Subgroups — #12068618

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10611071	C₂	1	1	yes	maximal, characteristic
2	#10611024	C₂	1	1	yes	maximal, characteristic
3	#10611009	C₂	1	1	yes	maximal, characteristic
4	C₅×#1572	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601588	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601542	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601539	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599367	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599367	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599364	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599361	C₂	1	1	yes	maximal, characteristic, complemented
12	#10599326	C₂	1	1	yes	maximal, characteristic, complemented
13	#10599325	C₂	1	1	yes	maximal, characteristic, complemented
14	#10599323	C₂	1	1	yes	maximal, characteristic, complemented
15	D₅×#334	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#709	C₂²	1	1	yes	characteristic
17	C₅×#432	C₂²	1	1	yes	characteristic
18	C₅×#431	C₂²	1	1	yes	characteristic
19	C₅×#431	C₂²	1	1	yes	characteristic
20	#65213	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#168	C₂²	1	1	yes	characteristic
22	C₄×#681	C₂²	1	1	yes	characteristic
23	#65126	C₂²	1	1	yes	characteristic
24	#65125	C₄	1	1	yes	characteristic
25	#65125	C₄	1	1	yes	characteristic
26	#65124	C₂²	1	1	yes	characteristic
27	#65124	C₂²	1	1	yes	characteristic
28	#65124	C₂²	1	1	yes	characteristic
29	#65122	C₂²	1	1	yes	characteristic
30	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	#65117	C₄	1	1	yes	characteristic
34	#65117	C₄	1	1	yes	characteristic
35	#65019	—	2	1	no	—
36	#65018	C₄	1	1	yes	characteristic
37	#65018	C₄	1	1	yes	characteristic
38	#65017	—	2	1	no	—
39	#65017	—	2	1	no	—
40	#65017	C₄	1	1	yes	characteristic
41	#65017	C₄	1	1	yes	characteristic
42	#65014	—	2	1	no	—
43	#64995	—	2	1	no	—
44	#64990	—	2	1	no	—
45	C₄×#676	C₂²	1	1	yes	characteristic
46	C₈×D₂₀	—	2	1	no	—
47	#64974	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
50	#64968	—	2	1	no	—
51	C₅×#335	C₂²	1	1	yes	characteristic
52	C₅×#335	C₂²	1	1	yes	characteristic
53	C₅×#334	C₂²	1	1	yes	characteristic
54	C₅×#334	C₂²	1	1	yes	characteristic
55	#64700	C₂²	1	1	yes	characteristic
56	#64700	C₂²	1	1	yes	characteristic
57	#64700	C₂²	1	1	yes	characteristic
58	#64700	C₂²	1	1	yes	characteristic
59	#64699	C₂²	1	1	yes	characteristic
60	#64699	C₂²	1	1	yes	characteristic
61	#64699	C₂²	1	1	yes	characteristic
62	#64699	C₂²	1	1	yes	characteristic
63	#64677	C₂²	1	1	yes	characteristic
64	#64677	C₂²	1	1	yes	characteristic
65	#64677	C₂²	1	1	yes	characteristic
66	#64677	C₂²	1	1	yes	characteristic
67	#17838	—	5	1	no	maximal, Sylow
