Subgroups — #36604230

Order 22784.

732 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030627	C₂	1	1	yes	maximal, characteristic
2	#26030057	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151798	C₂	1	1	yes	maximal, characteristic
4	#26029199	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021613	C₂	1	2	yes	maximal, complemented
6	#26021511	C₂	1	2	yes	maximal, complemented
7	#26021156	C₂	1	2	yes	maximal, complemented
8	#26021092	C₂	1	1	yes	maximal, characteristic
9	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020912	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13083561	C₂²	1	2	yes	—
13	#19152155	C₂²	1	1	yes	characteristic
14	C₂×#15668009	C₂²	1	1	yes	characteristic
15	#19151963	—	2	2	no	—
16	#19151945	—	2	1	no	—
17	#19151945	—	2	1	no	—
18	#19151905	—	2	2	no	—
19	#19151893	—	2	1	no	—
20	#19151883	—	2	1	no	—
21	#19151798	—	2	1	no	—
22	#19151798	—	2	2	no	—
23	#19151798	—	2	1	no	—
24	#19151728	—	2	1	no	—
25	#19151726	—	2	2	no	—
26	C₈×Dic₁₇₈	—	2	1	no	—
27	C₂×#15667947	C₂²	1	2	yes	—
28	#19151638	C₂²	1	2	yes	—
29	#19151626	C₂²	1	2	yes	—
30	#19151622	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151607	C₂²	1	2	yes	—
33	#19151604	C₂²	1	2	yes	—
34	#19151604	C₂²	1	2	yes	—
35	C₂×#15667932	C₂²	1	2	yes	—
36	C₂×#15667928	C₂²	1	2	yes	—
37	C₂×#15667928	C₂²	1	2	yes	—
38	#19151556	C₂²	1	2	yes	—
39	#19151362	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#101×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
45	#343×C₈₉	C₂²	1	1	yes	characteristic
46	#343×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×D₃₅₆	—	2	1	no	—
48	C₂²×D₃₅₆	—	2	1	no	—
49	C₂²×D₃₅₆	C₂³	1	2	yes	—
50	C₂×#13083561	—	2	2	no	—
51	C₂×#13083561	—	2	2	no	—
52	C₂×#13083561	—	2	4	no	—
53	C₂×#13083561	—	4	2	no	—
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂²×#10623494	C₂³	1	2	yes	—
56	#15668012	D₄	1	1	yes	characteristic
57	#15668012	D₄	1	1	yes	characteristic
58	#15668009	—	2	1	no	—
59	#15668009	—	2	1	no	—
60	#15668009	—	2	1	no	—
61	#15668009	—	2	1	no	—
62	#15668004	D₄	1	2	yes	—
63	#15667991	—	2	1	no	—
64	#15667991	—	2	1	no	—
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×Dic₁₇₈	—	2	1	no	—
67	#15667971	C₂³	1	2	yes	—
68	#15667947	—	4	2	no	—
69	#15667945	—	2	2	no	—
70	#15667943	—	2	2	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	D₄	1	1	yes	characteristic
74	C₄⋊#10623494	D₄	1	2	yes	—
75	C₄⋊#10623494	D₄	1	1	yes	characteristic
76	#15667941	—	2	2	no	—
77	#15667941	—	2	2	no	—
78	#15667936	—	2	2	no	—
79	#15667936	—	2	2	no	—
80	#15667934	—	2	2	no	—
81	#15667934	—	2	2	no	—
82	#15667934	—	2	2	no	—
83	#15667934	—	2	2	no	—
84	#15667932	—	2	2	no	—
85	#15667932	—	2	2	no	—
86	#15667928	—	2	4	no	—
87	#15667928	—	4	2	no	—
88	#15667922	—	2	2	no	—
89	C₈×Dic₈₉	—	2	2	no	—
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₄×Q₈×C₈₉	—	2	1	no	—
97	C₄×Q₈×C₈₉	—	2	1	no	—
98	C₄×Q₈×C₈₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	—	2	1	no	—
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	#101×C₈₉	—	2	2	no	—
104	#101×C₈₉	—	2	2	no	—
105	#97×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	—	2	1	no	—
109	C₂³×D₈₉	—	2	2	no	—
