Subgroups — C₈₉×#25593 #36403441

Order 22784.

1234 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	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3140	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3040	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2657	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2004	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2002	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1887	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1885	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1759	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	1	yes	characteristic
14	#559×C₈₉	—	2	2	no	—
15	#550×C₈₉	—	2	2	no	—
16	#546×C₈₉	—	2	4	no	—
17	#540×C₈₉	—	2	2	no	—
18	#535×C₈₉	C₂²	1	2	yes	—
19	#533×C₈₉	C₂²	1	1	yes	characteristic
20	#532×C₈₉	—	2	2	no	—
21	C₂×#127×C₈₉	C₂²	1	2	yes	—
22	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#124×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
25	#518×C₈₉	C₂²	1	2	yes	—
26	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
27	#489×C₈₉	—	2	2	no	—
28	#488×C₈₉	—	2	2	no	—
29	#464×C₈₉	—	2	2	no	—
30	#463×C₈₉	—	2	2	no	—
31	#423×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#104×C₈₉	C₂²	1	2	yes	—
33	#419×C₈₉	C₂²	1	2	yes	—
34	#419×C₈₉	C₂²	1	1	yes	characteristic
35	#418×C₈₉	C₂²	1	2	yes	—
36	#418×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#100×C₈₉	C₂²	1	2	yes	—
38	C₂×#100×C₈₉	C₂²	1	2	yes	—
39	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	#392×C₈₉	—	2	4	no	—
41	#376×C₈₉	C₂²	1	1	yes	characteristic
42	#339×C₈₉	C₂²	1	2	yes	—
43	#339×C₈₉	C₂²	1	2	yes	—
44	#339×C₈₉	C₂²	1	2	yes	—
45	C₂×#41×C₈₉	—	2	4	no	—
46	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₈₉	—	2	4	no	—
49	C₂²×D₄×C₈₉	D₄	1	4	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
52	#137×C₈₉	—	4	2	no	—
53	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
54	C₂×Q₁₆×C₈₉	—	2	1	no	—
55	C₂×SD₁₆×C₈₉	—	2	1	no	—
56	C₂×SD₁₆×C₈₉	—	2	1	no	—
57	C₂×D₈×C₈₉	—	2	1	no	—
58	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₈₉	D₄	1	2	yes	complemented
62	#127×C₈₉	—	2	2	no	—
63	#127×C₈₉	—	2	1	no	—
64	#127×C₈₉	—	2	1	no	—
65	#127×C₈₉	—	2	2	no	—
66	#127×C₈₉	—	2	4	no	—
67	#127×C₈₉	—	4	2	no	—
68	#125×C₈₉	D₄	1	2	yes	complemented
69	#124×C₈₉	—	2	4	no	—
70	#124×C₈₉	—	2	2	no	—
71	#124×C₈₉	—	2	2	no	—
72	#124×C₈₉	—	2	1	no	—
73	#124×C₈₉	—	2	1	no	—
74	#124×C₈₉	—	2	4	no	—
75	#124×C₈₉	—	4	2	no	—
76	#123×C₈₉	—	2	8	no	—
77	C₂²⋊Q₈×C₈₉	—	2	2	no	—
78	#121×C₈₉	—	2	4	no	—
79	#121×C₈₉	—	2	8	no	—
80	#121×C₈₉	—	2	4	no	—
81	#120×C₈₉	—	2	4	no	—
82	C₄×Q₈×C₈₉	—	2	2	no	—
83	C₄×Q₈×C₈₉	D₄	1	2	yes	complemented
84	C₄×D₄×C₈₉	—	2	4	no	—
