Subgroups — C₃×#10615125 #14425300

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4144	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66156	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3965	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65366	C₂	1	4	yes	maximal, complemented
6	C₃×#65350	C₂	1	4	yes	maximal, complemented
7	C₃×#65294	C₂	1	2	yes	maximal, complemented
8	#10615125	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	—	2	2	no	—
12	C₃×#4144	—	2	2	no	—
13	C₃×#4144	—	2	4	no	—
14	C₃×#4144	C₂²	1	4	yes	—
15	C₂×C₃×#711	—	2	2	no	—
16	C₂×C₃×D₄×D₅	—	2	2	no	—
17	C₂×C₃×#709	C₂²	1	2	yes	—
18	C₃×C₅×#127	C₂²	1	2	yes	complemented
19	C₃×C₅×#124	C₂²	1	2	yes	complemented
20	C₃×C₅×#121	—	2	2	no	—
21	C₃×C₅×#120	—	2	2	no	—
22	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
23	C₃×#4097	—	2	2	no	—
24	C₃×#4096	—	2	4	no	—
25	C₃×#4095	—	2	2	no	—
26	C₃×#4088	C₂²	1	4	yes	complemented
27	C₃×#4078	C₂²	1	4	yes	complemented
28	C₂×C₃×#681	C₂²	1	2	yes	complemented
29	C₃×#3965	C₂²	1	4	yes	complemented
30	C₃×#3937	C₂²	1	8	yes	complemented
31	C₃×#3019	—	5	1	no	maximal, Hall
32	C₂×#4144	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
34	#66156	C₂×C₃	1	2	yes	complemented
35	C₂×#3965	C₂×C₃	1	1	yes	characteristic, complemented
36	#65366	C₂×C₃	1	4	yes	complemented
37	#65350	C₂×C₃	1	4	yes	complemented
38	#65294	C₂×C₃	1	2	yes	complemented
39	C₂⁴×C₃×C₅	D₄	1	2	yes	—
40	C₂³×C₃×D₅	—	2	2	no	—
41	C₃×C₅×#41	—	2	2	no	—
42	C₃×C₅×#41	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
54	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
55	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
56	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
57	C₂²×C₃×Dic₅	—	2	2	no	—
58	C₃×#711	—	2	8	no	—
59	C₃×#711	—	2	8	no	—
60	C₃×D₄×D₅	—	2	8	no	—
61	C₃×D₄×D₅	—	2	8	no	—
62	C₃×#709	—	2	2	no	—
63	C₃×#709	—	2	2	no	—
64	C₃×#709	D₄	1	4	yes	complemented
65	C₃×#709	C₂³	1	4	yes	—
66	C₂×C₃×D₂₀	D₄	1	2	yes	complemented
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×Dic₁₀	D₄	1	2	yes	complemented
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
73	C₃×#689	—	2	4	no	—
74	C₃×#688	—	2	4	no	—
75	C₃×#687	—	2	4	no	—
76	C₃×#686	—	2	4	no	—
77	C₃×#681	—	2	2	no	—
78	C₃×#681	C₂³	1	4	yes	complemented
79	C₂×C₃×#168	—	2	2	no	—
80	C₂×C₃×H(5,𝔽₂)	—	5	1	no	—
81	C₃×#575	—	5	2	no	—
82	C₃×#535	D₅	1	1	yes	characteristic, complemented
83	C₃×#455	—	5	4	no	—
84	C₃×#453	—	5	4	no	—
85	C₃×#421	—	5	2	no	—
86	C₂×C₃×#100	—	5	1	no	—
87	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₂²⋊D₅	—	2	2	no	—
90	#4144	—	2	2	no	—
91	#4144	—	2	4	no	—
92	#4144	C₂²×C₃	1	4	yes	—
93	C₂×#711	—	2	2	no	—
94	C₂×D₄×D₅	—	2	2	no	—
95	C₂×#709	C₂²×C₃	1	2	yes	—
96	C₅×#127	C₂²×C₃	1	2	yes	complemented
