Subgroups — C₂×#11748075 #14417966

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×C₅×#901	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91297	C₂	1	1	yes	maximal, characteristic
4	C₂×#91099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#90992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#90978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90976	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748075	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65434	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃×#709	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
14	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#901	—	2	2	no	—
17	C₅×#901	C₂²	1	4	yes	complemented
18	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
19	C₂×C₅×D₃×C₈	—	2	1	no	—
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₃×#4047	—	2	2	no	—
22	C₃×#4047	C₂²	1	4	yes	complemented
23	C₂×C₃×#676	—	2	1	no	—
24	C₂×C₃×C₈×D₅	—	2	1	no	—
25	C₂×#6661	C₄	1	1	yes	characteristic, complemented
26	C₂×#6656	C₄	1	1	yes	characteristic, complemented
27	C₂×#6655	C₄	1	1	yes	characteristic, complemented
28	#91297	C₄	1	4	yes	complemented
29	#91297	C₂²	1	4	yes	—
30	C₂×#6652	C₄	1	1	yes	characteristic, complemented
31	#91099	C₂²	1	4	yes	complemented
32	#90992	C₂²	1	4	yes	complemented
33	#90978	C₂²	1	4	yes	complemented
34	#90976	C₂²	1	4	yes	complemented
35	C₂×#5145	—	5	1	no	maximal, Hall
36	C₂×C₅×#131	—	3	1	no	—
37	C₂×#4096	—	3	1	no	—
38	C₂×#4047	D₃	1	1	yes	characteristic, complemented
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₅	—	2	1	no	—
46	C₂×C₅×#67	—	2	1	no	—
47	C₅×#235	—	2	1	no	—
48	C₅×#235	—	2	1	no	—
49	C₅×#235	C₂×C₄	1	2	yes	—
50	C₅×#235	C₂³	1	2	yes	—
51	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×C₅×D₃	—	2	1	no	—
53	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
55	C₃×#709	—	2	1	no	—
56	C₃×#709	—	2	1	no	—
57	C₃×#709	C₂×C₄	1	2	yes	—
58	C₃×#709	C₂³	1	2	yes	—
59	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	—	2	1	no	—
61	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₄×Dic₁₅	—	2	1	no	—
67	C₄×Dic₁₅	C₂³	1	2	yes	—
68	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
70	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃⋊#168	C₂³	1	2	yes	—
72	C₅×#208	—	2	1	no	—
73	C₅×#208	C₂³	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	—	2	1	no	—
75	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
76	C₅×D₃×C₈	—	2	4	no	—
77	C₃×#681	—	2	1	no	—
78	C₃×#681	C₂³	1	2	yes	—
79	C₂×C₃×#168	—	2	1	no	—
80	C₃×#676	—	2	4	no	—
81	C₃×C₈×D₅	—	2	4	no	—
82	#6661	C₂×C₄	1	4	yes	complemented
83	#6656	C₂×C₄	1	4	yes	complemented
84	#6655	C₂×C₄	1	4	yes	complemented
85	#6652	C₂×C₄	1	4	yes	complemented
86	C₂×C₃×#131	—	5	1	no	—
87	C₂×#950	—	5	1	no	—
88	C₂×#901	D₅	1	1	yes	characteristic, complemented
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	—	3	1	no	—
95	C₂×#709	C₂×D₃	1	1	yes	characteristic
96	C₅×#131	—	3	4	no	—
97	C₅×#131	—	6	2	no	—
98	C₂×C₅×M₁₆	—	3	1	no	—
99	C₂×C₅×M₁₆	—	6	1	no	—
100	C₂²×C₅×C₈	—	6	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	C₂×D₃	1	1	yes	characteristic
110	C₂²×#168	—	3	1	no	—
111	#4047	—	2	2	no	—
112	#4047	C₂×D₃	1	4	yes	complemented
113	C₂×#676	—	2	1	no	—
114	C₂×C₈×D₅	—	2	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	#41	1	1	yes	characteristic
121	C₂²×C₅×D₃	—	2	1	no	—
