Subgroups — C₃×#10613308 #14458450

Order 1920.

924 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66064	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66051	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65364	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65067	C₂	1	2	yes	maximal, complemented
7	C₃×#65066	C₂	1	2	yes	maximal, complemented
8	C₃×#65065	C₂	1	2	yes	maximal, complemented
9	C₃×D₅×#102	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×#677	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613308	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×D₄×D₅	—	2	1	no	—
14	C₂×C₃×D₄×D₅	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic
17	C₃×#4092	—	2	2	no	—
18	C₃×#4084	—	2	1	no	—
19	C₃×#4084	C₂²	1	2	yes	—
20	C₃×#4083	—	2	2	no	—
21	C₂×C₃×#687	C₂²	1	2	yes	complemented
22	C₂×C₃×#677	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₈×D₅	C₂²	1	2	yes	complemented
24	C₃×#4043	C₂²	1	2	yes	complemented
25	C₃×#4039	—	2	1	no	—
26	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
27	C₃×#4036	—	2	1	no	—
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	2	yes	complemented
33	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3964	C₂²	1	2	yes	complemented
35	C₃×#3953	C₂²	1	1	yes	characteristic
36	C₃×#3952	C₂²	1	2	yes	complemented
37	C₃×#3949	C₂²	1	1	yes	characteristic, complemented
38	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3941	C₂²	1	2	yes	—
40	C₃×#3940	C₂²	1	2	yes	complemented
41	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3295	—	5	1	no	maximal, Hall
43	#66064	C₂×C₃	1	1	yes	characteristic, complemented
44	#66051	C₂×C₃	1	1	yes	characteristic
45	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
46	#65373	C₂×C₃	1	1	yes	characteristic, complemented
47	#65364	C₂×C₃	1	1	yes	characteristic, complemented
48	#65067	C₂×C₃	1	2	yes	complemented
49	#65066	C₂×C₃	1	2	yes	complemented
50	#65065	C₂×C₃	1	2	yes	complemented
51	D₅×#102	C₂×C₃	1	2	yes	complemented
52	C₄×#677	C₂×C₃	1	1	yes	characteristic, complemented
53	C₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂³×C₃×D₅	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×D₄	—	2	1	no	—
57	C₂×C₃×C₅×D₄	—	2	1	no	—
58	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
59	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₃×D₄×D₅	—	2	4	no	—
62	C₃×D₄×D₅	—	4	2	no	—
63	C₃×D₄×D₅	—	4	4	no	—
64	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
65	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	1	no	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
69	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×C₂²⋊Dic₅	—	2	2	no	—
76	C₃×#687	—	4	2	no	—
77	C₃×#685	—	2	2	no	—
78	C₃×#685	—	2	1	no	—
79	C₃×#685	D₄	1	2	yes	—
80	C₃×C₄⋊Dic₅	—	2	2	no	—
81	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
84	C₃×#683	—	2	1	no	—
85	C₃×#683	—	2	2	no	—
86	C₃×C₄×Dic₅	—	2	1	no	—
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₃×#677	—	2	2	no	—
89	C₃×C₈×D₅	—	4	2	no	—
90	C₃×#554	—	5	1	no	—
