Subgroups — #28595641

Order 15104.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433817	C₂	1	1	yes	maximal, characteristic
2	#21433000	C₂	1	2	yes	maximal, complemented
3	C₂×#16837525	C₂	1	1	yes	maximal, characteristic, complemented
4	#21432521	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424992	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424887	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424766	C₂	1	2	yes	maximal, complemented
8	#21424596	C₂	1	2	yes	maximal, complemented
9	#21424147	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423897	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	#16838202	C₂²	1	2	yes	—
13	C₂×#14273749	C₂²	1	1	yes	characteristic
14	C₂×#14273733	C₂²	1	2	yes	—
15	C₂×#14273733	C₂²	1	1	yes	characteristic
16	C₂×#14273733	C₂²	1	1	yes	characteristic
17	C₄×#11745685	C₂²	1	1	yes	characteristic
18	#16837678	C₄	1	2	yes	complemented
19	#16837673	C₄	1	2	yes	complemented
20	#16837666	C₄	1	4	yes	complemented
21	#16837525	—	2	4	no	—
22	#16837525	—	2	1	no	—
23	#16837525	—	2	1	no	—
24	#16837525	—	2	1	no	—
25	#16837525	—	2	1	no	—
26	#16837520	—	2	4	no	—
27	#16837451	C₂²	1	2	yes	—
28	C₂×#14273663	C₂²	1	1	yes	characteristic
29	#16837420	C₂²	1	2	yes	—
30	#16837420	C₂²	1	2	yes	—
31	C₂×#14273655	C₂²	1	2	yes	—
32	#16837384	C₂²	1	2	yes	—
33	#16837375	C₂²	1	2	yes	—
34	#16837359	—	2	1	no	—
35	#16837359	—	2	1	no	—
36	#16837357	C₂²	1	1	yes	characteristic
37	#16837357	C₂²	1	1	yes	characteristic
38	C₄×#11745664	C₂²	1	1	yes	characteristic
39	#16837354	—	2	1	no	—
40	#97×D₅₉	—	2	1	no	—
41	#16837174	C₂²	1	2	yes	—
42	#16837172	C₂²	1	2	yes	—
43	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
44	C₅₉×#427	C₂²	1	1	yes	characteristic
45	C₅₉×#405	C₂²	1	2	yes	—
46	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#339	C₂²	1	2	yes	—
48	C₂×#11745685	C₂³	1	2	yes	—
49	C₂×#11745685	C₂³	1	1	yes	characteristic
50	#14273760	—	2	2	no	—
51	#14273760	C₂×C₄	1	4	yes	—
52	#14273755	—	2	2	no	—
53	#14273755	C₂×C₄	1	4	yes	—
54	#14273749	—	2	4	no	—
55	#14273749	—	2	1	no	—
56	#14273749	—	2	1	no	—
57	#14273749	—	2	1	no	—
58	#14273749	—	2	1	no	—
59	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#11745660	C₂×C₄	1	2	yes	complemented
61	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic, complemented
62	#14273733	—	2	1	no	—
63	#14273733	—	2	1	no	—
64	#14273733	—	2	2	no	—
65	#14273733	—	2	2	no	—
66	#14273733	—	2	2	no	—
67	#14273733	—	2	2	no	—
68	#14273733	—	2	2	no	—
69	#14273733	C₂×C₄	1	2	yes	—
70	#14273733	C₂×C₄	1	2	yes	—
71	#14273733	D₄	1	4	yes	—
72	C₂×#11745664	C₂³	1	2	yes	—
