Subgroups — C₈₉×#35251 #36413099

Order 22784.

5426 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#537×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2848	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2847	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2616	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2615	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2430	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2410	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2409	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2408	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2407	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2311	C₂	1	2	yes	maximal, complemented
14	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	—	2	16	no	—
16	C₂²×#41×C₈₉	—	2	8	no	—
17	C₂²×#41×C₈₉	C₂²	1	2	yes	—
18	C₂²×#41×C₈₉	C₂²	1	2	yes	—
19	C₂²×#41×C₈₉	C₂²	1	2	yes	—
20	C₂²×#41×C₈₉	C₂²	1	2	yes	—
21	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
25	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
26	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
27	#537×C₈₉	—	2	16	no	—
28	#525×C₈₉	—	2	8	no	—
29	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
34	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
36	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
38	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
39	C₂×#120×C₈₉	C₂²	1	2	yes	—
40	C₂×#120×C₈₉	C₂²	1	4	yes	—
41	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
43	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
45	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
46	#395×C₈₉	C₂²	1	4	yes	complemented
47	#394×C₈₉	C₂²	1	8	yes	complemented
48	#394×C₈₉	C₂²	1	4	yes	complemented
49	#393×C₈₉	C₂²	1	4	yes	complemented
50	#392×C₈₉	C₂²	1	8	yes	complemented
51	#392×C₈₉	C₂²	1	4	yes	complemented
52	#391×C₈₉	C₂²	1	4	yes	complemented
53	#390×C₈₉	C₂²	1	4	yes	complemented
54	#386×C₈₉	C₂²	1	4	yes	—
55	#386×C₈₉	C₂²	1	8	yes	complemented
56	#386×C₈₉	C₂²	1	8	yes	complemented
57	#385×C₈₉	C₂²	1	4	yes	—
58	#385×C₈₉	C₂²	1	8	yes	complemented
59	#380×C₈₉	C₂²	1	2	yes	—
60	#380×C₈₉	C₂²	1	2	yes	—
61	#380×C₈₉	C₂²	1	4	yes	complemented
62	#380×C₈₉	C₂²	1	4	yes	complemented
63	#380×C₈₉	C₂²	1	2	yes	complemented
64	#380×C₈₉	C₂²	1	2	yes	complemented
65	#379×C₈₉	C₂²	1	4	yes	—
66	C₂×#95×C₈₉	C₂²	1	2	yes	complemented
67	C₂⁵×C₈₉	C₂³	1	2	yes	—
68	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×#41×C₈₉	—	2	128	no	—
70	C₂×#41×C₈₉	—	2	8	no	—
71	C₂×#41×C₈₉	—	2	8	no	—
72	C₂×#41×C₈₉	—	2	16	no	—
73	C₂×#41×C₈₉	—	2	8	no	—
74	C₂×#41×C₈₉	—	2	16	no	—
75	C₂×#41×C₈₉	—	2	8	no	—
76	C₂×#41×C₈₉	—	2	8	no	—
77	C₂×#41×C₈₉	—	2	8	no	—
78	C₂×#41×C₈₉	—	2	8	no	—
79	C₂×#41×C₈₉	—	2	4	no	—
80	C₂×#41×C₈₉	—	2	8	no	—
81	C₂×#41×C₈₉	D₄	1	16	yes	complemented
82	C₂²×Q₈×C₈₉	—	2	8	no	—
83	C₂²×Q₈×C₈₉	—	2	4	no	—
84	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
87	C₂²×D₄×C₈₉	—	2	8	no	—
88	C₂²×D₄×C₈₉	—	2	8	no	—
89	C₂²×D₄×C₈₉	—	2	16	no	—
90	C₂²×D₄×C₈₉	—	2	4	no	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
93	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₈₉	—	2	8	no	—
101	C₂³×C₄×C₈₉	—	2	16	no	—
102	C₂³×C₄×C₈₉	—	2	8	no	—
103	C₂³×C₄×C₈₉	D₄	1	8	yes	complemented
104	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
106	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