91	C₃×D₄²	—	5	1	no	—
92	C₃×#486	D₅	1	1	yes	characteristic, complemented
93	C₃×#481	—	5	2	no	—
94	C₃×#476	—	5	1	no	—
95	C₃×#465	—	5	2	no	—
96	C₃×#460	—	5	1	no	—
97	C₃×#450	—	5	2	no	—
98	C₃×C₄×SD₁₆	—	5	1	no	—
99	C₃×C₈×D₄	—	5	1	no	—
100	C₂×C₃×#102	—	5	2	no	—
101	C₂×D₄×D₅	—	2	1	no	—
102	C₂×D₄×D₅	C₂²×C₃	1	2	yes	—
103	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₅×#127	C₂²×C₃	1	1	yes	characteristic
105	#4092	—	2	2	no	—
106	#4084	—	2	1	no	—
107	#4084	C₂²×C₃	1	2	yes	—
108	#4083	—	2	2	no	—
109	C₂×#687	C₂²×C₃	1	2	yes	complemented
110	C₂×#677	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₈×D₅	C₂²×C₃	1	2	yes	complemented
112	#4043	C₂²×C₃	1	2	yes	complemented
113	#4039	—	2	1	no	—
114	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
115	#4036	—	2	1	no	—
116	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
117	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
118	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
119	C₅×#102	C₂²×C₃	1	2	yes	complemented
120	C₅×#102	C₂²×C₃	1	2	yes	complemented
121	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	#3964	C₂²×C₃	1	2	yes	complemented
123	#3953	C₂²×C₃	1	1	yes	characteristic
124	#3952	C₂²×C₃	1	2	yes	complemented
125	#3949	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
127	#3941	C₂²×C₃	1	2	yes	—
128	#3940	C₂²×C₃	1	2	yes	complemented
129	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3295	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	2	no	—
132	C₂²×C₃×D₅	—	2	1	no	—
133	C₂²×C₃×D₅	—	4	4	no	—
134	C₂²×C₃×D₅	—	4	4	no	—
135	C₂²×C₃×D₅	—	8	2	no	—
136	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
137	C₃×C₅×Q₈	—	8	1	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	2	no	—
141	C₃×C₅×D₄	—	8	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₂²⋊D₅	—	4	4	no	—
147	C₃×C₂²⋊D₅	—	4	4	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	2	1	no	—
150	C₂×C₃×Dic₅	—	2	1	no	—
151	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
152	C₃×D₂₀	—	2	1	no	—
153	C₃×D₂₀	SD₁₆	1	4	yes	complemented
154	C₃×D₂₀	#41	1	2	yes	—
155	C₃×C₄×D₅	—	2	2	no	—
156	C₃×C₄×D₅	—	2	2	no	—
157	C₃×C₄×D₅	—	4	2	no	—
158	C₃×C₄×D₅	—	8	2	no	—
159	C₃×Dic₁₀	—	2	1	no	—
160	C₃×Dic₁₀	—	2	1	no	—
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₃×#168	—	2	2	no	—
164	C₂²×C₃×D₄	—	5	2	no	—
165	C₂²×C₃×D₄	—	10	1	no	—
166	C₂×C₃×SD₁₆	—	5	2	no	—
167	C₂×C₃×SD₁₆	—	5	1	no	—
168	C₂²×C₃×C₈	—	5	2	no	—
169	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
170	C₃×#127	C₂×D₅	1	1	yes	characteristic
171	C₃×#125	—	10	1	no	—
172	C₃×C₂²⋊Q₈	—	5	2	no	—
173	C₃×C₂²⋊Q₈	—	10	2	no	—
174	C₃×#121	—	5	2	no	—
175	C₃×#121	—	10	1	no	—
176	C₃×#120	—	10	2	no	—
177	C₃×C₄×Q₈	—	5	1	no	—
178	C₃×C₄×D₄	—	5	1	no	—
179	C₃×C₄×D₄	—	5	1	no	—
180	C₃×C₄×D₄	—	10	1	no	—
181	C₂×C₃×C₄⋊C₄	—	5	2	no	—
182	C₃×#106	—	5	1	no	—
183	C₃×#106	—	5	2	no	—
184	C₃×C₄⋊C₈	—	5	1	no	—
185	C₃×#103	—	5	1	no	—
186	C₃×#102	—	5	2	no	—
187	C₃×#102	—	5	1	no	—
188	C₃×#102	—	5	2	no	—
189	C₃×#102	C₂×D₅	1	2	yes	complemented
