Subgroups — C₈₉×#35565 #36413413

Order 22784.

4146 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	C₂×#537×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2541	C₂	1	8	yes	maximal, complemented
6	C₈₉×#2540	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2539	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2433	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
14	#537×C₈₉	—	2	8	no	—
15	#535×C₈₉	—	2	16	no	—
16	C₂×#127×C₈₉	C₂²	1	4	yes	complemented
17	C₂×#127×C₈₉	C₂²	1	8	yes	complemented
18	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
19	#525×C₈₉	—	2	16	no	—
20	C₂×#123×C₈₉	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
23	C₂×#121×C₈₉	—	2	8	no	—
24	C₂×#121×C₈₉	C₂²	1	8	yes	—
25	C₂×#121×C₈₉	C₂²	1	4	yes	—
26	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
27	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
28	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
29	C₂×#120×C₈₉	C₂²	1	4	yes	—
30	C₂×#120×C₈₉	C₂²	1	8	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
32	C₂×#117×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
35	#399×C₈₉	C₂²	1	8	yes	complemented
36	#392×C₈₉	C₂²	1	16	yes	complemented
37	#392×C₈₉	C₂²	1	8	yes	complemented
38	#390×C₈₉	C₂²	1	8	yes	complemented
39	#390×C₈₉	C₂²	1	16	yes	complemented
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	complemented
41	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
42	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
43	C₂⁵×C₈₉	C₂³	1	2	yes	—
44	C₂×#41×C₈₉	—	2	8	no	—
45	C₂×#41×C₈₉	—	2	8	no	—
46	C₂×#41×C₈₉	—	2	8	no	—
47	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×D₄×C₈₉	—	2	8	no	—
49	C₂²×D₄×C₈₉	—	2	4	no	—
50	C₂²×D₄×C₈₉	—	2	8	no	—
51	C₂²×D₄×C₈₉	—	4	8	no	—
52	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
53	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
56	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
57	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
59	C₂³×C₄×C₈₉	—	2	4	no	—
60	C₂³×C₄×C₈₉	—	2	8	no	—
61	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
64	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	#127×C₈₉	—	2	16	no	—
67	#127×C₈₉	—	4	16	no	—
68	#124×C₈₉	—	2	16	no	—
69	#123×C₈₉	—	2	16	no	—
70	C₂²⋊Q₈×C₈₉	—	2	16	no	—
71	C₂²⋊Q₈×C₈₉	—	2	16	no	—
72	#121×C₈₉	—	2	16	no	—
73	#121×C₈₉	—	2	32	no	—
74	#121×C₈₉	—	2	16	no	—
75	#121×C₈₉	—	2	16	no	—
76	#121×C₈₉	—	2	32	no	—
77	#120×C₈₉	—	2	16	no	—
78	#120×C₈₉	—	2	32	no	—
79	C₄×D₄×C₈₉	—	2	32	no	—
80	#117×C₈₉	D₄	1	16	yes	complemented
81	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
92	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
94	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
95	#95×C₈₉	C₂³	1	8	yes	—
96	C₂⁴×C₈₉	—	2	2	no	—
97	C₂⁴×C₈₉	—	2	4	no	—
98	C₂⁴×C₈₉	—	2	4	no	—
99	C₂⁴×C₈₉	—	2	4	no	—
100	C₂⁴×C₈₉	—	2	8	no	—
101	C₂⁴×C₈₉	—	4	2	no	—
102	C₂⁴×C₈₉	—	4	4	no	—
103	C₂⁴×C₈₉	—	4	4	no	—
104	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
105	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
106	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
107	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
108	#41×C₈₉	—	4	32	no	—
109	C₂×Q₈×C₈₉	—	2	4	no	—
110	C₂×Q₈×C₈₉	—	2	4	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×D₄×C₈₉	—	2	8	no	—