122	C₂²×C₃×D₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₂×Dic₁₅	—	2	2	no	—
130	C₂×Dic₁₅	—	4	2	no	—
131	C₅×#67	—	2	2	no	—
132	C₅×#67	—	2	2	no	—
133	C₂×C₅×Dic₃	—	2	1	no	—
134	C₅×D₁₂	—	2	1	no	—
135	C₅×D₁₂	C₂²×C₄	1	2	yes	—
136	C₄×C₅×D₃	—	2	2	no	—
137	C₄×C₅×D₃	—	2	2	no	—
138	C₅×Dic₆	—	2	1	no	—
139	C₅×Dic₆	C₂²×C₄	1	2	yes	—
140	C₃×C₂²⋊D₅	—	2	2	no	—
141	C₃×C₂²⋊D₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₃×D₂₀	—	2	1	no	—
144	C₃×D₂₀	C₂²×C₄	1	2	yes	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×Dic₁₀	—	2	1	no	—
148	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
149	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₃⋊#168	C₂²×C₄	1	2	yes	—
152	C₃⋊#168	C₂²×C₄	1	2	yes	—
153	C₃×#168	—	2	2	no	—
154	C₅×C₃⋊C₈	—	2	2	no	—
155	C₂×C₃×#41	—	5	1	no	—
156	C₂×#235	C₂×D₅	1	1	yes	characteristic
157	C₃×#131	—	5	4	no	—
158	C₃×#131	—	10	2	no	—
159	C₂×C₃×M₁₆	—	5	1	no	—
160	C₂×C₃×M₁₆	—	10	1	no	—
161	C₂²×C₃×C₈	—	10	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	C₂×D₅	1	1	yes	characteristic
171	C₂²×C₃⋊C₈	—	5	1	no	—
172	#901	—	2	2	no	—
173	#901	C₂×D₅	1	4	yes	complemented
174	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
175	C₂×D₃×C₈	—	2	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	—	3	2	no	—
181	C₅×#41	—	3	2	no	—
182	C₅×#41	—	6	1	no	—
183	C₅×#41	—	6	1	no	—
184	C₂×C₅×Q₈	—	3	1	no	—
185	C₂×C₅×D₄	—	3	1	no	—
186	C₂×C₅×D₄	—	6	1	no	—
187	C₂²×C₄×C₅	—	6	1	no	—
188	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂×C₂²⋊D₅	—	2	1	no	—
190	C₂²×Dic₅	—	6	1	no	—
191	#709	—	2	1	no	—
192	#709	—	2	1	no	—
193	#709	C₄×D₃	1	2	yes	—
194	#709	C₂²×D₃	1	2	yes	—
195	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
196	C₂×C₄×D₅	—	2	1	no	—
197	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
198	C₅×M₁₆	—	3	2	no	—
199	C₅×M₁₆	—	6	1	no	—
200	C₅×M₁₆	—	6	4	no	—
201	C₂×C₅×C₈	—	6	1	no	—
202	C₂×C₅×C₈	—	6	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	—	2	1	no	—
214	#681	C₂²×D₃	1	2	yes	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	3	2	no	—
217	C₂×#168	—	3	1	no	—
218	C₂×#168	—	3	1	no	—
219	C₂×#168	—	3	2	no	—
220	#676	—	2	4	no	—
221	C₈×D₅	—	2	4	no	—
222	C₂×#135	—	15	1	no	—
223	C₂×#131	—	3	1	no	—
224	C₂×#131	—	5	1	no	—
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	C₄×D₄	1	1	yes	characteristic
232	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	—	4	2	no	—
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	—	4	2	no	—
238	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
242	Dic₁₅	—	4	2	no	—
243	C₃×Dic₅	—	2	2	no	—
244	C₅×Dic₃	—	2	2	no	—
245	C₃×#41	—	5	2	no	—
246	C₃×#41	—	5	2	no	—
247	C₃×#41	—	10	1	no	—
248	C₃×#41	—	10	1	no	—
249	C₂×C₃×Q₈	—	5	1	no	—
250	C₂×C₃×D₄	—	5	1	no	—
251	C₂×C₃×D₄	—	10	1	no	—
252	C₂²×C₃×C₄	—	10	1	no	—
253	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
254	C₂×#67	—	2	1	no	—
255	C₂²×Dic₃	—	10	1	no	—
256	#235	—	2	1	no	—
257	#235	—	2	1	no	—
258	#235	C₄×D₅	1	2	yes	—
259	#235	C₂²×D₅	1	2	yes	—
260	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
261	C₂×C₄×D₃	—	2	1	no	—
262	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
263	C₃×M₁₆	—	5	2	no	—
264	C₃×M₁₆	—	10	1	no	—
265	C₃×M₁₆	—	10	4	no	—
266	C₂×C₃×C₈	—	10	1	no	—
267	C₂×C₃×C₈	—	10	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	—	2	1	no	—
279	#208	C₂²×D₅	1	2	yes	—
280	C₂×C₃⋊C₈	—	2	1	no	—
281	C₂×C₃⋊C₈	—	5	1	no	—
282	C₂×C₃⋊C₈	—	5	1	no	—
