Subgroups — #36597024

Order 22784.

830 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029976	C₂	1	2	yes	maximal, complemented
2	C₂×#19151865	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029153	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028860	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021650	C₂	1	2	yes	maximal, complemented
6	#26021522	C₂	1	2	yes	maximal, complemented
7	#26021163	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021043	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020735	C₂	1	2	yes	maximal, complemented
10	#26020302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#472×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152396	C₂²	1	1	yes	characteristic
13	C₂×#15668038	C₂²	1	2	yes	—
14	#19152364	C₂²	1	2	yes	—
15	C₂×#15668018	C₂²	1	1	yes	characteristic
16	#19151865	—	2	4	no	—
17	#19151865	—	2	2	no	—
18	#19151865	—	2	2	no	—
19	#19151858	—	2	4	no	—
20	#19151718	—	2	2	no	—
21	#19151713	—	2	2	no	—
22	#19151647	C₂²	1	2	yes	—
23	#19151646	C₂²	1	1	yes	characteristic
24	#19151646	C₂²	1	2	yes	—
25	#19151645	—	2	2	no	—
26	C₂×#15667948	C₂²	1	1	yes	characteristic
27	C₂×#15667948	C₂²	1	1	yes	characteristic
28	#108×D₈₉	—	2	2	no	—
29	#19151615	C₂²	1	1	yes	characteristic
30	#19151614	C₂²	1	1	yes	characteristic
31	#19151603	C₂²	1	2	yes	—
32	#19151582	C₂²	1	2	yes	—
33	C₂×#15667929	C₂²	1	2	yes	—
34	C₂×#15667929	C₂²	1	2	yes	—
35	#19151553	C₂²	1	1	yes	characteristic
36	#19151370	C₂²	1	2	yes	—
37	#19151356	C₂²	1	2	yes	—
38	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
39	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
41	#472×C₈₉	—	2	2	no	—
42	#472×C₈₉	—	2	2	no	—
43	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#100×C₈₉	C₂²	1	2	yes	—
45	C₂×#13083574	C₂³	1	1	yes	characteristic
46	#15668043	D₄	1	2	yes	—
47	#15668042	—	2	1	no	—
48	#15668038	—	2	4	no	—
49	#15668038	—	2	4	no	—
50	#15668038	D₄	1	2	yes	—
51	#15668037	—	2	1	no	—
52	#15668032	—	2	2	no	—
53	C₂×#13083562	—	2	2	no	—
54	C₂×#13083559	—	2	2	no	—
55	#15668020	—	4	2	no	—
56	#15668018	—	2	4	no	—
57	#15668018	—	2	1	no	—
58	#15668018	—	2	1	no	—
59	#15668018	D₄	1	2	yes	—
60	#15668018	D₄	1	2	yes	—
61	C₂×#13083558	C₂³	1	2	yes	—
62	C₂×#13083558	C₂³	1	2	yes	—
63	C₂×#13083558	C₂³	1	1	yes	characteristic
64	C₂×#13083558	C₂³	1	1	yes	characteristic
65	C₂×#13083557	—	2	1	no	—
66	M₁₆×D₈₉	—	2	4	no	—
67	C₂×C₈×D₈₉	—	2	1	no	—
68	#15667971	C₂³	1	1	yes	characteristic
69	#15667948	—	2	4	no	—
70	#15667948	—	2	1	no	—
71	#15667948	—	2	1	no	—
72	#15667948	—	2	1	no	—
73	#15667948	—	2	1	no	—
74	#15667947	—	2	2	no	—
75	#15667947	—	2	4	no	—
76	#15667939	—	2	2	no	—
77	#15667938	—	2	2	no	—
78	#15667933	—	4	2	no	—
79	#15667931	—	2	2	no	—
80	#15667929	—	2	4	no	—
81	#15667929	—	2	4	no	—
82	#15667929	—	2	2	no	—
83	#15667922	—	2	1	no	—
