Subgroups — C₂×#11751246 #14417924

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#91839	C₂	1	1	yes	maximal, characteristic
3	C₂×#91790	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91121	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751246	C₂	1	8	yes	maximal, direct product factor
6	C₂×#91109	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#91106	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#91099	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65434	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×#6817	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	—	2	2	no	—
13	C₃×C₅×#131	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×M₁₆	—	2	1	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	—	2	1	no	—
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	#91839	C₄	1	4	yes	complemented
19	#91839	C₂²	1	4	yes	—
20	C₂×#6718	C₄	1	1	yes	characteristic, complemented
21	C₂×#6717	C₄	1	1	yes	characteristic, complemented
22	C₂×#6716	C₄	1	1	yes	characteristic, complemented
23	C₂×#6715	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
25	C₂×#6710	C₂²	1	1	yes	characteristic
26	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
27	#91790	—	2	2	no	—
28	#91790	C₂²	1	4	yes	complemented
29	C₂×#6705	—	2	1	no	—
30	C₂×C₈×D₁₅	—	2	1	no	—
31	#91121	C₂²	1	4	yes	complemented
32	#91109	C₂²	1	4	yes	complemented
33	#91106	C₂²	1	4	yes	complemented
34	#91099	C₂²	1	4	yes	complemented
35	C₂×#5145	—	5	1	no	maximal, Hall
36	C₂×C₅×#131	D₃	1	1	yes	characteristic, complemented
37	C₂×#4096	—	3	1	no	—
38	C₂×#4047	—	3	1	no	—
39	C₂×#3969	—	3	1	no	—
40	#65434	—	3	8	no	—
41	C₂×#3957	—	3	1	no	—
42	C₂×#3954	—	3	1	no	—
43	C₂×#3947	—	3	1	no	—
44	C₃×C₅×#41	—	2	1	no	—
45	C₃×C₅×#41	—	2	1	no	—
46	C₃×C₅×#41	C₂×C₄	1	2	yes	—
47	C₃×C₅×#41	C₂³	1	2	yes	—
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×#1220	—	2	1	no	—
54	C₂²×Dic₁₅	—	2	1	no	—
55	#6817	—	2	1	no	—
56	#6817	—	2	1	no	—
57	#6817	C₂×C₄	1	2	yes	—
58	#6817	C₂³	1	2	yes	—
59	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×D₁₅	—	2	1	no	—
61	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	—	2	1	no	—
63	C₃×C₅×M₁₆	—	2	4	no	—
64	C₃×C₅×M₁₆	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₂×C₃×C₅×C₈	—	2	4	no	—
67	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	#6718	C₂×C₄	1	4	yes	complemented
72	#6717	C₂×C₄	1	4	yes	complemented
73	#6716	C₂×C₄	1	4	yes	complemented
74	#6715	C₂×C₄	1	4	yes	complemented
75	C₄×Dic₁₅	—	2	1	no	—
76	C₄×Dic₁₅	C₂³	1	2	yes	—
77	#6710	—	2	1	no	—
78	#6710	C₂³	1	2	yes	—
79	C₂×C₃⋊#168	—	2	1	no	—
80	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
83	C₂×C₃⋊#168	C₂³	1	2	yes	—
84	#6705	—	2	4	no	—
85	C₈×D₁₅	—	2	4	no	—
86	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
87	C₂×#950	—	5	1	no	—
88	C₂×#901	—	5	1	no	—
89	C₂×#837	—	5	1	no	—
90	#5145	—	5	8	no	—
91	C₂×#825	—	5	1	no	—
92	C₂×#822	—	5	1	no	—
93	C₂×#815	—	5	1	no	—