107	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
114	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
115	#123×C₈₉	—	2	8	no	—
116	C₂²⋊Q₈×C₈₉	—	2	16	no	—
117	C₂²⋊Q₈×C₈₉	—	2	4	no	—
118	C₂²⋊Q₈×C₈₉	—	2	4	no	—
119	C₂²⋊Q₈×C₈₉	—	2	16	no	—
120	#121×C₈₉	—	2	16	no	—
121	#121×C₈₉	—	2	32	no	—
122	#121×C₈₉	—	2	4	no	—
123	#121×C₈₉	—	2	4	no	—
124	#121×C₈₉	—	2	16	no	—
125	#120×C₈₉	—	2	8	no	—
126	#120×C₈₉	—	4	8	no	—
127	C₄×D₄×C₈₉	—	2	8	no	—
128	C₄×D₄×C₈₉	—	2	8	no	—
129	#117×C₈₉	—	2	4	no	—
130	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
151	#95×C₈₉	C₂³	1	4	yes	—
152	#95×C₈₉	C₂³	1	4	yes	—
153	#95×C₈₉	C₂³	1	8	yes	—
154	#95×C₈₉	C₂³	1	8	yes	—
155	C₂⁴×C₈₉	—	2	8	no	—
156	C₂⁴×C₈₉	—	2	4	no	—
157	C₂⁴×C₈₉	—	2	4	no	—
158	C₂⁴×C₈₉	—	2	2	no	—
159	C₂⁴×C₈₉	—	2	2	no	—
160	C₂⁴×C₈₉	—	2	4	no	—
161	C₂⁴×C₈₉	—	2	4	no	—
162	C₂⁴×C₈₉	—	4	2	no	—
163	C₂⁴×C₈₉	—	4	4	no	—
164	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
165	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
166	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
168	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
170	#41×C₈₉	—	2	64	no	—
171	#41×C₈₉	—	2	64	no	—
172	#41×C₈₉	—	2	64	no	—
173	#41×C₈₉	—	2	64	no	—
174	#41×C₈₉	—	4	16	no	—
175	C₂×Q₈×C₈₉	—	2	32	no	—
176	C₂×Q₈×C₈₉	—	2	8	no	—
177	C₂×Q₈×C₈₉	—	2	4	no	—
178	C₂×Q₈×C₈₉	—	2	4	no	—
179	C₂×Q₈×C₈₉	—	2	4	no	—
180	C₂×Q₈×C₈₉	—	2	2	no	—
181	C₂×Q₈×C₈₉	—	2	4	no	—
182	C₂×Q₈×C₈₉	C₂×D₄	1	8	yes	—
183	C₂×D₄×C₈₉	—	2	64	no	—
184	C₂×D₄×C₈₉	—	2	32	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	2	8	no	—
187	C₂×D₄×C₈₉	—	2	8	no	—
188	C₂×D₄×C₈₉	—	2	8	no	—
189	C₂×D₄×C₈₉	—	2	8	no	—
190	C₂×D₄×C₈₉	—	2	4	no	—
191	C₂×D₄×C₈₉	—	2	4	no	—
192	C₂×D₄×C₈₉	—	2	4	no	—
193	C₂×D₄×C₈₉	—	2	8	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	16	no	—
197	C₂×D₄×C₈₉	—	2	8	no	—
198	C₂×D₄×C₈₉	—	2	4	no	—
199	C₂×D₄×C₈₉	—	2	4	no	—
200	C₂×D₄×C₈₉	—	2	4	no	—
201	C₂×D₄×C₈₉	—	2	2	no	—
202	C₂×D₄×C₈₉	—	2	4	no	—
203	C₂×D₄×C₈₉	—	4	4	no	—
204	C₂×D₄×C₈₉	—	4	8	no	—
205	C₂×D₄×C₈₉	—	4	8	no	—
206	C₂×D₄×C₈₉	C₂×D₄	1	16	yes	—
207	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
208	C₂²×C₄×C₈₉	—	2	64	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	2	8	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	2	32	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	2	8	no	—
215	C₂²×C₄×C₈₉	—	2	4	no	—
216	C₂²×C₄×C₈₉	—	2	8	no	—
217	C₂²×C₄×C₈₉	—	2	8	no	—
218	C₂²×C₄×C₈₉	—	2	4	no	—
219	C₂²×C₄×C₈₉	—	2	8	no	—
220	C₂²×C₄×C₈₉	—	2	8	no	—
221	C₂²×C₄×C₈₉	—	2	4	no	—
222	C₂²×C₄×C₈₉	—	2	8	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	2	8	no	—
225	C₂²×C₄×C₈₉	—	4	4	no	—
226	C₂²×C₄×C₈₉	—	4	4	no	—
227	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
228	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
230	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	—
231	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
232	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
233	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
234	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₈₉	—	2	8	no	—
245	C₄⋊C₄×C₈₉	—	2	8	no	—
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	—	2	2	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	16	no	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	16	no	—
255	C₂²⋊C₄×C₈₉	—	2	8	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	16	no	—