110	C₂×Dic₁₇₈	—	2	1	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×D₃₅₆	—	2	2	no	—
113	C₂×D₃₅₆	—	2	2	no	—
114	C₂×D₃₅₆	—	2	2	no	—
115	C₂×D₃₅₆	—	2	2	no	—
116	C₂×D₃₅₆	—	2	2	no	—
117	C₂×D₃₅₆	—	2	2	no	—
118	C₂×D₃₅₆	—	4	1	no	—
119	C₂×D₃₅₆	—	4	1	no	—
120	C₂×D₃₅₆	—	4	1	no	—
121	C₂×D₃₅₆	—	4	1	no	—
122	C₂×D₃₅₆	—	8	2	no	—
123	C₂×D₃₅₆	—	8	2	no	—
124	#13083561	—	4	4	no	—
125	#13083561	—	4	4	no	—
126	#13083558	—	2	2	no	—
127	#13083558	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₂×#10623494	—	2	2	no	—
131	C₂×#10623494	C₂×D₄	1	2	yes	—
132	C₂×#10623494	C₂×D₄	1	2	yes	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
136	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
137	#13083553	—	2	2	no	—
138	#13083553	—	2	2	no	—
139	C₂²⋊Dic₈₉	—	2	2	no	—
140	C₄×Dic₈₉	—	2	2	no	—
141	C₂×Q₈×C₈₉	—	2	1	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	#41	1	2	yes	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	M₁₆×C₈₉	—	2	1	no	—
153	M₁₆×C₈₉	—	2	1	no	—
154	M₁₆×C₈₉	—	2	1	no	—
155	M₁₆×C₈₉	—	2	1	no	—
156	M₁₆×C₈₉	—	2	1	no	—
157	M₁₆×C₈₉	—	2	1	no	—
158	M₁₆×C₈₉	—	2	1	no	—
159	M₁₆×C₈₉	#41	1	2	yes	—
160	C₂×C₈×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	1	no	—
165	C₄⋊C₄×C₈₉	—	2	1	no	—
166	C₄⋊C₄×C₈₉	—	4	1	no	—
167	C₄⋊C₄×C₈₉	—	4	1	no	—
168	C₄²×C₈₉	—	4	1	no	—
169	C₄²×C₈₉	—	4	1	no	—
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂²×D₈₉	—	4	2	no	—
176	C₂²×D₈₉	—	4	2	no	—
177	C₂²×D₈₉	—	4	2	no	—
178	C₂²×D₈₉	—	8	2	no	—
179	C₂²×D₈₉	—	8	2	no	—
180	Q₈×C₈₉	—	2	2	no	—
181	Q₈×C₈₉	—	2	2	no	—
182	Q₈×C₈₉	—	4	1	no	—
183	Q₈×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	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	1	no	—
190	C₂×C₄×C₈₉	—	8	1	no	—
191	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×Dic₈₉	—	2	2	no	—
202	C₂×Dic₈₉	—	2	2	no	—
203	D₃₅₆	—	4	2	no	—
204	D₃₅₆	—	4	2	no	—
205	D₃₅₆	—	4	2	no	—
206	D₃₅₆	—	4	2	no	—
207	D₃₅₆	—	8	2	no	—
208	D₃₅₆	—	8	2	no	—
209	D₃₅₆	—	8	2	no	—
210	D₃₅₆	—	8	2	no	—
211	Dic₁₇₈	—	4	2	no	—
212	Dic₁₇₈	—	8	1	no	—
213	C₈×C₈₉	—	2	2	no	—
214	C₈×C₈₉	—	4	1	no	—
215	C₈×C₈₉	—	4	1	no	—
216	C₈×C₈₉	—	4	1	no	—
217	#10623494	—	2	2	no	—
218	#10623494	—	2	2	no	—
219	#10623494	—	4	2	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	—	8	2	no	—
226	C₂×D₈₉	—	8	2	no	—
227	C₂×D₈₉	—	8	2	no	—
228	C₂×D₈₉	—	16	2	no	—
229	C₂×D₈₉	—	16	2	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	#471	1	2	yes	—
236	C₄×C₈₉	#546	1	1	yes	characteristic
237	C₄×C₈₉	#548	1	1	yes	characteristic
238	C₄×C₈₉	#548	1	1	yes	characteristic
239	C₄×C₈₉	#550	1	1	yes	characteristic
240	Dic₈₉	—	4	2	no	—
241	Dic₈₉	—	4	2	no	—
242	#25315	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	2	1	no	—
244	C₂×C₈₉	—	2	1	no	—
245	C₂×C₈₉	#2426	1	1	yes	characteristic
246	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
247	C₂×C₈₉	#3068	1	1	yes	characteristic
248	D₈₉	—	16	2	no	—
249	#3138	—	89	1	no	—
250	#3078	—	89	1	no	—
251	C₂×#460	—	89	1	no	—
252	#2962	—	89	1	no	—
253	#2063	—	89	2	no	—
254	#2046	—	89	2	no	—
255	#1977	—	89	2	no	—
256	#1965	—	89	1	no	—
257	#1950	—	89	1	no	—
258	#1931	—	89	2	no	—
259	C₄×#101	D₈₉	1	1	yes	characteristic, complemented
260	C₈₉	#25315	1	1	yes	characteristic, complemented, Sylow
261	C₂²×SD₁₆	—	89	2	no	—
