Subgroups — C₃×#10615749 #14458222

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66172	C₂	1	2	yes	maximal, complemented
3	C₃×#66105	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65535	C₂	1	2	yes	maximal, complemented
5	C₃×#65494	C₂	1	2	yes	maximal, complemented
6	C₃×#65493	C₂	1	2	yes	maximal, complemented
7	C₃×#65485	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65470	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65432	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615749	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₃×#4150	C₂²	1	2	yes	—
15	C₃×C₅×#137	—	2	2	no	—
16	C₃×C₅×#137	C₂²	1	2	yes	—
17	C₃×C₅×#135	—	2	1	no	—
18	C₃×C₅×#135	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×#131	C₂²	1	1	yes	characteristic
22	C₃×#4097	—	2	2	no	—
23	C₃×#4097	C₂²	1	2	yes	—
24	C₃×#4097	C₂²	1	2	yes	—
25	C₃×#4096	—	2	2	no	—
26	C₃×#4096	C₂²	1	1	yes	characteristic
27	C₃×#4094	C₂²	1	2	yes	—
28	C₃×#4090	C₂²	1	2	yes	—
29	C₂×C₃×#689	—	2	2	no	—
30	C₂×C₃×#689	C₂²	1	2	yes	—
31	C₃×#4088	—	2	2	no	—
32	C₃×#4088	C₂²	1	2	yes	—
33	C₃×D₅×Q₁₆	—	2	1	no	—
34	C₃×#4061	—	2	2	no	—
35	C₃×#4058	—	2	1	no	—
36	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic
37	C₃×#4047	C₂²	1	1	yes	characteristic
38	C₃×#3969	C₂²	1	1	yes	characteristic
39	C₃×#3969	C₂²	1	2	yes	—
40	C₃×#3968	C₂²	1	2	yes	—
41	C₃×#3957	C₂²	1	1	yes	characteristic
42	C₃×#3956	C₂²	1	2	yes	—
43	C₃×#3954	C₂²	1	1	yes	characteristic
44	C₃×#3951	C₂²	1	1	yes	characteristic
45	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
46	C₃×#3293	—	5	1	no	maximal, Hall
47	C₅×#578	C₂×C₃	1	1	yes	characteristic, complemented
48	#66172	C₂×C₃	1	2	yes	complemented
49	#66105	C₂×C₃	1	1	yes	characteristic, complemented
50	#65535	C₂×C₃	1	2	yes	complemented
51	#65494	C₂×C₃	1	2	yes	complemented
52	#65493	C₂×C₃	1	2	yes	complemented
53	#65485	C₂×C₃	1	1	yes	characteristic, complemented
54	#65481	C₂×C₃	1	1	yes	characteristic, complemented
55	#65470	C₂×C₃	1	1	yes	characteristic, complemented
56	#65433	C₂×C₃	1	1	yes	characteristic, complemented
57	#65432	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	4	2	no	—
61	C₃×C₅×#41	C₂³	1	2	yes	—
62	C₃×C₅×#41	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×Q₈	—	2	2	no	—
64	C₂×C₃×C₅×Q₈	—	2	2	no	—
65	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
66	C₃×Q₈×D₅	—	2	2	no	—
67	C₃×#711	—	2	2	no	—
68	C₃×#711	—	4	2	no	—
69	C₃×#709	—	2	2	no	—
70	C₃×#709	C₂³	1	1	yes	characteristic
71	C₂×C₃×Dic₁₀	—	2	2	no	—
72	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
73	C₃×C₅×Q₁₆	—	2	2	no	—
74	C₃×C₅×Q₁₆	—	2	1	no	—