73	C₂×#11745664	C₂³	1	1	yes	characteristic
74	C₂×#11745664	C₂³	1	1	yes	characteristic
75	C₂×#11745659	—	2	1	no	—
76	C₂×#11745659	—	2	1	no	—
77	C₂×#11745659	—	2	2	no	—
78	C₂×C₈×D₅₉	—	2	1	no	—
79	C₂×C₈×D₅₉	—	2	1	no	—
80	C₂×C₈×D₅₉	—	2	2	no	—
81	C₄×Dic₁₁₈	—	2	1	no	—
82	C₄×D₂₃₆	—	2	1	no	—
83	C₄×C₂²⋊D₅₉	—	2	2	no	—
84	#14273686	C₂³	1	1	yes	characteristic
85	#14273684	—	2	1	no	—
86	C₄²×D₅₉	—	2	1	no	—
87	#14273663	—	2	1	no	—
88	#14273663	—	2	1	no	—
89	#14273663	—	2	4	no	—
90	#14273655	—	2	4	no	—
91	#14273655	—	2	2	no	—
92	#14273655	—	2	2	no	—
93	#14273655	—	2	4	no	—
94	#14273645	C₂×C₄	1	4	yes	complemented
95	#14273643	C₂×C₄	1	4	yes	complemented
96	#14273641	—	2	4	no	—
97	#14273638	—	2	1	no	—
98	#14273637	—	2	1	no	—
99	#14273637	—	2	1	no	—
100	C₄×C₅₉⋊C₈	—	2	1	no	—
101	C₈×Dic₅₉	—	2	1	no	—
102	C₈×Dic₅₉	—	2	1	no	—
103	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
106	#117×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	#108×C₅₉	C₂×C₄	1	2	yes	complemented
109	#108×C₅₉	C₂×C₄	1	2	yes	complemented
110	#107×C₅₉	—	2	1	no	—
111	#106×C₅₉	—	2	1	no	—
112	#97×C₅₉	—	2	2	no	—
113	#97×C₅₉	D₄	1	1	yes	characteristic
114	#97×C₅₉	D₄	1	1	yes	characteristic
115	#97×C₅₉	D₄	1	1	yes	characteristic
116	#97×C₅₉	D₄	1	1	yes	characteristic
117	C₄×C₈×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₅₉	—	2	1	no	—
121	C₂×C₂²⋊D₅₉	—	2	2	no	—
122	#11745685	—	2	1	no	—
123	#11745685	—	2	1	no	—
124	#11745685	—	2	2	no	—
125	#11745685	—	2	2	no	—
126	#11745685	—	2	2	no	—
127	#11745685	—	2	2	no	—
128	#11745685	C₂²×C₄	1	2	yes	—
129	#11745685	C₂×D₄	1	2	yes	—
130	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
131	C₂×D₂₃₆	#41	1	1	yes	characteristic
132	C₂×C₄×D₅₉	—	2	1	no	—
133	C₂×C₄×D₅₉	—	2	2	no	—
134	C₂×C₄×D₅₉	—	2	2	no	—
135	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
136	C₂×Dic₁₁₈	#41	1	1	yes	characteristic
137	M₁₆×C₅₉	—	2	2	no	—
138	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
148	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
149	C₂×C₈×C₅₉	#41	1	2	yes	—
150	C₄⋊C₄×C₅₉	—	2	2	no	—
151	C₂²⋊C₄×C₅₉	—	2	2	no	—
152	C₄²×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	—	2	2	no	—
154	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊Dic₅₉	#41	1	2	yes	—
157	(C₂×D₅₉)⋊C₄	—	2	2	no	—
158	C₄⋊Dic₅₉	—	2	1	no	—
159	Dic₅₉⋊C₄	—	2	2	no	—
160	C₄×Dic₅₉	—	2	2	no	—
161	C₄×Dic₅₉	—	2	1	no	—
162	#11745664	—	2	1	no	—
163	#11745664	—	2	1	no	—
164	#11745664	—	2	2	no	—
165	#11745664	—	2	2	no	—
166	#11745664	C₂²×C₄	1	2	yes	—
167	#11745664	C₂×D₄	1	2	yes	—
168	C₂×C₅₉⋊C₈	—	2	1	no	—
169	C₂×C₅₉⋊C₈	—	2	1	no	—
170	C₂×C₅₉⋊C₈	—	2	2	no	—
