Subgroups — #28602598

Order 15104.

796 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433013	C₂	1	1	yes	maximal, characteristic, complemented
2	#21432956	C₂	1	1	yes	maximal, characteristic, complemented
3	#21425001	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424995	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424634	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424629	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424624	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424619	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424592	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424585	C₂	1	1	yes	maximal, characteristic, complemented
11	#21424578	C₂	1	1	yes	maximal, characteristic, complemented
12	#21424571	C₂	1	1	yes	maximal, characteristic, complemented
13	#21424220	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423851	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#3154	C₂	1	1	yes	maximal, characteristic
16	#16838169	C₂²	1	1	yes	characteristic
17	#16838169	C₂²	1	1	yes	characteristic
18	#16837880	C₂²	1	1	yes	characteristic
19	#16837877	C₂²	1	1	yes	characteristic
20	#16837524	—	2	2	no	—
21	#16837519	—	2	2	no	—
22	#16837503	—	2	2	no	—
23	SD₁₆×Dic₅₉	—	2	2	no	—
24	C₂×#14273663	C₂²	1	1	yes	characteristic
25	#16837440	C₂²	1	1	yes	characteristic
26	#16837419	C₂²	1	1	yes	characteristic
27	#16837419	C₂²	1	1	yes	characteristic
28	#16837419	C₂²	1	1	yes	characteristic
29	#16837419	C₂²	1	1	yes	characteristic
30	#16837411	C₂²	1	1	yes	characteristic
31	#16837411	C₂²	1	1	yes	characteristic
32	#16837407	C₂²	1	1	yes	characteristic
33	#16837407	C₂²	1	1	yes	characteristic
34	C₂×#14273646	C₂²	1	1	yes	characteristic
35	C₂×#14273644	C₂²	1	1	yes	characteristic
36	#16837376	C₂²	1	1	yes	characteristic
37	#16837376	C₂²	1	1	yes	characteristic
38	#16837357	C₂²	1	1	yes	characteristic
39	#16837357	C₂²	1	1	yes	characteristic
40	#16837173	C₂²	1	1	yes	characteristic
41	#16837173	C₂²	1	1	yes	characteristic
42	C₅₉⋊#338	C₂²	1	1	yes	characteristic
43	#16837159	C₂²	1	1	yes	characteristic
44	#16837158	C₂²	1	1	yes	characteristic
45	#16837158	C₂²	1	1	yes	characteristic
46	#16837158	C₂²	1	1	yes	characteristic
47	#16837158	C₂²	1	1	yes	characteristic
48	C₂×#137×C₅₉	C₂²	1	1	yes	characteristic
49	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	1	yes	characteristic
50	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
51	C₂²×SD₁₆×C₅₉	C₂²	1	1	yes	characteristic
52	C₅₉×#536	C₂²	1	1	yes	characteristic
53	C₅₉×#535	C₂²	1	1	yes	characteristic
54	C₅₉×#497	C₄	1	2	yes	complemented
55	C₅₉×#496	C₄	1	2	yes	complemented
56	C₅₉×#495	C₄	1	2	yes	complemented
57	C₅₉×#492	C₄	1	2	yes	complemented
58	C₅₉×#405	C₂²	1	1	yes	characteristic
59	#14273734	—	2	2	no	—
60	#14273734	—	2	2	no	—
61	#14273734	—	4	1	no	—
62	#14273734	—	4	1	no	—
63	C₂×#11745664	—	4	1	no	—
64	C₂×#11745664	—	4	1	no	—
65	C₂×#11745664	C₂³	1	1	yes	characteristic