85	C₄×D₄×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	—	2	4	no	—
87	C₄×D₄×C₈₉	—	2	4	no	—
88	C₄×D₄×C₈₉	D₄	1	2	yes	complemented
89	#117×C₈₉	—	2	1	no	—
90	#117×C₈₉	C₂³	1	1	yes	characteristic
91	#117×C₈₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₄²×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	—	2	2	no	—
99	#104×C₈₉	—	2	4	no	—
100	#103×C₈₉	—	2	2	no	—
101	#103×C₈₉	—	2	4	no	—
102	#102×C₈₉	—	2	2	no	—
103	#102×C₈₉	—	2	4	no	—
104	#100×C₈₉	—	4	2	no	—
105	#100×C₈₉	—	4	2	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	#95×C₈₉	—	2	2	no	—
109	C₂⁴×C₈₉	—	2	1	no	—
110	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
111	#41×C₈₉	—	2	2	no	—
112	#41×C₈₉	—	2	2	no	—
113	#41×C₈₉	—	8	8	no	—
114	C₂×Q₈×C₈₉	—	2	2	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	—	2	1	no	—
117	C₂×Q₈×C₈₉	—	2	2	no	—
118	C₂×Q₈×C₈₉	—	2	2	no	—
119	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂×D₄×C₈₉	—	2	1	no	—
121	C₂×D₄×C₈₉	—	2	8	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	4	no	—
124	C₂×D₄×C₈₉	—	2	2	no	—
125	C₂×D₄×C₈₉	—	2	2	no	—
126	C₂×D₄×C₈₉	—	2	1	no	—
127	C₂×D₄×C₈₉	—	2	1	no	—
128	C₂×D₄×C₈₉	—	2	2	no	—
129	C₂×D₄×C₈₉	—	2	2	no	—
130	C₂×D₄×C₈₉	—	2	2	no	—
131	C₂×D₄×C₈₉	—	2	2	no	—
132	C₂×D₄×C₈₉	—	2	2	no	—
133	C₂×D₄×C₈₉	—	2	2	no	—
134	C₂×D₄×C₈₉	—	4	8	no	—
135	C₂×D₄×C₈₉	—	8	4	no	—
136	C₂×D₄×C₈₉	—	8	8	no	—
137	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	—	2	2	no	—
139	C₂²×C₄×C₈₉	—	2	8	no	—
140	C₂²×C₄×C₈₉	—	2	2	no	—
141	C₂²×C₄×C₈₉	—	2	1	no	—
142	C₂²×C₄×C₈₉	—	2	1	no	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₈₉	—	4	2	no	—
146	SD₁₆×C₈₉	—	4	2	no	—
147	SD₁₆×C₈₉	—	4	2	no	—
148	D₈×C₈₉	—	4	2	no	—
149	M₁₆×C₈₉	—	2	2	no	—
150	M₁₆×C₈₉	—	2	2	no	—
151	M₁₆×C₈₉	—	2	2	no	—
152	M₁₆×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	2	1	no	—
155	C₂×C₈×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	2	2	no	—
157	C₄⋊C₄×C₈₉	—	2	2	no	—
158	C₄⋊C₄×C₈₉	—	2	4	no	—
159	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₈₉	—	2	8	no	—
162	C₂²⋊C₄×C₈₉	—	2	8	no	—
163	C₂²⋊C₄×C₈₉	—	2	1	no	—
164	C₂²⋊C₄×C₈₉	—	2	2	no	—
165	C₂²⋊C₄×C₈₉	—	2	2	no	—
166	C₂²⋊C₄×C₈₉	—	4	8	no	—
167	C₂²⋊C₄×C₈₉	—	4	2	no	—
168	C₂²⋊C₄×C₈₉	—	4	2	no	—
169	C₄²×C₈₉	—	2	2	no	—
170	C₄²×C₈₉	—	2	1	no	—
171	C₄²×C₈₉	—	2	2	no	—
172	C₄²×C₈₉	—	2	2	no	—
173	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₈₉	C₂×D₄	1	2	yes	—
176	C₄²×C₈₉	#41	1	4	yes	complemented
177	C₂³×C₈₉	—	2	4	no	—
178	C₂³×C₈₉	—	2	1	no	—
179	C₂³×C₈₉	—	2	4	no	—
180	C₂³×C₈₉	—	2	4	no	—
181	C₂³×C₈₉	—	4	8	no	—
182	C₂³×C₈₉	—	4	4	no	—
183	C₂³×C₈₉	—	4	1	no	—
184	C₂³×C₈₉	—	4	2	no	—
185	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₈₉	—	2	1	no	—
187	Q₈×C₈₉	—	2	1	no	—
188	Q₈×C₈₉	—	4	4	no	—
189	Q₈×C₈₉	—	4	1	no	—