75	C₃×C₅×Q₁₆	—	2	1	no	—
76	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
77	C₃×C₅×SD₁₆	—	2	2	no	—
78	C₃×C₅×SD₁₆	D₄	1	2	yes	—
79	C₃×C₅×D₈	D₄	1	1	yes	characteristic
80	C₃×C₅×M₁₆	—	2	1	no	—
81	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	—	2	1	no	—
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₃×#689	—	2	2	no	—
85	C₃×#689	—	2	2	no	—
86	C₃×#689	—	2	2	no	—
87	C₃×#689	—	2	2	no	—
88	C₃×#689	—	2	2	no	—
89	C₃×#689	D₄	1	1	yes	characteristic
90	C₃×#688	—	2	2	no	—
91	C₃×#688	D₄	1	1	yes	characteristic
92	C₃×#687	—	2	2	no	—
93	C₃×#687	—	2	2	no	—
94	C₃×#687	D₄	1	1	yes	characteristic
95	C₃×#686	D₄	1	1	yes	characteristic
96	C₃×#683	—	4	2	no	—
97	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
98	C₃×#681	—	2	2	no	—
99	C₃×#681	C₂³	1	2	yes	—
100	C₃×#681	C₂³	1	1	yes	characteristic
101	C₂×C₃×#168	—	2	2	no	—
102	C₂×C₃×#168	C₂³	1	1	yes	characteristic
103	C₃×Dic₂₀	—	2	1	no	—
104	C₃×Dic₂₀	—	2	1	no	—
105	C₃×#676	—	2	1	no	—
106	C₃×C₈×D₅	—	2	1	no	—
107	C₃×#578	—	5	2	no	—
108	C₃×#578	—	5	1	no	—
109	C₃×#578	D₅	1	1	yes	characteristic, complemented
110	C₃×#494	—	5	1	no	—
111	C₃×#473	—	5	2	no	—
112	C₃×#473	—	5	1	no	—
113	C₃×#473	—	5	1	no	—
114	C₃×#456	—	5	2	no	—
115	C₃×#456	—	5	2	no	—
116	C₃×#443	—	5	1	no	—
117	C₃×#443	—	5	1	no	—
118	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
119	#4150	C₂²×C₃	1	2	yes	—
120	C₅×#137	—	2	2	no	—
121	C₅×#137	C₂²×C₃	1	2	yes	—
122	C₅×#135	—	2	1	no	—
123	C₅×#135	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₅×Q₁₆	—	2	1	no	—
125	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₅×#131	C₂²×C₃	1	1	yes	characteristic
127	#4097	—	2	2	no	—
128	#4097	C₂²×C₃	1	2	yes	—
129	#4097	C₂²×C₃	1	2	yes	—
130	#4096	—	2	2	no	—
131	#4096	C₂²×C₃	1	1	yes	characteristic
132	#4094	C₂²×C₃	1	2	yes	—
133	#4090	C₂²×C₃	1	2	yes	—
134	C₂×#689	—	2	2	no	—
135	C₂×#689	C₂²×C₃	1	2	yes	—
136	#4088	—	2	2	no	—
137	#4088	C₂²×C₃	1	2	yes	—
138	D₅×Q₁₆	—	2	1	no	—
139	#4061	—	2	2	no	—
140	#4058	—	2	1	no	—
141	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic
142	#4047	C₂²×C₃	1	1	yes	characteristic
143	#3969	C₂²×C₃	1	1	yes	characteristic
144	#3969	C₂²×C₃	1	2	yes	—
145	#3968	C₂²×C₃	1	2	yes	—
146	#3957	C₂²×C₃	1	1	yes	characteristic
147	#3956	C₂²×C₃	1	2	yes	—
148	#3954	C₂²×C₃	1	1	yes	characteristic
149	#3951	C₂²×C₃	1	1	yes	characteristic
150	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
151	#3293	—	5	1	no	Sylow
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	—	2	2	no	—
154	C₃×C₅×Q₈	—	4	2	no	—
155	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
156	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
