Subgroups — #36565057

Order 22784.

704 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	#26028883	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151654	C₂	1	1	yes	maximal, characteristic
3	#423×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26021028	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021027	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021025	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020458	C₂	1	2	yes	maximal
8	#26020455	C₂	1	2	yes	maximal
9	#26020425	C₂	1	2	yes	maximal, complemented
10	#26020391	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₈₉	C₂²	1	2	yes	—
13	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
14	#19151654	C₄	1	2	yes	—
15	#19151654	C₄	1	2	yes	—
16	#19151654	C₄	1	2	yes	—
17	#19151654	C₄	1	2	yes	—
18	#19151653	—	2	1	no	—
19	#19151653	—	2	1	no	—
20	#19151649	—	2	1	no	—
21	#19151649	—	2	1	no	—
22	C₂×#15667948	C₂²	1	2	yes	—
23	C₂×#15667947	C₂²	1	2	yes	—
24	C₂×#15667947	C₂²	1	2	yes	—
25	#19151622	C₂²	1	1	yes	characteristic
26	#19151621	C₂²	1	2	yes	—
27	#19151621	C₂²	1	1	yes	characteristic
28	#19151621	C₂²	1	1	yes	characteristic
29	#19151620	—	2	1	no	—
30	#19151620	—	2	1	no	—
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₈₉	—	2	1	no	—
33	C₄⋊C₈×D₈₉	—	2	1	no	—
34	#19151561	C₂²	1	1	yes	characteristic
35	#19151561	C₂²	1	1	yes	characteristic
36	C₂×#15667924	C₂²	1	2	yes	—
37	C₄×#13083558	C₂²	1	1	yes	characteristic
38	C₂×#15667922	C₂²	1	2	yes	—
39	#19151363	C₂²	1	2	yes	—
40	#19151362	C₂²	1	2	yes	—
41	#19151362	C₂²	1	2	yes	—
42	C₂×#108×C₈₉	C₂²	1	2	yes	—
43	#423×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	#341×C₈₉	C₂²	1	2	yes	—
47	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₈₉	C₂³	1	1	yes	characteristic
50	C₂×#13083558	C₂³	1	1	yes	characteristic
51	C₂×#13083558	C₂³	1	2	yes	—
52	C₂×#13083558	C₂³	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	M₁₆×D₈₉	—	4	2	no	—
55	M₁₆×D₈₉	—	4	2	no	—
56	C₂²×#10623494	C₂³	1	2	yes	—
57	C₂×C₈×D₈₉	—	2	2	no	—
58	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
60	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
61	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₈₉	D₄	1	1	yes	characteristic
66	C₄²×D₈₉	D₄	1	1	yes	characteristic
67	C₄²×D₈₉	D₄	1	1	yes	characteristic
68	C₄²×D₈₉	D₄	1	1	yes	characteristic
69	#15667948	—	4	2	no	—
70	#15667947	—	4	2	no	—
71	#15667947	—	4	2	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	—	2	1	no	—
74	C₄⋊#10623494	C₂×C₄	1	2	yes	—
75	C₄⋊#10623494	C₂×C₄	1	2	yes	—
76	#15667941	—	2	2	no	—
77	#15667941	—	2	2	no	—
78	#15667941	—	2	1	no	—
79	#15667941	—	2	1	no	—
80	#15667941	—	2	1	no	—
81	#15667941	—	2	1	no	—
82	#15667924	—	2	1	no	—
83	#15667924	—	2	1	no	—