66	C₂×#11745664	C₂³	1	1	yes	characteristic
67	C₂×#11745664	C₂³	1	1	yes	characteristic
68	C₂×#11745664	C₂³	1	1	yes	characteristic
69	Q₈×Dic₅₉	—	2	2	no	—
70	Q₈×Dic₅₉	—	4	1	no	—
71	D₄×Dic₅₉	—	2	2	no	—
72	D₄×Dic₅₉	—	4	1	no	—
73	#14273686	—	4	1	no	—
74	#14273686	C₂³	1	1	yes	characteristic
75	#14273686	C₂³	1	1	yes	characteristic
76	#14273686	C₂³	1	1	yes	characteristic
77	#14273686	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊Dic₅₉	—	4	1	no	—
79	#14273663	—	2	1	no	—
80	#14273663	—	2	1	no	—
81	#14273661	—	2	1	no	—
82	#14273659	—	2	1	no	—
83	#14273654	—	2	2	no	—
84	#14273654	—	2	2	no	—
85	#14273654	—	4	1	no	—
86	#14273654	—	4	1	no	—
87	#14273651	—	2	2	no	—
88	#14273651	—	4	1	no	—
89	#14273648	—	2	2	no	—
90	#14273648	—	4	1	no	—
91	#14273646	—	4	1	no	—
92	#14273644	—	4	1	no	—
93	#14273642	—	4	1	no	—
94	#14273642	—	4	1	no	—
95	#14273637	—	2	1	no	—
96	#14273637	D₄	1	2	yes	complemented
97	C₈×Dic₅₉	—	2	1	no	—
98	C₈×Dic₅₉	D₄	1	2	yes	complemented
99	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
103	#137×C₅₉	—	4	1	no	—
104	#137×C₅₉	—	4	1	no	—
105	AGL(1,ℤ/8)×C₅₉	—	4	1	no	—
106	AGL(1,ℤ/8)×C₅₉	—	4	1	no	—
107	#135×C₅₉	—	2	1	no	—
108	#135×C₅₉	—	2	1	no	—
109	#135×C₅₉	—	2	1	no	—
110	#135×C₅₉	—	2	1	no	—
111	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
112	C₂×Q₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
113	C₂×SD₁₆×C₅₉	—	2	1	no	—
114	C₂×SD₁₆×C₅₉	—	2	1	no	—
115	C₂×SD₁₆×C₅₉	—	2	1	no	—
116	C₂×SD₁₆×C₅₉	—	2	1	no	—
117	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
118	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
119	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
120	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
121	C₂×SD₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
122	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
123	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
124	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
127	C₄⋊Q₈×C₅₉	C₂×C₄	1	2	yes	complemented
128	#127×C₅₉	C₂×C₄	1	2	yes	—
129	#124×C₅₉	C₂×C₄	1	2	yes	—
130	#124×C₅₉	C₂×C₄	1	2	yes	complemented
131	#123×C₅₉	—	4	1	no	—
132	C₂²⋊Q₈×C₅₉	—	4	1	no	—
133	#121×C₅₉	—	4	1	no	—
134	#120×C₅₉	—	4	1	no	—
135	#117×C₅₉	C₂³	1	1	yes	characteristic
136	#97×C₅₉	C₂×C₄	1	2	yes	complemented
137	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	complemented
138	C₂⁴×C₅₉	—	2	1	no	—
139	#41×C₅₉	—	2	1	no	—
140	#41×C₅₉	—	2	1	no	—
141	#41×C₅₉	—	2	1	no	—
142	#41×C₅₉	—	2	1	no	—
143	#41×C₅₉	—	2	1	no	—
144	#41×C₅₉	—	2	1	no	—
145	#41×C₅₉	—	2	1	no	—
146	#41×C₅₉	—	2	1	no	—
147	C₂×Q₈×C₅₉	—	2	1	no	—
148	C₂×Q₈×C₅₉	—	2	1	no	—
149	C₂×Q₈×C₅₉	—	2	1	no	—
150	C₂×Q₈×C₅₉	—	2	1	no	—
151	C₂×Q₈×C₅₉	—	2	1	no	—
152	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
154	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×D₄×C₅₉	—	2	1	no	—
156	C₂×D₄×C₅₉	—	2	1	no	—
157	C₂×D₄×C₅₉	—	2	1	no	—
158	C₂×D₄×C₅₉	—	2	1	no	—
159	C₂×D₄×C₅₉	—	2	1	no	—
160	C₂×D₄×C₅₉	—	2	1	no	—
