Subgroups — #36604836

Order 22784.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030648	C₂	1	1	yes	maximal, characteristic
2	#26029724	C₂	1	1	yes	maximal, characteristic
3	#26028995	C₂	1	1	yes	maximal, characteristic
4	#26021698	C₂	1	2	yes	maximal, complemented
5	#26021552	C₂	1	2	yes	maximal, complemented
6	#26021242	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020770	C₂	1	2	yes	maximal, complemented
9	#26020312	C₂	1	2	yes	maximal, complemented
10	C₄×#15667931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#475×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668043	C₂²	1	2	yes	—
13	C₂×#15668018	C₂²	1	2	yes	—
14	#19152148	C₂²	1	1	yes	characteristic
15	#19151960	—	2	2	no	—
16	#19151950	—	2	1	no	—
17	#19151946	—	2	1	no	—
18	#19151820	—	2	2	no	—
19	#19151808	—	2	1	no	—
20	#19151798	—	2	1	no	—
21	#19151675	—	2	1	no	—
22	#19151668	—	2	2	no	—
23	#19151663	—	2	1	no	—
24	C₂×#15667948	C₂²	1	2	yes	—
25	#19151622	C₂²	1	1	yes	characteristic
26	#19151597	C₂²	1	2	yes	—
27	#19151597	C₂²	1	2	yes	—
28	#19151597	C₂²	1	2	yes	—
29	C₂×#15667931	C₂²	1	1	yes	characteristic
30	C₂×#15667931	C₂²	1	1	yes	characteristic
31	#19151564	C₂²	1	2	yes	—
32	C₄×#13083558	C₂²	1	1	yes	characteristic
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151367	C₂²	1	1	yes	characteristic
35	#19151367	C₂²	1	2	yes	—
36	#19151367	C₂²	1	2	yes	—
37	#19151367	C₂²	1	1	yes	characteristic
38	#19151363	C₂²	1	2	yes	—
39	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#475×C₈₉	—	2	1	no	—
42	#475×C₈₉	—	2	2	no	—
43	#475×C₈₉	—	2	1	no	—
44	C₂×#106×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂³	1	2	yes	—
48	#15668043	—	2	4	no	—
49	#15668043	—	4	2	no	—
50	C₂×#13083564	—	2	2	no	—
51	C₂×#13083561	—	2	2	no	—
52	#15668018	—	2	4	no	—
53	#15668018	—	4	2	no	—
54	C₂×#13083558	C₂³	1	1	yes	characteristic
55	C₂×#13083558	C₂³	1	2	yes	—
56	C₂×#13083558	C₂³	1	1	yes	characteristic
57	C₂×#13083558	C₂³	1	1	yes	characteristic
58	C₂×#13083558	C₂³	1	1	yes	characteristic
59	C₂×#13083557	—	2	2	no	—
60	C₂×C₈×D₈₉	—	2	2	no	—
61	#15668012	D₄	1	1	yes	characteristic
62	#15668009	D₄	1	1	yes	characteristic
63	#15668000	D₄	1	2	yes	—
64	#15667986	—	2	1	no	—
65	#15667986	—	2	1	no	—
66	C₄×D₃₅₆	—	2	1	no	—
67	C₄×D₃₅₆	—	2	1	no	—
68	#15667948	—	4	2	no	—
69	C₄⋊#10623494	—	2	1	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	#15667935	—	2	2	no	—
72	#15667935	—	2	2	no	—
73	#15667935	—	2	2	no	—
74	#15667932	—	2	2	no	—
75	#15667932	—	2	2	no	—
76	#15667932	—	2	2	no	—
77	#15667931	—	2	2	no	—
78	#15667931	—	2	2	no	—
79	#15667924	—	2	2	no	—
80	#15667924	—	2	2	no	—
81	#15667923	—	2	1	no	—
82	#15667923	—	2	1	no	—
83	C₄×#10623494	—	2	1	no	—
84	C₄×#10623494	—	2	1	no	—
85	C₂²×Q₈×C₈₉	—	2	1	no	—
86	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
88	C₄⋊Q₈×C₈₉	—	2	1	no	—
89	C₄⋊Q₈×C₈₉	—	2	1	no	—
90	C₄⋊Q₈×C₈₉	—	2	1	no	—
91	C₄⋊Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	#106×C₈₉	—	2	2	no	—
103	#106×C₈₉	—	2	2	no	—
104	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
106	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
107	#103×C₈₉	—	2	2	no	—
108	#103×C₈₉	—	2	2	no	—
109	#13083574	—	2	2	no	—
110	#13083574	—	2	2	no	—
111	#13083574	—	2	2	no	—