84	#15667924	—	2	1	no	—
85	#15667924	—	2	1	no	—
86	#15667924	C₂×C₄	1	4	yes	—
87	#15667924	C₂×C₄	1	4	yes	—
88	#15667923	—	2	1	no	—
89	#15667922	C₂×C₄	1	4	yes	—
90	#15667922	C₂×C₄	1	4	yes	—
91	C₄×#10623494	—	2	1	no	—
92	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
94	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#108×C₈₉	—	4	2	no	—
98	C₄⋊C₈×C₈₉	—	2	1	no	—
99	C₄⋊C₈×C₈₉	—	2	1	no	—
100	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
101	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
102	#97×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	—	2	1	no	—
104	C₂³×D₈₉	C₂×Q₈	1	1	yes	characteristic
105	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
106	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	2	1	no	—
110	C₂×C₄×D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	C₂×C₄×D₈₉	—	4	2	no	—
113	C₂×C₄×D₈₉	—	4	2	no	—
114	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
126	#13083558	—	2	2	no	—
127	#13083558	—	2	2	no	—
128	#13083558	—	2	1	no	—
129	#13083558	—	2	1	no	—
130	#13083558	—	2	1	no	—
131	#13083558	—	2	1	no	—
132	#13083557	—	4	4	no	—
133	C₂×#10623494	—	2	2	no	—
134	C₂×#10623494	—	2	2	no	—
135	C₂×#10623494	—	2	2	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	C₂²×C₄	1	4	yes	—
139	C₈×D₈₉	—	4	4	no	—
140	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
141	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
143	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	M₁₆×C₈₉	—	2	2	no	—
156	M₁₆×C₈₉	—	2	2	no	—
157	M₁₆×C₈₉	—	2	1	no	—
158	M₁₆×C₈₉	—	2	1	no	—
159	M₁₆×C₈₉	—	2	1	no	—
160	M₁₆×C₈₉	—	2	1	no	—
161	C₂×C₈×C₈₉	—	2	2	no	—
162	C₂×C₈×C₈₉	—	2	2	no	—
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
167	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂³×C₈₉	C₂²×Q₈	1	1	yes	characteristic
172	C₂²×D₈₉	—	2	1	no	—
173	C₂²×D₈₉	—	2	1	no	—
174	C₂²×D₈₉	—	2	2	no	—
175	C₂²×D₈₉	—	4	1	no	—
176	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×Dic₈₉	—	2	1	no	—
191	C₂×Dic₈₉	—	2	1	no	—
192	C₂×Dic₈₉	—	4	1	no	—
193	C₂×Dic₈₉	—	4	1	no	—
194	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₄×D₈₉	—	2	2	no	—
201	C₄×D₈₉	—	2	2	no	—
202	C₄×D₈₉	—	2	1	no	—
203	C₄×D₈₉	—	2	1	no	—
204	C₄×D₈₉	—	2	1	no	—
205	C₄×D₈₉	—	2	1	no	—
206	C₄×D₈₉	—	2	1	no	—
207	C₄×D₈₉	—	2	1	no	—
208	C₄×D₈₉	—	2	1	no	—
209	C₄×D₈₉	—	2	1	no	—
210	C₄×D₈₉	—	2	2	no	—
211	C₄×D₈₉	—	2	2	no	—
212	C₄×D₈₉	—	4	1	no	—
213	C₄×D₈₉	—	4	1	no	—
214	C₄×D₈₉	—	4	1	no	—
215	C₄×D₈₉	—	4	1	no	—
216	C₈×C₈₉	—	2	4	no	—
217	C₈×C₈₉	—	4	1	no	—
218	C₈×C₈₉	—	4	2	no	—
219	C₈×C₈₉	—	4	1	no	—
220	#10623494	—	2	4	no	—
221	#10623494	—	4	2	no	—
222	#10623494	—	4	1	no	—
223	#10623494	—	4	1	no	—
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₂²×C₈₉	#544	1	1	yes	characteristic
