Subgroups — C₂×#11747018 #14417880

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×#91303	C₂	1	1	yes	maximal, characteristic
2	C₂×#91290	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91286	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90991	C₂	1	1	yes	maximal, characteristic, complemented
8	#11747018	C₂	1	8	yes	maximal, direct product factor
9	C₂×#65113	—	3	1	no	maximal, Hall
10	C₂×#6817	C₂²	1	1	yes	characteristic
11	C₂×C₅×#235	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
16	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
17	C₂×#6663	C₄	1	1	yes	characteristic, complemented
18	C₂×#6660	C₄	1	1	yes	characteristic, complemented
19	C₂×#6659	C₄	1	1	yes	characteristic, complemented
20	#91303	C₄	1	4	yes	complemented
21	#91303	C₂²	1	4	yes	—
22	C₂×#6654	C₄	1	1	yes	characteristic, complemented
23	C₂×#6651	—	2	1	no	—
24	C₂×#6650	—	2	1	no	—
25	#91290	—	2	2	no	—
26	#91290	C₂²	1	4	yes	complemented
27	C₂×#6648	—	2	1	no	—
28	#91286	—	2	2	no	—
29	#91286	C₂²	1	4	yes	complemented
30	C₂×D₃×#168	—	2	1	no	—
31	#91089	C₂²	1	4	yes	complemented
32	C₅×#805	C₂²	1	4	yes	complemented
33	C₃×C₄×#168	C₂²	1	4	yes	complemented
34	#90991	C₂²	1	4	yes	complemented
35	C₂×#4700	—	5	1	no	maximal, Hall
36	C₂×#4096	—	3	1	no	—
37	C₂×#4094	—	3	1	no	—
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	D₃	1	1	yes	characteristic, complemented
43	#65113	—	3	8	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×#1220	—	2	1	no	—
47	#6817	—	2	1	no	—
48	#6817	—	2	1	no	—
49	#6817	C₂×C₄	1	2	yes	—
50	#6817	C₂³	1	2	yes	—
51	C₂×D₆₀	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×D₁₅	—	2	1	no	—
53	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×#67	—	2	1	no	—
55	C₅×#235	—	2	1	no	—
56	C₅×#235	—	2	1	no	—
57	C₅×#235	C₂×C₄	1	2	yes	—
58	C₅×#235	C₂³	1	2	yes	—
59	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	—	2	1	no	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	#6710	—	2	1	no	—
65	#6710	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	—	2	1	no	—
67	C₅×#208	—	2	1	no	—
68	C₅×#208	C₂³	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	—	2	1	no	—
70	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
71	C₂×C₃×#168	C₂×C₄	1	2	yes	—
72	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×#168	D₄	1	1	yes	characteristic
74	C₂×C₃×#168	D₄	1	2	yes	—
75	C₂×C₃×#168	D₄	1	1	yes	characteristic
76	C₂×C₃×#168	C₂³	1	2	yes	—
77	C₂×C₃×#168	C₂³	1	2	yes	—
78	#6663	C₂×C₄	1	4	yes	complemented
79	#6660	C₂×C₄	1	4	yes	complemented
80	#6659	C₂×C₄	1	4	yes	complemented
81	#6654	C₂×C₄	1	4	yes	complemented
82	#6651	—	2	4	no	—
83	#6650	—	2	4	no	—
84	#6648	—	2	4	no	—
85	D₃×#168	—	2	4	no	—
86	C₂×#904	—	5	1	no	—
87	C₂×#901	—	5	1	no	—
88	C₂×#901	—	5	1	no	—
89	C₂×C₃×C₄×C₈	—	5	1	no	—
90	C₂×#819	—	5	1	no	—
91	C₂×#805	—	5	1	no	—
92	C₂×#805	D₅	1	1	yes	characteristic, complemented
93	#4700	—	5	8	no	—
94	C₂×C₅×#41	—	3	1	no	—
95	C₂×#709	—	3	1	no	—
96	C₂×C₅×M₁₆	—	3	1	no	—
97	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
98	#4096	—	3	4	no	—
99	#4096	—	3	4	no	—
100	#4094	—	3	4	no	—
101	#4094	—	6	2	no	—
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	—	3	1	no	—
107	C₂×#681	—	6	1	no	—
108	C₂²×#168	—	6	1	no	—
109	C₂²×#168	C₂×D₃	1	1	yes	characteristic
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	C₂×D₃	1	4	yes	complemented
119	C₂×#443	—	15	1	no	Sylow
120	C₂³×C₃×C₅	#41	1	1	yes	characteristic