68	C₂×#709	Q₈	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₅	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
73	C₄×C₂²⋊D₅	D₄	1	1	yes	characteristic
74	#4072	Q₈	1	1	yes	characteristic
75	C₂×#681	—	2	1	no	—
76	C₂×#681	C₂×C₄	1	1	yes	characteristic
77	C₂×#681	C₂×C₄	1	1	yes	characteristic
78	C₂²×#168	—	2	1	no	—
79	C₂×#676	—	2	1	no	—
80	C₂×#676	C₂×C₄	1	1	yes	characteristic
81	C₂×#676	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₅	—	2	1	no	—
83	C₂×C₈×D₅	—	2	1	no	—
84	C₂×C₈×D₅	—	2	1	no	—
85	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
86	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
87	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₀	D₄	1	1	yes	characteristic
89	#4018	Q₈	1	1	yes	characteristic
90	#4018	Q₈	1	1	yes	characteristic
91	C₄²×D₅	C₂³	1	1	yes	characteristic
92	C₄²×D₅	C₂³	1	1	yes	characteristic
93	C₄×Dic₁₀	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₁₀	D₄	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
99	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
104	C₅×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
105	C₅×#97	—	2	1	no	—
106	C₄×C₅×C₈	—	2	1	no	—
107	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
109	#3952	—	2	1	no	—
110	#3952	—	2	1	no	—
111	#3952	—	2	1	no	—
112	#3952	—	2	1	no	—
113	#3952	C₂×C₄	1	1	yes	characteristic
114	#3952	C₂×C₄	1	1	yes	characteristic
115	#3952	C₂×C₄	1	1	yes	characteristic
116	#3952	C₂×C₄	1	1	yes	characteristic
117	#3947	—	2	1	no	—
118	#3947	—	2	1	no	—
119	#3947	—	2	1	no	—
120	#3947	C₂×C₄	1	1	yes	characteristic
121	#3947	C₂×C₄	1	1	yes	characteristic
122	#3946	—	2	1	no	—
123	#3946	—	2	1	no	—
124	#3946	—	2	1	no	—
125	#3946	—	2	1	no	—
126	#3946	C₂×C₄	1	1	yes	characteristic
127	#3946	C₂×C₄	1	1	yes	characteristic
128	#3946	C₂×C₄	1	1	yes	characteristic
129	#3946	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₅	—	2	1	no	—
131	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic
133	C₄⋊#168	—	2	1	no	—
134	C₄⋊#168	—	2	1	no	—
135	C₄⋊#168	C₂³	1	1	yes	characteristic
136	C₄⋊#168	C₂³	1	1	yes	characteristic
137	C₄⋊#168	C₂³	1	1	yes	characteristic
138	C₄⋊#168	C₂³	1	1	yes	characteristic
139	#3935	C₂×C₄	1	1	yes	characteristic
140	#3935	C₂×C₄	1	1	yes	characteristic
141	C₄×#168	C₂³	1	1	yes	characteristic
142	C₄×#168	C₂³	1	1	yes	characteristic
143	#2990	—	5	1	no	—
144	#2990	—	5	1	no	—
145	#2965	—	5	1	no	—
146	#1573	—	5	1	no	—
147	#1573	—	5	1	no	—
148	#1572	—	5	1	no	—
149	#1572	D₅	1	1	yes	characteristic, complemented
150	#1570	—	5	1	no	—
151	#1570	—	5	1	no	—
152	#1569	—	5	1	no	—
153	#1569	—	5	1	no	—
154	#1568	—	5	1	no	—
155	#1565	—	5	1	no	—
156	#1565	—	5	1	no	—
157	C₂×#334	—	5	1	no	—
158	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
