C₃×#3302	5

Subgroups — C3×#10615241 #14459950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615241 #14459950