190	Q₈×C₈₉	—	4	1	no	—
191	Q₈×C₈₉	—	4	2	no	—
192	D₄×C₈₉	—	2	1	no	—
193	D₄×C₈₉	—	2	1	no	—
194	D₄×C₈₉	—	4	8	no	—
195	D₄×C₈₉	—	4	2	no	—
196	D₄×C₈₉	—	4	2	no	—
197	D₄×C₈₉	—	4	1	no	—
198	D₄×C₈₉	—	4	2	no	—
199	D₄×C₈₉	—	4	1	no	—
200	D₄×C₈₉	—	4	2	no	—
201	D₄×C₈₉	—	4	2	no	—
202	D₄×C₈₉	—	4	2	no	—
203	D₄×C₈₉	—	8	4	no	—
204	D₄×C₈₉	—	8	8	no	—
205	D₄×C₈₉	—	8	16	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	4	no	—
209	C₂×C₄×C₈₉	—	2	4	no	—
210	C₂×C₄×C₈₉	—	4	2	no	—
211	C₂×C₄×C₈₉	—	4	4	no	—
212	C₂×C₄×C₈₉	—	4	4	no	—
213	C₂×C₄×C₈₉	—	4	2	no	—
214	C₂×C₄×C₈₉	—	4	1	no	—
215	C₂×C₄×C₈₉	—	4	2	no	—
216	C₂×C₄×C₈₉	—	8	8	no	—
217	C₂×C₄×C₈₉	#120	1	2	yes	—
218	C₂×C₄×C₈₉	#120	1	2	yes	—
219	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
222	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
223	C₈×C₈₉	—	4	1	no	—
224	C₈×C₈₉	—	4	1	no	—
225	C₈×C₈₉	—	4	2	no	—
226	C₂²×C₈₉	—	2	2	no	—
227	C₂²×C₈₉	—	4	1	no	—
228	C₂²×C₈₉	—	4	4	no	—
229	C₂²×C₈₉	—	4	2	no	—
230	C₂²×C₈₉	—	4	8	no	—
231	C₂²×C₈₉	—	8	4	no	—
232	C₂²×C₈₉	—	8	4	no	—
233	C₂²×C₈₉	—	8	4	no	—
234	C₂²×C₈₉	—	8	1	no	—
235	C₂²×C₈₉	—	8	2	no	—
236	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
237	C₂²×C₈₉	#546	1	2	yes	—
238	C₄×C₈₉	—	2	2	no	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	4	4	no	—
241	C₄×C₈₉	—	4	1	no	—
242	C₄×C₈₉	—	4	2	no	—
243	C₄×C₈₉	—	4	4	no	—
244	C₄×C₈₉	—	8	1	no	—
245	C₄×C₈₉	#532	1	1	yes	characteristic
246	C₄×C₈₉	#535	1	1	yes	characteristic
247	C₄×C₈₉	#550	1	2	yes	—
248	#25593	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂×C₈₉	—	2	2	no	—
250	C₂×C₈₉	—	8	1	no	—
251	C₂×C₈₉	—	8	4	no	—
252	C₂×C₈₉	—	16	1	no	—
253	C₂×C₈₉	#2431	1	1	yes	characteristic
254	C₂×C₈₉	#3019	1	2	yes	—
255	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
256	#3140	C₂×C₈₉	1	1	yes	characteristic, complemented
257	#3040	C₂×C₈₉	1	1	yes	characteristic, complemented
258	#2657	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#2004	C₂×C₈₉	1	2	yes	complemented
260	#2002	C₂×C₈₉	1	2	yes	complemented
261	#1995	C₂×C₈₉	1	1	yes	characteristic, complemented
262	#1965	C₂×C₈₉	1	1	yes	characteristic, complemented
263	#1887	C₂×C₈₉	1	2	yes	complemented
264	#1885	C₂×C₈₉	1	2	yes	complemented
265	#1759	C₂×C₈₉	1	1	yes	characteristic, complemented
266	C₈₉	#25593	1	1	yes	characteristic, direct product factor, Sylow
267	C₂×#137	C₂²×C₈₉	1	1	yes	characteristic
268	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	1	yes	characteristic
269	#559	—	2	2	no	—
270	#550	—	2	2	no	—
271	#546	—	2	4	no	—
272	#540	—	2	2	no	—
273	#535	C₂²×C₈₉	1	2	yes	—
274	#533	C₂²×C₈₉	1	1	yes	characteristic
275	#532	—	2	2	no	—
276	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
277	C₂×#127	C₂²×C₈₉	1	2	yes	—