84	C₈×Dic₈₉	—	2	1	no	—
85	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
87	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
88	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
89	C₂×SD₁₆×C₈₉	—	2	2	no	—
90	C₂×D₈×C₈₉	—	2	2	no	—
91	C₂×D₈×C₈₉	—	2	1	no	—
92	C₂×D₈×C₈₉	—	2	1	no	—
93	C₂×D₈×C₈₉	—	2	1	no	—
94	C₂×D₈×C₈₉	—	2	1	no	—
95	C₂×D₈×C₈₉	—	2	1	no	—
96	C₂×D₈×C₈₉	—	2	1	no	—
97	#131×C₈₉	—	2	1	no	—
98	#131×C₈₉	—	2	1	no	—
99	#131×C₈₉	—	2	1	no	—
100	#131×C₈₉	—	2	1	no	—
101	C₂×M₁₆×C₈₉	—	2	1	no	—
102	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₈₉	—	2	1	no	—
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	#108×C₈₉	D₄	1	2	yes	—
107	#108×C₈₉	D₄	1	2	yes	—
108	#100×C₈₉	—	2	4	no	—
109	#13083574	—	2	1	no	—
110	#13083574	—	2	1	no	—
111	#13083574	C₂×D₄	1	2	yes	—
112	#13083574	C₂×D₄	1	2	yes	—
113	C₂×Dic₁₇₈	#41	1	1	yes	characteristic
114	C₂×D₃₅₆	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	#13083564	—	2	2	no	—
118	#13083562	—	2	2	no	—
119	#13083562	—	4	4	no	—
120	#13083561	—	2	2	no	—
121	#13083559	—	2	2	no	—
122	#13083559	—	4	4	no	—
123	#13083558	—	2	1	no	—
124	#13083558	—	2	1	no	—
125	#13083558	—	2	2	no	—
126	#13083558	—	2	2	no	—
127	#13083558	—	2	2	no	—
128	#13083558	—	2	2	no	—
129	#13083558	C₂×D₄	1	2	yes	—
130	#13083558	C₂×D₄	1	2	yes	—
131	#13083557	—	2	2	no	—
132	#13083557	—	2	2	no	—
133	#13083557	—	4	4	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	2	no	—
137	C₂×#10623494	—	2	2	no	—
138	C₈×D₈₉	—	2	2	no	—
139	C₈×D₈₉	—	2	2	no	—
140	C₈×D₈₉	—	4	4	no	—
141	C₄⋊Dic₈₉	—	2	1	no	—
142	C₂²⋊Dic₈₉	—	2	1	no	—
143	C₄×Dic₈₉	—	2	1	no	—
144	C₂⁴×C₈₉	—	2	2	no	—
145	#41×C₈₉	—	2	1	no	—
146	#41×C₈₉	—	2	1	no	—
147	#41×C₈₉	—	2	1	no	—
148	#41×C₈₉	—	2	1	no	—
149	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₈₉	—	2	1	no	—
151	C₂×D₄×C₈₉	—	2	2	no	—
152	C₂×D₄×C₈₉	—	2	2	no	—
153	C₂×D₄×C₈₉	—	2	2	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂×D₄×C₈₉	—	2	2	no	—
156	C₂×D₄×C₈₉	—	2	2	no	—
157	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	SD₁₆×C₈₉	—	4	4	no	—
161	D₈×C₈₉	—	4	4	no	—
162	D₈×C₈₉	—	4	1	no	—
163	D₈×C₈₉	—	4	1	no	—
164	D₈×C₈₉	—	4	1	no	—
165	D₈×C₈₉	—	4	1	no	—
166	M₁₆×C₈₉	—	2	2	no	—
167	M₁₆×C₈₉	—	2	1	no	—
168	M₁₆×C₈₉	—	2	1	no	—
169	M₁₆×C₈₉	—	4	1	no	—
170	M₁₆×C₈₉	—	4	1	no	—
171	M₁₆×C₈₉	C₂×D₄	1	4	yes	—
172	C₂×C₈×C₈₉	—	2	2	no	—
173	C₂×C₈×C₈₉	—	2	1	no	—
174	C₂×C₈×C₈₉	—	4	1	no	—
175	C₂×C₈×C₈₉	—	4	1	no	—
176	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
181	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
182	C₂³×C₈₉	—	2	1	no	—
183	C₂³×C₈₉	—	4	2	no	—
184	C₂³×C₈₉	—	4	2	no	—
185	C₂³×C₈₉	—	4	2	no	—
186	C₂³×C₈₉	—	16	2	no	—
187	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂²×D₈₉	—	2	1	no	—
189	Q₈×C₈₉	—	2	1	no	—
190	Q₈×C₈₉	—	2	1	no	—
191	D₄×C₈₉	—	2	1	no	—
