Subgroups — C₂×#11749432 #14417876

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×C₅×#950	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#91286	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91121	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749432	C₂	1	8	yes	maximal, direct product factor
6	C₂×#90993	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#90978	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#90951	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65485	—	3	1	no	maximal, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×C₅×#235	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₁₅	C₂²	1	1	yes	characteristic
13	C₂×#6710	C₂²	1	1	yes	characteristic
14	C₅×#950	C₄	1	4	yes	complemented
15	C₅×#950	C₂²	1	4	yes	—
16	C₂×C₅×#216	C₄	1	1	yes	characteristic, complemented
17	C₂×C₅×#215	C₄	1	1	yes	characteristic, complemented
18	C₂×C₅×#214	C₄	1	1	yes	characteristic, complemented
19	C₂×C₅×#213	C₄	1	1	yes	characteristic, complemented
20	C₂²×C₅×C₃⋊C₈	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×#6650	—	2	1	no	—
28	#91286	—	2	2	no	—
29	#91286	C₂²	1	4	yes	complemented
30	C₂×D₃×#168	—	2	1	no	—
31	#91121	C₂²	1	4	yes	complemented
32	#90993	C₂²	1	4	yes	complemented
33	#90978	C₂²	1	4	yes	complemented
34	#90951	C₂²	1	4	yes	complemented
35	C₂×#5144	—	5	1	no	maximal, Hall
36	C₂×C₅×#135	—	3	1	no	—
37	C₂×#4094	—	3	1	no	—
38	C₂×#4094	D₃	1	1	yes	characteristic, complemented
39	C₂×#3969	—	3	1	no	—
40	C₂×#3969	—	3	1	no	—
41	#65485	—	3	8	no	—
42	C₂×#3951	—	3	1	no	—
43	C₂×C₈×Dic₅	—	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	C₂²×Dic₁₅	—	2	1	no	—
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	C₄×Dic₁₅	—	2	1	no	—
63	C₄×Dic₁₅	C₂³	1	2	yes	—
64	#6710	—	2	1	no	—
65	#6710	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	—	2	1	no	—
67	C₅×#216	C₂×C₄	1	4	yes	complemented
68	C₅×#215	C₂×C₄	1	4	yes	complemented
69	C₅×#214	C₂×C₄	1	4	yes	complemented
70	C₅×#213	C₂×C₄	1	4	yes	complemented
71	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
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	#6650	—	2	4	no	—
85	D₃×#168	—	2	4	no	—
86	C₂×C₃×#131	—	5	1	no	—
87	C₂×#950	D₅	1	1	yes	characteristic
88	C₂×#901	—	5	1	no	—
89	C₂×#837	—	5	1	no	—
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	—	3	1	no	—
95	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
96	C₅×#135	—	3	4	no	—
97	C₅×#135	—	3	4	no	—
98	C₂×C₅×Q₁₆	—	3	1	no	—
99	C₂×C₅×SD₁₆	—	3	1	no	—
100	C₂×C₅×SD₁₆	—	3	1	no	—
101	C₂×C₅×D₈	—	3	1	no	—
102	C₂²×C₅×C₈	—	3	1	no	—
103	#4094	—	2	2	no	—
104	#4094	—	3	4	no	—
105	#4094	—	6	2	no	—
106	#4094	C₂×D₃	1	4	yes	complemented
107	C₂×C₄×Dic₅	—	3	1	no	—
108	C₂×#681	—	2	1	no	—
109	C₂×#681	—	3	1	no	—
110	C₂×#681	—	6	1	no	—
111	C₂×#681	C₂×D₃	1	1	yes	characteristic
112	C₂²×#168	—	2	1	no	—
113	C₂²×#168	—	6	1	no	—
114	C₂²×#168	C₂×D₃	1	1	yes	characteristic
115	#3969	—	3	4	no	—
116	#3969	—	3	4	no	—
117	#3951	—	3	4	no	—
118	C₈×Dic₅	—	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×C₅×D₃	—	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	C₂×Dic₁₅	—	2	4	no	—
139	C₂×Dic₁₅	—	2	2	no	—
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	—	2	2	no	—
151	C₃×#168	C₂×D₄	1	2	yes	—
152	C₃×#168	C₂×D₄	1	2	yes	—
153	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