112	#13083574	—	2	2	no	—
113	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
114	C₂×D₃₅₆	—	2	1	no	—
115	C₂×D₃₅₆	—	2	1	no	—
116	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
117	C₂×C₂²⋊D₈₉	—	2	2	no	—
118	C₂×C₄×D₈₉	—	2	2	no	—
119	#13083564	—	4	4	no	—
120	#13083561	—	4	4	no	—
121	#13083558	—	2	1	no	—
122	#13083558	—	2	2	no	—
123	#13083558	—	2	1	no	—
124	#13083558	—	2	1	no	—
125	#13083558	—	2	1	no	—
126	#13083558	—	2	2	no	—
127	#13083558	—	2	1	no	—
128	#13083558	—	2	1	no	—
129	#13083558	—	2	1	no	—
130	#13083558	#41	1	2	yes	—
131	#13083557	—	4	4	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	—	2	2	no	—
134	C₂×#10623494	—	2	1	no	—
135	C₂×#10623494	—	2	1	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₈×D₈₉	—	4	4	no	—
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	—	2	1	no	—
140	#13083551	—	2	2	no	—
141	#13083551	—	2	2	no	—
142	C₂×Q₈×C₈₉	—	2	1	no	—
143	C₂×Q₈×C₈₉	—	2	1	no	—
144	C₂×Q₈×C₈₉	—	2	1	no	—
145	C₂×Q₈×C₈₉	—	2	1	no	—
146	C₂×Q₈×C₈₉	—	2	1	no	—
147	C₂×Q₈×C₈₉	—	4	1	no	—
148	C₂×Q₈×C₈₉	—	4	1	no	—
149	C₂×Q₈×C₈₉	—	8	2	no	—
150	C₂×Q₈×C₈₉	#41	1	2	yes	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	2	no	—
154	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₈×C₈₉	—	2	2	no	—
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₈₉	—	2	2	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₄⋊C₄×C₈₉	—	4	1	no	—
166	C₄⋊C₄×C₈₉	—	4	1	no	—
167	C₄⋊C₄×C₈₉	—	4	1	no	—
168	C₄⋊C₄×C₈₉	—	4	1	no	—
169	C₄²×C₈₉	—	4	1	no	—
170	C₄²×C₈₉	—	4	1	no	—
171	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂²×D₈₉	—	2	2	no	—
177	Q₈×C₈₉	—	2	2	no	—
178	Q₈×C₈₉	—	2	2	no	—
179	Q₈×C₈₉	—	4	1	no	—
180	Q₈×C₈₉	—	4	1	no	—
181	Q₈×C₈₉	—	8	2	no	—
182	Q₈×C₈₉	—	8	2	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	4	1	no	—
186	C₂×C₄×C₈₉	—	4	1	no	—
187	C₂×C₄×C₈₉	—	4	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	8	1	no	—
191	C₂×C₄×C₈₉	—	8	2	no	—
192	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
193	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂²⋊D₈₉	—	4	2	no	—
203	C₂²⋊D₈₉	—	4	2	no	—
204	C₂×Dic₈₉	—	2	2	no	—
205	D₃₅₆	—	2	2	no	—
206	D₃₅₆	—	2	2	no	—
207	D₃₅₆	—	4	2	no	—
208	D₃₅₆	—	8	1	no	—
209	C₄×D₈₉	—	4	2	no	—
210	C₄×D₈₉	—	4	2	no	—
211	Dic₁₇₈	—	2	2	no	—
212	Dic₁₇₈	—	2	2	no	—
213	C₈×C₈₉	—	2	2	no	—
214	C₈×C₈₉	—	2	2	no	—
215	#10623494	—	2	2	no	—
216	#10623494	—	4	1	no	—
217	#10623494	—	4	2	no	—
218	#10623494	—	4	1	no	—
219	#10623494	—	4	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	1	no	—
222	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
223	C₂²×C₈₉	#529	1	1	yes	characteristic
224	C₂²×C₈₉	#542	1	1	yes	characteristic
225	C₂×D₈₉	—	4	2	no	—
226	C₂×D₈₉	—	4	2	no	—
227	C₂×D₈₉	—	4	2	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	4	2	no	—
232	C₄×C₈₉	—	8	2	no	—
233	C₄×C₈₉	—	8	1	no	—
234	C₄×C₈₉	#471	1	2	yes	—
235	C₄×C₈₉	#546	1	1	yes	characteristic
236	C₄×C₈₉	#546	1	1	yes	characteristic
237	C₄×C₈₉	#547	1	1	yes	characteristic
238	C₄×C₈₉	#548	1	1	yes	characteristic
239	Dic₈₉	—	4	2	no	—
240	#25361	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	1	no	—
242	C₂×C₈₉	—	2	1	no	—
243	C₂×C₈₉	#2427	1	1	yes	characteristic
244	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