192	D₄×C₈₉	—	2	1	no	—
193	D₄×C₈₉	—	4	1	no	—
194	D₄×C₈₉	—	4	1	no	—
195	D₄×C₈₉	—	4	2	no	—
196	D₄×C₈₉	—	4	2	no	—
197	D₄×C₈₉	—	4	2	no	—
198	D₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	—	2	1	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²⋊D₈₉	—	2	2	no	—
209	C₂²⋊D₈₉	—	2	2	no	—
210	C₂×Dic₈₉	—	2	1	no	—
211	C₂×Dic₈₉	—	4	1	no	—
212	D₃₅₆	—	2	1	no	—
213	D₃₅₆	#121	1	2	yes	—
214	C₄×D₈₉	—	2	2	no	—
215	C₄×D₈₉	—	2	2	no	—
216	Dic₁₇₈	—	2	1	no	—
217	Dic₁₇₈	#121	1	2	yes	—
218	C₈×C₈₉	—	2	4	no	—
219	C₈×C₈₉	—	4	1	no	—
220	C₈×C₈₉	#121	1	1	yes	characteristic
221	C₈×C₈₉	#121	1	1	yes	characteristic
222	C₈×C₈₉	#121	1	1	yes	characteristic
223	C₈×C₈₉	#121	1	1	yes	characteristic
224	#10623494	—	2	2	no	—
225	#10623494	—	2	2	no	—
226	#10623494	—	4	2	no	—
227	#10623494	—	4	2	no	—
228	C₂²×C₈₉	—	4	1	no	—
229	C₂²×C₈₉	—	4	1	no	—
230	C₂²×C₈₉	—	8	1	no	—
231	C₂²×C₈₉	—	8	2	no	—
232	C₂²×C₈₉	—	16	2	no	—
233	C₂²×C₈₉	—	16	2	no	—
234	C₂²×C₈₉	—	16	2	no	—
235	C₂²×C₈₉	#537	1	1	yes	characteristic
236	C₂²×C₈₉	#547	1	1	yes	characteristic
237	C₂²×C₈₉	#548	1	1	yes	characteristic
238	C₂×D₈₉	—	2	2	no	—
239	C₂×D₈₉	—	8	1	no	—
240	C₄×C₈₉	—	4	1	no	—
241	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
242	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
243	C₄×C₈₉	D₄²	1	1	yes	characteristic
244	C₄×C₈₉	#553	1	1	yes	characteristic
245	Dic₈₉	—	2	2	no	—
246	Dic₈₉	—	8	1	no	—
247	#24809	—	89	1	no	maximal, Sylow
248	C₂×C₈₉	—	2	1	no	—
249	C₂×C₈₉	—	2	1	no	—
250	C₂×C₈₉	—	2	1	no	—
251	C₂×C₈₉	—	8	1	no	—
252	C₂×C₈₉	—	16	2	no	—
253	C₂×C₈₉	#2416	1	1	yes	characteristic
254	D₈₉	—	4	2	no	—
255	#3068	—	89	2	no	—
256	C₂×#472	—	89	1	no	—
257	C₂×#472	D₈₉	1	1	yes	characteristic, complemented
258	#2955	—	89	1	no	—
259	#2916	—	89	1	no	—
260	#2069	—	89	2	no	—
261	#2048	—	89	2	no	—
262	#1978	—	89	1	no	—
263	#1953	—	89	1	no	—
264	#1903	—	89	2	no	—
265	#1813	—	89	1	no	—
266	C₈₉	#24809	1	1	yes	characteristic, complemented, Sylow
267	#575	—	89	1	no	—
268	C₂×AGL(1,ℤ/8)	—	89	2	no	—
269	C₂×AGL(1,ℤ/8)	C₂×D₈₉	1	2	yes	—
270	C₂²×D₈	C₂×D₈₉	1	1	yes	characteristic
271	#568	—	89	2	no	—
272	C₂×#131	—	89	1	no	—
273	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
274	#472	—	2	2	no	—
275	#472	—	2	2	no	—
276	#472	—	178	2	no	—
277	#472	—	178	2	no	—
278	#472	—	178	4	no	—
279	#471	—	178	4	no	—
280	#444	—	178	2	no	—
281	#443	—	178	2	no	—
282	#430	—	89	2	no	—
283	#430	—	89	1	no	—
284	#430	—	89	2	no	—
285	#430	—	178	2	no	—
286	C₂×#108	—	89	1	no	—
287	C₂×#108	—	89	1	no	—
288	C₂×#108	—	178	2	no	—
289	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
290	#421	—	89	1	no	—
291	#421	—	89	1	no	—
292	#418	—	89	2	no	—
293	#413	—	89	2	no	—
294	C₂×#100	—	89	2	no	—
295	C₂×#100	—	89	2	no	—
296	C₂×#100	C₂×D₈₉	1	2	yes	—
297	#405	—	89	1	no	—
298	#344	—	89	2	no	—
299	#338	—	89	2	no	—
300	C₂×#41	—	89	1	no	—