94	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
95	C₂×#709	—	3	1	no	—
96	C₅×#131	—	2	2	no	—
97	C₅×#131	C₂×D₃	1	4	yes	complemented
98	C₂×C₅×M₁₆	—	2	1	no	—
99	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
100	C₂²×C₅×C₈	—	2	1	no	—
101	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
102	#4096	—	3	4	no	—
103	#4096	—	3	4	no	—
104	C₂×#689	—	3	1	no	—
105	C₂×#688	—	3	1	no	—
106	C₂×#687	—	3	1	no	—
107	C₂×#686	—	3	1	no	—
108	C₂×C₄×Dic₅	—	3	1	no	—
109	C₂×#681	—	3	1	no	—
110	C₂²×#168	—	3	1	no	—
111	#4047	—	3	4	no	—
112	#4047	—	6	2	no	—
113	C₂×#676	—	6	1	no	—
114	C₂×C₈×D₅	—	6	1	no	—
115	#3969	—	3	4	no	—
116	#3957	—	3	4	no	—
117	#3954	—	3	4	no	—
118	#3947	—	3	4	no	—
119	C₂×#444	—	15	1	no	Sylow
120	C₂³×C₃×C₅	—	2	1	no	—
121	C₂³×C₃×C₅	#41	1	1	yes	characteristic
122	C₂²×D₁₅	—	2	1	no	—
123	C₃×C₅×Q₈	—	2	1	no	—
124	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	1	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	#1220	—	2	2	no	—
139	#1220	—	2	2	no	—
140	C₂×Dic₁₅	—	2	1	no	—
141	C₂×Dic₁₅	—	2	2	no	—
142	C₂×Dic₁₅	—	4	2	no	—
143	D₆₀	—	2	1	no	—
144	D₆₀	C₂²×C₄	1	2	yes	—
145	C₄×D₁₅	—	2	2	no	—
146	C₄×D₁₅	—	2	2	no	—
147	Dic₃₀	—	2	1	no	—
148	Dic₃₀	C₂²×C₄	1	2	yes	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₃⋊#168	—	2	2	no	—
153	C₃⋊#168	C₂²×C₄	1	2	yes	—
154	C₃⋊#168	C₂²×C₄	1	2	yes	—
155	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
156	C₂×#235	—	5	1	no	—
157	C₃×#131	—	2	2	no	—
158	C₃×#131	C₂×D₅	1	4	yes	complemented
159	C₂×C₃×M₁₆	—	2	1	no	—
160	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
161	C₂²×C₃×C₈	—	2	1	no	—
162	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
163	#950	—	5	4	no	—
164	#950	—	5	4	no	—
165	C₂×#216	—	5	1	no	—
166	C₂×#215	—	5	1	no	—
167	C₂×#214	—	5	1	no	—
168	C₂×#213	—	5	1	no	—
169	C₂×C₄×Dic₃	—	5	1	no	—
170	C₂×#208	—	5	1	no	—
171	C₂²×C₃⋊C₈	—	5	1	no	—
172	#901	—	5	4	no	—
173	#901	—	10	2	no	—
174	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
175	C₂×D₃×C₈	—	10	1	no	—
176	#837	—	5	4	no	—
177	#825	—	5	4	no	—
178	#822	—	5	4	no	—
179	#815	—	5	4	no	—
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	C₄×D₃	1	2	yes	—
183	C₅×#41	C₂²×D₃	1	2	yes	—
184	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₂²⋊D₅	—	6	1	no	—
190	C₂²×Dic₅	—	6	1	no	—
191	#709	—	3	2	no	—
192	#709	—	3	2	no	—
193	#709	—	6	1	no	—
194	#709	—	6	1	no	—
195	C₂×D₂₀	—	3	1	no	—
196	C₂×C₄×D₅	—	6	1	no	—
197	C₂×Dic₁₀	—	3	1	no	—
198	C₅×M₁₆	—	2	1	no	—
199	C₅×M₁₆	—	2	4	no	—
200	C₅×M₁₆	C₂²×D₃	1	2	yes	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	4	no	—
203	C₂×C₅×C₈	#67	1	1	yes	characteristic
204	C₂×C₅×C₈	#67	1	1	yes	characteristic
205	C₂×C₅×C₈	#67	1	2	yes	—
206	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
207	#689	—	3	4	no	—
208	#688	—	3	4	no	—
209	#687	—	3	4	no	—
210	#686	—	3	4	no	—
211	C₄×Dic₅	—	3	2	no	—
212	C₄×Dic₅	—	6	1	no	—
213	#681	—	3	2	no	—
214	#681	—	6	1	no	—
215	C₂×#168	—	3	2	no	—
216	C₂×#168	—	3	1	no	—
217	C₂×#168	—	3	1	no	—
218	C₂×#168	—	3	2	no	—