190	C₃×#102	C₂×D₅	1	2	yes	complemented
191	C₃×C₂²⋊C₈	—	5	2	no	—
192	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
193	C₂³×D₅	—	2	2	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
198	C₂×C₂²⋊D₅	—	2	2	no	—
199	C₂×C₂²⋊D₅	—	2	2	no	—
200	D₄×D₅	—	2	4	no	—
201	D₄×D₅	—	4	2	no	—
202	D₄×D₅	—	4	4	no	—
203	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
204	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄×D₅	—	2	1	no	—
206	C₂×C₄×D₅	—	2	2	no	—
207	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
208	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
213	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
214	C₂²⋊Dic₅	—	2	2	no	—
215	#687	—	4	2	no	—
216	#685	—	2	2	no	—
217	#685	—	2	1	no	—
218	#685	C₃×D₄	1	2	yes	—
219	C₄⋊Dic₅	—	2	2	no	—
220	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
222	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
223	#683	—	2	1	no	—
224	#683	—	2	2	no	—
225	C₄×Dic₅	—	2	1	no	—
226	C₂×#168	C₂³×C₃	1	2	yes	—
227	#677	—	2	2	no	—
228	C₈×D₅	—	4	2	no	—
229	#554	—	5	1	no	—
230	D₄²	—	5	1	no	—
231	#486	C₃×D₅	1	1	yes	characteristic, complemented
232	#481	—	5	2	no	—
233	#476	—	5	1	no	—
234	#465	—	5	2	no	—
235	#460	—	5	1	no	—
236	#450	—	5	2	no	—
237	C₄×SD₁₆	—	5	1	no	—
238	C₈×D₄	—	5	1	no	—
239	C₂×#102	—	5	2	no	—
240	C₂²×C₃×C₅	—	4	2	no	—
241	C₂²×C₃×C₅	—	4	2	no	—
242	C₂²×C₃×C₅	—	4	2	no	—
243	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₃×D₅	—	2	2	no	—
245	C₂×C₃×D₅	—	2	2	no	—
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	4	1	no	—
248	C₂×C₃×D₅	—	4	1	no	—
249	C₂×C₃×D₅	—	8	8	no	—
250	C₂×C₃×D₅	C₂×SD₁₆	1	4	yes	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
254	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
255	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
256	C₃×Dic₅	—	2	2	no	—
257	C₃×Dic₅	—	4	1	no	—
258	C₃×Dic₅	—	4	1	no	—
259	C₃×Dic₅	—	4	1	no	—
260	C₂⁴×C₃	—	10	2	no	—
261	C₂×C₃×Q₈	—	2	1	no	—
262	C₂×C₃×Q₈	—	5	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	5	1	no	—
266	C₂×C₃×D₄	—	5	1	no	—
267	C₂×C₃×D₄	—	10	2	no	—
268	C₂×C₃×D₄	—	10	4	no	—
269	C₂×C₃×D₄	—	10	2	no	—
270	C₂×C₃×D₄	—	20	2	no	—
271	C₂×C₃×D₄	—	20	4	no	—
272	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
273	C₂²×C₃×C₄	—	5	2	no	—
274	C₂²×C₃×C₄	—	10	2	no	—
275	C₂²×C₃×C₄	—	10	1	no	—
276	C₃×SD₁₆	—	10	2	no	—
277	C₃×SD₁₆	—	20	2	no	—
278	C₂×C₃×C₈	—	5	2	no	—
279	C₂×C₃×C₈	—	20	2	no	—
280	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
281	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	5	1	no	—
284	C₃×C₄⋊C₄	—	5	1	no	—
285	C₃×C₄⋊C₄	—	5	1	no	—
286	C₃×C₄⋊C₄	—	10	2	no	—
287	C₃×C₄⋊C₄	—	10	2	no	—
288	C₃×C₄⋊C₄	—	10	1	no	—
289	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
290	C₃×C₂²⋊C₄	—	5	2	no	—
291	C₃×C₂²⋊C₄	—	10	2	no	—
292	C₃×C₂²⋊C₄	—	10	2	no	—
293	C₃×C₂²⋊C₄	—	10	1	no	—
294	C₃×C₄²	—	10	1	no	—
295	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
296	C₂³×C₅	—	2	2	no	—
297	C₂²×D₅	—	2	1	no	—
298	C₂²×D₅	—	4	4	no	—
299	C₂²×D₅	—	4	4	no	—
300	C₂²×D₅	—	8	2	no	—