171	Dic₂₃₆	—	2	4	no	—
172	Dic₂₃₆	—	2	1	no	—
173	Dic₂₃₆	—	2	1	no	—
174	D₄₇₂	—	2	4	no	—
175	D₄₇₂	—	2	1	no	—
176	D₄₇₂	—	2	1	no	—
177	#11745660	—	2	4	no	—
178	#11745660	—	2	4	no	—
179	#11745660	—	2	2	no	—
180	#11745660	—	2	2	no	—
181	#11745659	—	2	2	no	—
182	#11745659	—	2	2	no	—
183	#11745659	—	2	4	no	—
184	#11745659	—	4	2	no	—
185	#11745659	—	4	2	no	—
186	C₈×D₅₉	—	2	2	no	—
187	C₈×D₅₉	—	2	2	no	—
188	C₈×D₅₉	—	2	4	no	—
189	C₈×D₅₉	—	4	2	no	—
190	C₈×D₅₉	—	4	2	no	—
191	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
192	C₂²×D₅₉	—	2	1	no	—
193	C₂²×D₅₉	—	2	2	no	—
194	C₂×C₄×C₅₉	—	2	1	no	—
195	C₂×C₄×C₅₉	—	2	1	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	—	8	1	no	—
198	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
204	C₂²⋊D₅₉	—	2	2	no	—
205	C₂²⋊D₅₉	—	2	2	no	—
206	C₂²⋊D₅₉	—	4	2	no	—
207	C₂²⋊D₅₉	—	4	2	no	—
208	C₂×Dic₅₉	—	2	1	no	—
209	C₂×Dic₅₉	—	2	2	no	—
210	C₂×Dic₅₉	—	2	2	no	—
211	D₂₃₆	—	2	2	no	—
212	D₂₃₆	—	2	2	no	—
213	D₂₃₆	—	2	1	no	—
214	D₂₃₆	C₄×D₄	1	2	yes	—
215	C₄×D₅₉	—	2	2	no	—
216	C₄×D₅₉	—	2	2	no	—
217	C₄×D₅₉	—	4	2	no	—
218	C₄×D₅₉	—	4	2	no	—
219	C₄×D₅₉	—	8	2	no	—
220	Dic₁₁₈	—	2	1	no	—
221	Dic₁₁₈	—	2	2	no	—
222	Dic₁₁₈	—	2	2	no	—
223	Dic₁₁₈	C₄×D₄	1	2	yes	—
224	C₈×C₅₉	—	2	4	no	—
225	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
226	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
227	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
228	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
229	C₈×C₅₉	#121	1	2	yes	—
230	C₈×C₅₉	#121	1	2	yes	—
231	C₅₉⋊C₈	—	2	2	no	—
232	C₅₉⋊C₈	—	2	2	no	—
233	C₅₉⋊C₈	—	4	2	no	—
234	#21559	—	59	1	no	maximal, Sylow
235	C₂²×C₅₉	—	4	1	no	—
236	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
237	C₂²×C₅₉	#525	1	1	yes	characteristic
238	C₂²×C₅₉	#532	1	1	yes	characteristic
239	C₂×D₅₉	—	2	2	no	—
240	C₂×D₅₉	—	4	2	no	—
241	C₂×D₅₉	—	4	2	no	—
242	C₂×D₅₉	—	8	2	no	—
243	C₄×C₅₉	—	4	1	no	—
244	C₄×C₅₉	—	4	1	no	—
245	C₄×C₅₉	—	8	2	no	—
246	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
249	C₄×C₅₉	#529	1	1	yes	characteristic
250	Dic₅₉	—	2	2	no	—
251	Dic₅₉	—	4	2	no	—
252	Dic₅₉	—	4	2	no	—
253	#3067	—	59	1	no	—
254	#2955	—	59	2	no	—
255	C₂×#444	—	59	1	no	—
256	#2875	—	59	1	no	—
257	#1976	—	59	1	no	—
258	#1953	—	59	1	no	—
259	#1932	—	59	2	no	—
260	#1906	—	59	2	no	—
261	#1814	—	59	1	no	—
262	#1773	D₅₉	1	1	yes	characteristic, complemented
263	#1757	—	59	2	no	—
264	C₂×C₅₉	—	2	1	no	—
265	C₂×C₅₉	—	2	1	no	—
266	C₂×C₅₉	—	2	1	no	—
267	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
268	D₅₉	—	4	2	no	—
269	D₅₉	—	8	2	no	—
270	#575	—	59	2	no	—
271	C₂×#135	—	59	1	no	—
