Subgroups — C₃×#10615383 #14460091

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65885	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65373	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65330	C₂	1	2	yes	maximal, complemented
6	C₃×#65326	C₂	1	2	yes	maximal, complemented
7	C₃×#65308	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#686	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65291	C₂	1	2	yes	maximal, complemented
11	C₃×#65285	C₂	1	2	yes	maximal, complemented
12	#10615383	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#124	—	2	2	no	—
16	C₃×C₅×#121	—	2	1	no	—
17	C₃×C₅×#121	C₂²	1	2	yes	—
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	—	2	1	no	—
21	C₃×C₅×#117	C₂²	1	2	yes	—
22	C₃×#4084	—	2	1	no	—
23	C₂×C₃×#687	C₂²	1	2	yes	—
24	C₂×C₃×#686	C₂²	1	1	yes	characteristic
25	C₃×#4070	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	2	yes	—
27	C₃×D₅×C₄⋊C₄	—	2	1	no	—
28	C₃×#4029	—	2	2	no	—
29	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
30	C₃×#4015	C₂²	1	1	yes	characteristic
31	C₃×#3964	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊#168	C₂²	1	2	yes	—
33	C₃×#3942	C₂²	1	2	yes	—
34	C₃×#3942	C₂²	1	2	yes	—
35	C₃×#3942	C₂²	1	2	yes	—
36	C₃×#3941	C₂²	1	1	yes	characteristic
37	C₃×#3941	C₂²	1	2	yes	—
38	C₃×#3940	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3303	—	5	1	no	maximal, Hall
43	C₅×#555	C₂×C₃	1	1	yes	characteristic, complemented
44	#65885	C₂×C₃	1	1	yes	characteristic, complemented
45	#65382	C₂×C₃	1	1	yes	characteristic, complemented
46	#65373	C₂×C₃	1	1	yes	characteristic, complemented
47	#65330	C₂×C₃	1	2	yes	complemented
48	#65326	C₂×C₃	1	2	yes	complemented
49	#65308	C₂×C₃	1	1	yes	characteristic, complemented
50	C₄×#686	C₂×C₃	1	1	yes	characteristic, complemented
51	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
52	#65291	C₂×C₃	1	2	yes	complemented
53	#65285	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×D₄	—	2	2	no	—
56	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
57	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	—	2	1	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₃×#709	—	2	4	no	—
62	C₃×#709	—	4	2	no	—
63	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	—	2	1	no	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
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×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
74	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
75	C₃×C₄²×C₅	—	2	2	no	—
76	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₃×C₂²⋊Dic₅	—	2	2	no	—
78	C₃×#687	—	4	2	no	—
79	C₃×#686	—	2	2	no	—
80	C₃×#685	—	2	1	no	—
81	C₃×C₄⋊Dic₅	—	2	1	no	—
82	C₃×C₄⋊Dic₅	—	2	1	no	—
83	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
84	C₃×#683	—	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×#555	D₅	1	1	yes	characteristic, complemented
90	C₃×#547	—	5	1	no	—
91	C₃×#487	—	5	1	no	—
92	C₃×#485	—	5	2	no	—
93	C₃×#476	—	5	1	no	—
94	C₃×#465	—	5	2	no	—
95	C₃×#461	—	5	1	no	—
96	C₃×#449	—	5	2	no	—
97	C₃×C₄×D₈	—	5	1	no	—
98	C₃×C₈×D₄	—	5	1	no	—
99	C₃×#416	—	5	2	no	—
100	C₂×#709	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×#124	—	2	2	no	—
103	C₅×#121	—	2	1	no	—
104	C₅×#121	C₂²×C₃	1	2	yes	—
105	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
106	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
107	C₅×#117	—	2	1	no	—
108	C₅×#117	C₂²×C₃	1	2	yes	—
109	#4084	—	2	1	no	—
110	C₂×#687	C₂²×C₃	1	2	yes	—
111	C₂×#686	C₂²×C₃	1	1	yes	characteristic
112	#4070	C₂²×C₃	1	2	yes	—
113	C₂²×#168	C₂²×C₃	1	2	yes	—
114	D₅×C₄⋊C₄	—	2	1	no	—
115	#4029	—	2	2	no	—
116	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
117	#4015	C₂²×C₃	1	1	yes	characteristic
118	#3964	C₂²×C₃	1	1	yes	characteristic
119	C₂²⋊#168	C₂²×C₃	1	2	yes	—
120	#3942	C₂²×C₃	1	2	yes	—