301	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
302	C₅×Q₈	—	8	1	no	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	—	2	2	no	—
305	C₅×D₄	—	4	2	no	—
306	C₅×D₄	—	8	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²⋊D₅	—	4	4	no	—
312	C₂²⋊D₅	—	4	4	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	2	1	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
317	D₂₀	—	2	1	no	—
318	D₂₀	C₃×SD₁₆	1	4	yes	complemented
319	D₂₀	C₃×#41	1	2	yes	—
320	C₄×D₅	—	2	2	no	—
321	C₄×D₅	—	2	2	no	—
322	C₄×D₅	—	4	2	no	—
323	C₄×D₅	—	8	2	no	—
324	Dic₁₀	—	2	1	no	—
325	Dic₁₀	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	#168	—	2	2	no	—
329	C₂²×D₄	—	5	2	no	—
330	C₂²×D₄	—	10	1	no	—
331	C₂×SD₁₆	—	5	2	no	—
332	C₂×SD₁₆	—	5	1	no	—
333	C₂²×C₈	—	5	2	no	—
334	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
335	#127	C₂×C₃×D₅	1	1	yes	characteristic
336	#125	—	10	1	no	—
337	C₂²⋊Q₈	—	5	2	no	—
338	C₂²⋊Q₈	—	10	2	no	—
339	#121	—	5	2	no	—
340	#121	—	10	1	no	—
341	#120	—	10	2	no	—
342	C₄×Q₈	—	5	1	no	—
343	C₄×D₄	—	5	1	no	—
344	C₄×D₄	—	5	1	no	—
345	C₄×D₄	—	10	1	no	—
346	C₂×C₄⋊C₄	—	5	2	no	—
347	#106	—	5	1	no	—
348	#106	—	5	2	no	—
349	C₄⋊C₈	—	5	1	no	—
350	#103	—	5	1	no	—
351	#102	—	5	2	no	—
352	#102	—	5	1	no	—
353	#102	—	5	2	no	—
354	#102	C₂×C₃×D₅	1	2	yes	complemented
355	#102	C₂×C₃×D₅	1	2	yes	complemented
356	C₂²⋊C₈	—	5	2	no	—
357	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
358	C₂×C₃×C₅	—	8	2	no	—
359	C₂×C₃×C₅	#546	1	1	yes	characteristic
360	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
361	C₂×C₃×C₅	#576	1	1	yes	characteristic
362	C₃×D₅	—	2	4	no	—
363	C₃×D₅	—	4	2	no	—
364	C₂³×C₃	—	2	2	no	—
365	C₂³×C₃	—	5	2	no	—
366	C₂³×C₃	—	10	1	no	—
367	C₂³×C₃	—	20	4	no	—
368	C₂³×C₃	—	20	4	no	—
369	C₂³×C₃	—	40	2	no	—
370	C₃×Q₈	—	8	1	no	—
371	C₃×Q₈	—	10	1	no	—
372	C₃×Q₈	—	10	1	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	4	2	no	—
376	C₃×D₄	—	5	2	no	—
377	C₃×D₄	—	5	4	no	—
378	C₃×D₄	—	8	1	no	—
379	C₃×D₄	—	10	1	no	—
380	C₃×D₄	—	20	4	no	—
381	C₃×D₄	—	20	4	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	5	2	no	—
384	C₂×C₃×C₄	—	10	2	no	—
385	C₂×C₃×C₄	—	10	2	no	—
386	C₂×C₃×C₄	—	10	1	no	—
387	C₂×C₃×C₄	—	10	1	no	—
388	C₂×C₃×C₄	—	10	1	no	—
389	C₂×C₃×C₄	—	20	2	no	—
390	C₂×C₃×C₄	—	40	2	no	—
391	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
392	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	1	no	—
396	C₃×C₈	—	10	2	no	—
397	C₂²×C₅	—	4	2	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	2	no	—
400	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
401	C₂×D₅	—	2	2	no	—
402	C₂×D₅	—	2	2	no	—
403	C₂×D₅	—	2	2	no	—
404	C₂×D₅	—	4	1	no	—
405	C₂×D₅	—	4	1	no	—
406	C₂×D₅	—	8	8	no	—
407	C₂×D₅	C₂×C₃×SD₁₆	1	4	yes	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
411	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
412	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
413	Dic₅	—	2	2	no	—
414	Dic₅	—	4	1	no	—
415	Dic₅	—	4	1	no	—
416	Dic₅	—	4	1	no	—