121	C₂²×D₁₅	—	2	1	no	—
122	C₂²×C₅×D₃	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	2	4	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	#1220	—	2	2	no	—
132	#1220	—	2	2	no	—
133	C₂×Dic₁₅	—	2	1	no	—
134	D₆₀	—	2	1	no	—
135	D₆₀	C₂²×C₄	1	2	yes	—
136	C₄×D₁₅	—	2	2	no	—
137	C₄×D₁₅	—	2	2	no	—
138	Dic₃₀	—	2	1	no	—
139	Dic₃₀	C₂²×C₄	1	2	yes	—
140	C₅×#67	—	2	2	no	—
141	C₅×#67	—	2	2	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₅×D₁₂	—	2	1	no	—
144	C₅×D₁₂	C₂²×C₄	1	2	yes	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₅×Dic₆	—	2	1	no	—
148	C₅×Dic₆	C₂²×C₄	1	2	yes	—
149	C₃⋊#168	—	2	2	no	—
150	C₃×#168	C₂²×C₄	1	2	yes	—
151	C₃×#168	C₂²×C₄	1	2	yes	—
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×#235	—	5	1	no	—
156	C₂×#235	C₂×D₅	1	1	yes	characteristic
157	C₂²×C₃×C₈	—	5	1	no	—
158	C₂²×C₃×C₈	—	5	1	no	—
159	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
160	C₂×#208	—	5	1	no	—
161	C₂×#208	C₂×D₅	1	1	yes	characteristic
162	C₂×Dic₁₂	—	5	1	no	—
163	#904	—	5	4	no	—
164	#904	—	5	4	no	—
165	C₂×D₂₄	—	5	1	no	—
166	C₂×#204	—	5	1	no	—
167	C₂×#204	—	5	1	no	—
168	#901	—	5	4	no	—
169	#901	—	5	4	no	—
170	#901	—	10	2	no	—
171	#901	—	10	2	no	—
172	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
173	C₂×ΓL(1,𝔽₂₅)	—	10	1	no	—
174	C₂×D₃×C₈	—	10	1	no	—
175	C₂×D₃×C₈	—	10	1	no	—
176	C₃×C₄×C₈	—	5	4	no	—
177	#819	—	5	4	no	—
178	#805	—	5	4	no	—
179	#805	C₂×D₅	1	4	yes	complemented
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	—	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	—	2	1	no	—
202	C₄²×C₅	C₂²×D₃	1	2	yes	—
203	#689	—	3	4	no	—
204	#688	—	3	4	no	—
205	#687	—	3	4	no	—
206	#686	—	3	4	no	—
207	#681	—	3	2	no	—
208	#681	—	6	1	no	—
209	#681	—	6	4	no	—
210	C₂×#168	—	6	1	no	—
211	C₂×#168	—	6	4	no	—
212	C₂×#168	C₄×D₃	1	2	yes	—
213	C₂×#168	C₄×D₃	1	1	yes	characteristic
214	C₂×#168	C₄×D₃	1	1	yes	characteristic
215	C₂×#168	D₁₂	1	1	yes	characteristic
216	C₂×#168	D₁₂	1	1	yes	characteristic
217	C₂×#168	D₁₂	1	2	yes	—
218	C₂×#168	C₂²×D₃	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	—	15	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	—	5	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×D₁₅	—	2	2	no	—
235	C₂×D₁₅	—	4	2	no	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	4	2	no	—
238	C₃×C₄×C₅	—	2	4	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	2	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
247	C₂×#67	—	2	1	no	—
248	C₂×#67	—	10	1	no	—
249	#235	—	2	1	no	—
250	#235	—	2	1	no	—
251	#235	—	5	2	no	—
252	#235	—	5	2	no	—
253	#235	—	10	1	no	—
254	#235	—	10	1	no	—
255	#235	C₄×D₅	1	2	yes	—
256	#235	C₂²×D₅	1	2	yes	—
257	C₂×D₁₂	—	5	1	no	—
258	C₂×D₁₂	C₄×D₅	1	1	yes	characteristic
259	C₂×C₄×D₃	—	2	1	no	—
260	C₂×C₄×D₃	—	10	1	no	—
261	C₂×Dic₆	—	5	1	no	—
262	C₂×Dic₆	C₄×D₅	1	1	yes	characteristic
263	C₂×C₃×C₈	—	5	1	no	—
264	C₂×C₃×C₈	—	5	1	no	—
265	C₂×C₃×C₈	—	5	2	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	—	5	2	no	—
271	C₃×C₄²	—	2	1	no	—
272	C₃×C₄²	C₂²×D₅	1	2	yes	—
273	#208	—	2	1	no	—
274	#208	—	5	2	no	—
275	#208	—	10	1	no	—
276	#208	C₂²×D₅	1	2	yes	—
277	C₂×C₃⋊C₈	—	2	1	no	—
278	C₂×C₃⋊C₈	—	10	1	no	—
279	Dic₁₂	—	5	4	no	—
280	D₂₄	—	5	4	no	—
281	#204	—	5	4	no	—
282	#204	—	5	4	no	—
283	ΓL(1,𝔽₂₅)	—	10	4	no	—
284	ΓL(1,𝔽₂₅)	—	10	4	no	—
285	D₃×C₈	—	10	4	no	—
286	D₃×C₈	—	10	4	no	—
287	C₂³×C₅	—	6	1	no	—
288	C₂³×C₅	#235	1	1	yes	characteristic
