Subgroups — C₂×#11749434 #14417871

Order 1920.

944 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×#91839	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91290	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749434	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90992	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90980	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65113	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×#6817	C₂²	1	1	yes	characteristic
12	#91839	C₄	1	4	yes	complemented
13	#91839	C₂²	1	4	yes	—
14	C₂×#6718	C₄	1	1	yes	characteristic, complemented
15	C₂×#6717	C₄	1	1	yes	characteristic, complemented
16	C₂×#6716	C₄	1	1	yes	characteristic, complemented
17	C₂×#6715	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₃×#4094	—	2	2	no	—
22	C₃×#4094	C₂²	1	4	yes	complemented
23	C₂×C₃×#681	—	2	1	no	—
24	C₂×C₃×#681	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	—	2	1	no	—
26	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
27	C₂×#6651	—	2	1	no	—
28	#91290	—	2	2	no	—
29	#91290	C₂²	1	4	yes	complemented
30	C₂×#6648	—	2	1	no	—
31	C₅×#837	C₂²	1	4	yes	complemented
32	#90992	C₂²	1	4	yes	complemented
33	#90980	C₂²	1	4	yes	complemented
34	Dic₃×#168	C₂²	1	4	yes	complemented
35	C₂×#5144	—	5	1	no	maximal, Hall
36	C₂×#4096	—	3	1	no	—
37	C₂×#4094	D₃	1	1	yes	characteristic, complemented
38	C₂×#4053	—	3	1	no	—
39	C₂×C₅×#104	—	3	1	no	—
40	C₂×#3954	—	3	1	no	—
41	C₂×#3937	—	3	1	no	—
42	C₂×C₄×#168	—	3	1	no	—
43	#65113	—	3	8	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	#6817	—	2	1	no	—
55	#6817	—	2	1	no	—
56	#6817	C₂×C₄	1	2	yes	—
57	#6817	C₂³	1	2	yes	—
58	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	—	2	1	no	—
60	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₅×Dic₃	—	2	1	no	—
62	#6718	C₂×C₄	1	4	yes	complemented
63	#6717	C₂×C₄	1	4	yes	complemented
64	#6716	C₂×C₄	1	4	yes	complemented
65	#6715	C₂×C₄	1	4	yes	complemented
66	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
67	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃⋊#168	C₂×C₄	1	2	yes	—
69	C₂×C₃⋊#168	C₂³	1	2	yes	—
70	C₄×C₅×Dic₃	—	2	1	no	—
71	C₄×C₅×Dic₃	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	C₃×#681	—	2	1	no	—
76	C₃×#681	—	2	4	no	—
77	C₃×#681	C₂³	1	2	yes	—
78	C₂×C₃×#168	—	2	1	no	—
79	C₂×C₃×#168	—	2	4	no	—
80	C₂×C₃×#168	D₄	1	2	yes	—
81	C₂×C₃×#168	D₄	1	1	yes	characteristic
82	C₂×C₃×#168	D₄	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	#6651	—	2	4	no	—
85	#6648	—	2	4	no	—
86	C₂×C₃×#131	—	5	1	no	—
87	C₂×#950	—	5	1	no	—
88	C₂×#901	—	5	1	no	—
89	C₂×#837	D₅	1	1	yes	characteristic, complemented
90	#5144	—	5	8	no	—
91	C₂×#825	—	5	1	no	—
92	C₂×#822	—	5	1	no	—
93	C₂×C₈×Dic₃	—	5	1	no	—
94	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
95	C₂×#709	—	3	1	no	—
96	C₂×C₅×M₁₆	—	3	1	no	—
97	C₂×C₄²×C₅	—	3	1	no	—
98	#4096	—	3	4	no	—
99	#4096	—	3	4	no	—
100	#4094	—	2	2	no	—
101	#4094	C₂×D₃	1	4	yes	complemented
102	C₂×#689	—	3	1	no	—
103	C₂×#688	—	3	1	no	—
104	C₂×#687	—	3	1	no	—
105	C₂×#686	—	3	1	no	—
106	C₂×#681	—	2	1	no	—
107	C₂×#681	C₂×D₃	1	1	yes	characteristic
108	C₂²×#168	—	2	1	no	—
109	C₂²×#168	—	3	1	no	—
110	C₂²×#168	C₂×D₃	1	1	yes	characteristic
111	#4053	—	3	4	no	—
112	#4053	—	6	2	no	—
113	C₂×#676	—	6	1	no	—
114	C₂×C₈×D₅	—	6	1	no	—
115	C₅×#104	—	3	4	no	—
116	#3954	—	3	4	no	—
117	#3937	—	3	4	no	—
118	C₄×#168	—	3	4	no	—
119	C₂×#443	—	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	D₆₀	—	2	1	no	—
142	D₆₀	C₂²×C₄	1	2	yes	—
143	C₄×D₁₅	—	2	2	no	—
144	C₄×D₁₅	—	2	2	no	—
145	Dic₃₀	—	2	1	no	—
146	Dic₃₀	C₂²×C₄	1	2	yes	—
147	C₂×C₅×Dic₃	—	2	4	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₃⋊#168	C₂²×C₄	1	2	yes	—
150	C₃⋊#168	C₂²×C₄	1	2	yes	—
151	C₃×#168	—	2	2	no	—
152	C₃×#168	C₂×D₄	1	2	yes	—
153	C₃×#168	C₂×D₄	1	2	yes	—
154	C₅×C₃⋊C₈	—	2	2	no	—
155	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