301	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
302	C₂²×D₄	C₂²×D₈₉	1	2	yes	—
303	#137	—	89	2	no	—
304	#137	—	178	1	no	—
305	AGL(1,ℤ/8)	—	2	4	no	—
306	AGL(1,ℤ/8)	—	4	2	no	—
307	AGL(1,ℤ/8)	—	89	2	no	—
308	AGL(1,ℤ/8)	—	178	4	no	—
309	AGL(1,ℤ/8)	—	178	4	no	—
310	AGL(1,ℤ/8)	—	178	1	no	—
311	#135	—	178	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	178	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	1	no	—
316	C₂×D₈	—	2	1	no	—
317	C₂×D₈	—	2	1	no	—
318	C₂×D₈	—	2	1	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	1	no	—
321	C₂×D₈	—	178	2	no	—
322	#131	—	2	1	no	—
323	#131	—	2	1	no	—
324	#131	—	2	1	no	—
325	#131	—	2	1	no	—
326	#131	—	89	2	no	—
327	#131	—	89	2	no	—
328	#131	—	356	2	no	—
329	#131	—	178	4	no	—
330	#131	—	178	1	no	—
331	#131	—	178	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	89	1	no	—
334	C₂×M₁₆	—	89	1	no	—
335	C₂×M₁₆	—	89	2	no	—
336	C₂×M₁₆	—	89	2	no	—
337	C₂×M₁₆	—	178	4	no	—
338	C₂×M₁₆	—	178	1	no	—
339	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
340	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	178	1	no	—
343	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
344	#117	—	89	1	no	—
345	#108	—	178	4	no	—
346	#108	—	178	2	no	—
347	#108	—	178	4	no	—
348	#108	—	178	1	no	—
349	#108	—	178	1	no	—
350	#108	—	178	1	no	—
351	#108	—	178	1	no	—
352	#108	C₂²⋊D₈₉	1	2	yes	—
353	#108	C₂²⋊D₈₉	1	2	yes	—
354	#104	—	178	2	no	—
355	#104	—	178	2	no	—
356	#102	—	356	2	no	—
357	#101	—	178	2	no	—
358	#100	—	2	4	no	—
359	#100	—	178	4	no	—
360	#100	—	178	4	no	—
361	#100	—	178	2	no	—
362	#97	—	178	1	no	—
363	C₄×C₈	—	178	1	no	—
364	C₂⁴	—	2	2	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	89	2	no	—
370	#41	—	89	2	no	—
371	#41	—	178	1	no	—
372	#41	—	178	1	no	—
373	C₂×Q₈	—	89	1	no	—
374	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	89	1	no	—
383	C₂×D₄	—	178	1	no	—
384	C₂×D₄	D₄×D₈₉	1	1	yes	characteristic
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	178	1	no	—
387	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
388	Q₁₆	—	178	2	no	—
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	356	4	no	—
391	SD₁₆	—	178	2	no	—
392	SD₁₆	—	178	2	no	—
393	D₈	—	4	4	no	—
394	D₈	—	4	1	no	—
395	D₈	—	4	1	no	—
396	D₈	—	4	1	no	—
397	D₈	—	4	1	no	—
398	D₈	—	356	4	no	—
399	D₈	—	178	2	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	4	1	no	—
404	M₁₆	—	4	1	no	—
405	M₁₆	—	89	2	no	—
406	M₁₆	—	89	2	no	—
407	M₁₆	—	356	4	no	—
408	M₁₆	—	178	2	no	—
409	M₁₆	—	178	2	no	—
410	M₁₆	—	178	2	no	—
411	M₁₆	—	178	2	no	—
412	M₁₆	—	178	1	no	—
413	M₁₆	—	178	1	no	—
414	M₁₆	—	178	2	no	—
415	M₁₆	—	178	2	no	—
416	M₁₆	C₂×C₂²⋊D₈₉	1	4	yes	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	4	1	no	—
420	C₂×C₈	—	4	1	no	—
421	C₂×C₈	—	356	4	no	—
422	C₂×C₈	—	178	2	no	—
423	C₂×C₈	—	178	2	no	—