219	C₂×#168	—	6	1	no	—
220	#676	—	6	4	no	—
221	C₈×D₅	—	6	4	no	—
222	C₂×#135	—	15	1	no	—
223	C₂×#131	—	15	1	no	—
224	C₂×#131	D₁₅	1	1	yes	characteristic, complemented
225	#444	—	15	8	no	—
226	C₂×#108	—	15	1	no	—
227	C₂×#104	—	15	1	no	—
228	C₂×#104	—	15	1	no	—
229	C₂×#97	—	15	1	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×D₁₅	—	2	2	no	—
237	C₂×D₁₅	—	4	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	Dic₁₅	—	2	2	no	—
244	Dic₁₅	—	4	2	no	—
245	C₃×#41	—	2	1	no	—
246	C₃×#41	—	2	1	no	—
247	C₃×#41	C₄×D₅	1	2	yes	—
248	C₃×#41	C₂²×D₅	1	2	yes	—
249	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	C₂×#67	—	10	1	no	—
255	C₂²×Dic₃	—	10	1	no	—
256	#235	—	5	2	no	—
257	#235	—	5	2	no	—
258	#235	—	10	1	no	—
259	#235	—	10	1	no	—
260	C₂×D₁₂	—	5	1	no	—
261	C₂×C₄×D₃	—	10	1	no	—
262	C₂×Dic₆	—	5	1	no	—
263	C₃×M₁₆	—	2	1	no	—
264	C₃×M₁₆	—	2	4	no	—
265	C₃×M₁₆	C₂²×D₅	1	2	yes	—
266	C₂×C₃×C₈	—	2	1	no	—
267	C₂×C₃×C₈	—	2	4	no	—
268	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
270	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
271	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
272	#216	—	5	4	no	—
273	#215	—	5	4	no	—
274	#214	—	5	4	no	—
275	#213	—	5	4	no	—
276	C₄×Dic₃	—	5	2	no	—
277	C₄×Dic₃	—	10	1	no	—
278	#208	—	5	2	no	—
279	#208	—	10	1	no	—
280	C₂×C₃⋊C₈	—	5	1	no	—
281	C₂×C₃⋊C₈	—	5	1	no	—
282	C₂×C₃⋊C₈	—	5	2	no	—
283	C₂×C₃⋊C₈	—	5	2	no	—
284	C₂×C₃⋊C₈	—	10	1	no	—
285	ΓL(1,𝔽₂₅)	—	10	4	no	—
286	D₃×C₈	—	10	4	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	#235	1	1	yes	characteristic
289	C₂²×D₅	—	6	1	no	—
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
301	C₂×C₄×C₅	#235	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
305	C₂²⋊D₅	—	6	2	no	—
306	C₂²⋊D₅	—	6	2	no	—
307	C₂×Dic₅	—	6	1	no	—
308	C₂×Dic₅	—	6	2	no	—
309	C₂×Dic₅	—	12	2	no	—
310	D₂₀	—	3	2	no	—
311	D₂₀	—	6	1	no	—
312	C₄×D₅	—	6	2	no	—
313	C₄×D₅	—	6	2	no	—
314	Dic₁₀	—	3	2	no	—
315	Dic₁₀	—	6	1	no	—
316	C₅×C₈	—	2	2	no	—
317	C₅×C₈	C₂×#67	1	2	yes	—
318	C₅×C₈	C₂×#67	1	2	yes	—
319	#168	—	3	2	no	—
320	#168	—	3	2	no	—
321	#168	—	6	2	no	—
322	C₂×#41	—	15	1	no	—
323	C₂×#41	C₂×D₁₅	1	1	yes	characteristic
324	#135	—	15	4	no	—
325	#135	—	15	4	no	—
326	C₂×Q₁₆	—	15	1	no	—
327	C₂×SD₁₆	—	15	1	no	—
328	C₂×SD₁₆	—	15	1	no	—
329	C₂×D₈	—	15	1	no	—
330	#131	—	2	2	no	—
331	#131	—	15	4	no	—
332	#131	—	30	2	no	—
333	#131	C₂×D₁₅	1	4	yes	complemented
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	15	1	no	—
336	C₂×M₁₆	—	30	1	no	—
337	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	15	1	no	—
340	C₂²×C₈	—	30	1	no	—
341	C₂²×C₈	C₂×D₁₅	1	1	yes	characteristic
342	C₂×C₄²	—	15	1	no	—
343	#108	—	15	4	no	—
344	#104	—	15	4	no	—
345	#104	—	15	4	no	—
346	#97	—	15	4	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	—	4	2	no	—
350	C₂×C₃×C₅	#444	1	2	yes	complemented
351	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	D₁₅	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	#709	1	1	yes	characteristic