161	C₂×D₄×C₅₉	—	2	1	no	—
162	C₂×D₄×C₅₉	—	4	2	no	—
163	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
165	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	—	2	1	no	—
167	C₂²×C₄×C₅₉	—	2	1	no	—
168	C₂²×C₄×C₅₉	—	2	1	no	—
169	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
170	C₂²×Dic₅₉	—	4	2	no	—
171	Q₁₆×C₅₉	—	2	1	no	—
172	Q₁₆×C₅₉	—	2	1	no	—
173	Q₁₆×C₅₉	—	4	2	no	—
174	SD₁₆×C₅₉	—	2	2	no	—
175	SD₁₆×C₅₉	—	2	2	no	—
176	SD₁₆×C₅₉	—	2	2	no	—
177	SD₁₆×C₅₉	—	2	2	no	—
178	SD₁₆×C₅₉	—	2	1	no	—
179	SD₁₆×C₅₉	—	2	1	no	—
180	SD₁₆×C₅₉	—	2	1	no	—
181	SD₁₆×C₅₉	—	2	1	no	—
182	SD₁₆×C₅₉	—	4	2	no	—
183	SD₁₆×C₅₉	—	4	2	no	—
184	D₈×C₅₉	—	2	1	no	—
185	D₈×C₅₉	—	2	1	no	—
186	D₈×C₅₉	—	4	2	no	—
187	M₁₆×C₅₉	—	2	1	no	—
188	M₁₆×C₅₉	—	2	1	no	—
189	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
190	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
195	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
196	C₄⋊C₄×C₅₉	—	2	1	no	—
197	C₄⋊C₄×C₅₉	—	4	2	no	—
198	C₂²⋊C₄×C₅₉	—	2	1	no	—
199	C₂²⋊C₄×C₅₉	—	4	2	no	—
200	C₂²⋊C₄×C₅₉	—	4	2	no	—
201	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
202	C₂²⋊Dic₅₉	—	2	1	no	—
203	C₂²⋊Dic₅₉	—	2	1	no	—
204	C₂²⋊Dic₅₉	—	2	1	no	—
205	C₂²⋊Dic₅₉	—	2	1	no	—
206	C₂²⋊Dic₅₉	—	4	2	no	—
207	C₄⋊Dic₅₉	—	2	1	no	—
208	C₄⋊Dic₅₉	—	2	1	no	—
209	C₄⋊Dic₅₉	—	2	1	no	—
210	C₄⋊Dic₅₉	—	2	1	no	—
211	C₄⋊Dic₅₉	—	4	2	no	—
212	C₄×Dic₅₉	—	2	1	no	—
213	C₄×Dic₅₉	—	2	1	no	—
214	C₄×Dic₅₉	—	2	1	no	—
215	C₄×Dic₅₉	—	4	2	no	—
216	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
217	#11745664	—	2	1	no	—
218	#11745664	—	2	1	no	—
219	#11745664	—	2	1	no	—
220	#11745664	—	2	1	no	—
221	#11745664	—	2	1	no	—
222	#11745664	—	2	1	no	—
223	#11745664	—	2	1	no	—
224	#11745664	—	2	1	no	—
225	#11745664	—	4	2	no	—
226	#11745664	—	4	2	no	—
227	C₂×C₅₉⋊C₈	—	2	1	no	—
228	C₂×C₅₉⋊C₈	—	2	1	no	—
229	C₂×C₅₉⋊C₈	—	2	1	no	—
230	C₂×C₅₉⋊C₈	—	4	2	no	—
231	C₂×C₅₉⋊C₈	—	4	2	no	—
232	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
233	C₂³×C₅₉	—	2	1	no	—
234	C₂³×C₅₉	—	2	2	no	—
235	C₂³×C₅₉	—	2	1	no	—
236	C₂³×C₅₉	—	4	1	no	—
237	C₂³×C₅₉	—	4	1	no	—
238	C₂³×C₅₉	—	16	1	no	—
239	C₂³×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
240	Q₈×C₅₉	—	2	2	no	—
241	Q₈×C₅₉	—	2	1	no	—
242	Q₈×C₅₉	—	2	1	no	—
243	Q₈×C₅₉	—	2	1	no	—
244	Q₈×C₅₉	—	2	2	no	—
245	Q₈×C₅₉	—	2	1	no	—
246	Q₈×C₅₉	—	4	1	no	—
247	Q₈×C₅₉	—	4	1	no	—
248	D₄×C₅₉	—	2	1	no	—
249	D₄×C₅₉	—	2	1	no	—
250	D₄×C₅₉	—	2	2	no	—
251	D₄×C₅₉	—	2	1	no	—
252	D₄×C₅₉	—	2	2	no	—
253	D₄×C₅₉	—	2	1	no	—
254	D₄×C₅₉	—	4	1	no	—
255	D₄×C₅₉	—	4	1	no	—
256	D₄×C₅₉	—	4	1	no	—
257	D₄×C₅₉	—	4	1	no	—
258	D₄×C₅₉	—	4	1	no	—
259	D₄×C₅₉	—	4	1	no	—
260	D₄×C₅₉	—	16	2	no	—
261	C₂×C₄×C₅₉	—	2	2	no	—
262	C₂×C₄×C₅₉	—	2	1	no	—
263	C₂×C₄×C₅₉	—	2	2	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	4	1	no	—
266	C₂×C₄×C₅₉	—	4	1	no	—
267	C₂×C₄×C₅₉	—	4	1	no	—
268	C₂×C₄×C₅₉	—	4	1	no	—
269	C₂×C₄×C₅₉	—	4	1	no	—
270	C₂×C₄×C₅₉	—	4	1	no	—
271	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