278	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
279	C₂×#124	C₂²×C₈₉	1	2	yes	—
280	#518	C₂²×C₈₉	1	2	yes	—
281	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
282	#489	—	2	2	no	—
283	#488	—	2	2	no	—
284	#464	—	2	2	no	—
285	#463	—	2	2	no	—
286	#423	C₂²×C₈₉	1	1	yes	characteristic
287	C₂×#104	C₂²×C₈₉	1	2	yes	—
288	#419	C₂²×C₈₉	1	2	yes	—
289	#419	C₂²×C₈₉	1	1	yes	characteristic
290	#418	C₂²×C₈₉	1	2	yes	—
291	#418	C₂²×C₈₉	1	1	yes	characteristic
292	C₂×#100	C₂²×C₈₉	1	2	yes	—
293	C₂×#100	C₂²×C₈₉	1	2	yes	—
294	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
295	#392	—	2	4	no	—
296	#376	C₂²×C₈₉	1	1	yes	characteristic
297	#339	C₂²×C₈₉	1	2	yes	—
298	#339	C₂²×C₈₉	1	2	yes	—
299	#339	C₂²×C₈₉	1	2	yes	—
300	C₂×#41	—	2	4	no	—
301	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
302	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
303	C₂²×D₄	—	2	4	no	—
304	C₂²×D₄	D₄×C₈₉	1	4	yes	—
305	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
306	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
307	#137	—	4	2	no	—
308	AGL(1,ℤ/8)	—	4	2	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×SD₁₆	—	2	1	no	—
311	C₂×SD₁₆	—	2	1	no	—
312	C₂×D₈	—	2	1	no	—
313	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
316	C₄⋊Q₈	D₄×C₈₉	1	2	yes	complemented
317	#127	—	2	2	no	—
318	#127	—	2	1	no	—
319	#127	—	2	1	no	—
320	#127	—	2	2	no	—
321	#127	—	2	4	no	—
322	#127	—	4	2	no	—
323	#125	D₄×C₈₉	1	2	yes	complemented
324	#124	—	2	4	no	—
325	#124	—	2	2	no	—
326	#124	—	2	2	no	—
327	#124	—	2	1	no	—
328	#124	—	2	1	no	—
329	#124	—	2	4	no	—
330	#124	—	4	2	no	—
331	#123	—	2	8	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	#121	—	2	4	no	—
334	#121	—	2	8	no	—
335	#121	—	2	4	no	—
336	#120	—	2	4	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	D₄×C₈₉	1	2	yes	complemented
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	D₄×C₈₉	1	2	yes	complemented
344	#117	—	2	1	no	—
345	#117	C₂³×C₈₉	1	1	yes	characteristic
346	#117	C₂³×C₈₉	1	2	yes	—
347	C₂×C₂²⋊C₄	—	2	4	no	—
348	C₂×C₂²⋊C₄	—	2	4	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
352	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
353	C₄⋊C₈	—	2	2	no	—
354	#104	—	2	4	no	—
355	#103	—	2	2	no	—
356	#103	—	2	4	no	—
357	#102	—	2	2	no	—
358	#102	—	2	4	no	—
359	#100	—	4	2	no	—
360	#100	—	4	2	no	—
361	#97	—	2	1	no	—
362	C₄×C₈	—	2	1	no	—
363	#95	—	2	2	no	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	8	8	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	8	4	no	—
391	C₂×D₄	—	8	8	no	—
392	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
400	Q₁₆	—	4	2	no	—
401	SD₁₆	—	4	2	no	—
402	SD₁₆	—	4	2	no	—
403	D₈	—	4	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