157	C₃×C₅×D₄	—	2	2	no	—
158	C₃×C₅×D₄	—	2	1	no	—
159	C₃×C₅×D₄	—	4	2	no	—
160	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
161	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	4	2	no	—
166	C₂×C₃×C₄×C₅	—	4	2	no	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₃×C₂²⋊D₅	—	2	1	no	—
169	C₃×C₂²⋊D₅	—	4	2	no	—
170	C₂×C₃×Dic₅	—	2	1	no	—
171	C₂×C₃×Dic₅	—	2	2	no	—
172	C₂×C₃×Dic₅	—	4	2	no	—
173	C₃×D₂₀	C₂×D₄	1	1	yes	characteristic
174	C₃×C₄×D₅	—	2	1	no	—
175	C₃×C₄×D₅	—	4	2	no	—
176	C₃×Dic₁₀	—	2	2	no	—
177	C₃×Dic₁₀	—	2	2	no	—
178	C₃×Dic₁₀	—	4	2	no	—
179	C₃×Dic₁₀	C₂×D₄	1	1	yes	characteristic
180	C₃×C₅×C₈	—	2	1	no	—
181	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
182	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
183	C₃×#168	—	2	1	no	—
184	C₃×#168	—	2	2	no	—
185	C₃×#168	C₂×D₄	1	1	yes	characteristic
186	C₃×#168	C₂×D₄	1	1	yes	characteristic
187	C₃×2₋¹⁺⁴	—	5	2	no	—
188	C₃×2₋¹⁺⁴	C₂×D₅	1	2	yes	—
189	C₃×#137	—	2	2	no	—
190	C₃×#137	—	5	2	no	—
191	C₃×#137	—	5	2	no	—
192	C₃×#137	—	5	2	no	—
193	C₃×#137	—	10	2	no	—
194	C₃×#137	—	10	2	no	—
195	C₃×#137	—	10	2	no	—
196	C₃×#137	C₂×D₅	1	2	yes	—
197	C₃×#135	—	2	1	no	—
198	C₃×#135	—	5	1	no	—
199	C₃×#135	—	10	2	no	—
200	C₃×#135	—	10	1	no	—
201	C₃×#135	C₂×D₅	1	1	yes	characteristic
202	C₂×C₃×Q₁₆	—	2	1	no	—
203	C₂×C₃×Q₁₆	—	5	2	no	—
204	C₂×C₃×Q₁₆	—	5	1	no	—
205	C₂×C₃×Q₁₆	—	10	2	no	—
206	C₂×C₃×Q₁₆	—	10	1	no	—
207	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
208	C₃×#131	—	5	2	no	—
209	C₃×#131	—	5	1	no	—
210	C₃×#131	C₂×D₅	1	1	yes	characteristic
211	C₃×C₄⋊Q₈	—	5	2	no	—
212	C₃×#108	—	5	1	no	—
213	C₃×#108	—	5	1	no	—
214	C₃×#104	—	5	1	no	—
215	C₃×#104	—	5	2	no	—
216	C₃×#104	—	5	1	no	—
217	C₃×#101	—	5	2	no	—
218	C₃×#101	—	5	2	no	—
219	C₃×C₄×C₈	—	5	1	no	—
220	C₅×#41	—	2	2	no	—
221	C₅×#41	—	2	2	no	—
222	C₅×#41	—	4	2	no	—
223	C₅×#41	C₂³×C₃	1	1	yes	characteristic
224	C₅×#41	C₂³×C₃	1	2	yes	—
225	C₂×C₅×Q₈	—	2	2	no	—
226	C₂×C₅×Q₈	—	2	2	no	—
227	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
228	Q₈×D₅	—	2	2	no	—
229	#711	—	2	2	no	—
230	#711	—	4	2	no	—
231	#709	—	2	2	no	—
232	#709	C₂³×C₃	1	1	yes	characteristic
233	C₂×Dic₁₀	—	2	2	no	—
234	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
235	C₅×Q₁₆	—	2	2	no	—
236	C₅×Q₁₆	—	2	1	no	—
237	C₅×Q₁₆	—	2	1	no	—
238	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic
239	C₅×SD₁₆	—	2	2	no	—
240	C₅×SD₁₆	C₃×D₄	1	2	yes	—
241	C₅×D₈	C₃×D₄	1	1	yes	characteristic
242	C₅×M₁₆	—	2	1	no	—
243	C₅×M₁₆	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
246	#689	—	2	2	no	—
247	#689	—	2	2	no	—