272	C₂×#131	—	59	1	no	—
273	C₂×#131	—	59	1	no	—
274	C₂×#131	—	59	2	no	—
275	C₄×#41	—	59	1	no	—
276	#473	—	59	2	no	—
277	#472	—	59	2	no	—
278	#471	—	59	4	no	—
279	#444	—	118	4	no	—
280	#444	—	118	1	no	—
281	#444	—	118	1	no	—
282	#444	—	118	1	no	—
283	#444	—	118	1	no	—
284	#443	—	118	4	no	—
285	#430	—	59	2	no	—
286	C₂×#108	—	59	1	no	—
287	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
288	#427	C₂×D₅₉	1	1	yes	characteristic
289	#421	—	59	2	no	—
290	#421	—	59	2	no	—
291	C₂×#104	—	59	2	no	—
292	#413	—	59	2	no	—
293	#410	—	59	2	no	—
294	#405	—	59	1	no	—
295	#405	—	59	1	no	—
296	#405	—	118	1	no	—
297	#405	—	118	1	no	—
298	#405	C₂×D₅₉	1	2	yes	—
299	C₄×M₁₆	—	59	1	no	—
300	C₄×M₁₆	—	118	1	no	—
301	C₂×#97	—	118	1	no	—
302	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
303	#344	—	59	2	no	—
304	#344	—	59	2	no	—
305	#339	C₂×D₅₉	1	2	yes	—
306	C₅₉	#21559	1	1	yes	characteristic, complemented, Sylow
307	C₂×#41	—	59	1	no	—
308	C₂×#41	—	59	2	no	—
309	#137	—	59	4	no	—
310	#137	—	118	2	no	—
311	AGL(1,ℤ/8)	—	59	4	no	—
312	AGL(1,ℤ/8)	—	118	2	no	—
313	#135	—	118	4	no	—
314	#135	—	118	1	no	—
315	#135	—	118	1	no	—
316	#135	—	118	1	no	—
317	#135	—	118	1	no	—
318	C₂×Q₁₆	—	59	1	no	—
319	C₂×SD₁₆	—	59	2	no	—
320	C₂×D₈	—	59	1	no	—
321	#131	—	59	2	no	—
322	#131	—	59	2	no	—
323	#131	—	59	4	no	—
324	#131	—	118	1	no	—
325	#131	—	118	1	no	—
326	#131	—	118	2	no	—
327	#131	—	118	2	no	—
328	#131	—	118	2	no	—
329	#131	—	118	2	no	—
330	#131	—	118	2	no	—
331	C₂×M₁₆	—	59	1	no	—
332	C₂×M₁₆	—	59	1	no	—
333	C₂×M₁₆	—	59	2	no	—
334	C₂×M₁₆	—	118	1	no	—
335	C₂×M₁₆	—	118	1	no	—
336	C₂×M₁₆	—	118	2	no	—
337	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
338	C₂²×C₈	—	118	1	no	—
339	C₂²×C₈	—	118	1	no	—
340	C₂²×C₈	—	118	2	no	—
341	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
342	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
343	C₄×Q₈	—	118	1	no	—
344	C₄×D₄	—	118	1	no	—
345	C₄×D₄	—	118	2	no	—
346	#117	—	59	1	no	—
347	#117	—	118	1	no	—
348	#117	C₂²×D₅₉	1	2	yes	—
349	C₂×C₄²	—	118	1	no	—
350	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
351	#108	—	118	4	no	—
352	#108	—	118	1	no	—
353	#108	—	118	1	no	—
354	#108	C₄×D₅₉	1	2	yes	complemented
355	#108	C₄×D₅₉	1	2	yes	complemented
356	#107	—	2	1	no	—
357	#106	—	2	1	no	—
358	#104	—	118	4	no	—
359	#104	—	118	4	no	—
360	#104	—	118	2	no	—
361	#104	—	118	2	no	—
362	#101	—	59	4	no	—
363	#100	—	59	4	no	—
364	#99	—	118	4	no	—
365	#97	—	2	2	no	—
366	#97	—	118	1	no	—
367	#97	—	118	1	no	—
368	#97	—	118	1	no	—
369	#97	D₂₃₆	1	1	yes	characteristic
370	#97	D₂₃₆	1	1	yes	characteristic