161	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₂²⋊D₅	C₄⋊C₄	1	1	yes	characteristic
163	#709	—	4	2	no	—
164	C₂×D₂₀	C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
171	C₂×Dic₁₀	C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₅×C₈	—	2	1	no	—
173	C₂×C₅×C₈	—	2	1	no	—
174	C₂×C₅×C₈	—	2	1	no	—
175	C₂×C₅×C₈	—	2	1	no	—
176	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
183	C₄²×C₅	C₂⁴	1	1	yes	characteristic
184	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
185	C₂²⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
186	#685	C₄⋊C₄	1	1	yes	characteristic
187	#685	C₄⋊C₄	1	1	yes	characteristic
188	#685	C₄⋊C₄	1	1	yes	characteristic
189	#685	C₄⋊C₄	1	1	yes	characteristic
190	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
191	C₄⋊Dic₅	C₄⋊C₄	1	1	yes	characteristic
192	#683	C₄⋊C₄	1	1	yes	characteristic
193	#683	C₄⋊C₄	1	1	yes	characteristic
194	#683	C₄⋊C₄	1	1	yes	characteristic
195	#683	C₄⋊C₄	1	1	yes	characteristic
196	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
198	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
199	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
200	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
201	C₄×Dic₅	C₂×Q₈	1	1	yes	characteristic
202	#681	—	2	2	no	—
203	#681	—	4	1	no	—
204	#681	—	8	1	no	—
205	C₂×#168	—	2	1	no	—
206	C₂×#168	—	2	1	no	—
207	C₂×#168	—	2	1	no	—
208	C₂×#168	—	2	1	no	—
209	C₂×#168	—	8	1	no	—
210	C₂×#168	C₂²×C₄	1	1	yes	characteristic
211	C₂×#168	C₂²×C₄	1	1	yes	characteristic
212	C₂×#168	C₂²×C₄	1	1	yes	characteristic
213	C₂×#168	C₂²×C₄	1	1	yes	characteristic
214	#676	—	2	2	no	—
215	#676	—	4	1	no	—
216	#676	—	8	1	no	—
217	C₈×D₅	—	2	2	no	—
218	C₈×D₅	—	4	1	no	—
219	C₈×D₅	—	8	1	no	—
220	C₈×D₅	—	8	1	no	—
221	C₈×D₅	—	8	1	no	—
222	C₄×#41	—	5	1	no	—
223	#446	—	5	1	no	—
224	#446	—	5	1	no	—
225	#446	—	10	1	no	—
226	#446	—	10	1	no	—
227	#436	—	5	1	no	—
228	#436	—	5	1	no	—
229	#435	—	5	1	no	—
230	#435	—	5	1	no	—
231	#435	—	5	1	no	—
232	#435	—	5	1	no	—
233	#435	—	10	1	no	—
234	#435	—	10	1	no	—
235	#435	—	10	1	no	—
236	#435	—	10	1	no	—
237	C₈×D₄	—	10	1	no	—
238	C₈×D₄	—	10	1	no	—
239	#432	—	5	1	no	—
240	#432	—	5	1	no	—
241	#432	—	5	1	no	—
242	#432	C₂×D₅	1	1	yes	characteristic
243	#431	—	5	1	no	—
244	#431	—	5	1	no	—
245	#431	—	5	1	no	—
246	#431	C₂×D₅	1	1	yes	characteristic
247	#431	C₂×D₅	1	1	yes	characteristic
248	#423	—	5	1	no	—
249	#423	—	5	1	no	—
250	C₂×C₄⋊C₈	—	5	1	no	—
251	C₂×C₄⋊C₈	—	5	1	no	—
252	C₂×C₄⋊C₈	—	5	1	no	—
253	C₂×C₄⋊C₈	—	5	1	no	—
254	C₄×M₁₆	—	5	1	no	—
255	C₄×M₁₆	—	5	1	no	—
256	C₂×C₄×C₈	—	5	1	no	—
257	#335	—	5	1	no	—
258	#335	—	5	1	no	—
259	#335	—	5	1	no	—
260	#335	—	5	1	no	—
261	#335	C₂×D₅	1	1	yes	characteristic
262	#335	C₂×D₅	1	1	yes	characteristic