248	#689	—	2	2	no	—
249	#689	—	2	2	no	—
250	#689	—	2	2	no	—
251	#689	C₃×D₄	1	1	yes	characteristic
252	#688	—	2	2	no	—
253	#688	C₃×D₄	1	1	yes	characteristic
254	#687	—	2	2	no	—
255	#687	—	2	2	no	—
256	#687	C₃×D₄	1	1	yes	characteristic
257	#686	C₃×D₄	1	1	yes	characteristic
258	#683	—	4	2	no	—
259	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
260	#681	—	2	2	no	—
261	#681	C₂³×C₃	1	1	yes	characteristic
262	#681	C₂³×C₃	1	2	yes	—
263	C₂×#168	—	2	2	no	—
264	C₂×#168	C₂³×C₃	1	1	yes	characteristic
265	Dic₂₀	—	2	1	no	—
266	Dic₂₀	—	2	1	no	—
267	#676	—	2	1	no	—
268	C₈×D₅	—	2	1	no	—
269	#578	—	5	2	no	—
270	#578	—	5	1	no	—
271	#578	C₃×D₅	1	1	yes	characteristic, complemented
272	#494	—	5	1	no	—
273	#473	—	5	2	no	—
274	#473	—	5	1	no	—
275	#473	—	5	1	no	—
276	#456	—	5	2	no	—
277	#456	—	5	2	no	—
278	#443	—	5	1	no	—
279	#443	—	5	1	no	—
280	C₂²×C₃×C₅	—	2	2	no	—
281	C₂²×C₃×C₅	—	2	1	no	—
282	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×C₃×D₅	—	2	1	no	—
284	C₃×C₄×C₅	—	2	2	no	—
285	C₃×C₄×C₅	—	2	1	no	—
286	C₃×C₄×C₅	—	4	2	no	—
287	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
289	C₃×Dic₅	—	2	2	no	—
290	C₃×Dic₅	—	2	1	no	—
291	C₃×Dic₅	—	4	2	no	—
292	C₃×#41	—	2	2	no	—
293	C₃×#41	—	2	2	no	—
294	C₃×#41	—	4	2	no	—
295	C₃×#41	—	5	1	no	—
296	C₃×#41	—	10	2	no	—
297	C₃×#41	—	10	2	no	—
298	C₃×#41	—	20	2	no	—
299	C₃×#41	C₂²×D₅	1	1	yes	characteristic
300	C₃×#41	C₂²×D₅	1	2	yes	—
301	C₂×C₃×Q₈	—	2	2	no	—
302	C₂×C₃×Q₈	—	2	2	no	—
303	C₂×C₃×Q₈	—	5	2	no	—
304	C₂×C₃×Q₈	—	10	2	no	—
305	C₂×C₃×Q₈	—	10	2	no	—
306	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
307	C₃×Q₁₆	—	2	2	no	—
308	C₃×Q₁₆	—	2	1	no	—
309	C₃×Q₁₆	—	2	1	no	—
310	C₃×Q₁₆	—	5	1	no	—
311	C₃×Q₁₆	—	10	2	no	—
312	C₃×Q₁₆	—	10	2	no	—
313	C₃×Q₁₆	—	10	2	no	—
314	C₃×Q₁₆	—	10	2	no	—
315	C₃×Q₁₆	—	10	2	no	—
316	C₃×Q₁₆	—	10	1	no	—
317	C₃×Q₁₆	—	10	1	no	—
318	C₃×Q₁₆	C₂²⋊D₅	1	1	yes	characteristic
319	C₃×SD₁₆	—	2	2	no	—
320	C₃×SD₁₆	—	5	1	no	—
321	C₃×SD₁₆	—	5	1	no	—
322	C₃×SD₁₆	—	10	2	no	—
323	C₃×SD₁₆	—	10	2	no	—
324	C₃×SD₁₆	—	10	2	no	—
325	C₃×SD₁₆	C₂²⋊D₅	1	2	yes	—
326	C₃×D₈	—	5	1	no	—
327	C₃×D₈	C₂²⋊D₅	1	1	yes	characteristic
328	C₃×M₁₆	—	2	1	no	—
329	C₃×M₁₆	—	5	2	no	—
330	C₃×M₁₆	—	5	1	no	—
331	C₃×M₁₆	—	10	2	no	—
332	C₃×M₁₆	—	10	1	no	—
333	C₃×M₁₆	C₂²×D₅	1	1	yes	characteristic
334	C₂×C₃×C₈	—	2	1	no	—
335	C₂×C₃×C₈	—	5	1	no	—
336	C₂×C₃×C₈	—	10	2	no	—
337	C₂×C₃×C₈	—	10	1	no	—
338	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
339	C₃×C₄⋊C₄	—	20	2	no	—
340	C₃×C₄²	—	5	1	no	—
341	C₅×Q₈	—	2	2	no	—
342	C₅×Q₈	—	2	2	no	—
343	C₅×Q₈	—	4	2	no	—
344	C₅×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