274	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×Dic₅₉	—	2	2	no	—
278	C₂×Dic₅₉	—	4	1	no	—
279	C₂×Dic₅₉	—	4	1	no	—
280	C₂×Dic₅₉	—	4	1	no	—
281	C₂×Dic₅₉	—	16	2	no	—
282	C₈×C₅₉	—	2	2	no	—
283	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
284	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
285	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
286	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
287	C₅₉⋊C₈	—	2	2	no	—
288	C₅₉⋊C₈	—	4	1	no	—
289	C₅₉⋊C₈	—	4	1	no	—
290	C₅₉⋊C₈	—	4	1	no	—
291	#22284	—	59	1	no	maximal, Sylow
292	C₂²×C₅₉	—	4	1	no	—
293	C₂²×C₅₉	—	4	1	no	—
294	C₂²×C₅₉	—	4	1	no	—
295	C₂²×C₅₉	—	4	2	no	—
296	C₂²×C₅₉	—	8	1	no	—
297	C₂²×C₅₉	—	8	2	no	—
298	C₂²×C₅₉	—	8	1	no	—
299	C₂²×C₅₉	—	8	2	no	—
300	C₂²×C₅₉	—	16	1	no	—
301	C₂²×C₅₉	#518	1	1	yes	characteristic
302	C₂²×C₅₉	#535	1	1	yes	characteristic
303	C₂²×C₅₉	#540	1	1	yes	characteristic
304	C₄×C₅₉	—	4	2	no	—
305	C₄×C₅₉	—	4	1	no	—
306	C₄×C₅₉	—	4	1	no	—
307	C₄×C₅₉	—	4	2	no	—
308	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
309	C₄×C₅₉	#518	1	1	yes	characteristic
310	C₄×C₅₉	#535	1	1	yes	characteristic
311	C₄×C₅₉	#540	1	1	yes	characteristic
312	Dic₅₉	—	4	2	no	—
313	Dic₅₉	—	8	1	no	—
314	Dic₅₉	—	8	1	no	—
315	Dic₅₉	—	8	1	no	—
316	#3154	D₅₉	1	1	yes	characteristic
317	#2957	—	59	1	no	—
318	#2949	—	59	1	no	—
319	#1977	—	59	1	no	—
320	#1976	—	59	1	no	—
321	#1912	—	59	1	no	—
322	#1911	—	59	1	no	—
323	#1910	—	59	1	no	—
324	#1909	—	59	1	no	—
325	#1905	—	59	1	no	—
326	#1904	—	59	1	no	—
327	#1903	—	59	1	no	—
328	#1902	—	59	1	no	—
329	#1833	—	59	1	no	—
330	#1747	—	59	1	no	—
331	C₂×C₅₉	—	2	1	no	—
332	C₂×C₅₉	—	2	1	no	—
333	C₂×C₅₉	—	2	1	no	—
334	C₂×C₅₉	—	8	1	no	—
335	C₂×C₅₉	—	8	1	no	—
336	C₂×C₅₉	—	8	2	no	—
337	C₂×C₅₉	#2328	1	1	yes	characteristic
338	C₂×#137	C₂×D₅₉	1	1	yes	characteristic
339	C₂×AGL(1,ℤ/8)	C₂×D₅₉	1	1	yes	characteristic
340	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
341	C₂²×SD₁₆	C₂×D₅₉	1	1	yes	characteristic
342	#568	—	59	1	no	—
343	#568	—	59	1	no	—
344	#536	C₂×D₅₉	1	1	yes	characteristic
345	#535	C₂×D₅₉	1	1	yes	characteristic
346	#519	—	59	1	no	—
347	#518	—	59	1	no	—
348	#497	Dic₅₉	1	2	yes	complemented
349	#496	Dic₅₉	1	2	yes	complemented
350	#495	Dic₅₉	1	2	yes	complemented
351	#492	Dic₅₉	1	2	yes	complemented
352	#444	—	118	2	no	—
353	#443	—	118	2	no	—
354	#440	—	118	2	no	—
355	C₄×SD₁₆	—	118	2	no	—
356	C₂×#108	—	59	1	no	—
357	#427	—	59	1	no	—
358	#421	—	59	1	no	—
359	#421	—	59	1	no	—
360	#421	—	59	1	no	—
361	#421	—	59	1	no	—
362	#419	—	59	1	no	—
363	#419	—	59	1	no	—
364	#418	—	59	1	no	—
365	#418	—	59	1	no	—
366	C₂×#101	—	59	1	no	—
367	C₂×#100	—	59	1	no	—
368	#410	—	59	1	no	—
369	#410	—	59	1	no	—
370	#405	—	59	1	no	—
371	#405	—	59	1	no	—
372	#405	C₂×D₅₉	1	1	yes	characteristic
373	#344	—	59	1	no	—
374	#344	—	59	1	no	—
375	#338	—	59	1	no	—
376	H(3,ℤ/4)	—	59	1	no	—
377	H(3,ℤ/4)	—	59	1	no	—
378	H(3,ℤ/4)	—	59	1	no	—
379	H(3,ℤ/4)	—	59	1	no	—