263	#334	—	5	1	no	—
264	#334	—	5	1	no	—
265	#334	—	5	1	no	—
266	#334	—	5	1	no	—
267	#334	—	5	1	no	—
268	#334	—	5	1	no	—
269	#334	—	5	1	no	—
270	#334	—	5	1	no	—
271	#334	C₂×D₅	1	1	yes	characteristic
272	#334	C₂×D₅	1	1	yes	characteristic
273	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₂²×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	—	2	1	no	—
277	C₂×C₄×C₅	—	2	1	no	—
278	C₂×C₄×C₅	—	2	1	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
287	C₂²⋊D₅	—	2	2	no	—
288	C₂²⋊D₅	—	4	1	no	—
289	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
292	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
293	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
295	D₂₀	—	2	2	no	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	2	1	no	—
298	C₄×D₅	—	2	1	no	—
299	C₄×D₅	—	2	1	no	—
300	C₄×D₅	—	2	1	no	—
301	C₄×D₅	—	2	1	no	—
302	C₄×D₅	—	2	1	no	—
303	C₄×D₅	—	2	1	no	—
304	C₄×D₅	—	2	1	no	—
305	C₄×D₅	—	4	1	no	—
306	Dic₁₀	—	4	1	no	—
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	—	2	1	no	—
309	C₅×C₈	—	2	1	no	—
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	4	1	no	—
312	C₅×C₈	—	4	1	no	—
313	C₅×C₈	—	4	1	no	—
314	C₅×C₈	—	4	1	no	—
315	#168	—	2	1	no	—
316	#168	—	2	1	no	—
317	#168	—	2	1	no	—
318	#168	—	4	1	no	—
319	#168	—	4	1	no	—
320	#168	—	4	1	no	—
321	#168	—	4	1	no	—
322	#168	#131	1	2	yes	—
323	C₂×#41	—	5	1	no	—
324	C₂×M₁₆	—	5	1	no	—
325	C₂×M₁₆	—	5	1	no	—
326	C₂×M₁₆	—	5	1	no	—
327	C₂×M₁₆	—	5	1	no	—
328	C₂×M₁₆	—	10	1	no	—
329	C₂×M₁₆	—	10	1	no	—
330	C₂²×C₈	—	5	1	no	—
331	C₂²×C₈	—	5	1	no	—
332	C₂²×C₈	—	10	1	no	—
333	C₂²×C₈	—	10	1	no	—
334	C₂²×C₈	—	10	1	no	—
335	C₂²×C₈	—	10	1	no	—
336	C₄×Q₈	—	5	1	no	—
337	C₄×Q₈	—	5	1	no	—
338	C₄×D₄	—	5	1	no	—
339	C₄×D₄	—	5	1	no	—
340	C₄×D₄	—	5	1	no	—
341	C₄×D₄	—	5	1	no	—
342	C₄×D₄	—	5	1	no	—
343	C₄×D₄	—	5	1	no	—
344	#117	—	5	1	no	—
345	#117	—	5	1	no	—
346	#117	—	5	1	no	—
347	C₂×C₄²	—	5	1	no	—
348	C₂×C₄²	—	5	1	no	—
349	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
350	C₄⋊C₈	—	5	1	no	—
351	C₄⋊C₈	—	5	1	no	—
352	C₄⋊C₈	—	5	1	no	—
353	C₄⋊C₈	—	5	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	—	5	1	no	—
357	C₄⋊C₈	—	5	1	no	—
358	C₄⋊C₈	—	10	1	no	—
359	C₄⋊C₈	—	10	1	no	—
360	C₄⋊C₈	—	10	1	no	—
361	C₄⋊C₈	—	10	1	no	—
362	C₄⋊C₈	—	10	1	no	—
363	C₄⋊C₈	—	10	1	no	—
364	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
365	C₄⋊C₈	C₄×D₅	1	1	yes	characteristic
366	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
367	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
368	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
369	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
370	C₂²⋊C₈	—	2	1	no	—
371	C₂²⋊C₈	—	2	1	no	—
372	C₂²⋊C₈	—	5	1	no	—
373	C₂²⋊C₈	—	5	1	no	—
374	C₂²⋊C₈	—	5	1	no	—