97	C₅×#124	C₂²×C₃	1	2	yes	complemented
98	C₅×#121	—	2	2	no	—
99	C₅×#120	—	2	2	no	—
100	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
101	#4097	—	2	2	no	—
102	#4096	—	2	4	no	—
103	#4095	—	2	2	no	—
104	#4088	C₂²×C₃	1	4	yes	complemented
105	#4078	C₂²×C₃	1	4	yes	complemented
106	C₂×#681	C₂²×C₃	1	2	yes	complemented
107	#3965	C₂²×C₃	1	4	yes	complemented
108	#3937	C₂²×C₃	1	8	yes	complemented
109	#3019	—	5	1	no	Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	1	no	—
113	C₂³×C₃×C₅	—	8	2	no	—
114	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₃×D₅	—	2	2	no	—
117	C₂²×C₃×D₅	—	2	8	no	—
118	C₂²×C₃×D₅	—	8	4	no	—
119	C₃×C₅×Q₈	—	2	2	no	—
120	C₃×C₅×D₄	—	2	4	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	4	1	no	—
124	C₃×C₅×D₄	—	4	1	no	—
125	C₃×C₅×D₄	—	8	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	4	2	no	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₃×C₂²⋊D₅	—	2	16	no	—
134	C₃×C₂²⋊D₅	—	2	4	no	—
135	C₃×C₂²⋊D₅	—	2	4	no	—
136	C₂×C₃×Dic₅	—	2	8	no	—
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₃×D₂₀	—	2	2	no	—
139	C₃×D₂₀	C₂×D₄	1	4	yes	—
140	C₃×C₄×D₅	—	2	4	no	—
141	C₃×C₄×D₅	—	2	4	no	—
142	C₃×Dic₁₀	—	2	2	no	—
143	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
144	C₃×#168	—	2	4	no	—
145	C₃×H(5,𝔽₂)	—	5	4	no	—
146	C₃×H(5,𝔽₂)	—	10	4	no	—
147	C₃×H(5,𝔽₂)	—	10	2	no	—
148	C₂×C₃×#41	—	5	2	no	—
149	C₂×C₃×#41	—	10	2	no	—
150	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic, complemented
151	C₂²×C₃×D₄	—	10	2	no	—
152	C₂²×C₃×D₄	—	10	2	no	—
153	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
154	C₃×#137	—	5	4	no	—
155	C₃×#137	—	10	2	no	—
156	C₃×AGL(1,ℤ/8)	—	5	4	no	—
157	C₃×AGL(1,ℤ/8)	—	10	2	no	—
158	C₃×#135	—	10	4	no	—
159	C₂×C₃×M₁₆	—	5	2	no	—
160	C₃×#127	C₂×D₅	1	2	yes	complemented
161	C₃×#124	C₂×D₅	1	2	yes	complemented
162	C₃×#121	—	2	2	no	—
163	C₃×#120	—	2	2	no	—
164	C₃×#117	C₂×D₅	1	1	yes	characteristic, complemented
165	C₃×#104	—	5	8	no	—
166	C₃×#100	—	5	4	no	—
167	C₂⁴×C₅	C₃×D₄	1	2	yes	—
168	C₂³×D₅	—	2	2	no	—
169	C₅×#41	—	2	2	no	—
170	C₅×#41	—	2	2	no	—
171	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic, complemented
172	C₂×C₅×D₄	—	2	1	no	—
173	C₂×C₅×D₄	—	2	4	no	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	2	2	no	—
176	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
177	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
178	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic, complemented
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₂²⋊D₅	—	2	4	no	—
182	C₂×C₂²⋊D₅	—	2	8	no	—
183	C₂×C₂²⋊D₅	—	2	2	no	—
184	C₂×C₂²⋊D₅	—	2	8	no	—
185	C₂²×Dic₅	—	2	2	no	—
186	#711	—	2	8	no	—
187	#711	—	2	8	no	—
188	D₄×D₅	—	2	8	no	—
189	D₄×D₅	—	2	8	no	—
190	#709	—	2	2	no	—
191	#709	—	2	2	no	—
192	#709	C₃×D₄	1	4	yes	complemented