424	C₂×C₈	—	178	1	no	—
425	C₂×C₈	—	178	1	no	—
426	C₂×C₈	—	178	2	no	—
427	C₂×C₈	—	178	2	no	—
428	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
429	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂×C₈	#13083573	1	1	yes	characteristic
433	C₂×C₈	#13083573	1	1	yes	characteristic
434	C₄⋊C₄	—	178	1	no	—
435	C₂²⋊C₄	—	178	1	no	—
436	C₄²	—	178	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	16	2	no	—
442	C₂³	—	178	1	no	—
443	C₂³	#15668059	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	89	2	no	—
447	Q₈	—	178	1	no	—
448	D₄	—	2	1	no	—
449	D₄	—	2	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	89	2	no	—
457	D₄	—	178	2	no	—
458	D₄	—	178	2	no	—
459	D₄	—	178	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	356	1	no	—
464	C₂×C₄	—	178	1	no	—
465	C₂×C₄	—	178	2	no	—
466	C₂×C₄	—	178	2	no	—
467	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
470	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
471	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
472	C₂×C₄	#15668057	1	1	yes	characteristic
473	C₈	—	2	4	no	—
474	C₈	—	4	1	no	—
475	C₈	—	356	2	no	—
476	C₈	—	356	2	no	—
477	C₈	—	178	2	no	—
478	C₈	—	178	2	no	—
479	C₈	#15667983	1	1	yes	characteristic
480	C₈	#15667983	1	1	yes	characteristic
481	C₈	#15667983	1	1	yes	characteristic
482	C₈	#15667983	1	1	yes	characteristic
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	16	2	no	—
488	C₂²	—	16	2	no	—
489	C₂²	—	16	2	no	—
490	C₂²	—	178	2	no	—
491	C₂²	—	712	1	no	—
492	C₂²	#19152177	1	1	yes	characteristic
493	C₂²	#19152248	1	1	yes	characteristic
494	C₂²	#19152255	1	1	yes	characteristic
495	C₄	—	4	1	no	—
496	C₄	—	178	2	no	—
497	C₄	—	712	1	no	—
498	C₄	#121×D₈₉	1	1	yes	characteristic
499	C₄	C₂×#15667983	1	1	yes	characteristic
500	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
501	C₄	#19152295	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	1	no	—
506	C₂	—	16	2	no	—
507	C₂	—	356	2	no	—
508	C₂	#26023688	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26023688
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×#472×C₈₉	C₂
socle	C₂×C₈₉	#2416
hypercenter	C₂×#472	D₈₉
hypocenter	C₈₉	#24809
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. #26029976	C₂	semidirect
2. C₂×#19151865	C₂	semidirect
3. #26029153	C₂	semidirect
4. #26028860	C₂	semidirect
5. #26021650	C₂	semidirect
6. #26021522	C₂	semidirect
7. #26021163	C₂	semidirect
8. #26021043	C₂	semidirect
9. #26020735	C₂	semidirect
10. #26020302	C₂	semidirect
11. C₂×#472×C₈₉	C₂	semidirect
257. C₂×#472	D₈₉	semidirect
266. C₈₉	#24809	semidirect

Maximal subgroups

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

subgroup	index
#26029976	2
C₂×#19151865	2
#26029153	2
#26028860	2
#26021650	2
#26021522	2
#26021163	2
#26021043	2
#26020735	2
#26020302	2
C₂×#472×C₈₉	2
#24809	89