283	C₂×C₃⋊C₈	—	5	2	no	—
284	C₂×C₃⋊C₈	—	5	2	no	—
285	ΓL(1,𝔽₂₅)	—	2	4	no	—
286	D₃×C₈	—	2	4	no	—
287	C₂³×C₅	—	6	1	no	—
288	C₂³×C₅	#235	1	1	yes	characteristic
289	C₂²×D₅	—	2	1	no	—
290	C₅×Q₈	—	3	2	no	—
291	C₅×Q₈	—	6	1	no	—
292	C₅×D₄	—	3	2	no	—
293	C₅×D₄	—	6	2	no	—
294	C₅×D₄	—	6	2	no	—
295	C₅×D₄	—	6	1	no	—
296	C₂×C₄×C₅	—	6	1	no	—
297	C₂×C₄×C₅	—	6	2	no	—
298	C₂×C₄×C₅	—	6	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	—	2	2	no	—
306	C₂²⋊D₅	—	2	2	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	6	2	no	—
309	C₂×Dic₅	—	12	2	no	—
310	D₂₀	—	2	1	no	—
311	D₂₀	C₂×C₄×D₃	1	2	yes	—
312	C₄×D₅	—	2	2	no	—
313	C₄×D₅	—	2	2	no	—
314	Dic₁₀	—	2	1	no	—
315	Dic₁₀	C₂×C₄×D₃	1	2	yes	—
316	C₅×C₈	—	6	2	no	—
317	C₅×C₈	C₂×#67	1	2	yes	—
318	C₅×C₈	C₂×#67	1	2	yes	—
319	#168	—	2	2	no	—
320	#168	—	3	2	no	—
321	#168	—	3	2	no	—
322	C₂×#41	—	3	1	no	—
323	C₂×#41	—	5	1	no	—
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	—	3	4	no	—
331	#131	—	5	4	no	—
332	#131	—	6	2	no	—
333	#131	—	10	2	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	5	1	no	—
336	C₂×M₁₆	—	6	1	no	—
337	C₂×M₁₆	—	10	1	no	—
338	C₂²×C₈	—	6	1	no	—
339	C₂²×C₈	—	10	1	no	—
340	C₂²×C₈	—	15	1	no	—
341	C₂²×C₈	D₃×D₅	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	#444	1	2	yes	complemented
350	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
351	C₃×D₅	—	4	2	no	—
352	C₅×D₃	—	4	2	no	—
353	C₂³×C₃	—	10	1	no	—
354	C₂³×C₃	#709	1	1	yes	characteristic
355	C₂²×D₃	—	2	1	no	—
356	C₃×Q₈	—	5	2	no	—
357	C₃×Q₈	—	10	1	no	—
358	C₃×D₄	—	5	2	no	—
359	C₃×D₄	—	10	2	no	—
360	C₃×D₄	—	10	2	no	—
361	C₃×D₄	—	10	1	no	—
362	C₂×C₃×C₄	—	10	1	no	—
363	C₂×C₃×C₄	—	10	2	no	—
364	C₂×C₃×C₄	—	10	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	—	2	2	no	—
372	#67	—	2	2	no	—
373	C₂×Dic₃	—	2	1	no	—
374	C₂×Dic₃	—	10	2	no	—
375	C₂×Dic₃	—	20	2	no	—
376	D₁₂	—	2	1	no	—
377	D₁₂	C₂×C₄×D₅	1	2	yes	—
378	C₄×D₃	—	2	2	no	—
379	C₄×D₃	—	2	2	no	—
380	Dic₆	—	2	1	no	—
381	Dic₆	C₂×C₄×D₅	1	2	yes	—
382	C₃×C₈	—	10	2	no	—
383	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
384	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
385	C₃⋊C₈	—	2	2	no	—
386	C₃⋊C₈	—	5	2	no	—
387	C₃⋊C₈	—	5	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	6	2	no	—
390	C₂²×C₅	—	12	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	—	2	2	no	—
395	C₂×D₅	—	4	2	no	—
396	C₄×C₅	—	6	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	—	2	2	no	—
402	Dic₅	—	12	2	no	—
403	#41	—	3	2	no	—
404	#41	—	3	2	no	—
405	#41	—	5	2	no	—
406	#41	—	5	2	no	—
407	#41	—	6	1	no	—
408	#41	—	6	1	no	—
409	#41	—	10	1	no	—
410	#41	—	10	1	no	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	—	5	1	no	—
413	C₂×D₄	—	3	1	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	6	1	no	—
416	C₂×D₄	—	10	1	no	—
417	C₂²×C₄	—	6	1	no	—
418	C₂²×C₄	—	10	1	no	—
419	C₂²×C₄	—	30	1	no	—
420	C₂²×C₄	C₂×D₃×D₅	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	—	3	2	no	—
426	M₁₆	—	5	2	no	—
427	M₁₆	—	6	1	no	—
428	M₁₆	—	6	4	no	—
429	M₁₆	—	10	1	no	—
430	M₁₆	—	10	4	no	—
431	C₂×C₈	—	6	1	no	—
432	C₂×C₈	—	6	4	no	—
433	C₂×C₈	—	10	1	no	—
434	C₂×C₈	—	10	4	no	—
435	C₂×C₈	—	15	1	no	—
436	C₂×C₈	—	15	1	no	—
437	C₂×C₈	—	15	2	no	—
438	C₂×C₈	—	15	2	no	—
439	C₂×C₈	#1201	1	2	yes	—
440	C₂×C₈	#1201	1	1	yes	characteristic
441	C₂×C₈	#1201	1	1	yes	characteristic
442	C₂×C₈	C₂×D₃×D₅	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	—	10	2	no	—