228	C₂²×C₈₉	#544	1	1	yes	characteristic
229	C₂×D₈₉	—	2	1	no	—
230	C₂×D₈₉	—	2	1	no	—
231	C₂×D₈₉	—	2	1	no	—
232	C₂×D₈₉	—	2	1	no	—
233	C₂×D₈₉	—	2	1	no	—
234	C₂×D₈₉	—	4	2	no	—
235	C₂×D₈₉	—	4	2	no	—
236	C₂×D₈₉	#430	1	2	yes	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	2	1	no	—
240	C₄×C₈₉	#430	1	2	yes	—
241	C₄×C₈₉	#520	1	1	yes	characteristic
242	C₄×C₈₉	#520	1	1	yes	characteristic
243	C₄×C₈₉	#535	1	1	yes	characteristic
244	C₄×C₈₉	#536	1	1	yes	characteristic
245	Dic₈₉	—	2	1	no	—
246	Dic₈₉	—	2	1	no	—
247	Dic₈₉	—	2	1	no	—
248	Dic₈₉	—	2	1	no	—
249	Dic₈₉	—	2	1	no	—
250	Dic₈₉	—	2	1	no	—
251	#21994	—	89	1	no	maximal, Sylow
252	C₂×C₈₉	—	2	1	no	—
253	C₂×C₈₉	—	2	1	no	—
254	C₂×C₈₉	#2317	1	1	yes	characteristic
255	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
256	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
257	D₈₉	—	2	2	no	—
258	D₈₉	—	4	1	no	—
259	#2920	—	89	1	no	—
260	C₂×#432	—	89	1	no	—
261	C₂×#423	—	89	1	no	—
262	#1950	—	89	1	no	—
263	#1950	—	89	1	no	—
264	#1950	—	89	1	no	—
265	#1950	D₈₉	1	1	yes	characteristic, complemented
266	#1855	—	89	2	no	—
267	#1855	—	89	2	no	—
268	#1849	—	89	2	no	—
269	#1838	—	89	2	no	—
270	C₈₉	#21994	1	1	yes	characteristic, complemented, Sylow
271	C₂²×M₁₆	—	89	2	no	—
272	C₂²×C₄²	—	89	1	no	—
273	#432	—	89	2	no	—
274	#432	—	89	2	no	—
275	#432	—	89	2	no	—
276	#432	—	89	2	no	—
277	#432	—	178	1	no	—
278	#432	—	178	1	no	—
279	#431	—	178	1	no	—
280	#431	—	178	1	no	—
281	C₂×#108	—	89	2	no	—
282	C₂×#108	—	89	2	no	—
283	C₂×#108	—	89	2	no	—
284	C₂×#108	C₂×D₈₉	1	2	yes	—
285	#423	—	89	1	no	—
286	#423	—	89	2	no	—
287	#423	—	89	1	no	—
288	#423	—	89	1	no	—
289	#423	—	178	1	no	—
290	#423	—	178	1	no	—
291	#423	C₂×D₈₉	1	1	yes	characteristic
292	C₂×C₄⋊C₈	—	89	1	no	—
293	C₂×C₄⋊C₈	—	178	1	no	—
294	C₂×C₄⋊C₈	—	178	1	no	—
295	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
296	#407	—	89	1	no	—
297	#407	—	89	1	no	—
298	C₂×C₂²⋊C₈	—	89	2	no	—
299	C₄×M₁₆	—	89	1	no	—
300	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
301	C₂×#97	—	89	2	no	—
302	#341	—	89	2	no	—
303	#341	—	89	2	no	—
304	#341	—	89	2	no	—
305	#341	C₂×D₈₉	1	2	yes	—
306	C₂³×C₄	—	89	1	no	—
307	C₂³×C₄	—	89	1	no	—
308	C₂³×C₄	—	89	1	no	—
309	C₂×M₁₆	—	89	2	no	—
310	C₂×M₁₆	—	89	1	no	—
311	C₂×M₁₆	—	89	1	no	—
312	C₂×M₁₆	—	356	2	no	—
313	C₂×M₁₆	—	356	2	no	—
314	C₂×M₁₆	—	178	2	no	—
315	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
316	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
317	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
318	C₂²×C₈	—	89	2	no	—
319	C₂²×C₈	—	178	2	no	—
320	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
321	C₂×C₄²	—	89	1	no	—
322	C₂×C₄²	—	89	1	no	—