156	C₂×#235	—	5	1	no	—
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	—	5	1	no	—
162	C₂²×C₃×C₈	—	10	1	no	—
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	C₂×D₅	1	1	yes	characteristic
170	C₂×#208	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	4	yes	complemented
177	#825	—	5	4	no	—
178	#822	—	5	4	no	—
179	C₈×Dic₃	—	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	—	6	1	no	—
189	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₂×C₂²⋊D₅	—	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	—	3	2	no	—
199	C₅×M₁₆	—	6	1	no	—
200	C₂×C₅×C₈	—	6	1	no	—
201	C₄²×C₅	—	3	2	no	—
202	C₄²×C₅	—	6	1	no	—
203	#689	—	3	4	no	—
204	#688	—	3	4	no	—
205	#687	—	3	4	no	—
206	#686	—	3	4	no	—
207	#681	—	2	1	no	—
208	#681	—	2	4	no	—
209	#681	C₂²×D₃	1	2	yes	—
210	C₂×#168	—	2	1	no	—
211	C₂×#168	—	2	4	no	—
212	C₂×#168	—	3	2	no	—
213	C₂×#168	—	3	1	no	—
214	C₂×#168	—	3	1	no	—
215	C₂×#168	—	3	2	no	—
216	C₂×#168	#67	1	1	yes	characteristic
217	C₂×#168	#67	1	1	yes	characteristic
218	C₂×#168	#67	1	2	yes	—
219	C₂×#168	C₂²×D₃	1	2	yes	—
220	#676	—	6	4	no	—
221	C₈×D₅	—	6	4	no	—
222	C₂×#135	—	15	1	no	—
223	C₂×#131	—	5	1	no	—
224	C₂×#131	—	15	1	no	—
225	#443	—	15	8	no	—
226	C₂×#108	—	15	1	no	—
227	C₂×#104	—	3	1	no	—
228	C₂×#104	—	15	1	no	—
229	C₂×C₄×C₈	—	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	C₅×Dic₃	—	2	4	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	—	2	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	—	5	2	no	—
264	C₃×M₁₆	—	10	4	no	—
265	C₃×M₁₆	—	10	1	no	—
266	C₂×C₃×C₈	—	5	1	no	—
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	5	2	no	—
269	C₂×C₃×C₈	—	5	2	no	—
270	C₂×C₃×C₈	—	10	4	no	—
271	C₂×C₃×C₈	—	10	1	no	—
272	#216	—	5	4	no	—
273	#215	—	5	4	no	—
274	#214	—	5	4	no	—
275	#213	—	5	4	no	—
276	C₄×Dic₃	—	2	1	no	—
277	C₄×Dic₃	C₂²×D₅	1	2	yes	—
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)	—	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	—	6	4	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
303	C₂×C₄×C₅	#235	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
307	C₂²⋊D₅	—	6	2	no	—
308	C₂²⋊D₅	—	6	2	no	—
309	C₂×Dic₅	—	6	1	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	—	6	2	no	—
317	#168	—	2	2	no	—
318	#168	—	3	2	no	—
319	#168	—	3	2	no	—
320	#168	C₂×#67	1	2	yes	—
321	#168	C₂×#67	1	2	yes	—
322	C₂×#41	—	15	1	no	—
323	C₂×#41	D₃×D₅	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	—	5	4	no	—
331	#131	—	10	2	no	—
332	#131	—	15	4	no	—
333	#131	—	30	2	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	5	1	no	—
336	C₂×M₁₆	—	10	1	no	—
337	C₂×M₁₆	—	30	1	no	—
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	10	1	no	—
340	C₂²×C₈	—	15	1	no	—
341	C₂²×C₈	—	30	1	no	—
342	C₂×C₄²	—	3	1	no	—
343	#108	—	15	4	no	—
344	#104	—	3	4	no	—
345	#104	—	15	4	no	—
346	C₄×C₈	—	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	#443	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	#711	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	D₄×D₅	1	1	yes	characteristic
368	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
369	C₂×C₃×C₄	#711	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	—	2	4	no	—
374	C₂×Dic₃	—	2	2	no	—
375	C₂×Dic₃	—	10	1	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	—	5	2	no	—
383	C₃×C₈	—	5	2	no	—
384	C₃×C₈	—	10	2	no	—
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	—	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	—	6	4	no	—
398	C₄×C₅	C₄×#67	1	1	yes	characteristic
399	C₄×C₅	C₄×#67	1	1	yes	characteristic
400	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
401	C₄×C₅	C₂²×#67	1	1	yes	characteristic
402	Dic₅	—	6	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	#1200	1	2	yes	—
410	#41	C₂×D₃×D₅	1	2	yes	—
411	C₂×Q₈	—	15	1	no	—
412	C₂×Q₈	#1200	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	#1200	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	6	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	—	10	4	no	—