448	C₂²×C₃	—	20	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	—	2	2	no	—
453	C₂×D₃	—	4	2	no	—
454	C₃×C₄	—	10	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	—	2	2	no	—
460	Dic₃	—	20	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	12	2	no	—
464	C₂×C₅	#5145	1	2	yes	complemented
465	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
466	D₅	—	4	2	no	—
467	C₂³	—	6	1	no	—
468	C₂³	—	10	1	no	—
469	C₂³	#6771	1	1	yes	characteristic
470	Q₈	—	3	2	no	—
471	Q₈	—	5	2	no	—
472	Q₈	—	6	1	no	—
473	Q₈	—	10	1	no	—
474	D₄	—	3	2	no	—
475	D₄	—	5	2	no	—
476	D₄	—	6	2	no	—
477	D₄	—	6	2	no	—
478	D₄	—	6	1	no	—
479	D₄	—	10	2	no	—
480	D₄	—	10	2	no	—
481	D₄	—	10	1	no	—
482	C₂×C₄	—	6	1	no	—
483	C₂×C₄	—	6	2	no	—
484	C₂×C₄	—	6	2	no	—
485	C₂×C₄	—	10	1	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	30	2	no	—
489	C₂×C₄	—	60	2	no	—
490	C₂×C₄	#6771	1	1	yes	characteristic
491	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
492	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
493	C₂×C₄	C₂×#1201	1	1	yes	characteristic
494	C₂×C₄	C₂×#1201	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
496	C₈	—	6	2	no	—
497	C₈	—	10	2	no	—
498	C₈	—	15	2	no	—
499	C₈	—	15	2	no	—
500	C₈	C₂×#1201	1	2	yes	—
501	C₈	C₂×#1201	1	2	yes	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	20	2	no	—
505	C₂×C₃	#65434	1	2	yes	complemented
506	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
507	D₃	—	4	2	no	—
508	C₅	C₂×#5145	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	6	2	no	—
511	C₂²	—	10	2	no	—
512	C₂²	—	12	2	no	—
513	C₂²	—	20	2	no	—
514	C₂²	C₄×#1201	1	1	yes	characteristic
515	C₂²	C₄×#1201	1	1	yes	characteristic
516	C₂²	C₂×#6771	1	1	yes	characteristic
517	C₄	—	6	2	no	—
518	C₄	—	10	2	no	—
519	C₄	—	60	2	no	—
520	C₄	C₄×#1201	1	1	yes	characteristic
521	C₄	C₄×#1201	1	1	yes	characteristic
522	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
523	C₄	C₂²×#1201	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	—	12	2	no	—
528	C₂	—	20	2	no	—
529	C₂	#11748075	1	2	yes	direct product factor
530	C₂	C₂×C₄×#1201	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#1201
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×#91297	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#444
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#901	C₂	semidirect
2. C₂×C₃×#4047	C₂	semidirect
4. C₂×#91099	C₂	semidirect
5. C₂×#90992	C₂	semidirect
6. C₂×#90978	C₂	semidirect
7. C₂×#90976	C₂	semidirect
8. #11748075	C₂	direct (N × H)
17. C₅×#901	C₂²	semidirect
22. C₃×#4047	C₂²	semidirect
25. C₂×#6661	C₄	semidirect
26. C₂×#6656	C₄	semidirect
27. C₂×#6655	C₄	semidirect
28. #91297	C₄	semidirect
30. C₂×#6652	C₄	semidirect
31. #91099	C₂²	semidirect
32. #90992	C₂²	semidirect
33. #90978	C₂²	semidirect
34. #90976	C₂²	semidirect
38. C₂×#4047	D₃	semidirect
82. #6661	C₂×C₄	semidirect
83. #6656	C₂×C₄	semidirect
84. #6655	C₂×C₄	semidirect
85. #6652	C₂×C₄	semidirect
88. C₂×#901	D₅	semidirect
112. #4047	C₂×D₃	semidirect
173. #901	C₂×D₅	semidirect
349. 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	#11748075	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×C₅×#901	2
C₂×C₃×#4047	2
C₂×#91297	2
C₂×#91099	2
C₂×#90992	2
C₂×#90978	2
C₂×#90976	2
#11748075	2
C₂×#65434	3
C₂×#5145	5

Subgroups — C2×#11748075 #14417966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11748075 #14417966