121	#3942	C₂²×C₃	1	2	yes	—
122	#3942	C₂²×C₃	1	2	yes	—
123	#3941	C₂²×C₃	1	1	yes	characteristic
124	#3941	C₂²×C₃	1	2	yes	—
125	#3940	C₂²×C₃	1	2	yes	—
126	#3939	C₂²×C₃	1	1	yes	characteristic
127	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
128	C₄×#168	C₂²×C₃	1	1	yes	characteristic
129	#3303	—	5	1	no	Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₂²×C₃×D₅	—	2	1	no	—
133	C₃×C₅×Q₈	—	8	1	no	—
134	C₃×C₅×D₄	—	2	2	no	—
135	C₃×C₅×D₄	—	2	1	no	—
136	C₃×C₅×D₄	—	2	1	no	—
137	C₃×C₅×D₄	—	8	2	no	—
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	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
147	C₃×C₂²⋊D₅	—	4	4	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	2	2	no	—
150	C₃×D₂₀	—	2	1	no	—
151	C₃×D₂₀	#41	1	2	yes	—
152	C₃×C₄×D₅	—	4	4	no	—
153	C₃×C₄×D₅	—	4	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	2	2	no	—
156	C₃×#168	—	2	1	no	—
157	C₃×#168	—	2	1	no	—
158	C₃×#168	—	2	2	no	—
159	C₂×C₃×#41	—	5	2	no	—
160	C₂×C₃×SD₁₆	—	5	2	no	—
161	C₂×C₃×D₈	—	5	1	no	—
162	C₂²×C₃×C₈	—	5	2	no	—
163	C₃×C₄⋊Q₈	—	5	1	no	—
164	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
165	C₃×#124	—	2	2	no	—
166	C₃×#123	—	10	2	no	—
167	C₃×C₂²⋊Q₈	—	5	2	no	—
168	C₃×#121	—	2	1	no	—
169	C₃×#121	—	10	1	no	—
170	C₃×#121	C₂×D₅	1	2	yes	—
171	C₃×C₄×D₄	—	5	1	no	—
172	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
173	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
174	C₃×#117	—	2	1	no	—
175	C₃×#117	C₂×D₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	—	10	1	no	—
177	C₃×#107	—	5	1	no	—
178	C₃×#106	—	5	2	no	—
179	C₃×C₄⋊C₈	—	5	1	no	—
180	C₃×#103	—	5	2	no	—
181	C₃×#103	—	5	2	no	—
182	C₃×#103	—	5	2	no	—
183	C₃×#102	—	5	1	no	—
184	C₃×#102	—	5	1	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×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	C₂³×C₃	1	2	yes	—
194	C₂×C₂²⋊D₅	—	2	2	no	—
195	#709	—	2	4	no	—
196	#709	—	4	2	no	—
197	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₄×D₅	—	2	2	no	—
199	C₂×C₄×D₅	—	2	1	no	—
200	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
203	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
209	C₄²×C₅	—	2	2	no	—
210	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₂²⋊Dic₅	—	2	2	no	—
212	#687	—	4	2	no	—
213	#686	—	2	2	no	—
214	#685	—	2	1	no	—
215	C₄⋊Dic₅	—	2	1	no	—
216	C₄⋊Dic₅	—	2	1	no	—
217	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
218	#683	—	2	2	no	—
219	C₂×#168	—	4	2	no	—
220	C₂×#168	C₂³×C₃	1	1	yes	characteristic
221	C₂×#168	C₂³×C₃	1	1	yes	characteristic
222	C₂×#168	C₂³×C₃	1	2	yes	—
223	#555	C₃×D₅	1	1	yes	characteristic, complemented
224	#547	—	5	1	no	—
225	#487	—	5	1	no	—
226	#485	—	5	2	no	—
227	#476	—	5	1	no	—
228	#465	—	5	2	no	—
229	#461	—	5	1	no	—
230	#449	—	5	2	no	—
231	C₄×D₈	—	5	1	no	—
232	C₈×D₄	—	5	1	no	—
233	#416	—	5	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	—	4	1	no	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₃×D₅	—	2	2	no	—
242	C₂×C₃×D₅	—	4	1	no	—
243	C₂×C₃×D₅	—	4	1	no	—
244	C₃×C₄×C₅	—	2	2	no	—
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	—	4	1	no	—
247	C₃×C₄×C₅	—	4	2	no	—
248	C₃×C₄×C₅	#135	1	2	yes	—
249	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
251	C₃×Dic₅	—	4	2	no	—
252	C₃×Dic₅	—	4	1	no	—
253	C₃×#41	—	10	4	no	—
254	C₃×#41	—	20	2	no	—
255	C₂×C₃×Q₈	—	2	1	no	—
256	C₂×C₃×Q₈	—	5	2	no	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	5	1	no	—
259	C₂×C₃×D₄	—	10	2	no	—
260	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	—	10	1	no	—
264	C₂²×C₃×C₄	—	10	2	no	—
265	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
266	C₃×SD₁₆	—	20	2	no	—
267	C₃×D₈	—	10	2	no	—
268	C₂×C₃×C₈	—	5	1	no	—
269	C₂×C₃×C₈	—	5	1	no	—
270	C₂×C₃×C₈	—	5	2	no	—
271	C₂×C₃×C₈	—	20	2	no	—
272	C₃×C₄⋊C₄	—	2	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	—	10	1	no	—