289	C₂²×D₅	—	6	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	—	2	4	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	2	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	C₂×D₁₂	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
305	C₂×C₄×C₅	#235	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	—	6	2	no	—
318	#168	C₂×C₄×D₃	1	2	yes	—
319	#168	C₂×C₄×D₃	1	2	yes	—
320	#168	C₂×D₁₂	1	2	yes	—
321	#168	C₂×D₁₂	1	2	yes	—
322	C₂×#41	—	3	1	no	—
323	C₂×#41	—	15	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	—	15	4	no	—
331	#131	—	15	4	no	—
332	#131	—	30	2	no	—
333	#131	—	30	2	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	15	1	no	—
336	C₂×M₁₆	—	30	1	no	—
337	C₂×M₁₆	—	30	1	no	—
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	30	1	no	—
341	C₂²×C₈	—	30	1	no	—
342	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
343	#108	—	15	4	no	—
344	#104	—	3	4	no	—
345	#104	—	15	4	no	—
346	C₄×C₈	—	5	4	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	#443	1	2	yes	complemented
350	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
351	D₁₅	—	4	2	no	—
352	C₅×D₃	—	4	2	no	—
353	C₂³×C₃	#711	1	1	yes	characteristic
354	C₂²×D₃	—	2	1	no	—
355	C₂²×D₃	—	10	1	no	—
356	C₂×C₃×C₄	—	2	4	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
360	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
361	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
362	C₂×C₃×C₄	#711	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
364	#67	—	2	2	no	—
365	#67	—	2	2	no	—
366	#67	—	10	2	no	—
367	#67	—	10	2	no	—
368	C₂×Dic₃	—	2	1	no	—
369	C₂×Dic₃	—	10	1	no	—
370	D₁₂	—	2	1	no	—
371	D₁₂	—	5	2	no	—
372	D₁₂	—	10	1	no	—
373	D₁₂	C₂×C₄×D₅	1	2	yes	—
374	C₄×D₃	—	2	2	no	—
375	C₄×D₃	—	2	2	no	—
376	C₄×D₃	—	10	2	no	—
377	C₄×D₃	—	10	2	no	—
378	Dic₆	—	2	1	no	—
379	Dic₆	—	5	2	no	—
380	Dic₆	—	10	1	no	—
381	Dic₆	C₂×C₄×D₅	1	2	yes	—
382	C₃×C₈	—	5	2	no	—
383	C₃×C₈	—	5	2	no	—
384	C₃×C₈	—	5	2	no	—
385	C₃×C₈	—	5	2	no	—
386	C₃⋊C₈	—	2	2	no	—
387	C₃⋊C₈	—	10	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	6	2	no	—
390	C₂²×C₅	—	12	2	no	—
391	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
392	C₂²×C₅	C₄×D₁₂	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	4	no	—
397	C₄×C₅	—	6	2	no	—
398	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
399	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
400	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
401	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
402	Dic₅	—	6	2	no	—
403	#41	—	3	2	no	—
404	#41	—	3	2	no	—
405	#41	—	6	1	no	—
406	#41	—	6	1	no	—
407	#41	—	15	2	no	—
408	#41	—	15	2	no	—
409	#41	—	30	1	no	—
410	#41	—	30	1	no	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	—	15	1	no	—
413	C₂×D₄	—	3	1	no	—
414	C₂×D₄	—	6	1	no	—
415	C₂×D₄	—	15	1	no	—
416	C₂×D₄	—	30	1	no	—
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	—	6	1	no	—
427	M₁₆	—	15	2	no	—
428	M₁₆	—	30	4	no	—
429	M₁₆	—	30	4	no	—
430	M₁₆	—	30	1	no	—
431	C₂×C₈	—	5	1	no	—
432	C₂×C₈	—	5	1	no	—
433	C₂×C₈	—	5	2	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	—	5	1	no	—
436	C₂×C₈	—	5	1	no	—
437	C₂×C₈	—	5	2	no	—
438	C₂×C₈	—	5	2	no	—
439	C₂×C₈	—	6	1	no	—
440	C₂×C₈	—	30	4	no	—
441	C₂×C₈	—	30	4	no	—
442	C₂×C₈	—	30	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	C₂×D₃×D₅	1	2	yes	—
445	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	#4027	1	1	yes	characteristic
448	C₂²×C₃	#4027	1	1	yes	characteristic