417	C₂⁴	—	10	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	5	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	5	1	no	—
423	C₂×D₄	—	5	1	no	—
424	C₂×D₄	—	10	2	no	—
425	C₂×D₄	—	10	4	no	—
426	C₂×D₄	—	10	2	no	—
427	C₂×D₄	—	20	2	no	—
428	C₂×D₄	—	20	4	no	—
429	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
430	C₂²×C₄	—	5	2	no	—
431	C₂²×C₄	—	10	2	no	—
432	C₂²×C₄	—	10	1	no	—
433	SD₁₆	—	10	2	no	—
434	SD₁₆	—	20	2	no	—
435	C₂×C₈	—	5	2	no	—
436	C₂×C₈	—	20	2	no	—
437	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
438	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	5	1	no	—
441	C₄⋊C₄	—	5	1	no	—
442	C₄⋊C₄	—	5	1	no	—
443	C₄⋊C₄	—	10	2	no	—
444	C₄⋊C₄	—	10	2	no	—
445	C₄⋊C₄	—	10	1	no	—
446	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
447	C₂²⋊C₄	—	5	2	no	—
448	C₂²⋊C₄	—	10	2	no	—
449	C₂²⋊C₄	—	10	2	no	—
450	C₂²⋊C₄	—	10	1	no	—
451	C₄²	—	10	1	no	—
452	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
453	C₃×C₅	#3295	1	1	yes	characteristic, complemented, Hall
454	C₂²×C₃	—	4	2	no	—
455	C₂²×C₃	—	4	2	no	—
456	C₂²×C₃	—	4	2	no	—
457	C₂²×C₃	—	5	4	no	—
458	C₂²×C₃	—	10	2	no	—
459	C₂²×C₃	—	10	2	no	—
460	C₂²×C₃	—	10	2	no	—
461	C₂²×C₃	—	20	1	no	—
462	C₂²×C₃	—	20	1	no	—
463	C₂²×C₃	—	40	8	no	—
464	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	2	no	—
467	C₃×C₄	—	10	2	no	—
468	C₃×C₄	—	20	1	no	—
469	C₃×C₄	—	20	1	no	—
470	C₃×C₄	—	20	1	no	—
471	C₃×C₄	D₅×SD₁₆	1	2	yes	—
472	C₃×C₄	D₅×#41	1	1	yes	characteristic
473	C₃×C₄	#4149	1	1	yes	characteristic
474	C₂×C₅	—	8	2	no	—
475	C₂×C₅	C₃×#546	1	1	yes	characteristic
476	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
477	C₂×C₅	C₃×#576	1	1	yes	characteristic
478	D₅	—	2	4	no	—
479	D₅	—	4	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	5	2	no	—
482	C₂³	—	10	1	no	—
483	C₂³	—	20	4	no	—
484	C₂³	—	20	4	no	—
485	C₂³	—	40	2	no	—
486	Q₈	—	8	1	no	—
487	Q₈	—	10	1	no	—
488	Q₈	—	10	1	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	5	2	no	—
493	D₄	—	5	4	no	—
494	D₄	—	8	1	no	—
495	D₄	—	10	1	no	—
496	D₄	—	20	4	no	—
497	D₄	—	20	4	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	5	2	no	—
500	C₂×C₄	—	10	2	no	—
501	C₂×C₄	—	10	2	no	—
502	C₂×C₄	—	10	1	no	—
503	C₂×C₄	—	10	1	no	—
504	C₂×C₄	—	10	1	no	—
505	C₂×C₄	—	20	2	no	—
506	C₂×C₄	—	40	2	no	—
507	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
508	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
509	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	10	2	no	—
513	C₂×C₃	—	8	2	no	—
514	C₂×C₃	—	10	4	no	—
515	C₂×C₃	—	20	2	no	—
516	C₂×C₃	#66010	1	1	yes	characteristic
517	C₂×C₃	#66091	1	1	yes	characteristic
518	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
519	C₅	C₃×#3295	1	1	yes	characteristic, complemented, Sylow
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	5	4	no	—
524	C₂²	—	10	2	no	—
525	C₂²	—	10	2	no	—
526	C₂²	—	10	2	no	—
527	C₂²	—	20	1	no	—
528	C₂²	—	20	1	no	—
529	C₂²	—	40	8	no	—
530	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	4	2	no	—
533	C₄	—	10	2	no	—
534	C₄	—	20	1	no	—
535	C₄	—	20	1	no	—
536	C₄	—	20	1	no	—