245	C₂×C₈₉	#3069	1	1	yes	characteristic
246	D₈₉	—	8	2	no	—
247	#3141	—	89	1	no	—
248	C₂×#475	D₈₉	1	1	yes	characteristic, complemented
249	#3037	—	89	1	no	—
250	#2935	—	89	1	no	—
251	#2079	—	89	2	no	—
252	#2052	—	89	2	no	—
253	#1997	—	89	1	no	—
254	#1950	—	89	1	no	—
255	#1908	—	89	2	no	—
256	#1815	—	89	2	no	—
257	C₄×#101	—	89	1	no	—
258	C₈₉	#25361	1	1	yes	characteristic, complemented, Sylow
259	C₂×#137	—	89	2	no	—
260	C₂×#131	—	89	2	no	—
261	#532	—	89	1	no	—
262	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
264	#489	—	178	2	no	—
265	#487	—	178	1	no	—
266	#486	—	178	1	no	—
267	#475	—	2	1	no	—
268	#475	—	2	2	no	—
269	#475	—	2	1	no	—
270	#464	—	178	2	no	—
271	#462	—	178	1	no	—
272	#460	—	178	1	no	—
273	#436	—	178	1	no	—
274	#435	—	178	2	no	—
275	C₈×D₄	—	178	1	no	—
276	C₂×#108	—	89	2	no	—
277	C₂×#106	C₂×D₈₉	1	2	yes	—
278	#423	—	89	1	no	—
279	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
280	#417	—	89	2	no	—
281	#417	—	89	2	no	—
282	#417	—	89	2	no	—
283	C₂×#103	C₂×D₈₉	1	2	yes	—
284	C₂×#101	—	89	1	no	—
285	C₂×#101	—	89	1	no	—
286	#408	—	89	2	no	—
287	C₄×M₁₆	—	89	1	no	—
288	C₄×M₁₆	—	89	1	no	—
289	#343	—	89	2	no	—
290	#343	—	89	1	no	—
291	#343	—	89	2	no	—
292	#343	—	89	1	no	—
293	#341	—	89	2	no	—
294	C₂×#41	—	89	2	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	#137	—	356	2	no	—
298	#137	—	178	4	no	—
299	C₂×Q₁₆	—	178	2	no	—
300	C₂×SD₁₆	—	178	2	no	—
301	#131	—	356	2	no	—
302	#131	—	178	4	no	—
303	C₂×M₁₆	—	89	1	no	—
304	C₂×M₁₆	—	89	2	no	—
305	C₂×M₁₆	—	89	1	no	—
306	C₂×M₁₆	—	89	1	no	—
307	C₂×M₁₆	—	89	1	no	—
308	C₂×M₁₆	—	178	2	no	—
309	C₂²×C₈	—	178	2	no	—
310	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	89	1	no	—
316	#127	—	89	1	no	—
317	#124	—	89	2	no	—
318	#121	—	178	1	no	—
319	#121	—	178	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×D₄	—	178	1	no	—
325	C₄×D₄	—	178	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
332	#108	—	356	2	no	—
333	#106	—	2	2	no	—
334	#106	—	2	2	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	—	178	1	no	—
337	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
338	C₄⋊C₈	C₂²⋊D₈₉	1	2	yes	—
339	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
340	#103	—	2	2	no	—
341	#103	—	2	2	no	—
342	#103	—	178	2	no	—
343	#103	—	178	2	no	—
344	#103	—	178	2	no	—
345	#102	—	178	2	no	—
346	#102	—	178	2	no	—
347	#102	—	178	2	no	—
348	#101	—	178	2	no	—
349	#101	—	178	2	no	—
350	C₂²⋊C₈	—	178	2	no	—
351	C₂²⋊C₈	—	178	2	no	—
352	#97	—	178	1	no	—
353	#97	—	178	1	no	—
354	C₄×C₈	—	178	1	no	—
355	C₄×C₈	—	178	1	no	—
356	#41	—	178	2	no	—
357	#41	—	178	2	no	—
358	#41	—	178	2	no	—
359	#41	—	178	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	4	1	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×Q₈	—	8	2	no	—
368	C₂×Q₈	—	89	2	no	—
369	C₂×Q₈	#13083575	1	2	yes	—
370	C₂×D₄	—	89	2	no	—
371	C₂×D₄	—	178	2	no	—
372	C₂×D₄	—	178	1	no	—
373	C₂×D₄	—	178	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	178	2	no	—
378	C₂²×C₄	#13083573	1	1	yes	characteristic
379	C₂²×C₄	#13083573	1	1	yes	characteristic
380	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
381	Q₁₆	—	356	4	no	—
382	SD₁₆	—	356	4	no	—
383	M₁₆	—	89	2	no	—
384	M₁₆	—	356	4	no	—
385	M₁₆	—	178	1	no	—
386	M₁₆	—	178	1	no	—