380	H(3,ℤ/4)	—	59	1	no	—
381	C₅₉	#22284	1	1	yes	characteristic, complemented, Sylow
382	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
383	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
384	C₂²×Q₈	C₂²×D₅₉	1	1	yes	characteristic
385	C₂²×D₄	C₂²×D₅₉	1	1	yes	characteristic
386	#137	—	4	1	no	—
387	#137	—	4	1	no	—
388	AGL(1,ℤ/8)	—	4	1	no	—
389	AGL(1,ℤ/8)	—	4	1	no	—
390	#135	—	2	1	no	—
391	#135	—	2	1	no	—
392	#135	—	2	1	no	—
393	#135	—	2	1	no	—
394	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic, complemented
395	C₂×Q₁₆	C₂×Dic₅₉	1	2	yes	complemented
396	C₂×SD₁₆	—	2	1	no	—
397	C₂×SD₁₆	—	2	1	no	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×SD₁₆	—	2	1	no	—
400	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
401	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
402	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
403	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic, complemented
404	C₂×SD₁₆	C₂×Dic₅₉	1	1	yes	characteristic, complemented
405	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	complemented
406	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
407	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic, complemented
408	#131	—	118	2	no	—
409	#131	—	118	2	no	—
410	#131	—	236	1	no	—
411	#131	—	236	1	no	—
412	C₂×M₁₆	—	59	1	no	—
413	C₂×M₁₆	—	59	1	no	—
414	C₂×M₁₆	—	59	1	no	—
415	C₂×M₁₆	—	59	1	no	—
416	C₂×M₁₆	—	236	1	no	—
417	C₂×M₁₆	—	236	1	no	—
418	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
419	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
420	C₄⋊Q₈	C₂×Dic₅₉	1	2	yes	complemented
421	#127	C₂×Dic₅₉	1	2	yes	—
422	#124	C₂×Dic₅₉	1	2	yes	—
423	#124	C₂×Dic₅₉	1	2	yes	complemented
424	#123	—	4	1	no	—
425	C₂²⋊Q₈	—	4	1	no	—
426	#121	—	4	1	no	—
427	#120	—	4	1	no	—
428	C₄×Q₈	—	118	2	no	—
429	C₄×Q₈	—	236	1	no	—
430	C₄×D₄	—	118	2	no	—
431	C₄×D₄	—	236	1	no	—
432	#117	—	59	1	no	—
433	#117	—	59	1	no	—
434	#117	—	59	1	no	—
435	#117	—	59	1	no	—
436	#117	—	236	1	no	—
437	#117	C₂²×D₅₉	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	236	1	no	—
439	#108	—	118	1	no	—
440	#108	—	118	1	no	—
441	#107	—	118	1	no	—
442	#106	—	118	1	no	—
443	#104	—	118	2	no	—
444	#104	—	118	2	no	—
445	#104	—	236	1	no	—
446	#104	—	236	1	no	—
447	#103	—	118	2	no	—
448	#103	—	236	1	no	—
449	#102	—	118	2	no	—
450	#102	—	236	1	no	—
451	#101	—	236	1	no	—
452	#100	—	236	1	no	—
453	#99	—	236	1	no	—
454	#99	—	236	1	no	—
455	#97	—	59	2	no	—
456	#97	—	118	1	no	—
457	#97	C₂×Dic₅₉	1	2	yes	complemented
458	C₄×C₈	—	59	2	no	—
459	C₄×C₈	—	118	1	no	—
460	C₄×C₈	C₂×Dic₅₉	1	2	yes	complemented
461	C₂⁴	—	2	1	no	—
462	#41	—	2	1	no	—
463	#41	—	2	1	no	—
464	#41	—	2	1	no	—
465	#41	—	2	1	no	—
466	#41	—	2	1	no	—
467	#41	—	2	1	no	—
468	#41	—	2	1	no	—
469	#41	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
476	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
477	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