355	C₂²×D₃	—	10	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
367	C₂×C₃×C₄	#709	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
371	#67	—	10	2	no	—
372	#67	—	10	2	no	—
373	C₂×Dic₃	—	10	1	no	—
374	C₂×Dic₃	—	10	2	no	—
375	C₂×Dic₃	—	20	2	no	—
376	D₁₂	—	5	2	no	—
377	D₁₂	—	10	1	no	—
378	C₄×D₃	—	10	2	no	—
379	C₄×D₃	—	10	2	no	—
380	Dic₆	—	5	2	no	—
381	Dic₆	—	10	1	no	—
382	C₃×C₈	—	2	2	no	—
383	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
384	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
385	C₃⋊C₈	—	5	2	no	—
386	C₃⋊C₈	—	5	2	no	—
387	C₃⋊C₈	—	10	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	C₄×#67	1	1	yes	characteristic
392	C₂²×C₅	C₄×#67	1	1	yes	characteristic
393	C₂²×C₅	C₂×#235	1	1	yes	characteristic
394	C₂×D₅	—	6	2	no	—
395	C₂×D₅	—	12	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	C₄×#67	1	1	yes	characteristic
398	C₄×C₅	C₄×#67	1	1	yes	characteristic
399	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
400	C₄×C₅	C₂²×#67	1	1	yes	characteristic
401	Dic₅	—	6	2	no	—
402	Dic₅	—	12	2	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	15	2	no	—
406	#41	—	15	2	no	—
407	#41	—	30	1	no	—
408	#41	—	30	1	no	—
409	#41	C₄×D₁₅	1	2	yes	—
410	#41	C₂²×D₁₅	1	2	yes	—
411	C₂×Q₈	—	15	1	no	—
412	C₂×Q₈	C₄×D₁₅	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	15	1	no	—
415	C₂×D₄	—	30	1	no	—
416	C₂×D₄	C₄×D₁₅	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	30	1	no	—
419	C₂²×C₄	—	30	1	no	—
420	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
421	Q₁₆	—	15	4	no	—
422	SD₁₆	—	15	4	no	—
423	SD₁₆	—	15	4	no	—
424	D₈	—	15	4	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	—	15	2	no	—
428	M₁₆	—	30	1	no	—
429	M₁₆	—	30	4	no	—
430	M₁₆	C₂²×D₁₅	1	2	yes	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	—	15	1	no	—
434	C₂×C₈	—	15	1	no	—
435	C₂×C₈	—	15	2	no	—
436	C₂×C₈	—	15	2	no	—
437	C₂×C₈	—	30	1	no	—
438	C₂×C₈	—	30	4	no	—
439	C₂×C₈	#1220	1	2	yes	—
440	C₂×C₈	#1220	1	1	yes	characteristic
441	C₂×C₈	#1220	1	1	yes	characteristic
442	C₂×C₈	C₂²×D₁₅	1	2	yes	—
443	C₄²	—	15	2	no	—
444	C₄²	—	30	1	no	—
445	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	4	2	no	—
449	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
450	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
451	C₂²×C₃	C₂×#709	1	1	yes	characteristic
452	C₂×D₃	—	10	2	no	—
453	C₂×D₃	—	20	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
456	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
457	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
458	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
459	Dic₃	—	10	2	no	—
460	Dic₃	—	20	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	#5145	1	2	yes	complemented
465	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
466	D₅	—	12	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	30	1	no	—
469	C₂³	#6817	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	15	2	no	—
472	Q₈	—	30	1	no	—