371	#97	D₂₃₆	1	1	yes	characteristic
372	#97	D₂₃₆	1	1	yes	characteristic
373	C₄×C₈	—	2	2	no	—
374	C₄×C₈	—	118	1	no	—
375	C₄×C₈	—	118	1	no	—
376	C₄×C₈	—	118	1	no	—
377	#41	—	59	2	no	—
378	#41	—	59	2	no	—
379	#41	—	118	1	no	—
380	#41	—	118	1	no	—
381	#41	—	118	2	no	—
382	#41	—	118	2	no	—
383	#41	—	118	2	no	—
384	#41	—	118	2	no	—
385	C₂×Q₈	—	59	2	no	—
386	C₂×Q₈	—	59	1	no	—
387	C₂×D₄	—	59	2	no	—
388	C₂×D₄	—	59	1	no	—
389	C₂×D₄	—	118	1	no	—
390	C₂×D₄	—	118	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	118	2	no	—
393	C₂²×C₄	—	118	1	no	—
394	C₂²×C₄	—	118	2	no	—
395	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
396	Q₁₆	—	118	4	no	—
397	Q₁₆	—	118	1	no	—
398	Q₁₆	—	118	1	no	—
399	SD₁₆	—	118	4	no	—
400	SD₁₆	—	118	4	no	—
401	SD₁₆	—	118	2	no	—
402	SD₁₆	—	118	2	no	—
403	D₈	—	118	4	no	—
404	D₈	—	118	1	no	—
405	D₈	—	118	1	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	59	2	no	—
408	M₁₆	—	59	2	no	—
409	M₁₆	—	118	1	no	—
410	M₁₆	—	118	1	no	—
411	M₁₆	—	118	2	no	—
412	M₁₆	—	118	2	no	—
413	M₁₆	—	118	4	no	—
414	M₁₆	—	118	2	no	—
415	M₁₆	—	118	2	no	—
416	M₁₆	—	236	2	no	—
417	M₁₆	—	236	2	no	—
418	M₁₆	C₂×C₄×D₅₉	1	4	yes	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	118	1	no	—
421	C₂×C₈	—	118	1	no	—
422	C₂×C₈	—	118	2	no	—
423	C₂×C₈	—	118	2	no	—
424	C₂×C₈	—	118	4	no	—
425	C₂×C₈	—	118	2	no	—
426	C₂×C₈	—	236	2	no	—
427	C₂×C₈	—	236	2	no	—
428	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
429	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
430	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
431	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
432	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
433	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
434	C₂×C₈	#11745685	1	1	yes	characteristic
435	C₂×C₈	#11745685	1	1	yes	characteristic
436	C₂×C₈	D₄×D₅₉	1	2	yes	—
437	C₂×C₈	#11745689	1	2	yes	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	118	2	no	—
440	C₄⋊C₄	—	118	1	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	59	2	no	—
443	C₂²⋊C₄	—	118	2	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	118	2	no	—
447	C₄²	—	118	1	no	—
448	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
449	C₄²	C₂×D₂₃₆	1	1	yes	characteristic
450	C₂³	—	118	1	no	—
451	C₂³	—	118	2	no	—
452	C₂³	#41×D₅₉	1	1	yes	characteristic
453	Q₈	—	59	2	no	—
454	Q₈	—	118	1	no	—
455	Q₈	—	118	2	no	—
456	Q₈	—	118	2	no	—
457	D₄	—	59	2	no	—
458	D₄	—	118	2	no	—
459	D₄	—	118	2	no	—
460	D₄	—	118	1	no	—
461	D₄	—	118	2	no	—
462	D₄	—	118	2	no	—
463	D₄	—	236	2	no	—
464	D₄	—	236	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	118	1	no	—