277	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
278	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
279	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	2	no	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	10	2	no	—
284	C₃×C₂²⋊C₄	—	10	1	no	—
285	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
286	C₃×C₄²	—	2	2	no	—
287	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
290	C₂²×D₅	—	2	1	no	—
291	C₅×Q₈	—	8	1	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	—	8	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	4	2	no	—
301	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₂²⋊D₅	—	4	4	no	—
306	C₂×Dic₅	—	2	1	no	—
307	C₂×Dic₅	—	2	2	no	—
308	D₂₀	—	2	1	no	—
309	D₂₀	C₃×#41	1	2	yes	—
310	C₄×D₅	—	4	4	no	—
311	C₄×D₅	—	4	2	no	—
312	Dic₁₀	—	2	2	no	—
313	Dic₁₀	—	2	2	no	—
314	#168	—	2	1	no	—
315	#168	—	2	1	no	—
316	#168	—	2	2	no	—
317	C₂×#41	—	5	2	no	—
318	C₂×SD₁₆	—	5	2	no	—
319	C₂×D₈	—	5	1	no	—
320	C₂²×C₈	—	5	2	no	—
321	C₄⋊Q₈	—	5	1	no	—
322	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
323	#124	—	2	2	no	—
324	#123	—	10	2	no	—
325	C₂²⋊Q₈	—	5	2	no	—
326	#121	—	2	1	no	—
327	#121	—	10	1	no	—
328	#121	C₂×C₃×D₅	1	2	yes	—
329	C₄×D₄	—	5	1	no	—
330	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
331	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
332	#117	—	2	1	no	—
333	#117	C₂×C₃×D₅	1	2	yes	—
334	C₂×C₄⋊C₄	—	10	1	no	—
335	#107	—	5	1	no	—
336	#106	—	5	2	no	—
337	C₄⋊C₈	—	5	1	no	—
338	#103	—	5	2	no	—
339	#103	—	5	2	no	—
340	#103	—	5	2	no	—
341	#102	—	5	1	no	—
342	#102	—	5	1	no	—
343	#102	—	5	2	no	—
344	C₂²⋊C₈	—	5	2	no	—
345	C₄×C₈	—	5	1	no	—
346	C₂×C₃×C₅	—	4	2	no	—
347	C₂×C₃×C₅	—	8	1	no	—
348	C₂×C₃×C₅	#546	1	1	yes	characteristic
349	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
350	C₂×C₃×C₅	#577	1	1	yes	characteristic
351	C₃×D₅	—	4	2	no	—
352	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	—	10	1	no	—
354	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
355	C₃×Q₈	—	8	1	no	—
356	C₃×Q₈	—	10	2	no	—
357	C₃×Q₈	—	10	2	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	1	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	—	5	2	no	—
362	C₃×D₄	—	8	2	no	—
363	C₃×D₄	—	10	1	no	—
364	C₃×D₄	—	20	4	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	4	2	no	—
370	C₂×C₃×C₄	—	10	1	no	—
371	C₂×C₃×C₄	—	10	2	no	—
372	C₂×C₃×C₄	—	20	4	no	—
373	C₂×C₃×C₄	—	20	2	no	—
374	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
378	C₃×C₈	—	10	1	no	—
379	C₃×C₈	—	10	1	no	—
380	C₃×C₈	—	10	2	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	2	2	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	—	4	1	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
388	C₂×D₅	—	2	2	no	—
389	C₂×D₅	—	4	1	no	—
390	C₂×D₅	—	4	1	no	—
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	C₃×#135	1	2	yes	—
396	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
397	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
398	Dic₅	—	4	1	no	—
399	Dic₅	—	4	2	no	—
400	#41	—	10	4	no	—
401	#41	—	20	2	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	5	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	5	1	no	—
406	C₂×D₄	—	10	2	no	—
407	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
408	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	10	1	no	—
411	C₂²×C₄	—	10	2	no	—
412	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
413	SD₁₆	—	20	2	no	—
414	D₈	—	10	2	no	—
415	C₂×C₈	—	5	1	no	—
416	C₂×C₈	—	5	1	no	—
417	C₂×C₈	—	5	2	no	—
418	C₂×C₈	—	20	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	5	1	no	—
421	C₄⋊C₄	—	10	1	no	—
422	C₄⋊C₄	—	10	2	no	—
423	C₄⋊C₄	—	10	1	no	—
424	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
425	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