113	C₂×D₄×C₈₉	—	2	8	no	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	16	no	—
116	C₂×D₄×C₈₉	—	2	16	no	—
117	C₂×D₄×C₈₉	—	2	16	no	—
118	C₂×D₄×C₈₉	—	2	16	no	—
119	C₂×D₄×C₈₉	—	2	8	no	—
120	C₂×D₄×C₈₉	—	2	8	no	—
121	C₂×D₄×C₈₉	—	2	4	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	8	no	—
124	C₂×D₄×C₈₉	—	2	4	no	—
125	C₂×D₄×C₈₉	—	2	32	no	—
126	C₂×D₄×C₈₉	—	2	8	no	—
127	C₂×D₄×C₈₉	—	4	8	no	—
128	C₂×D₄×C₈₉	—	4	8	no	—
129	C₂×D₄×C₈₉	—	4	16	no	—
130	C₂×D₄×C₈₉	—	4	8	no	—
131	C₂×D₄×C₈₉	—	4	16	no	—
132	C₂×D₄×C₈₉	—	4	32	no	—
133	C₂×D₄×C₈₉	—	4	16	no	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	—	2	4	no	—
136	C₂²×C₄×C₈₉	—	2	8	no	—
137	C₂²×C₄×C₈₉	—	2	8	no	—
138	C₂²×C₄×C₈₉	—	2	8	no	—
139	C₂²×C₄×C₈₉	—	2	8	no	—
140	C₂²×C₄×C₈₉	—	2	8	no	—
141	C₂²×C₄×C₈₉	—	2	8	no	—
142	C₂²×C₄×C₈₉	—	4	4	no	—
143	C₂²×C₄×C₈₉	—	4	16	no	—
144	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
145	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
150	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	16	no	—
153	C₄⋊C₄×C₈₉	—	2	8	no	—
154	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
155	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	complemented
156	C₂²⋊C₄×C₈₉	—	2	16	no	—
157	C₂²⋊C₄×C₈₉	—	2	16	no	—
158	C₂²⋊C₄×C₈₉	—	2	16	no	—
159	C₂²⋊C₄×C₈₉	—	2	32	no	—
160	C₂²⋊C₄×C₈₉	—	2	16	no	—
161	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
162	C₄²×C₈₉	—	4	8	no	—
163	C₄²×C₈₉	C₂×D₄	1	16	yes	complemented
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	2	no	—
166	C₂³×C₈₉	—	2	8	no	—
167	C₂³×C₈₉	—	2	4	no	—
168	C₂³×C₈₉	—	2	2	no	—
169	C₂³×C₈₉	—	2	2	no	—
170	C₂³×C₈₉	—	2	4	no	—
171	C₂³×C₈₉	—	2	4	no	—
172	C₂³×C₈₉	—	2	4	no	—
173	C₂³×C₈₉	—	2	4	no	—
174	C₂³×C₈₉	—	2	8	no	—
175	C₂³×C₈₉	—	2	4	no	—
176	C₂³×C₈₉	—	2	8	no	—
177	C₂³×C₈₉	—	2	8	no	—
178	C₂³×C₈₉	—	2	8	no	—
179	C₂³×C₈₉	—	2	8	no	—
180	C₂³×C₈₉	—	4	16	no	—
181	C₂³×C₈₉	—	4	4	no	—
182	C₂³×C₈₉	—	4	8	no	—
183	C₂³×C₈₉	—	4	8	no	—
184	C₂³×C₈₉	—	4	4	no	—
185	C₂³×C₈₉	—	4	8	no	—
186	C₂³×C₈₉	—	8	16	no	—
187	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
188	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
189	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
190	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
191	Q₈×C₈₉	—	4	8	no	—
192	D₄×C₈₉	—	4	32	no	—
193	D₄×C₈₉	—	4	32	no	—
194	D₄×C₈₉	—	4	16	no	—
195	D₄×C₈₉	—	4	16	no	—
196	D₄×C₈₉	—	4	8	no	—
197	D₄×C₈₉	—	8	8	no	—
198	D₄×C₈₉	—	8	32	no	—
199	C₂×C₄×C₈₉	—	2	8	no	—
200	C₂×C₄×C₈₉	—	2	8	no	—
201	C₂×C₄×C₈₉	—	2	8	no	—
202	C₂×C₄×C₈₉	—	2	2	no	—
203	C₂×C₄×C₈₉	—	2	4	no	—
204	C₂×C₄×C₈₉	—	2	4	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	4	8	no	—
208	C₂×C₄×C₈₉	—	4	4	no	—
209	C₂×C₄×C₈₉	—	4	16	no	—
210	C₂×C₄×C₈₉	—	4	16	no	—
211	C₂×C₄×C₈₉	#127	1	16	yes	complemented
212	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
213	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
214	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
217	C₂²×C₈₉	—	2	2	no	—
218	C₂²×C₈₉	—	2	2	no	—
219	C₂²×C₈₉	—	2	8	no	—
220	C₂²×C₈₉	—	2	4	no	—
221	C₂²×C₈₉	—	2	8	no	—
222	C₂²×C₈₉	—	4	16	no	—
223	C₂²×C₈₉	—	4	2	no	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	4	4	no	—
226	C₂²×C₈₉	—	4	4	no	—
227	C₂²×C₈₉	—	4	4	no	—
228	C₂²×C₈₉	—	4	4	no	—
229	C₂²×C₈₉	—	4	4	no	—
230	C₂²×C₈₉	—	4	4	no	—
231	C₂²×C₈₉	—	4	4	no	—