154	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
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	—	5	1	no	—
162	C₂²×C₃×C₈	—	10	1	no	—
163	#950	Dic₅	1	4	yes	complemented
164	#950	C₂×D₅	1	4	yes	—
165	C₂×#216	Dic₅	1	1	yes	characteristic, complemented
166	C₂×#215	Dic₅	1	1	yes	characteristic, complemented
167	C₂×#214	Dic₅	1	1	yes	characteristic, complemented
168	C₂×#213	Dic₅	1	1	yes	characteristic, complemented
169	C₂×C₄×Dic₃	—	5	1	no	—
170	C₂×#208	—	5	1	no	—
171	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
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	C₈×Dic₃	—	5	4	no	—
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	3	2	no	—
183	C₅×#41	—	3	2	no	—
184	C₅×#41	—	6	1	no	—
185	C₅×#41	—	6	1	no	—
186	C₅×#41	C₄×D₃	1	2	yes	—
187	C₅×#41	C₂²×D₃	1	2	yes	—
188	C₂×C₅×Q₈	—	3	1	no	—
189	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
190	C₂×C₅×D₄	—	2	1	no	—
191	C₂×C₅×D₄	—	3	1	no	—
192	C₂×C₅×D₄	—	6	1	no	—
193	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	—	2	1	no	—
195	C₂²×C₄×C₅	—	6	1	no	—
196	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₂²×Dic₅	—	6	1	no	—
198	C₅×Q₁₆	—	3	4	no	—
199	C₅×SD₁₆	—	3	4	no	—
200	C₅×SD₁₆	—	3	4	no	—
201	C₅×D₈	—	3	4	no	—
202	C₂×C₅×C₈	—	3	1	no	—
203	C₂×C₅×C₈	—	3	1	no	—
204	C₂×C₅×C₈	—	3	2	no	—
205	C₂×C₅×C₈	—	3	2	no	—
206	C₄×Dic₅	—	3	2	no	—
207	C₄×Dic₅	—	6	1	no	—
208	#681	—	2	1	no	—
209	#681	—	2	4	no	—
210	#681	—	3	2	no	—
211	#681	—	6	1	no	—
212	#681	—	6	4	no	—
213	#681	C₂²×D₃	1	2	yes	—
214	C₂×#168	—	2	1	no	—
215	C₂×#168	—	2	4	no	—
216	C₂×#168	—	6	1	no	—
217	C₂×#168	—	6	4	no	—
218	C₂×#168	#67	1	1	yes	characteristic
219	C₂×#168	#67	1	1	yes	characteristic
220	C₂×#168	#67	1	2	yes	—
221	C₂×#168	C₂²×D₃	1	2	yes	—
222	C₂×#135	—	3	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	—	15	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×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	—	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	4	no	—
244	C₅×Dic₃	—	2	2	no	—
245	C₃×#41	—	2	1	no	—
246	C₃×#41	—	2	1	no	—
247	C₃×#41	C₂×Dic₅	1	2	yes	—
248	C₃×#41	C₂²×D₅	1	2	yes	—
249	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
250	C₂×C₃×D₄	—	2	1	no	—
251	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	—	2	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	C₂×Dic₅	1	2	yes	—
259	#235	C₂²×D₅	1	2	yes	—
260	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
261	C₂×C₄×D₃	—	2	1	no	—
262	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
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	C₂×Dic₅	1	4	yes	complemented
273	#215	C₂×Dic₅	1	4	yes	complemented
274	#214	C₂×Dic₅	1	4	yes	complemented
275	#213	C₂×Dic₅	1	4	yes	complemented
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	—	10	1	no	—
281	C₂×C₃⋊C₈	C₂×Dic₅	1	1	yes	characteristic
282	C₂×C₃⋊C₈	C₂×Dic₅	1	1	yes	characteristic
283	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
284	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
285	ΓL(1,𝔽₂₅)	—	10	4	no	—
286	D₃×C₈	—	10	4	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	—	6	1	no	—
289	C₂³×C₅	#235	1	1	yes	characteristic
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	—	3	2	no	—
292	C₅×Q₈	—	6	1	no	—
293	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	1	no	—
297	C₅×D₄	—	3	2	no	—
298	C₅×D₄	—	6	2	no	—