262	#533	—	89	1	no	—
263	C₂×#127	—	89	1	no	—
264	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
265	#490	—	178	2	no	—
266	#486	—	178	1	no	—
267	#486	—	178	1	no	—
268	#479	—	178	2	no	—
269	#477	—	178	1	no	—
270	#475	—	178	1	no	—
271	#460	—	178	1	no	—
272	#460	—	178	2	no	—
273	#460	—	178	1	no	—
274	#446	—	178	1	no	—
275	#446	—	178	2	no	—
276	C₈×Q₈	—	178	1	no	—
277	C₂×#108	—	89	2	no	—
278	#428	—	89	2	no	—
279	#424	—	89	2	no	—
280	#423	—	89	1	no	—
281	C₂×C₄⋊C₈	—	89	1	no	—
282	#419	—	89	2	no	—
283	#418	—	89	2	no	—
284	#418	—	89	2	no	—
285	C₂×#102	—	89	2	no	—
286	C₂×#101	C₂×D₈₉	1	1	yes	characteristic
287	C₂×#101	C₂×D₈₉	1	1	yes	characteristic
288	C₂×#100	—	89	2	no	—
289	C₂×#100	—	89	2	no	—
290	#405	—	89	2	no	—
291	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
292	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
293	#343	C₂×D₈₉	1	1	yes	characteristic
294	#343	C₂×D₈₉	1	1	yes	characteristic
295	#341	—	89	2	no	—
296	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₂²×D₄	—	89	2	no	—
298	C₂²×D₄	—	178	1	no	—
299	C₂²×D₄	—	178	1	no	—
300	C₂×SD₁₆	—	356	2	no	—
301	C₂×SD₁₆	—	178	2	no	—
302	C₂×SD₁₆	—	178	2	no	—
303	C₂×SD₁₆	—	178	4	no	—
304	C₂×M₁₆	—	89	2	no	—
305	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
306	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
307	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
308	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
309	C₂²×C₈	—	89	2	no	—
310	C₄⋊Q₈	—	89	1	no	—
311	C₄⋊Q₈	—	89	1	no	—
312	#127	—	178	1	no	—
313	#127	—	178	1	no	—
314	#127	—	178	1	no	—
315	#127	—	178	1	no	—
316	#125	—	89	2	no	—
317	C₂²⋊Q₈	—	178	1	no	—
318	C₂²⋊Q₈	—	178	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	178	1	no	—
324	C₄×Q₈	—	178	1	no	—
325	#117	—	89	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
330	#108	—	356	2	no	—
331	#107	—	178	2	no	—
332	#106	—	178	2	no	—
333	C₄⋊C₈	—	89	1	no	—
334	C₄⋊C₈	—	89	1	no	—
335	C₄⋊C₈	—	89	2	no	—
336	C₄⋊C₈	—	178	2	no	—
337	C₄⋊C₈	—	178	2	no	—
338	C₄⋊C₈	—	178	1	no	—
339	C₄⋊C₈	—	178	1	no	—
340	#103	—	178	2	no	—
341	#103	—	178	2	no	—
342	#102	—	178	2	no	—
343	#102	—	178	2	no	—
344	#102	—	178	2	no	—
345	#102	—	178	2	no	—
346	#102	—	178	2	no	—
347	#102	—	178	2	no	—
348	#101	—	2	2	no	—
349	#101	—	2	2	no	—
350	#100	—	356	2	no	—
351	#100	—	178	4	no	—
352	#97	—	2	1	no	—
353	#97	—	2	1	no	—
354	#97	—	178	2	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	2	1	no	—
357	C₄×C₈	—	178	2	no	—
358	C₂⁴	—	178	2	no	—
359	C₂×Q₈	—	2	1	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	—	178	1	no	—
365	C₂×Q₈	—	178	1	no	—
366	C₂×Q₈	#13083574	1	2	yes	—
367	C₂×D₄	—	356	1	no	—
368	C₂×D₄	—	356	1	no	—
369	C₂×D₄	—	356	1	no	—
370	C₂×D₄	—	356	1	no	—
371	C₂×D₄	—	178	2	no	—
372	C₂×D₄	—	178	2	no	—
373	C₂×D₄	—	178	2	no	—
374	C₂×D₄	—	178	2	no	—
375	C₂×D₄	—	178	2	no	—
376	C₂×D₄	—	178	2	no	—
377	C₂×D₄	—	712	2	no	—
378	C₂×D₄	—	712	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	#13083574	1	1	yes	characteristic
382	C₂²×C₄	#13083574	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
384	SD₁₆	—	356	4	no	—
385	SD₁₆	—	356	4	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	1	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	2	1	no	—