193	#709	C₂³×C₃	1	4	yes	—
194	C₂×D₂₀	C₃×D₄	1	2	yes	complemented
195	C₂×C₄×D₅	—	2	2	no	—
196	C₂×Dic₁₀	C₃×D₄	1	2	yes	complemented
197	C₅×C₄⋊C₄	—	2	1	no	—
198	C₅×C₂²⋊C₄	—	2	1	no	—
199	C₅×C₂²⋊C₄	—	2	4	no	—
200	C₄²×C₅	C₂³×C₃	1	2	yes	complemented
201	#689	—	2	4	no	—
202	#688	—	2	4	no	—
203	#687	—	2	4	no	—
204	#686	—	2	4	no	—
205	#681	—	2	2	no	—
206	#681	C₂³×C₃	1	4	yes	complemented
207	C₂×#168	—	2	2	no	—
208	C₂×H(5,𝔽₂)	—	5	1	no	—
209	#575	—	5	2	no	—
210	#535	C₃×D₅	1	1	yes	characteristic, complemented
211	#455	—	5	4	no	—
212	#453	—	5	4	no	—
213	#421	—	5	2	no	—
214	C₂×#100	—	5	1	no	—
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	—	4	4	no	—
218	C₂²×C₃×C₅	—	4	4	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	1	no	—
221	C₂²×C₃×C₅	—	8	2	no	—
222	C₂²×C₃×C₅	#120	1	1	yes	characteristic
223	C₂²×C₃×C₅	#120	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₃×D₅	—	2	4	no	—
226	C₂×C₃×D₅	—	4	4	no	—
227	C₂×C₃×D₅	—	8	8	no	—
228	C₃×C₄×C₅	—	4	2	no	—
229	C₃×C₄×C₅	—	4	1	no	—
230	C₃×C₄×C₅	#120	1	2	yes	—
231	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
232	C₃×Dic₅	—	2	4	no	—
233	C₂⁴×C₃	—	10	2	no	—
234	C₂⁴×C₃	C₂²⋊D₅	1	2	yes	—
235	C₃×#41	—	2	2	no	—
236	C₃×#41	—	2	2	no	—
237	C₃×#41	—	5	4	no	—
238	C₃×#41	—	5	4	no	—
239	C₃×#41	—	10	8	no	—
240	C₃×#41	—	10	8	no	—
241	C₃×#41	—	10	2	no	—
242	C₃×#41	—	10	2	no	—
243	C₂×C₃×Q₈	—	5	2	no	—
244	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic, complemented
245	C₂×C₃×D₄	—	2	1	no	—
246	C₂×C₃×D₄	—	2	4	no	—
247	C₂×C₃×D₄	—	2	2	no	—
248	C₂×C₃×D₄	—	2	2	no	—
249	C₂×C₃×D₄	—	5	2	no	—
250	C₂×C₃×D₄	—	10	8	no	—
251	C₂×C₃×D₄	—	10	8	no	—
252	C₂×C₃×D₄	—	10	4	no	—
253	C₂×C₃×D₄	—	10	8	no	—
254	C₂×C₃×D₄	—	10	2	no	—
255	C₂×C₃×D₄	—	10	8	no	—
256	C₂×C₃×D₄	C₂²⋊D₅	1	2	yes	—
257	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
258	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic, complemented
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	10	2	no	—
261	C₂²×C₃×C₄	—	10	2	no	—
262	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
263	C₃×Q₁₆	—	10	4	no	—
264	C₃×SD₁₆	—	10	4	no	—
265	C₃×SD₁₆	—	10	4	no	—
266	C₃×D₈	—	10	4	no	—
267	C₃×M₁₆	—	5	4	no	—
268	C₃×M₁₆	—	10	2	no	—
269	C₂×C₃×C₈	—	10	2	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	2	4	no	—
273	C₃×C₄²	C₂²×D₅	1	2	yes	complemented
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	8	2	no	—
278	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
279	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
280	C₂²×D₅	—	2	2	no	—
281	C₂²×D₅	—	2	8	no	—
282	C₂²×D₅	—	8	4	no	—
283	C₅×Q₈	—	2	2	no	—
284	C₅×D₄	—	2	4	no	—
285	C₅×D₄	—	2	4	no	—
286	C₅×D₄	—	2	2	no	—
287	C₅×D₄	—	4	1	no	—
288	C₅×D₄	—	4	1	no	—
289	C₅×D₄	—	8	4	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	C₂²⋊D₅	—	2	16	no	—