470	C₂×C₄	—	118	2	no	—
471	C₂×C₄	—	118	2	no	—
472	C₂×C₄	—	118	2	no	—
473	C₂×C₄	—	118	2	no	—
474	C₂×C₄	—	472	2	no	—
475	C₂×C₄	—	236	2	no	—
476	C₂×C₄	—	236	2	no	—
477	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
479	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
480	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
481	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
482	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
483	C₈	—	2	4	no	—
484	C₈	—	118	2	no	—
485	C₈	—	118	2	no	—
486	C₈	—	236	2	no	—
487	C₈	C₄×D₂₃₆	1	1	yes	characteristic
488	C₈	C₄×D₂₃₆	1	1	yes	characteristic
489	C₈	C₄×D₂₃₆	1	1	yes	characteristic
490	C₈	C₄×D₂₃₆	1	1	yes	characteristic
491	C₈	#14273702	1	2	yes	—
492	C₈	#14273702	1	2	yes	—
493	C₂²	—	4	1	no	—
494	C₂²	—	118	2	no	—
495	C₂²	—	472	2	no	—
496	C₂²	—	236	2	no	—
497	C₂²	—	236	2	no	—
498	C₂²	C₄×#11745689	1	1	yes	characteristic
499	C₂²	#16837914	1	1	yes	characteristic
500	C₂²	#16837949	1	1	yes	characteristic
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	2	no	—
504	C₄	—	118	2	no	—
505	C₄	—	236	2	no	—
506	C₄	—	236	2	no	—
507	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
508	C₄	C₂×C₄×D₂₃₆	1	1	yes	characteristic
509	C₄	C₂×#14273702	1	1	yes	characteristic
510	C₄	#16837939	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	472	2	no	—
515	C₂	—	236	2	no	—
516	C₂	C₄×#14273702	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14273702
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1773	C₂
socle	C₂×C₅₉	C₄×#121
prime radical	#21433817	C₂
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1773	D₅₉
hypocenter	C₅₉	#21559
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
2. #21433000	C₂	semidirect
3. C₂×#16837525	C₂	semidirect
4. #21432521	C₂	semidirect
5. #21424992	C₂	semidirect
6. #21424887	C₂	semidirect
7. #21424766	C₂	semidirect
8. #21424596	C₂	semidirect
9. #21424147	C₂	semidirect
10. #21423897	C₂	semidirect
11. C₅₉×#1773	C₂	semidirect
18. #16837678	C₄	semidirect
19. #16837673	C₄	semidirect
20. #16837666	C₄	semidirect
59. C₂×Dic₂₃₆	C₂×C₄	semidirect
60. C₂×#11745660	C₂×C₄	semidirect
61. C₂×D₄₇₂	C₂×C₄	semidirect
94. #14273645	C₂×C₄	semidirect
95. #14273643	C₂×C₄	semidirect
108. #108×C₅₉	C₂×C₄	semidirect
109. #108×C₅₉	C₂×C₄	semidirect
262. #1773	D₅₉	semidirect
306. C₅₉	#21559	semidirect
354. #108	C₄×D₅₉	semidirect
355. #108	C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433817	2
#21433000	2
C₂×#16837525	2
#21432521	2
#21424992	2
#21424887	2
#21424766	2
#21424596	2
#21424147	2
#21423897	2
C₅₉×#1773	2
#21559	59