345	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
346	C₅×D₄	—	2	2	no	—
347	C₅×D₄	—	2	1	no	—
348	C₅×D₄	—	4	2	no	—
349	C₅×D₄	C₂×C₃×D₄	1	1	yes	characteristic
350	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
351	C₂×C₄×C₅	—	2	2	no	—
352	C₂×C₄×C₅	—	2	1	no	—
353	C₂×C₄×C₅	—	2	2	no	—
354	C₂×C₄×C₅	—	4	2	no	—
355	C₂×C₄×C₅	—	4	2	no	—
356	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
357	C₂²⋊D₅	—	2	1	no	—
358	C₂²⋊D₅	—	4	2	no	—
359	C₂×Dic₅	—	2	1	no	—
360	C₂×Dic₅	—	2	2	no	—
361	C₂×Dic₅	—	4	2	no	—
362	D₂₀	C₂×C₃×D₄	1	1	yes	characteristic
363	C₄×D₅	—	2	1	no	—
364	C₄×D₅	—	4	2	no	—
365	Dic₁₀	—	2	2	no	—
366	Dic₁₀	—	2	2	no	—
367	Dic₁₀	—	4	2	no	—
368	Dic₁₀	C₂×C₃×D₄	1	1	yes	characteristic
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
371	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
372	#168	—	2	1	no	—
373	#168	—	2	2	no	—
374	#168	C₂×C₃×D₄	1	1	yes	characteristic
375	#168	C₂×C₃×D₄	1	1	yes	characteristic
376	2₋¹⁺⁴	—	5	2	no	—
377	2₋¹⁺⁴	C₂×C₃×D₅	1	2	yes	—
378	#137	—	2	2	no	—
379	#137	—	5	2	no	—
380	#137	—	5	2	no	—
381	#137	—	5	2	no	—
382	#137	—	10	2	no	—
383	#137	—	10	2	no	—
384	#137	—	10	2	no	—
385	#137	C₂×C₃×D₅	1	2	yes	—
386	#135	—	2	1	no	—
387	#135	—	5	1	no	—
388	#135	—	10	2	no	—
389	#135	—	10	1	no	—
390	#135	C₂×C₃×D₅	1	1	yes	characteristic
391	C₂×Q₁₆	—	2	1	no	—
392	C₂×Q₁₆	—	5	2	no	—
393	C₂×Q₁₆	—	5	1	no	—
394	C₂×Q₁₆	—	10	2	no	—
395	C₂×Q₁₆	—	10	1	no	—
396	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
397	#131	—	5	2	no	—
398	#131	—	5	1	no	—
399	#131	C₂×C₃×D₅	1	1	yes	characteristic
400	C₄⋊Q₈	—	5	2	no	—
401	#108	—	5	1	no	—
402	#108	—	5	1	no	—
403	#104	—	5	1	no	—
404	#104	—	5	2	no	—
405	#104	—	5	1	no	—
406	#101	—	5	2	no	—
407	#101	—	5	2	no	—
408	C₄×C₈	—	5	1	no	—
409	C₂×C₃×C₅	—	2	1	no	—
410	C₂×C₃×C₅	—	4	2	no	—
411	C₂×C₃×C₅	—	4	1	no	—
412	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
413	C₃×D₅	—	4	1	no	—
414	C₃×Q₈	—	2	2	no	—
415	C₃×Q₈	—	2	2	no	—
416	C₃×Q₈	—	4	2	no	—
417	C₃×Q₈	—	5	1	no	—
418	C₃×Q₈	—	10	2	no	—
419	C₃×Q₈	—	10	2	no	—
420	C₃×Q₈	—	20	2	no	—
421	C₃×Q₈	D₄×D₅	1	1	yes	characteristic
422	C₃×Q₈	C₂×C₂²⋊D₅	1	2	yes	—
423	C₃×D₄	—	2	1	no	—
424	C₃×D₄	—	2	2	no	—
425	C₃×D₄	—	4	2	no	—
426	C₃×D₄	—	5	1	no	—
427	C₃×D₄	—	10	1	no	—
428	C₃×D₄	—	20	2	no	—
429	C₃×D₄	D₄×D₅	1	1	yes	characteristic
430	C₃×D₄	C₂×C₂²⋊D₅	1	2	yes	—
431	C₂×C₃×C₄	—	2	2	no	—
432	C₂×C₃×C₄	—	2	1	no	—
433	C₂×C₃×C₄	—	2	2	no	—
434	C₂×C₃×C₄	—	4	2	no	—
435	C₂×C₃×C₄	—	4	2	no	—
436	C₂×C₃×C₄	—	10	1	no	—
437	C₂×C₃×C₄	—	10	1	no	—
438	C₂×C₃×C₄	—	10	2	no	—
439	C₂×C₃×C₄	—	20	2	no	—
440	C₂×C₃×C₄	—	20	2	no	—