298	C₂²⋊D₅	—	2	4	no	—
299	C₂²⋊D₅	—	2	4	no	—
300	C₂×Dic₅	—	2	8	no	—
301	C₂×Dic₅	—	2	2	no	—
302	D₂₀	—	2	2	no	—
303	D₂₀	C₂×C₃×D₄	1	4	yes	—
304	C₄×D₅	—	2	4	no	—
305	C₄×D₅	—	2	4	no	—
306	Dic₁₀	—	2	2	no	—
307	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
308	#168	—	2	4	no	—
309	H(5,𝔽₂)	—	5	4	no	—
310	H(5,𝔽₂)	—	10	4	no	—
311	H(5,𝔽₂)	—	10	2	no	—
312	C₂×#41	—	5	2	no	—
313	C₂×#41	—	10	2	no	—
314	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic, complemented
315	C₂²×D₄	—	10	2	no	—
316	C₂²×D₄	—	10	2	no	—
317	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
318	#137	—	5	4	no	—
319	#137	—	10	2	no	—
320	AGL(1,ℤ/8)	—	5	4	no	—
321	AGL(1,ℤ/8)	—	10	2	no	—
322	#135	—	10	4	no	—
323	C₂×M₁₆	—	5	2	no	—
324	#127	C₂×C₃×D₅	1	2	yes	complemented
325	#124	C₂×C₃×D₅	1	2	yes	complemented
326	#121	—	2	2	no	—
327	#120	—	2	2	no	—
328	#117	C₂×C₃×D₅	1	1	yes	characteristic, complemented
329	#104	—	5	8	no	—
330	#100	—	5	4	no	—
331	C₂×C₃×C₅	—	2	1	no	—
332	C₂×C₃×C₅	—	2	1	no	—
333	C₂×C₃×C₅	—	2	1	no	—
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	—	8	1	no	—
336	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
337	C₃×D₅	—	4	4	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	—	8	2	no	—
342	C₂³×C₃	—	10	8	no	—
343	C₂³×C₃	—	10	2	no	—
344	C₂³×C₃	—	40	4	no	—
345	C₂³×C₃	C₂×C₂²⋊D₅	1	4	yes	—
346	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	5	4	no	—
349	C₃×Q₈	—	10	2	no	—
350	C₃×D₄	—	2	4	no	—
351	C₃×D₄	—	2	2	no	—
352	C₃×D₄	—	2	4	no	—
353	C₃×D₄	—	4	1	no	—
354	C₃×D₄	—	4	1	no	—
355	C₃×D₄	—	5	4	no	—
356	C₃×D₄	—	8	4	no	—
357	C₃×D₄	—	10	16	no	—
358	C₃×D₄	—	10	4	no	—
359	C₃×D₄	—	10	4	no	—
360	C₃×D₄	—	10	2	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	4	2	no	—
364	C₂×C₃×C₄	—	10	8	no	—
365	C₂×C₃×C₄	—	10	2	no	—
366	C₂×C₃×C₄	—	10	4	no	—
367	C₂×C₃×C₄	—	10	4	no	—
368	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
369	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
370	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
372	C₃×C₈	—	10	4	no	—
373	C₂²×C₅	—	2	4	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	4	no	—
376	C₂²×C₅	—	4	4	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	8	2	no	—
380	C₂²×C₅	C₃×#120	1	1	yes	characteristic
381	C₂²×C₅	C₃×#120	1	1	yes	characteristic
382	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
383	C₂×D₅	—	2	4	no	—
384	C₂×D₅	—	4	4	no	—
385	C₂×D₅	—	8	8	no	—
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	C₃×#120	1	2	yes	—
389	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
390	Dic₅	—	2	4	no	—
391	C₂⁴	—	10	2	no	—
392	C₂⁴	C₃×C₂²⋊D₅	1	2	yes	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	5	4	no	—
396	#41	—	5	4	no	—
397	#41	—	10	8	no	—
398	#41	—	10	8	no	—
399	#41	—	10	2	no	—
400	#41	—	10	2	no	—