299	C₅×D₄	—	6	2	no	—
300	C₅×D₄	—	6	1	no	—
301	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	6	1	no	—
306	C₂×C₄×C₅	—	6	2	no	—
307	C₂×C₄×C₅	—	6	2	no	—
308	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
310	C₂×C₄×C₅	#235	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
314	C₂×Dic₅	—	6	4	no	—
315	C₂×Dic₅	—	6	2	no	—
316	C₅×C₈	—	3	2	no	—
317	C₅×C₈	—	3	2	no	—
318	#168	—	2	2	no	—
319	#168	—	6	2	no	—
320	#168	C₂×#67	1	2	yes	—
321	#168	C₂×#67	1	2	yes	—
322	C₂×#41	—	3	1	no	—
323	C₂×#41	D₃×D₅	1	1	yes	characteristic
324	#135	—	3	4	no	—
325	#135	—	3	4	no	—
326	C₂×Q₁₆	—	3	1	no	—
327	C₂×SD₁₆	—	3	1	no	—
328	C₂×SD₁₆	—	3	1	no	—
329	C₂×D₈	—	3	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	—	5	1	no	—
335	C₂×M₁₆	—	10	1	no	—
336	C₂×M₁₆	—	15	1	no	—
337	C₂×M₁₆	—	30	1	no	—
338	C₂²×C₈	—	3	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	10	1	no	—
341	C₂²×C₈	—	30	1	no	—
342	C₂×C₄²	—	15	1	no	—
343	#108	—	15	4	no	—
344	#104	—	15	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	C₅×D₃	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	#711	1	1	yes	characteristic
355	C₂²×D₃	—	2	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	C₂²×Dic₅	1	2	yes	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	C₂²×Dic₅	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	D₄×D₅	1	1	yes	characteristic
366	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
367	C₂×C₃×C₄	#711	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂²×Dic₅	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	4	no	—
375	C₂×Dic₃	—	10	2	no	—
376	D₁₂	—	2	1	no	—
377	D₁₂	C₂²×Dic₅	1	2	yes	—
378	C₄×D₃	—	2	2	no	—
379	C₄×D₃	—	2	2	no	—
380	Dic₆	—	2	1	no	—
381	Dic₆	C₂²×Dic₅	1	2	yes	—
382	C₃×C₈	—	5	2	no	—
383	C₃×C₈	—	5	2	no	—
384	C₃×C₈	—	10	2	no	—
385	C₃⋊C₈	—	10	2	no	—
386	C₃⋊C₈	C₂²×Dic₅	1	2	yes	—
387	C₃⋊C₈	C₂²×Dic₅	1	2	yes	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	6	2	no	—
392	C₂²×C₅	—	12	2	no	—
393	C₂²×C₅	C₄×#67	1	1	yes	characteristic
394	C₂²×C₅	C₄×#67	1	1	yes	characteristic
395	C₂²×C₅	C₂×#235	1	1	yes	characteristic
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	6	2	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	4	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	3	2	no	—
406	#41	—	3	2	no	—
407	#41	—	6	1	no	—
408	#41	—	6	1	no	—
409	#41	D₃×Dic₅	1	2	yes	—
410	#41	C₂×D₃×D₅	1	2	yes	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	3	1	no	—
415	C₂×D₄	—	6	1	no	—
416	C₂×D₄	D₃×Dic₅	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	—	3	4	no	—
422	SD₁₆	—	3	4	no	—
423	SD₁₆	—	3	4	no	—
424	D₈	—	3	4	no	—
425	M₁₆	—	5	2	no	—
426	M₁₆	—	10	4	no	—
427	M₁₆	—	10	1	no	—
428	M₁₆	—	15	2	no	—
429	M₁₆	—	30	4	no	—
430	M₁₆	—	30	1	no	—
431	C₂×C₈	—	3	1	no	—
432	C₂×C₈	—	3	1	no	—
433	C₂×C₈	—	3	2	no	—
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	—	5	2	no	—
436	C₂×C₈	—	5	1	no	—
437	C₂×C₈	—	5	1	no	—
438	C₂×C₈	—	5	2	no	—
439	C₂×C₈	—	10	4	no	—
440	C₂×C₈	—	10	1	no	—
441	C₂×C₈	—	30	4	no	—
442	C₂×C₈	—	30	1	no	—
443	C₄²	—	15	2	no	—
444	C₄²	—	30	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	D₄×Dic₅	1	1	yes	characteristic
450	C₂²×C₃	D₄×Dic₅	1	1	yes	characteristic
451	C₂²×C₃	C₂×#711	1	1	yes	characteristic
452	C₂×D₃	—	2	2	no	—
453	C₂×D₃	—	4	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