441	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
442	C₃×C₈	—	2	1	no	—
443	C₃×C₈	—	5	1	no	—
444	C₃×C₈	—	5	1	no	—
445	C₃×C₈	—	10	2	no	—
446	C₃×C₈	—	10	1	no	—
447	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
448	C₃×C₈	C₂×C₂²⋊D₅	1	1	yes	characteristic
449	C₂²×C₅	—	2	2	no	—
450	C₂²×C₅	—	2	1	no	—
451	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×D₅	—	2	1	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	1	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
457	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
458	Dic₅	—	2	2	no	—
459	Dic₅	—	2	1	no	—
460	Dic₅	—	4	2	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	4	2	no	—
464	#41	—	5	1	no	—
465	#41	—	10	2	no	—
466	#41	—	10	2	no	—
467	#41	—	20	2	no	—
468	#41	C₂²×C₃×D₅	1	1	yes	characteristic
469	#41	C₂²×C₃×D₅	1	2	yes	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	5	2	no	—
473	C₂×Q₈	—	10	2	no	—
474	C₂×Q₈	—	10	2	no	—
475	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
476	Q₁₆	—	2	2	no	—
477	Q₁₆	—	2	1	no	—
478	Q₁₆	—	2	1	no	—
479	Q₁₆	—	5	1	no	—
480	Q₁₆	—	10	2	no	—
481	Q₁₆	—	10	2	no	—
482	Q₁₆	—	10	2	no	—
483	Q₁₆	—	10	2	no	—
484	Q₁₆	—	10	2	no	—
485	Q₁₆	—	10	1	no	—
486	Q₁₆	—	10	1	no	—
487	Q₁₆	C₃×C₂²⋊D₅	1	1	yes	characteristic
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	5	1	no	—
490	SD₁₆	—	5	1	no	—
491	SD₁₆	—	10	2	no	—
492	SD₁₆	—	10	2	no	—
493	SD₁₆	—	10	2	no	—
494	SD₁₆	C₃×C₂²⋊D₅	1	2	yes	—
495	D₈	—	5	1	no	—
496	D₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
497	M₁₆	—	2	1	no	—
498	M₁₆	—	5	2	no	—
499	M₁₆	—	5	1	no	—
500	M₁₆	—	10	2	no	—
501	M₁₆	—	10	1	no	—
502	M₁₆	C₂²×C₃×D₅	1	1	yes	characteristic
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	5	1	no	—
505	C₂×C₈	—	10	2	no	—
506	C₂×C₈	—	10	1	no	—
507	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
508	C₄⋊C₄	—	20	2	no	—
509	C₄²	—	5	1	no	—
510	C₃×C₅	#3293	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	1	no	—
512	C₂²×C₃	—	2	2	no	—
513	C₂²×C₃	—	10	1	no	—
514	C₂²×C₃	#4144	1	1	yes	characteristic
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	—	10	2	no	—
519	C₃×C₄	—	10	1	no	—
520	C₃×C₄	—	20	2	no	—
521	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
522	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
523	C₂×C₅	—	2	1	no	—
524	C₂×C₅	—	4	2	no	—
525	C₂×C₅	—	4	1	no	—
526	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
527	D₅	—	4	1	no	—
528	Q₈	—	2	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	4	2	no	—
531	Q₈	—	5	1	no	—
532	Q₈	—	10	2	no	—
533	Q₈	—	10	2	no	—
534	Q₈	—	20	2	no	—
535	Q₈	C₃×D₄×D₅	1	1	yes	characteristic