401	C₂×Q₈	—	5	2	no	—
402	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	5	2	no	—
408	C₂×D₄	—	10	8	no	—
409	C₂×D₄	—	10	8	no	—
410	C₂×D₄	—	10	4	no	—
411	C₂×D₄	—	10	8	no	—
412	C₂×D₄	—	10	2	no	—
413	C₂×D₄	—	10	8	no	—
414	C₂×D₄	C₃×C₂²⋊D₅	1	2	yes	—
415	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
416	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	10	2	no	—
419	C₂²×C₄	—	10	2	no	—
420	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
421	Q₁₆	—	10	4	no	—
422	SD₁₆	—	10	4	no	—
423	SD₁₆	—	10	4	no	—
424	D₈	—	10	4	no	—
425	M₁₆	—	5	4	no	—
426	M₁₆	—	10	2	no	—
427	C₂×C₈	—	10	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₄²	C₂²×C₃×D₅	1	2	yes	complemented
432	C₃×C₅	#3019	1	1	yes	characteristic, complemented, Hall
433	C₂²×C₃	—	2	4	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	4	4	no	—
436	C₂²×C₃	—	4	4	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	8	2	no	—
440	C₂²×C₃	—	10	4	no	—
441	C₂²×C₃	—	20	4	no	—
442	C₂²×C₃	—	40	8	no	—
443	C₂²×C₃	#4083	1	1	yes	characteristic
444	C₂²×C₃	#4083	1	1	yes	characteristic
445	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	1	no	—
448	C₃×C₄	—	10	4	no	—
449	C₃×C₄	#4083	1	2	yes	—
450	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	4	4	no	—
455	C₂×C₅	—	8	1	no	—
456	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
457	D₅	—	4	4	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	8	2	no	—
462	C₂³	—	10	8	no	—
463	C₂³	—	10	2	no	—
464	C₂³	—	40	4	no	—
465	C₂³	C₂×C₃×C₂²⋊D₅	1	4	yes	—
466	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	5	4	no	—
469	Q₈	—	10	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	1	no	—
474	D₄	—	4	1	no	—
475	D₄	—	5	4	no	—
476	D₄	—	8	4	no	—
477	D₄	—	10	16	no	—
478	D₄	—	10	4	no	—
479	D₄	—	10	4	no	—
480	D₄	—	10	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	10	8	no	—
485	C₂×C₄	—	10	2	no	—
486	C₂×C₄	—	10	4	no	—
487	C₂×C₄	—	10	4	no	—
488	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
489	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
490	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
491	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
492	C₈	—	10	4	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	2	1	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	4	4	no	—
497	C₂×C₃	—	8	1	no	—
498	C₂×C₃	—	20	4	no	—
499	C₂×C₃	C₂×#4083	1	1	yes	characteristic
500	C₅	C₃×#3019	1	1	yes	characteristic, complemented, Sylow
501	C₂²	—	2	4	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	10	4	no	—
509	C₂²	—	20	4	no	—
510	C₂²	—	40	8	no	—
511	C₂²	C₃×#4083	1	1	yes	characteristic
512	C₂²	C₃×#4083	1	1	yes	characteristic
513	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
514	C₄	—	4	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	10	4	no	—