487	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
488	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	236	2	no	—
493	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
494	Q₁₆	—	2	1	no	—
495	Q₁₆	—	2	1	no	—
496	Q₁₆	—	4	2	no	—
497	SD₁₆	—	2	2	no	—
498	SD₁₆	—	2	2	no	—
499	SD₁₆	—	2	2	no	—
500	SD₁₆	—	2	2	no	—
501	SD₁₆	—	2	1	no	—
502	SD₁₆	—	2	1	no	—
503	SD₁₆	—	2	1	no	—
504	SD₁₆	—	2	1	no	—
505	SD₁₆	—	4	2	no	—
506	SD₁₆	—	4	2	no	—
507	D₈	—	2	1	no	—
508	D₈	—	2	1	no	—
509	D₈	—	4	2	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	118	1	no	—
513	M₁₆	—	118	1	no	—
514	M₁₆	—	118	1	no	—
515	M₁₆	—	118	1	no	—
516	M₁₆	—	118	1	no	—
517	M₁₆	—	118	1	no	—
518	M₁₆	—	118	1	no	—
519	M₁₆	—	118	1	no	—
520	M₁₆	—	236	2	no	—
521	M₁₆	—	236	2	no	—
522	C₂×C₈	—	59	2	no	—
523	C₂×C₈	—	118	1	no	—
524	C₂×C₈	—	118	1	no	—
525	C₂×C₈	—	118	1	no	—
526	C₂×C₈	—	236	2	no	—
527	C₂×C₈	—	236	2	no	—
528	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
529	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
530	C₂×C₈	#11745687	1	1	yes	characteristic
531	C₂×C₈	#11745687	1	1	yes	characteristic
532	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
533	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
534	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	118	1	no	—
538	C₄⋊C₄	—	118	1	no	—
539	C₄⋊C₄	—	118	1	no	—
540	C₄⋊C₄	—	118	1	no	—
541	C₄⋊C₄	—	236	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	4	2	no	—
544	C₂²⋊C₄	—	4	2	no	—
545	C₂²⋊C₄	—	118	1	no	—
546	C₂²⋊C₄	—	118	1	no	—
547	C₂²⋊C₄	—	118	1	no	—
548	C₂²⋊C₄	—	118	1	no	—
549	C₂²⋊C₄	—	236	2	no	—
550	C₄²	—	59	2	no	—
551	C₄²	—	118	1	no	—
552	C₄²	—	118	1	no	—
553	C₄²	—	118	1	no	—
554	C₄²	—	236	2	no	—
555	C₄²	C₂²×Dic₅₉	1	2	yes	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	2	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	4	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	16	1	no	—
562	C₂³	#14273772	1	1	yes	characteristic
563	Q₈	—	2	2	no	—
564	Q₈	—	2	1	no	—
565	Q₈	—	2	1	no	—
566	Q₈	—	2	1	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	2	1	no	—
569	Q₈	—	4	1	no	—
570	Q₈	—	4	1	no	—
571	D₄	—	2	1	no	—
572	D₄	—	2	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	1	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	1	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	4	1	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	16	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	118	2	no	—
595	C₂×C₄	—	944	2	no	—
596	C₂×C₄	—	236	1	no	—
597	C₂×C₄	—	236	1	no	—
598	C₂×C₄	—	236	1	no	—
599	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
600	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
601	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
602	C₂×C₄	#14273772	1	1	yes	characteristic
603	C₂×C₄	#14273772	1	1	yes	characteristic
604	C₂×C₄	#14273772	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	118	2	no	—
607	C₈	—	236	1	no	—
608	C₈	—	236	1	no	—
609	C₈	—	236	1	no	—
610	C₈	D₄×Dic₅₉	1	1	yes	characteristic