232	C₂²×C₈₉	—	4	8	no	—
233	C₂²×C₈₉	—	4	8	no	—
234	C₂²×C₈₉	—	4	16	no	—
235	C₂²×C₈₉	—	8	16	no	—
236	C₂²×C₈₉	C₂×#127	1	4	yes	—
237	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
238	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
239	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂²×C₈₉	#585	1	2	yes	—
241	C₄×C₈₉	—	2	8	no	—
242	C₄×C₈₉	—	2	16	no	—
243	C₄×C₈₉	—	4	2	no	—
244	C₄×C₈₉	—	4	4	no	—
245	C₄×C₈₉	C₂×#127	1	8	yes	—
246	#35565	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂×C₈₉	—	2	4	no	—
248	C₂×C₈₉	—	4	4	no	—
249	C₂×C₈₉	—	8	4	no	—
250	C₂×C₈₉	—	8	4	no	—
251	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
252	C₂×C₈₉	#3484	1	1	yes	characteristic
253	C₂×C₈₉	#3487	1	1	yes	characteristic
254	C₂×C₈₉	#3488	1	4	yes	—
255	C₂×#537	C₂×C₈₉	1	1	yes	characteristic, complemented
256	C₂×#535	C₂×C₈₉	1	2	yes	complemented
257	C₂×#525	C₂×C₈₉	1	2	yes	complemented
258	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#2541	C₂×C₈₉	1	8	yes	complemented
260	#2540	C₂×C₈₉	1	8	yes	complemented
261	#2539	C₂×C₈₉	1	4	yes	complemented
262	#2433	C₂×C₈₉	1	4	yes	complemented
263	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
264	C₈₉	#35565	1	1	yes	characteristic, direct product factor, Sylow
265	C₂²×#41	C₂²×C₈₉	1	2	yes	—
266	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
267	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
268	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
269	#537	—	2	8	no	—
270	#535	—	2	16	no	—
271	C₂×#127	C₂²×C₈₉	1	4	yes	complemented
272	C₂×#127	C₂²×C₈₉	1	8	yes	complemented
273	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
274	#525	—	2	16	no	—
275	C₂×#123	C₂²×C₈₉	1	4	yes	—
276	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
277	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
278	C₂×#121	—	2	8	no	—
279	C₂×#121	C₂²×C₈₉	1	8	yes	—
280	C₂×#121	C₂²×C₈₉	1	4	yes	—
281	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
282	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
283	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
284	C₂×#120	C₂²×C₈₉	1	4	yes	—
285	C₂×#120	C₂²×C₈₉	1	8	yes	—
286	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
287	C₂×#117	C₂²×C₈₉	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
290	#399	C₂²×C₈₉	1	8	yes	complemented
291	#392	C₂²×C₈₉	1	16	yes	complemented
292	#392	C₂²×C₈₉	1	8	yes	complemented
293	#390	C₂²×C₈₉	1	8	yes	complemented
294	#390	C₂²×C₈₉	1	16	yes	complemented
295	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	complemented
296	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
297	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
298	C₂⁵	C₂³×C₈₉	1	2	yes	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	2	8	no	—
301	C₂×#41	—	2	8	no	—
302	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
303	C₂²×D₄	—	2	8	no	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	2	8	no	—
306	C₂²×D₄	—	4	8	no	—
307	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
308	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
309	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
310	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
311	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
312	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