536	Q₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
537	D₄	—	2	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	5	1	no	—
541	D₄	—	10	1	no	—
542	D₄	—	20	2	no	—
543	D₄	C₃×D₄×D₅	1	1	yes	characteristic
544	D₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	10	2	no	—
553	C₂×C₄	—	20	2	no	—
554	C₂×C₄	—	20	2	no	—
555	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	5	1	no	—
558	C₈	—	5	1	no	—
559	C₈	—	10	2	no	—
560	C₈	—	10	1	no	—
561	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
562	C₈	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
563	C₂×C₃	—	2	1	no	—
564	C₂×C₃	—	4	1	no	—
565	C₂×C₃	—	4	2	no	—
566	C₂×C₃	—	20	1	no	—
567	C₂×C₃	D₄×C₂²⋊D₅	1	1	yes	characteristic
568	C₅	C₃×#3293	1	1	yes	characteristic, complemented, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	10	1	no	—
572	C₂²	C₃×#4144	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	10	2	no	—
577	C₄	—	10	1	no	—
578	C₄	—	20	2	no	—
579	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
580	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
581	C₃	#10615749	1	1	yes	characteristic, direct product factor, Sylow
582	C₂	—	2	1	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	20	1	no	—
586	C₂	C₃×D₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#578	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#578	D₅
hypocenter	C₅	C₃×#3293
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#578

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#578	C₂	semidirect
2. C₃×#66172	C₂	semidirect
3. C₃×#66105	C₂	semidirect
4. C₃×#65535	C₂	semidirect
5. C₃×#65494	C₂	semidirect
6. C₃×#65493	C₂	semidirect
7. C₃×#65485	C₂	semidirect
8. C₃×#65481	C₂	semidirect
9. C₃×#65470	C₂	semidirect
10. C₃×#65433	C₂	semidirect
11. C₃×#65432	C₂	semidirect
12. #10615749	C₃	direct (N × H)
47. C₅×#578	C₂×C₃	semidirect
48. #66172	C₂×C₃	semidirect
49. #66105	C₂×C₃	semidirect
50. #65535	C₂×C₃	semidirect
51. #65494	C₂×C₃	semidirect
52. #65493	C₂×C₃	semidirect
53. #65485	C₂×C₃	semidirect
54. #65481	C₂×C₃	semidirect
55. #65470	C₂×C₃	semidirect
56. #65433	C₂×C₃	semidirect
57. #65432	C₂×C₃	semidirect
109. C₃×#578	D₅	semidirect
271. #578	C₃×D₅	semidirect
510. C₃×C₅	#3293	semidirect
568. C₅	C₃×#3293	semidirect
581. C₃	#10615749	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×#578	2
C₃×#66172	2
C₃×#66105	2
C₃×#65535	2
C₃×#65494	2
C₃×#65493	2
C₃×#65485	2
C₃×#65481	2
C₃×#65470	2
C₃×#65433	2
C₃×#65432	2
#10615749	3
C₃×#3293	5

Subgroups — C3×#10615749 #14458222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615749 #14458222