323	C₂×C₄²	—	89	1	no	—
324	C₂×C₄²	—	89	1	no	—
325	C₂×C₄²	—	89	1	no	—
326	C₂×C₄²	—	89	1	no	—
327	C₂×C₄²	—	89	1	no	—
328	C₂×C₄²	—	89	1	no	—
329	C₂×C₄²	—	89	1	no	—
330	C₂×C₄²	—	89	1	no	—
331	C₂×C₄²	—	89	1	no	—
332	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
333	#108	—	4	2	no	—
334	#108	—	356	2	no	—
335	#108	—	356	2	no	—
336	#108	—	356	2	no	—
337	C₄⋊C₈	—	2	1	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	89	2	no	—
340	C₄⋊C₈	—	89	2	no	—
341	C₄⋊C₈	—	178	2	no	—
342	C₄⋊C₈	—	178	2	no	—
343	C₄⋊C₈	—	178	1	no	—
344	C₄⋊C₈	—	178	1	no	—
345	C₄⋊C₈	—	178	1	no	—
346	C₄⋊C₈	—	178	1	no	—
347	C₄⋊C₈	—	178	1	no	—
348	C₄⋊C₈	—	178	1	no	—
349	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
350	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
351	C₂²⋊C₈	—	89	4	no	—
352	C₂²⋊C₈	—	89	4	no	—
353	C₂²⋊C₈	—	178	1	no	—
354	C₂²⋊C₈	—	178	1	no	—
355	C₂²⋊C₈	—	178	1	no	—
356	C₂²⋊C₈	—	178	1	no	—
357	#97	—	2	1	no	—
358	#97	—	89	4	no	—
359	#97	—	89	4	no	—
360	#97	—	178	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₄×C₈	—	178	1	no	—
363	C₂⁴	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	—	89	1	no	—
366	C₂²×C₄	—	89	1	no	—
367	C₂²×C₄	—	89	1	no	—
368	C₂²×C₄	—	89	1	no	—
369	C₂²×C₄	—	89	1	no	—
370	C₂²×C₄	—	89	1	no	—
371	C₂²×C₄	—	89	1	no	—
372	C₂²×C₄	—	89	1	no	—
373	C₂²×C₄	—	89	1	no	—
374	C₂²×C₄	—	89	1	no	—
375	C₂²×C₄	—	89	1	no	—
376	C₂²×C₄	—	89	1	no	—
377	C₂²×C₄	—	89	1	no	—
378	C₂²×C₄	—	89	1	no	—
379	C₂²×C₄	—	356	2	no	—
380	C₂²×C₄	—	356	2	no	—
381	C₂²×C₄	—	178	1	no	—
382	C₂²×C₄	—	178	1	no	—
383	C₂²×C₄	—	178	1	no	—
384	C₂²×C₄	—	178	1	no	—
385	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
386	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
387	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	1	no	—
393	M₁₆	—	2	1	no	—
394	M₁₆	—	356	4	no	—
395	M₁₆	—	178	1	no	—
396	M₁₆	—	178	2	no	—
397	M₁₆	—	178	1	no	—
398	M₁₆	—	178	2	no	—
399	M₁₆	—	178	1	no	—
400	M₁₆	—	178	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	89	4	no	—
407	C₂×C₈	—	356	4	no	—
408	C₂×C₈	—	178	1	no	—
409	C₂×C₈	—	178	1	no	—
410	C₂×C₈	—	178	2	no	—
411	C₂×C₈	—	178	2	no	—
412	C₂×C₈	—	178	2	no	—
413	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
414	C₄²	—	89	1	no	—
415	C₄²	—	89	1	no	—
416	C₄²	—	89	1	no	—
417	C₄²	—	89	1	no	—
418	C₄²	—	89	1	no	—
419	C₄²	—	89	1	no	—
420	C₄²	—	89	1	no	—
421	C₄²	—	89	1	no	—
422	C₄²	—	89	1	no	—
423	C₄²	—	89	1	no	—
424	C₄²	—	89	1	no	—
425	C₄²	—	89	1	no	—
426	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
428	C₄²	D₄×D₈₉	1	1	yes	characteristic
429	C₄²	D₄×D₈₉	1	1	yes	characteristic
430	C₂³	—	89	1	no	—
431	C₂³	—	89	1	no	—
432	C₂³	—	356	1	no	—
433	C₂³	—	178	2	no	—
434	C₂³	—	178	1	no	—
435	C₂³	—	178	1	no	—