313	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	8	no	—
316	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
318	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
319	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
320	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
321	#127	—	2	16	no	—
322	#127	—	4	16	no	—
323	#124	—	2	16	no	—
324	#123	—	2	16	no	—
325	C₂²⋊Q₈	—	2	16	no	—
326	C₂²⋊Q₈	—	2	16	no	—
327	#121	—	2	16	no	—
328	#121	—	2	32	no	—
329	#121	—	2	16	no	—
330	#121	—	2	16	no	—
331	#121	—	2	32	no	—
332	#120	—	2	16	no	—
333	#120	—	2	32	no	—
334	C₄×D₄	—	2	32	no	—
335	#117	D₄×C₈₉	1	16	yes	complemented
336	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
337	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
341	C₂×C₂²⋊C₄	—	2	8	no	—
342	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
348	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
349	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
350	#95	C₂³×C₈₉	1	8	yes	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	4	no	—
355	C₂⁴	—	2	8	no	—
356	C₂⁴	—	4	2	no	—
357	C₂⁴	—	4	4	no	—
358	C₂⁴	—	4	4	no	—
359	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
360	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
361	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
362	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
363	#41	—	4	32	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	16	no	—
371	C₂×D₄	—	2	16	no	—
372	C₂×D₄	—	2	16	no	—
373	C₂×D₄	—	2	16	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	32	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	4	8	no	—
383	C₂×D₄	—	4	8	no	—
384	C₂×D₄	—	4	16	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	—	4	16	no	—
387	C₂×D₄	—	4	32	no	—
388	C₂×D₄	—	4	16	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	8	no	—
393	C₂²×C₄	—	2	8	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	4	16	no	—
399	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
400	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
402	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
405	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
407	C₄⋊C₄	—	2	16	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
410	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	complemented
411	C₂²⋊C₄	—	2	16	no	—
412	C₂²⋊C₄	—	2	16	no	—
413	C₂²⋊C₄	—	2	16	no	—
414	C₂²⋊C₄	—	2	32	no	—
415	C₂²⋊C₄	—	2	16	no	—
416	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
417	C₄²	—	4	8	no	—
418	C₄²	C₂×D₄×C₈₉	1	16	yes	complemented
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	8	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	4	16	no	—
436	C₂³	—	4	4	no	—
437	C₂³	—	4	8	no	—
438	C₂³	—	4	8	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	8	no	—
441	C₂³	—	8	16	no	—
442	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
443	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
444	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
445	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
446	Q₈	—	4	8	no	—
447	D₄	—	4	32	no	—
448	D₄	—	4	32	no	—
449	D₄	—	4	16	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	8	no	—
452	D₄	—	8	8	no	—
453	D₄	—	8	32	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	16	no	—
465	C₂×C₄	—	4	16	no	—
466	C₂×C₄	#127×C₈₉	1	16	yes	complemented