429	M₁₆	—	10	1	no	—
430	M₁₆	—	30	4	no	—
431	C₂×C₈	—	5	2	no	—
432	C₂×C₈	—	5	1	no	—
433	C₂×C₈	—	5	1	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	6	1	no	—
436	C₂×C₈	—	10	4	no	—
437	C₂×C₈	—	10	1	no	—
438	C₂×C₈	—	15	1	no	—
439	C₂×C₈	—	15	1	no	—
440	C₂×C₈	—	15	2	no	—
441	C₂×C₈	—	15	2	no	—
442	C₂×C₈	—	30	4	no	—
443	C₄²	—	3	2	no	—
444	C₄²	—	6	1	no	—
445	C₃×C₅	C₂×#443	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	#4027	1	1	yes	characteristic
450	C₂²×C₃	#4027	1	1	yes	characteristic
451	C₂²×C₃	C₂×#711	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	#4027	1	1	yes	characteristic
456	C₃×C₄	#4027	1	1	yes	characteristic
457	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
458	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
459	Dic₃	—	2	4	no	—
460	Dic₃	—	10	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	#5144	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	#6782	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	15	2	no	—
472	Q₈	—	30	1	no	—
473	Q₈	C₂×#1200	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×#1200	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	6	4	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	30	1	no	—
488	C₂×C₄	—	30	2	no	—
489	C₂×C₄	—	30	2	no	—
490	C₂×C₄	#6782	1	1	yes	characteristic
491	C₂×C₄	C₂×#1200	1	1	yes	characteristic
492	C₂×C₄	C₂×#1200	1	1	yes	characteristic
493	C₂×C₄	D₅×#67	1	1	yes	characteristic
494	C₂×C₄	D₅×#67	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
496	C₈	—	5	2	no	—
497	C₈	—	5	2	no	—
498	C₈	—	6	2	no	—
499	C₈	—	10	2	no	—
500	C₈	—	15	2	no	—
501	C₈	—	15	2	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	#65113	1	2	yes	complemented
506	C₂×C₃	C₂×#4027	1	1	yes	characteristic
507	D₃	—	20	2	no	—
508	C₅	C₂×#5144	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	#91552	1	1	yes	characteristic
515	C₂²	#91552	1	1	yes	characteristic
516	C₂²	C₂×#6782	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	6	4	no	—
519	C₄	—	30	2	no	—
520	C₄	#91552	1	1	yes	characteristic
521	C₄	#91552	1	1	yes	characteristic
522	C₄	C₂²×#1200	1	1	yes	characteristic
523	C₄	C₂×D₅×#67	1	1	yes	characteristic
524	C₃	C₂×#65113	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	#11749434	1	2	yes	direct product factor
530	C₂	C₂×#91552	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×#67
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₅×#41	C₂²
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×#91839	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×#41	D₃×D₅
hypocenter	C₃×C₅	C₂×#443
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₂×#91290	C₂	semidirect
4. C₂×C₅×#837	C₂	semidirect
5. #11749434	C₂	direct (N × H)
6. C₂×#90992	C₂	semidirect
7. C₂×#90980	C₂	semidirect
8. C₂×Dic₃×#168	C₂	semidirect
12. #91839	C₄	semidirect
14. C₂×#6718	C₄	semidirect
15. C₂×#6717	C₄	semidirect
16. C₂×#6716	C₄	semidirect
17. C₂×#6715	C₄	semidirect
22. C₃×#4094	C₂²	semidirect
29. #91290	C₂²	semidirect
31. C₅×#837	C₂²	semidirect
32. #90992	C₂²	semidirect
33. #90980	C₂²	semidirect
34. Dic₃×#168	C₂²	semidirect
37. C₂×#4094	D₃	semidirect
62. #6718	C₂×C₄	semidirect
63. #6717	C₂×C₄	semidirect
64. #6716	C₂×C₄	semidirect
65. #6715	C₂×C₄	semidirect
89. C₂×#837	D₅	semidirect
101. #4094	C₂×D₃	semidirect
176. #837	C₂×D₅	semidirect
350. C₂×C₃×C₅	#443	semidirect
445. C₃×C₅	C₂×#443	semidirect
464. C₂×C₅	#5144	semidirect
505. C₂×C₃	#65113	semidirect
508. C₅	C₂×#5144	semidirect
524. C₃	C₂×#65113	semidirect
529. C₂	#11749434	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×#91839	2
C₂×C₃×#4094	2
C₂×#91290	2
C₂×C₅×#837	2
#11749434	2
C₂×#90992	2
C₂×#90980	2
C₂×Dic₃×#168	2
C₂×#65113	3
C₂×#5144	5

Subgroups — C2×#11749434 #14417871

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11749434 #14417871