456	C₃×C₄	D₄×Dic₅	1	1	yes	characteristic
457	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
458	C₃×C₄	C₂³×Dic₅	1	1	yes	characteristic
459	Dic₃	—	2	2	no	—
460	Dic₃	—	10	4	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	—	12	2	no	—
465	C₂×C₅	#5144	1	2	yes	complemented
466	C₂×C₅	C₂×C₄×#67	1	1	yes	characteristic
467	C₂³	—	2	1	no	—
468	C₂³	—	6	1	no	—
469	C₂³	#6782	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	3	2	no	—
472	Q₈	—	6	1	no	—
473	Q₈	C₂×D₃×Dic₅	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	3	2	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	6	1	no	—
481	D₄	C₂×D₃×Dic₅	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	1	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	—	30	4	no	—
489	C₂×C₄	—	30	2	no	—
490	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
491	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
492	C₂×C₄	#6782	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	—	3	2	no	—
497	C₈	—	3	2	no	—
498	C₈	—	5	2	no	—
499	C₈	—	5	2	no	—
500	C₈	—	10	2	no	—
501	C₈	—	30	2	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	#65485	1	2	yes	complemented
506	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
507	D₃	—	4	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	—	6	2	no	—
513	C₂²	—	12	2	no	—
514	C₂²	Dic₅×#67	1	1	yes	characteristic
515	C₂²	Dic₅×#67	1	1	yes	characteristic
516	C₂²	C₂×#6782	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	6	2	no	—
519	C₄	—	30	4	no	—
520	C₄	Dic₅×#67	1	1	yes	characteristic
521	C₄	Dic₅×#67	1	1	yes	characteristic
522	C₄	C₂²×D₃×Dic₅	1	1	yes	characteristic
523	C₄	C₂×D₅×#67	1	1	yes	characteristic
524	C₃	C₂×#65485	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	4	2	no	—
528	C₂	—	12	2	no	—
529	C₂	#11749432	1	2	yes	direct product factor
530	C₂	C₂×Dic₅×#67	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×C₅×#950	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×#91286	C₂	semidirect
4. C₂×#91121	C₂	semidirect
5. #11749432	C₂	direct (N × H)
6. C₂×#90993	C₂	semidirect
7. C₂×#90978	C₂	semidirect
8. C₂×#90951	C₂	semidirect
14. C₅×#950	C₄	semidirect
16. C₂×C₅×#216	C₄	semidirect
17. C₂×C₅×#215	C₄	semidirect
18. C₂×C₅×#214	C₄	semidirect
19. C₂×C₅×#213	C₄	semidirect
22. C₃×#4094	C₂²	semidirect
29. #91286	C₂²	semidirect
31. #91121	C₂²	semidirect
32. #90993	C₂²	semidirect
33. #90978	C₂²	semidirect
34. #90951	C₂²	semidirect
38. C₂×#4094	D₃	semidirect
67. C₅×#216	C₂×C₄	semidirect
68. C₅×#215	C₂×C₄	semidirect
69. C₅×#214	C₂×C₄	semidirect
70. C₅×#213	C₂×C₄	semidirect
106. #4094	C₂×D₃	semidirect
163. #950	Dic₅	semidirect
165. C₂×#216	Dic₅	semidirect
166. C₂×#215	Dic₅	semidirect
167. C₂×#214	Dic₅	semidirect
168. C₂×#213	Dic₅	semidirect
272. #216	C₂×Dic₅	semidirect
273. #215	C₂×Dic₅	semidirect
274. #214	C₂×Dic₅	semidirect
275. #213	C₂×Dic₅	semidirect
350. C₂×C₃×C₅	#443	semidirect
445. C₃×C₅	C₂×#443	semidirect
465. C₂×C₅	#5144	semidirect
505. C₂×C₃	#65485	semidirect
508. C₅	C₂×#5144	semidirect
524. C₃	C₂×#65485	semidirect
529. C₂	#11749432	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×#950	2
C₂×C₃×#4094	2
C₂×#91286	2
C₂×#91121	2
#11749432	2
C₂×#90993	2
C₂×#90978	2
C₂×#90951	2
C₂×#65485	3
C₂×#5144	5

Subgroups — C2×#11749432 #14417876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11749432 #14417876