387	M₁₆	—	178	1	no	—
388	M₁₆	—	178	2	no	—
389	M₁₆	—	178	1	no	—
390	M₁₆	—	178	2	no	—
391	M₁₆	—	178	1	no	—
392	M₁₆	—	178	1	no	—
393	M₁₆	—	178	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	356	4	no	—
397	C₂×C₈	—	178	1	no	—
398	C₂×C₈	—	178	1	no	—
399	C₂×C₈	—	178	2	no	—
400	C₂×C₈	—	178	1	no	—
401	C₂×C₈	—	178	1	no	—
402	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
403	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	—	4	1	no	—
412	C₄⋊C₄	—	178	1	no	—
413	C₄⋊C₄	—	178	1	no	—
414	C₂²⋊C₄	—	178	2	no	—
415	C₂²⋊C₄	—	178	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	4	1	no	—
418	C₄²	D₄×D₈₉	1	1	yes	characteristic
419	C₄²	D₄×D₈₉	1	1	yes	characteristic
420	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
421	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
422	C₂³	—	178	2	no	—
423	C₂³	C₂×#13083573	1	1	yes	characteristic
424	Q₈	—	2	2	no	—
425	Q₈	—	2	2	no	—
426	Q₈	—	4	1	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	8	2	no	—
429	Q₈	—	8	2	no	—
430	Q₈	—	178	2	no	—
431	Q₈	—	178	2	no	—
432	D₄	—	356	2	no	—
433	D₄	—	356	2	no	—
434	D₄	—	356	2	no	—
435	D₄	—	178	2	no	—
436	D₄	—	178	2	no	—
437	D₄	—	712	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	—	356	2	no	—
448	C₂×C₄	—	356	2	no	—
449	C₂×C₄	—	178	2	no	—
450	C₂×C₄	#15667983	1	1	yes	characteristic
451	C₂×C₄	#15667983	1	1	yes	characteristic
452	C₂×C₄	#15667983	1	1	yes	characteristic
453	C₂×C₄	#15667983	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
456	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
458	C₂×C₄	#15668058	1	1	yes	characteristic
459	C₂×C₄	#15668060	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	356	1	no	—
463	C₈	—	356	2	no	—
464	C₈	—	356	1	no	—
465	C₈	—	356	1	no	—
466	C₈	—	178	2	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	356	2	no	—
470	C₂²	—	356	2	no	—
471	C₂²	—	356	2	no	—
472	C₂²	C₂×#15667983	1	1	yes	characteristic
473	C₂²	#19152134	1	1	yes	characteristic
474	C₂²	#19152221	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	356	2	no	—
482	C₄	#19151858	1	2	yes	—
483	C₄	#19152236	1	1	yes	characteristic
484	C₄	#19152239	1	1	yes	characteristic
485	C₄	#19152250	1	1	yes	characteristic
486	C₄	#19152259	1	1	yes	characteristic
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	712	2	no	—
490	C₂	#26023825	1	1	yes	characteristic
491	C₂	C₂×#19151858	1	1	yes	characteristic
492	C₂	#26029985	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×#475×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	C₂×#475	D₈₉
hypocenter	C₈₉	#25361
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#475

Complements

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

N	H ≅ G/N	type
4. #26021698	C₂	semidirect
5. #26021552	C₂	semidirect
6. #26021242	C₂	semidirect
7. #26021028	C₂	semidirect
8. #26020770	C₂	semidirect
9. #26020312	C₂	semidirect
10. C₄×#15667931	C₂	semidirect
11. C₂×#475×C₈₉	C₂	semidirect
248. C₂×#475	D₈₉	semidirect
258. C₈₉	#25361	semidirect

Maximal subgroups

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

subgroup	index
#26030648	2
#26029724	2
#26028995	2
#26021698	2
#26021552	2
#26021242	2
#26021028	2
#26020770	2
#26020312	2
C₄×#15667931	2
C₂×#475×C₈₉	2
#25361	89