537	C₄	C₃×D₅×SD₁₆	1	2	yes	—
538	C₄	C₃×D₅×#41	1	1	yes	characteristic
539	C₄	C₃×#4149	1	1	yes	characteristic
540	C₃	#10613308	1	1	yes	characteristic, direct product factor, Sylow
541	C₂	—	8	2	no	—
542	C₂	—	10	4	no	—
543	C₂	—	20	2	no	—
544	C₂	C₃×#66010	1	1	yes	characteristic
545	C₂	C₃×#66091	1	1	yes	characteristic
546	C₂	C₂×C₃×D₅×SD₁₆	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×#486	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66051	C₂
hypercenter	C₃×#486	D₅
hypocenter	C₅	C₃×#3295
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#486

Complements

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

N	H ≅ G/N	type
1. C₃×#66064	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×#65373	C₂	semidirect
5. C₃×#65364	C₂	semidirect
6. C₃×#65067	C₂	semidirect
7. C₃×#65066	C₂	semidirect
8. C₃×#65065	C₂	semidirect
9. C₃×D₅×#102	C₂	semidirect
10. C₃×C₄×#677	C₂	semidirect
11. C₃×C₈×D₂₀	C₂	semidirect
12. #10613308	C₃	direct (N × H)
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₃×#687	C₂²	semidirect
23. C₂×C₃×C₈×D₅	C₂²	semidirect
24. C₃×#4043	C₂²	semidirect
26. C₃×D₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₄×Dic₁₀	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#102	C₂²	semidirect
33. C₃×C₄×C₅×C₈	C₂²	semidirect
34. C₃×#3964	C₂²	semidirect
36. C₃×#3952	C₂²	semidirect
37. C₃×#3949	C₂²	semidirect
38. C₃×#3948	C₂²	semidirect
40. C₃×#3940	C₂²	semidirect
41. C₃×C₄⋊#168	C₂²	semidirect
43. #66064	C₂×C₃	semidirect
45. C₅×#486	C₂×C₃	semidirect
46. #65373	C₂×C₃	semidirect
47. #65364	C₂×C₃	semidirect
48. #65067	C₂×C₃	semidirect
49. #65066	C₂×C₃	semidirect
50. #65065	C₂×C₃	semidirect
51. D₅×#102	C₂×C₃	semidirect
52. C₄×#677	C₂×C₃	semidirect
53. C₈×D₂₀	C₂×C₃	semidirect
92. C₃×#486	D₅	semidirect
103. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
109. C₂×#687	C₂²×C₃	semidirect
111. C₂×C₈×D₅	C₂²×C₃	semidirect
112. #4043	C₂²×C₃	semidirect
114. D₅×C₄⋊C₄	C₂²×C₃	semidirect
118. C₄×Dic₁₀	C₂²×C₃	semidirect
119. C₅×#102	C₂²×C₃	semidirect
120. C₅×#102	C₂²×C₃	semidirect
121. C₄×C₅×C₈	C₂²×C₃	semidirect
122. #3964	C₂²×C₃	semidirect
124. #3952	C₂²×C₃	semidirect
125. #3949	C₂²×C₃	semidirect
126. #3948	C₂²×C₃	semidirect
128. #3940	C₂²×C₃	semidirect
129. C₄⋊#168	C₂²×C₃	semidirect
153. C₃×D₂₀	SD₁₆	semidirect
169. C₃×C₄⋊Q₈	C₂×D₅	semidirect
189. C₃×#102	C₂×D₅	semidirect
190. C₃×#102	C₂×D₅	semidirect
192. C₃×C₄×C₈	C₂×D₅	semidirect
231. #486	C₃×D₅	semidirect
318. D₂₀	C₃×SD₁₆	semidirect
334. C₄⋊Q₈	C₂×C₃×D₅	semidirect
354. #102	C₂×C₃×D₅	semidirect
355. #102	C₂×C₃×D₅	semidirect
357. C₄×C₈	C₂×C₃×D₅	semidirect
453. C₃×C₅	#3295	semidirect
519. C₅	C₃×#3295	semidirect
540. C₃	#10613308	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×#66064	2
C₃×#66051	2
C₃×C₅×#486	2
C₃×#65373	2
C₃×#65364	2
C₃×#65067	2
C₃×#65066	2
C₃×#65065	2
C₃×D₅×#102	2
C₃×C₄×#677	2
C₃×C₈×D₂₀	2
#10613308	3
C₃×#3295	5

Subgroups — C3×#10613308 #14458450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613308 #14458450