375	C₂²⋊C₈	—	5	1	no	—
376	C₂²⋊C₈	—	10	1	no	—
377	C₂²⋊C₈	—	10	1	no	—
378	C₂²⋊C₈	—	10	1	no	—
379	C₂²⋊C₈	—	10	1	no	—
380	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
381	C₂²⋊C₈	C₄×D₅	1	1	yes	characteristic
382	#97	—	2	1	no	—
383	#97	—	5	1	no	—
384	#97	—	5	1	no	—
385	#97	—	5	1	no	—
386	#97	—	5	1	no	—
387	#97	—	10	1	no	—
388	#97	—	10	1	no	—
389	#97	—	10	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	—	5	1	no	—
392	C₄×C₈	—	5	1	no	—
393	C₄×C₈	—	5	1	no	—
394	C₄×C₈	—	5	1	no	—
395	C₄×C₈	—	10	1	no	—
396	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
402	C₂×D₅	—	2	1	no	—
403	C₂×D₅	—	2	1	no	—
404	C₂×D₅	—	2	1	no	—
405	C₂×D₅	—	2	1	no	—
406	C₂×D₅	—	2	1	no	—
407	C₂×D₅	#430	1	2	yes	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	C₂×#131	1	1	yes	characteristic
413	C₄×C₅	#568	1	1	yes	characteristic
414	C₄×C₅	#577	1	1	yes	characteristic
415	C₄×C₅	#577	1	1	yes	characteristic
416	Dic₅	—	2	1	no	—
417	Dic₅	—	2	1	no	—
418	Dic₅	—	2	1	no	—
419	Dic₅	—	2	1	no	—
420	Dic₅	—	2	1	no	—
421	Dic₅	—	2	1	no	—
422	#41	—	20	2	no	—
423	C₂×Q₈	—	5	1	no	—
424	C₂×D₄	—	5	1	no	—
425	C₂×D₄	—	5	1	no	—
426	C₂×D₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	5	1	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	C₂×C₄×D₅	1	1	yes	characteristic
434	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
435	C₂²×C₄	Q₈×D₅	1	1	yes	characteristic
436	M₁₆	—	10	2	no	—
437	M₁₆	—	10	2	no	—
438	M₁₆	—	20	1	no	—
439	M₁₆	—	20	1	no	—
440	M₁₆	—	40	1	no	—
441	M₁₆	—	40	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	5	1	no	—
447	C₂×C₈	—	5	1	no	—
448	C₂×C₈	—	5	1	no	—
449	C₂×C₈	—	5	1	no	—
450	C₂×C₈	—	10	2	no	—
451	C₂×C₈	—	10	1	no	—
452	C₂×C₈	—	10	1	no	—
453	C₂×C₈	—	10	1	no	—
454	C₂×C₈	—	10	1	no	—
455	C₂×C₈	—	20	1	no	—
456	C₂×C₈	—	40	1	no	—
457	C₂×C₈	—	40	1	no	—
458	C₂×C₈	—	40	1	no	—
459	C₂×C₈	—	40	1	no	—
460	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
461	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
462	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
463	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
464	C₄⋊C₄	—	5	1	no	—
465	C₄⋊C₄	—	5	1	no	—
466	C₄⋊C₄	—	5	1	no	—
467	C₄⋊C₄	—	5	1	no	—
468	C₄⋊C₄	—	5	1	no	—
469	C₄⋊C₄	—	5	1	no	—
470	C₂²⋊C₄	—	5	1	no	—
471	C₂²⋊C₄	—	5	1	no	—
472	C₂²⋊C₄	—	5	1	no	—
473	C₂²⋊C₄	—	5	1	no	—
474	C₂²⋊C₄	—	5	1	no	—
475	C₂²⋊C₄	—	5	1	no	—
476	C₄²	—	5	1	no	—
477	C₄²	—	5	1	no	—
478	C₄²	—	5	1	no	—
479	C₄²	—	5	1	no	—
480	C₄²	—	5	1	no	—
481	C₄²	—	5	1	no	—
482	C₄²	C₂×C₄×D₅	1	1	yes	characteristic
483	C₄²	D₄×D₅	1	1	yes	characteristic
484	C₄²	Q₈×D₅	1	1	yes	characteristic
485	C₄²	C₂³×D₅	1	1	yes	characteristic
486	C₂×C₅	—	4	1	no	—
487	C₂×C₅	#2906	1	1	yes	characteristic
488	C₂×C₅	#2912	1	1	yes	characteristic