393	M₁₆	—	178	2	no	—
394	M₁₆	—	178	2	no	—
395	M₁₆	#13083574	1	2	yes	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	89	2	no	—
401	C₂×C₈	—	89	2	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	89	2	no	—
410	C₄⋊C₄	—	89	2	no	—
411	C₄⋊C₄	—	178	2	no	—
412	C₄⋊C₄	—	178	2	no	—
413	C₄⋊C₄	—	178	1	no	—
414	C₄⋊C₄	—	178	1	no	—
415	C₂²⋊C₄	—	178	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	178	2	no	—
419	C₄²	D₄×D₈₉	1	1	yes	characteristic
420	C₄²	D₄×D₈₉	1	1	yes	characteristic
421	C₄²	D₄×D₈₉	1	1	yes	characteristic
422	C₄²	D₄×D₈₉	1	1	yes	characteristic
423	C₂³	—	356	2	no	—
424	C₂³	—	356	2	no	—
425	C₂³	—	356	2	no	—
426	C₂³	—	712	2	no	—
427	C₂³	—	712	2	no	—
428	C₂³	C₂×#13083574	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	1	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	356	2	no	—
434	Q₈	—	712	1	no	—
435	D₄	—	356	2	no	—
436	D₄	—	356	2	no	—
437	D₄	—	356	2	no	—
438	D₄	—	356	2	no	—
439	D₄	—	712	2	no	—
440	D₄	—	712	2	no	—
441	D₄	—	712	2	no	—
442	D₄	—	712	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	1	no	—
450	C₂×C₄	—	178	2	no	—
451	C₂×C₄	—	178	2	no	—
452	C₂×C₄	#15667985	1	1	yes	characteristic
453	C₂×C₄	#15667985	1	1	yes	characteristic
454	C₂×C₄	#15667985	1	1	yes	characteristic
455	C₂×C₄	#15667985	1	1	yes	characteristic
456	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
459	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
460	C₂×C₄	#15668058	1	1	yes	characteristic
461	C₂×C₄	#15668059	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	356	2	no	—
467	C₈	—	178	2	no	—
468	C₈	—	178	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	1424	2	no	—
472	C₂²	—	1424	2	no	—
473	C₂²	—	712	2	no	—
474	C₂²	—	712	2	no	—
475	C₂²	—	712	2	no	—
476	C₂²	C₂×#15667985	1	1	yes	characteristic
477	C₂²	#19152132	1	1	yes	characteristic
478	C₂²	#19152219	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	356	2	no	—
485	C₄	—	356	2	no	—
486	C₄	#19151864	1	2	yes	—
487	C₄	#19152244	1	1	yes	characteristic
488	C₄	#19152257	1	1	yes	characteristic
489	C₄	#19152257	1	1	yes	characteristic
490	C₄	#19152269	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	1424	2	no	—
494	C₂	#26023818	1	1	yes	characteristic
495	C₂	C₂×#19151864	1	1	yes	characteristic
496	C₂	#26029983	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667985
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#101×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#15668009	C₂²
hypercenter	C₄×#101	D₈₉
hypocenter	C₈₉	#25315
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#101

Complements

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

N	H ≅ G/N	type
2. #26030057	C₂	semidirect
4. #26029199	C₂	semidirect
5. #26021613	C₂	semidirect
6. #26021511	C₂	semidirect
7. #26021156	C₂	semidirect
9. #26021027	C₂	semidirect
10. #26020912	C₂	semidirect
11. C₄×#101×C₈₉	C₂	semidirect
259. C₄×#101	D₈₉	semidirect
260. C₈₉	#25315	semidirect

Maximal subgroups

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

subgroup	index
#26030627	2
#26030057	2
C₂×#19151798	2
#26029199	2
#26021613	2
#26021511	2
#26021156	2
#26021092	2
#26021027	2
#26020912	2
C₄×#101×C₈₉	2
#25315	89