467	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
468	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
469	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
470	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	4	16	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	8	no	—
488	C₂²	—	4	8	no	—
489	C₂²	—	4	16	no	—
490	C₂²	—	8	16	no	—
491	C₂²	C₂×#127×C₈₉	1	4	yes	—
492	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
493	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
494	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
495	C₂²	#585×C₈₉	1	2	yes	—
496	C₄	—	2	8	no	—
497	C₄	—	2	16	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	4	no	—
500	C₄	C₂×#127×C₈₉	1	8	yes	—
501	C₂	—	2	4	no	—
502	C₂	—	4	4	no	—
503	C₂	—	8	4	no	—
504	C₂	—	8	4	no	—
505	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
506	C₂	C₈₉×#3484	1	1	yes	characteristic
507	C₂	C₈₉×#3487	1	1	yes	characteristic
508	C₂	C₈₉×#3488	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#537×C₈₉	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₂×#525×C₈₉	C₂	semidirect
4. C₂²×#121×C₈₉	C₂	semidirect
5. C₈₉×#2541	C₂	semidirect
6. C₈₉×#2540	C₂	semidirect
7. C₈₉×#2539	C₂	semidirect
8. C₈₉×#2433	C₂	semidirect
9. C₈₉×#2274	C₂	semidirect
16. C₂×#127×C₈₉	C₂²	semidirect
17. C₂×#127×C₈₉	C₂²	semidirect
18. C₂×#124×C₈₉	C₂²	semidirect
21. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
26. C₂×#121×C₈₉	C₂²	semidirect
27. C₂×#121×C₈₉	C₂²	semidirect
28. C₂×#121×C₈₉	C₂²	semidirect
31. C₂×C₄×D₄×C₈₉	C₂²	semidirect
35. #399×C₈₉	C₂²	semidirect
36. #392×C₈₉	C₂²	semidirect
37. #392×C₈₉	C₂²	semidirect
38. #390×C₈₉	C₂²	semidirect
39. #390×C₈₉	C₂²	semidirect
40. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
80. #117×C₈₉	D₄	semidirect
81. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
155. C₄⋊C₄×C₈₉	C₂×D₄	semidirect
163. C₄²×C₈₉	C₂×D₄	semidirect
211. C₂×C₄×C₈₉	#127	semidirect
246. #35565	C₈₉	direct (N × H)
255. C₂×#537	C₂×C₈₉	semidirect
256. C₂×#535	C₂×C₈₉	semidirect
257. C₂×#525	C₂×C₈₉	semidirect
258. C₂²×#121	C₂×C₈₉	semidirect
259. #2541	C₂×C₈₉	semidirect
260. #2540	C₂×C₈₉	semidirect
261. #2539	C₂×C₈₉	semidirect
262. #2433	C₂×C₈₉	semidirect
263. #2274	C₂×C₈₉	semidirect
264. C₈₉	#35565	direct (N × H)
271. C₂×#127	C₂²×C₈₉	semidirect
272. C₂×#127	C₂²×C₈₉	semidirect
273. C₂×#124	C₂²×C₈₉	semidirect
276. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
277. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
281. C₂×#121	C₂²×C₈₉	semidirect
282. C₂×#121	C₂²×C₈₉	semidirect
283. C₂×#121	C₂²×C₈₉	semidirect
286. C₂×C₄×D₄	C₂²×C₈₉	semidirect
290. #399	C₂²×C₈₉	semidirect
291. #392	C₂²×C₈₉	semidirect
292. #392	C₂²×C₈₉	semidirect
293. #390	C₂²×C₈₉	semidirect
294. #390	C₂²×C₈₉	semidirect
295. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
335. #117	D₄×C₈₉	semidirect
336. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
410. C₄⋊C₄	C₂×D₄×C₈₉	semidirect
418. C₄²	C₂×D₄×C₈₉	semidirect
466. C₂×C₄	#127×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#537×C₈₉	2
C₂×#535×C₈₉	2
C₂×#525×C₈₉	2
C₂²×#121×C₈₉	2
C₈₉×#2541	2
C₈₉×#2540	2
C₈₉×#2539	2
C₈₉×#2433	2
C₈₉×#2274	2
#35565	89

Subgroups — C89×#35565 #36413413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35565 #36413413