436	C₂³	C₂×Q₈×D₈₉	1	1	yes	characteristic
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	89	1	no	—
440	C₂×C₄	—	89	1	no	—
441	C₂×C₄	—	89	1	no	—
442	C₂×C₄	—	89	1	no	—
443	C₂×C₄	—	89	1	no	—
444	C₂×C₄	—	89	1	no	—
445	C₂×C₄	—	356	1	no	—
446	C₂×C₄	—	356	1	no	—
447	C₂×C₄	—	356	1	no	—
448	C₂×C₄	—	356	1	no	—
449	C₂×C₄	—	356	1	no	—
450	C₂×C₄	—	356	1	no	—
451	C₂×C₄	—	178	2	no	—
452	C₂×C₄	—	178	2	no	—
453	C₂×C₄	—	178	1	no	—
454	C₂×C₄	—	178	1	no	—
455	C₂×C₄	—	178	2	no	—
456	C₂×C₄	—	178	2	no	—
457	C₂×C₄	—	178	1	no	—
458	C₂×C₄	—	178	1	no	—
459	C₂×C₄	—	178	1	no	—
460	C₂×C₄	—	178	1	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	178	1	no	—
464	C₂×C₄	—	178	1	no	—
465	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
467	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
471	C₂×C₄	#15668057	1	1	yes	characteristic
472	C₂×C₄	#15668058	1	1	yes	characteristic
473	C₂×C₄	#15668059	1	1	yes	characteristic
474	C₂×C₄	#15668060	1	1	yes	characteristic
475	C₈	—	2	4	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	1	no	—
478	C₈	—	4	1	no	—
479	C₈	—	356	2	no	—
480	C₈	—	356	1	no	—
481	C₈	—	356	1	no	—
482	C₈	—	178	4	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	89	2	no	—
486	C₂²	—	356	2	no	—
487	C₂²	—	356	2	no	—
488	C₂²	—	178	1	no	—
489	C₂²	—	178	1	no	—
490	C₂²	—	178	1	no	—
491	C₂²	—	178	1	no	—
492	C₂²	—	178	1	no	—
493	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
494	C₂²	#19152225	1	1	yes	characteristic
495	C₂²	#19152228	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	178	1	no	—
500	C₄	—	178	1	no	—
501	C₄	—	178	1	no	—
502	C₄	—	178	1	no	—
503	C₄	—	178	1	no	—
504	C₄	—	178	1	no	—
505	C₄	#19151645	1	2	yes	—
506	C₄	#19152077	1	1	yes	characteristic
507	C₄	#19152080	1	1	yes	characteristic
508	C₄	#19152164	1	1	yes	characteristic
509	C₄	#19152171	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	356	1	no	—
513	C₂	—	178	2	no	—
514	C₂	#26022874	1	1	yes	characteristic
515	C₂	#430×D₈₉	1	1	yes	characteristic
516	C₂	C₂×#19151645	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1950	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₂×Q₈
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1950	D₈₉
hypocenter	C₈₉	#21994
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
4. #26021028	C₂	semidirect
5. #26021027	C₂	semidirect
6. #26021025	C₂	semidirect
9. #26020425	C₂	semidirect
10. #26020391	C₂	semidirect
11. C₈₉×#1950	C₂	semidirect
265. #1950	D₈₉	semidirect
270. C₈₉	#21994	semidirect

Maximal subgroups

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

subgroup	index
#26028883	2
C₂×#19151654	2
#423×D₈₉	2
#26021028	2
#26021027	2
#26021025	2
#26020458	2
#26020455	2
#26020425	2
#26020391	2
C₈₉×#1950	2
#21994	89