449	C₂²×C₃	C₂×#711	1	1	yes	characteristic
450	C₂×D₃	—	2	2	no	—
451	C₂×D₃	—	4	2	no	—
452	C₂×D₃	—	10	2	no	—
453	C₂×D₃	—	20	2	no	—
454	C₃×C₄	—	2	4	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	2	no	—
460	Dic₃	—	10	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	12	2	no	—
464	C₂×C₅	#4700	1	2	yes	complemented
465	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
466	D₅	—	12	2	no	—
467	C₂³	—	6	1	no	—
468	C₂³	—	30	1	no	—
469	C₂³	#6782	1	1	yes	characteristic
470	Q₈	—	3	2	no	—
471	Q₈	—	6	1	no	—
472	Q₈	—	15	2	no	—
473	Q₈	—	30	1	no	—
474	D₄	—	3	2	no	—
475	D₄	—	6	2	no	—
476	D₄	—	6	2	no	—
477	D₄	—	6	1	no	—
478	D₄	—	15	2	no	—
479	D₄	—	30	2	no	—
480	D₄	—	30	2	no	—
481	D₄	—	30	1	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	6	1	no	—
485	C₂×C₄	—	6	2	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	C₄×D₃×D₅	1	1	yes	characteristic
491	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
492	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
493	C₂×C₄	D₅×D₁₂	1	1	yes	characteristic
494	C₂×C₄	#6782	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	—	5	2	no	—
499	C₈	—	5	2	no	—
500	C₈	—	6	2	no	—
501	C₈	—	30	2	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	#65113	1	2	yes	complemented
505	C₂×C₃	C₂×#4027	1	1	yes	characteristic
506	D₃	—	4	2	no	—
507	D₃	—	20	2	no	—
508	C₅	C₂×#4700	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	6	2	no	—
511	C₂²	—	12	2	no	—
512	C₂²	—	30	2	no	—
513	C₂²	—	60	2	no	—
514	C₂²	#91405	1	1	yes	characteristic
515	C₂²	#91405	1	1	yes	characteristic
516	C₂²	C₂×#6782	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	6	2	no	—
519	C₄	—	30	2	no	—
520	C₄	#91405	1	1	yes	characteristic
521	C₄	#91405	1	1	yes	characteristic
522	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
523	C₄	C₂×D₅×D₁₂	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	—	12	2	no	—
528	C₂	—	60	2	no	—
529	C₂	#11747018	1	2	yes	direct product factor
530	C₂	C₂×#91405	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅×D₁₂
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×#91303	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₂×#443
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#91290	C₂	semidirect
3. C₂×#91286	C₂	semidirect
4. C₂×#91089	C₂	semidirect
5. C₂×C₅×#805	C₂	semidirect
6. C₂×C₃×C₄×#168	C₂	semidirect
7. C₂×#90991	C₂	semidirect
8. #11747018	C₂	direct (N × H)
17. C₂×#6663	C₄	semidirect
18. C₂×#6660	C₄	semidirect
19. C₂×#6659	C₄	semidirect
20. #91303	C₄	semidirect
22. C₂×#6654	C₄	semidirect
26. #91290	C₂²	semidirect
29. #91286	C₂²	semidirect
31. #91089	C₂²	semidirect
32. C₅×#805	C₂²	semidirect
33. C₃×C₄×#168	C₂²	semidirect
34. #90991	C₂²	semidirect
42. C₂×C₄×#168	D₃	semidirect
78. #6663	C₂×C₄	semidirect
79. #6660	C₂×C₄	semidirect
80. #6659	C₂×C₄	semidirect
81. #6654	C₂×C₄	semidirect
92. C₂×#805	D₅	semidirect
118. C₄×#168	C₂×D₃	semidirect
179. #805	C₂×D₅	semidirect
349. C₂×C₃×C₅	#443	semidirect
445. C₃×C₅	C₂×#443	semidirect
464. C₂×C₅	#4700	semidirect
504. C₂×C₃	#65113	semidirect
508. C₅	C₂×#4700	semidirect
524. C₃	C₂×#65113	semidirect
529. C₂	#11747018	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×#91303	2
C₂×#91290	2
C₂×#91286	2
C₂×#91089	2
C₂×C₅×#805	2
C₂×C₃×C₄×#168	2
C₂×#90991	2
#11747018	2
C₂×#65113	3
C₂×#4700	5

Subgroups — C2×#11747018 #14417880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11747018 #14417880