489	C₂×C₅	C₂×#430	1	1	yes	characteristic
490	D₅	—	2	2	no	—
491	D₅	—	4	1	no	—
492	C₂³	—	5	1	no	—
493	C₂³	—	5	1	no	—
494	C₂³	D₅×C₄⋊C₄	1	1	yes	characteristic
495	Q₈	—	20	1	no	—
496	D₄	—	10	2	no	—
497	D₄	—	10	2	no	—
498	D₄	—	20	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	1	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	10	2	no	—
511	C₂×C₄	—	10	1	no	—
512	C₂×C₄	—	10	1	no	—
513	C₂×C₄	—	10	1	no	—
514	C₂×C₄	—	10	1	no	—
515	C₂×C₄	—	10	1	no	—
516	C₂×C₄	—	10	1	no	—
517	C₂×C₄	—	10	1	no	—
518	C₂×C₄	—	10	1	no	—
519	C₂×C₄	—	20	1	no	—
520	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
521	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
522	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
524	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
525	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
526	C₈	—	2	1	no	—
527	C₈	—	2	1	no	—
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	5	2	no	—
535	C₈	—	10	1	no	—
536	C₈	—	10	1	no	—
537	C₈	—	10	1	no	—
538	C₈	—	20	1	no	—
539	C₈	—	20	1	no	—
540	C₈	—	20	1	no	—
541	C₈	—	20	1	no	—
542	C₅	#17838	1	1	yes	characteristic, complemented, Sylow
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	5	2	no	—
547	C₂²	—	10	1	no	—
548	C₂²	—	10	1	no	—
549	C₂²	—	10	1	no	—
550	C₂²	—	10	1	no	—
551	C₂²	—	10	1	no	—
552	C₂²	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	10	1	no	—
558	C₄	—	10	1	no	—
559	C₄	—	10	1	no	—
560	C₄	—	10	1	no	—
561	C₄	—	10	1	no	—
562	C₄	—	10	1	no	—
563	C₄	D₅×#131	1	1	yes	characteristic
564	C₄	#66084	1	1	yes	characteristic
565	C₄	#66104	1	1	yes	characteristic
566	C₄	#66104	1	1	yes	characteristic
567	C₂	—	4	1	no	—
568	C₂	—	10	2	no	—
569	C₂	—	20	1	no	—
570	C₂	#10610812	1	1	yes	characteristic
571	C₂	#10610909	1	1	yes	characteristic
572	C₂	D₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1572	C₂
socle	C₂²×C₅	C₂²×C₄⋊C₄
prime radical	C₂×#709	Q₈
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1572	D₅
hypocenter	C₅	#17838
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1572

Complements

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

N	H ≅ G/N	type
4. C₅×#1572	C₂	semidirect
5. #10601588	C₂	semidirect
6. #10601542	C₂	semidirect
7. #10601539	C₂	semidirect
8. #10599367	C₂	semidirect
9. #10599367	C₂	semidirect
10. #10599364	C₂	semidirect
11. #10599361	C₂	semidirect
12. #10599326	C₂	semidirect
13. #10599325	C₂	semidirect
14. #10599323	C₂	semidirect
15. D₅×#334	C₂	semidirect
149. #1572	D₅	semidirect
542. C₅	#17838	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10611071	2
#10611024	2
#10611009	2
C₅×#1572	2
#10601588	2
#10601542	2
#10601539	2
#10599367	2
#10599364	2
#10599361	2
#10599326	2
#10599325	2
#10599323	2
D₅×#334	2
#17838	5