415	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
429	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₈₉	1	2	yes	—
431	C₄²	#41×C₈₉	1	4	yes	complemented
432	C₂³	—	2	4	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	8	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	4	2	no	—
440	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
441	Q₈	—	2	1	no	—
442	Q₈	—	2	1	no	—
443	Q₈	—	4	4	no	—
444	Q₈	—	4	1	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	2	no	—
447	D₄	—	2	1	no	—
448	D₄	—	2	1	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	8	4	no	—
459	D₄	—	8	8	no	—
460	D₄	—	8	16	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	#120×C₈₉	1	2	yes	—
473	C₂×C₄	#120×C₈₉	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
477	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
478	C₈	—	4	1	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	8	no	—
486	C₂²	—	8	4	no	—
487	C₂²	—	8	4	no	—
488	C₂²	—	8	4	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	2	no	—
491	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
492	C₂²	#546×C₈₉	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	8	1	no	—
500	C₄	#532×C₈₉	1	1	yes	characteristic
501	C₄	#535×C₈₉	1	1	yes	characteristic
502	C₄	#550×C₈₉	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	8	1	no	—
505	C₂	—	8	4	no	—
506	C₂	—	16	1	no	—
507	C₂	C₈₉×#2431	1	1	yes	characteristic
508	C₂	C₈₉×#3019	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3508	C₂	semidirect
2. C₈₉×#3140	C₂	semidirect
3. C₈₉×#3040	C₂	semidirect
4. C₈₉×#2657	C₂	semidirect
5. C₈₉×#2004	C₂	semidirect
6. C₈₉×#2002	C₂	semidirect
7. C₈₉×#1995	C₂	semidirect
8. C₈₉×#1965	C₂	semidirect
9. C₈₉×#1887	C₂	semidirect
10. C₈₉×#1885	C₂	semidirect
11. C₈₉×#1759	C₂	semidirect
61. C₄⋊Q₈×C₈₉	D₄	semidirect
68. #125×C₈₉	D₄	semidirect
83. C₄×Q₈×C₈₉	D₄	semidirect
88. C₄×D₄×C₈₉	D₄	semidirect
176. C₄²×C₈₉	#41	semidirect
248. #25593	C₈₉	direct (N × H)
255. #3508	C₂×C₈₉	semidirect
256. #3140	C₂×C₈₉	semidirect
257. #3040	C₂×C₈₉	semidirect
258. #2657	C₂×C₈₉	semidirect
259. #2004	C₂×C₈₉	semidirect
260. #2002	C₂×C₈₉	semidirect
261. #1995	C₂×C₈₉	semidirect
262. #1965	C₂×C₈₉	semidirect
263. #1887	C₂×C₈₉	semidirect
264. #1885	C₂×C₈₉	semidirect
265. #1759	C₂×C₈₉	semidirect
266. C₈₉	#25593	direct (N × H)
316. C₄⋊Q₈	D₄×C₈₉	semidirect
323. #125	D₄×C₈₉	semidirect
338. C₄×Q₈	D₄×C₈₉	semidirect
343. C₄×D₄	D₄×C₈₉	semidirect
431. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3140	2
C₈₉×#3040	2
C₈₉×#2657	2
C₈₉×#2004	2
C₈₉×#2002	2
C₈₉×#1995	2
C₈₉×#1965	2
C₈₉×#1887	2
C₈₉×#1885	2
C₈₉×#1759	2
#25593	89

Subgroups — C89×#25593 #36403441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25593 #36403441