426	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	10	2	no	—
431	C₂²⋊C₄	—	10	1	no	—
432	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
435	C₃×C₅	#3303	1	1	yes	characteristic, complemented, Hall
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	2	2	no	—
439	C₂²×C₃	—	4	1	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	1	no	—
442	C₂²×C₃	—	10	2	no	—
443	C₂²×C₃	—	20	1	no	—
444	C₂²×C₃	—	20	1	no	—
445	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	2	1	no	—
448	C₃×C₄	—	4	1	no	—
449	C₃×C₄	—	4	2	no	—
450	C₃×C₄	—	20	1	no	—
451	C₃×C₄	—	20	2	no	—
452	C₃×C₄	#4096	1	2	yes	—
453	C₃×C₄	D₅×#41	1	1	yes	characteristic
454	C₃×C₄	#4149	1	1	yes	characteristic
455	C₂×C₅	—	4	2	no	—
456	C₂×C₅	—	8	1	no	—
457	C₂×C₅	C₃×#546	1	1	yes	characteristic
458	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
459	C₂×C₅	C₃×#577	1	1	yes	characteristic
460	D₅	—	4	2	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	10	1	no	—
463	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
464	Q₈	—	8	1	no	—
465	Q₈	—	10	2	no	—
466	Q₈	—	10	2	no	—
467	D₄	—	2	2	no	—
468	D₄	—	2	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	5	2	no	—
471	D₄	—	8	2	no	—
472	D₄	—	10	1	no	—
473	D₄	—	20	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	10	1	no	—
480	C₂×C₄	—	10	2	no	—
481	C₂×C₄	—	20	4	no	—
482	C₂×C₄	—	20	2	no	—
483	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
484	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
485	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
486	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
487	C₈	—	10	1	no	—
488	C₈	—	10	1	no	—
489	C₈	—	10	2	no	—
490	C₂×C₃	—	4	2	no	—
491	C₂×C₃	—	8	1	no	—
492	C₂×C₃	—	20	2	no	—
493	C₂×C₃	C₂×#4096	1	1	yes	characteristic
494	C₂×C₃	#66163	1	1	yes	characteristic
495	C₂×C₃	#66170	1	1	yes	characteristic
496	C₅	C₃×#3303	1	1	yes	characteristic, complemented, Sylow
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	10	2	no	—
504	C₂²	—	20	1	no	—
505	C₂²	—	20	1	no	—
506	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	2	no	—
511	C₄	—	20	1	no	—
512	C₄	—	20	2	no	—
513	C₄	C₃×#4096	1	2	yes	—
514	C₄	C₃×D₅×#41	1	1	yes	characteristic
515	C₄	C₃×#4149	1	1	yes	characteristic
516	C₃	#10615383	1	1	yes	characteristic, direct product factor, Sylow
517	C₂	—	4	2	no	—
518	C₂	—	8	1	no	—
519	C₂	—	20	2	no	—
520	C₂	C₂×C₃×#4096	1	1	yes	characteristic
521	C₂	C₃×#66163	1	1	yes	characteristic
522	C₂	C₃×#66170	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	C₃×C₅×#555	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#555	D₅
hypocenter	C₅	C₃×#3303
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×#555

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#555	C₂	semidirect
2. C₃×#65885	C₂	semidirect
3. C₃×#65382	C₂	semidirect
4. C₃×#65373	C₂	semidirect
5. C₃×#65330	C₂	semidirect
6. C₃×#65326	C₂	semidirect
7. C₃×#65308	C₂	semidirect
8. C₃×C₄×#686	C₂	semidirect
9. C₃×D₄×#168	C₂	semidirect
10. C₃×#65291	C₂	semidirect
11. C₃×#65285	C₂	semidirect
12. #10615383	C₃	direct (N × H)
43. C₅×#555	C₂×C₃	semidirect
44. #65885	C₂×C₃	semidirect
45. #65382	C₂×C₃	semidirect
46. #65373	C₂×C₃	semidirect
47. #65330	C₂×C₃	semidirect
48. #65326	C₂×C₃	semidirect
49. #65308	C₂×C₃	semidirect
50. C₄×#686	C₂×C₃	semidirect
51. D₄×#168	C₂×C₃	semidirect
52. #65291	C₂×C₃	semidirect
53. #65285	C₂×C₃	semidirect
89. C₃×#555	D₅	semidirect
223. #555	C₃×D₅	semidirect
435. C₃×C₅	#3303	semidirect
496. C₅	C₃×#3303	semidirect
516. C₃	#10615383	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×#555	2
C₃×#65885	2
C₃×#65382	2
C₃×#65373	2
C₃×#65330	2
C₃×#65326	2
C₃×#65308	2
C₃×C₄×#686	2
C₃×D₄×#168	2
C₃×#65291	2
C₃×#65285	2
#10615383	3
C₃×#3303	5

Subgroups — C3×#10615383 #14460091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615383 #14460091