517	C₄	C₃×#4083	1	2	yes	—
518	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
519	C₃	#10615125	1	1	yes	characteristic, direct product factor, Sylow
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	—	8	1	no	—
525	C₂	—	20	4	no	—
526	C₂	C₂×C₃×#4083	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×#4083
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#535	C₂
socle	C₂×C₃×C₅	C₂×#120
hypercenter	C₃×#535	D₅
hypocenter	C₅	C₃×#3019
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4144	C₂	semidirect
2. C₃×C₅×#535	C₂	semidirect
3. C₃×#66156	C₂	semidirect
4. C₂×C₃×#3965	C₂	semidirect
5. C₃×#65366	C₂	semidirect
6. C₃×#65350	C₂	semidirect
7. C₃×#65294	C₂	semidirect
8. #10615125	C₃	direct (N × H)
9. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₃×C₅×#124	C₂²	semidirect
22. C₃×C₅×#117	C₂²	semidirect
26. C₃×#4088	C₂²	semidirect
27. C₃×#4078	C₂²	semidirect
28. C₂×C₃×#681	C₂²	semidirect
29. C₃×#3965	C₂²	semidirect
30. C₃×#3937	C₂²	semidirect
32. C₂×#4144	C₂×C₃	semidirect
33. C₅×#535	C₂×C₃	semidirect
34. #66156	C₂×C₃	semidirect
35. C₂×#3965	C₂×C₃	semidirect
36. #65366	C₂×C₃	semidirect
37. #65350	C₂×C₃	semidirect
38. #65294	C₂×C₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂³	semidirect
50. C₂×C₃×C₅×D₄	C₂³	semidirect
64. C₃×#709	D₄	semidirect
66. C₂×C₃×D₂₀	D₄	semidirect
68. C₂×C₃×Dic₁₀	D₄	semidirect
72. C₃×C₄²×C₅	C₂³	semidirect
78. C₃×#681	C₂³	semidirect
82. C₃×#535	D₅	semidirect
87. C₂×C₅×#41	C₂²×C₃	semidirect
96. C₅×#127	C₂²×C₃	semidirect
97. C₅×#124	C₂²×C₃	semidirect
100. C₅×#117	C₂²×C₃	semidirect
104. #4088	C₂²×C₃	semidirect
105. #4078	C₂²×C₃	semidirect
106. C₂×#681	C₂²×C₃	semidirect
107. #3965	C₂²×C₃	semidirect
108. #3937	C₂²×C₃	semidirect
150. C₂×C₃×#41	C₂×D₅	semidirect
160. C₃×#127	C₂×D₅	semidirect
161. C₃×#124	C₂×D₅	semidirect
164. C₃×#117	C₂×D₅	semidirect
171. C₂×C₅×Q₈	C₂³×C₃	semidirect
178. C₂×C₅×D₄	C₂³×C₃	semidirect
192. #709	C₃×D₄	semidirect
194. C₂×D₂₀	C₃×D₄	semidirect
196. C₂×Dic₁₀	C₃×D₄	semidirect
200. C₄²×C₅	C₂³×C₃	semidirect
206. #681	C₂³×C₃	semidirect
210. #535	C₃×D₅	semidirect
244. C₂×C₃×Q₈	C₂²×D₅	semidirect
258. C₂×C₃×D₄	C₂²×D₅	semidirect
273. C₃×C₄²	C₂²×D₅	semidirect
314. C₂×#41	C₂×C₃×D₅	semidirect
324. #127	C₂×C₃×D₅	semidirect
325. #124	C₂×C₃×D₅	semidirect
328. #117	C₂×C₃×D₅	semidirect
402. C₂×Q₈	C₂²×C₃×D₅	semidirect
416. C₂×D₄	C₂²×C₃×D₅	semidirect
431. C₄²	C₂²×C₃×D₅	semidirect
432. C₃×C₅	#3019	semidirect
500. C₅	C₃×#3019	semidirect
519. C₃	#10615125	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#4144	2
C₃×C₅×#535	2
C₃×#66156	2
C₂×C₃×#3965	2
C₃×#65366	2
C₃×#65350	2
C₃×#65294	2
#10615125	3
C₃×#3019	5

Subgroups — C3×#10615125 #14425300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615125 #14425300