473	Q₈	C₂×C₄×D₁₅	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	15	2	no	—
478	D₄	—	30	2	no	—
479	D₄	—	30	2	no	—
480	D₄	—	30	1	no	—
481	D₄	C₂×C₄×D₁₅	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	30	1	no	—
486	C₂×C₄	—	30	2	no	—
487	C₂×C₄	—	30	2	no	—
488	C₂×C₄	—	30	2	no	—
489	C₂×C₄	—	60	2	no	—
490	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
491	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
492	C₂×C₄	#6817	1	1	yes	characteristic
493	C₂×C₄	C₂×#1220	1	1	yes	characteristic
494	C₂×C₄	C₂×#1220	1	1	yes	characteristic
495	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	15	2	no	—
498	C₈	—	15	2	no	—
499	C₈	—	30	2	no	—
500	C₈	C₂×#1220	1	2	yes	—
501	C₈	C₂×#1220	1	2	yes	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	#65434	1	2	yes	complemented
506	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
507	D₃	—	20	2	no	—
508	C₅	C₂×#5145	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	30	2	no	—
513	C₂²	—	60	2	no	—
514	C₂²	C₄×#1220	1	1	yes	characteristic
515	C₂²	C₄×#1220	1	1	yes	characteristic
516	C₂²	C₂×#6817	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	30	2	no	—
519	C₄	—	60	2	no	—
520	C₄	C₄×#1220	1	1	yes	characteristic
521	C₄	C₄×#1220	1	1	yes	characteristic
522	C₄	C₂²×C₄×D₁₅	1	1	yes	characteristic
523	C₄	C₂²×#1220	1	1	yes	characteristic
524	C₃	C₂×#65434	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	4	2	no	—
528	C₂	—	60	2	no	—
529	C₂	#11751246	1	2	yes	direct product factor
530	C₂	C₂×C₄×#1220	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#1220
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×#91839	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#131	D₁₅
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×#91790	C₂	semidirect
4. C₂×#91121	C₂	semidirect
5. #11751246	C₂	direct (N × H)
6. C₂×#91109	C₂	semidirect
7. C₂×#91106	C₂	semidirect
8. C₂×#91099	C₂	semidirect
13. C₃×C₅×#131	C₂²	semidirect
18. #91839	C₄	semidirect
20. C₂×#6718	C₄	semidirect
21. C₂×#6717	C₄	semidirect
22. C₂×#6716	C₄	semidirect
23. C₂×#6715	C₄	semidirect
28. #91790	C₂²	semidirect
31. #91121	C₂²	semidirect
32. #91109	C₂²	semidirect
33. #91106	C₂²	semidirect
34. #91099	C₂²	semidirect
36. C₂×C₅×#131	D₃	semidirect
71. #6718	C₂×C₄	semidirect
72. #6717	C₂×C₄	semidirect
73. #6716	C₂×C₄	semidirect
74. #6715	C₂×C₄	semidirect
86. C₂×C₃×#131	D₅	semidirect
97. C₅×#131	C₂×D₃	semidirect
158. C₃×#131	C₂×D₅	semidirect
224. C₂×#131	D₁₅	semidirect
333. #131	C₂×D₁₅	semidirect
350. C₂×C₃×C₅	#444	semidirect
445. C₃×C₅	C₂×#444	semidirect
464. C₂×C₅	#5145	semidirect
505. C₂×C₃	#65434	semidirect
508. C₅	C₂×#5145	semidirect
524. C₃	C₂×#65434	semidirect
529. C₂	#11751246	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×C₅×#131	2
C₂×#91839	2
C₂×#91790	2
C₂×#91121	2
#11751246	2
C₂×#91109	2
C₂×#91106	2
C₂×#91099	2
C₂×#65434	3
C₂×#5145	5

Subgroups — C2×#11751246 #14417924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11751246 #14417924