611	C₈	D₄×Dic₅₉	1	1	yes	characteristic
612	C₈	D₄×Dic₅₉	1	1	yes	characteristic
613	C₈	D₄×Dic₅₉	1	1	yes	characteristic
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	2	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	2	no	—
622	C₂²	—	16	1	no	—
623	C₂²	#16837877	1	1	yes	characteristic
624	C₂²	#16837965	1	1	yes	characteristic
625	C₂²	#16838006	1	1	yes	characteristic
626	C₄	—	4	2	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	472	1	no	—
631	C₄	—	472	1	no	—
632	C₄	—	472	1	no	—
633	C₄	—	236	2	no	—
634	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
635	C₄	#16837877	1	1	yes	characteristic
636	C₄	#16837965	1	1	yes	characteristic
637	C₄	#16838006	1	1	yes	characteristic
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	8	2	no	—
642	C₂	—	8	1	no	—
643	C₂	—	8	1	no	—
644	C₂	#21426822	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21426822
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting, prime radical	C₅₉×#3154	C₂
socle	C₂×C₅₉	#2328
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#3154	D₅₉
hypocenter	C₅₉	#22284
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3154

Complements

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

N	H ≅ G/N	type
1. #21433013	C₂	semidirect
2. #21432956	C₂	semidirect
3. #21425001	C₂	semidirect
4. #21424995	C₂	semidirect
5. #21424634	C₂	semidirect
6. #21424629	C₂	semidirect
7. #21424624	C₂	semidirect
8. #21424619	C₂	semidirect
9. #21424592	C₂	semidirect
10. #21424585	C₂	semidirect
11. #21424578	C₂	semidirect
12. #21424571	C₂	semidirect
13. #21424220	C₂	semidirect
14. #21423851	C₂	semidirect
54. C₅₉×#497	C₄	semidirect
55. C₅₉×#496	C₄	semidirect
56. C₅₉×#495	C₄	semidirect
57. C₅₉×#492	C₄	semidirect
96. #14273637	D₄	semidirect
98. C₈×Dic₅₉	D₄	semidirect
111. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
112. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
120. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
121. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
122. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
124. C₂×D₈×C₅₉	C₂×C₄	semidirect
127. C₄⋊Q₈×C₅₉	C₂×C₄	semidirect
130. #124×C₅₉	C₂×C₄	semidirect
136. #97×C₅₉	C₂×C₄	semidirect
137. C₄×C₈×C₅₉	C₂×C₄	semidirect
348. #497	Dic₅₉	semidirect
349. #496	Dic₅₉	semidirect
350. #495	Dic₅₉	semidirect
351. #492	Dic₅₉	semidirect
381. C₅₉	#22284	semidirect
394. C₂×Q₁₆	C₂×Dic₅₉	semidirect
395. C₂×Q₁₆	C₂×Dic₅₉	semidirect
403. C₂×SD₁₆	C₂×Dic₅₉	semidirect
404. C₂×SD₁₆	C₂×Dic₅₉	semidirect
405. C₂×SD₁₆	C₂×Dic₅₉	semidirect
407. C₂×D₈	C₂×Dic₅₉	semidirect
420. C₄⋊Q₈	C₂×Dic₅₉	semidirect
423. #124	C₂×Dic₅₉	semidirect
457. #97	C₂×Dic₅₉	semidirect
460. C₄×C₈	C₂×Dic₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433013	2
#21432956	2
#21425001	2
#21424995	2
#21424634	2
#21424629	2
#21424624	2
#21424619	2
#21424592	2
#21424585	2
#21424578	2
#21424571	2
#21424220	2
#21423851	2
C₅₉×#3154	2
#22284	59