259	C₂²⋊C₄×C₈₉	—	4	4	no	—
260	C₂²⋊C₄×C₈₉	—	4	8	no	—
261	C₂²⋊C₄×C₈₉	—	4	8	no	—
262	C₄²×C₈₉	—	2	4	no	—
263	C₂³×C₈₉	—	2	2	no	—
264	C₂³×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	—	2	1	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	16	no	—
269	C₂³×C₈₉	—	2	8	no	—
270	C₂³×C₈₉	—	2	8	no	—
271	C₂³×C₈₉	—	2	4	no	—
272	C₂³×C₈₉	—	2	4	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	2	1	no	—
275	C₂³×C₈₉	—	2	4	no	—
276	C₂³×C₈₉	—	2	1	no	—
277	C₂³×C₈₉	—	2	4	no	—
278	C₂³×C₈₉	—	2	4	no	—
279	C₂³×C₈₉	—	2	2	no	—
280	C₂³×C₈₉	—	2	4	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	4	no	—
283	C₂³×C₈₉	—	2	2	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	4	no	—
286	C₂³×C₈₉	—	4	4	no	—
287	C₂³×C₈₉	—	4	8	no	—
288	C₂³×C₈₉	—	4	16	no	—
289	C₂³×C₈₉	—	4	8	no	—
290	C₂³×C₈₉	—	4	16	no	—
291	C₂³×C₈₉	—	4	8	no	—
292	C₂³×C₈₉	—	4	8	no	—
293	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
294	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
295	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
296	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
297	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
298	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
299	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
300	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
301	Q₈×C₈₉	—	2	16	no	—
302	Q₈×C₈₉	—	2	16	no	—
303	Q₈×C₈₉	—	4	4	no	—
304	D₄×C₈₉	—	2	32	no	—
305	D₄×C₈₉	—	2	16	no	—
306	D₄×C₈₉	—	2	32	no	—
307	D₄×C₈₉	—	2	16	no	—
308	D₄×C₈₉	—	4	8	no	—
309	D₄×C₈₉	—	4	8	no	—
310	D₄×C₈₉	—	4	8	no	—
311	D₄×C₈₉	—	4	4	no	—
312	D₄×C₈₉	—	8	16	no	—
313	C₂×C₄×C₈₉	—	2	16	no	—
314	C₂×C₄×C₈₉	—	2	32	no	—
315	C₂×C₄×C₈₉	—	2	8	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	4	no	—
318	C₂×C₄×C₈₉	—	2	4	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	8	no	—
321	C₂×C₄×C₈₉	—	2	8	no	—
322	C₂×C₄×C₈₉	—	2	8	no	—
323	C₂×C₄×C₈₉	—	2	32	no	—
324	C₂×C₄×C₈₉	—	2	8	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	8	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	4	no	—
330	C₂×C₄×C₈₉	—	2	8	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	4	no	—
334	C₂×C₄×C₈₉	—	2	8	no	—
335	C₂×C₄×C₈₉	—	4	8	no	—
336	C₂×C₄×C₈₉	—	8	8	no	—
337	C₂×C₄×C₈₉	#120	1	16	yes	complemented
338	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
340	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	2	no	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	4	no	—
350	C₂²×C₈₉	—	2	4	no	—
351	C₂²×C₈₉	—	2	4	no	—
352	C₂²×C₈₉	—	2	4	no	—
353	C₂²×C₈₉	—	2	8	no	—
354	C₂²×C₈₉	—	2	2	no	—
355	C₂²×C₈₉	—	2	2	no	—
356	C₂²×C₈₉	—	2	2	no	—
357	C₂²×C₈₉	—	2	8	no	—
358	C₂²×C₈₉	—	2	8	no	—
359	C₂²×C₈₉	—	4	16	no	—
360	C₂²×C₈₉	—	4	32	no	—
361	C₂²×C₈₉	—	4	4	no	—
362	C₂²×C₈₉	—	4	4	no	—
363	C₂²×C₈₉	—	4	2	no	—
364	C₂²×C₈₉	—	4	4	no	—
365	C₂²×C₈₉	—	4	2	no	—
366	C₂²×C₈₉	—	4	4	no	—
367	C₂²×C₈₉	—	4	2	no	—
368	C₂²×C₈₉	—	4	2	no	—
369	C₂²×C₈₉	—	4	2	no	—
370	C₂²×C₈₉	—	4	4	no	—
371	C₂²×C₈₉	—	4	4	no	—
372	C₂²×C₈₉	C₂×#120	1	4	yes	—
373	C₂²×C₈₉	#537	1	4	yes	complemented
374	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
375	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
376	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₈₉	#585	1	2	yes	—
379	C₄×C₈₉	—	2	2	no	—
380	C₄×C₈₉	—	2	8	no	—
381	C₄×C₈₉	—	2	2	no	—
382	C₄×C₈₉	—	4	2	no	—
383	C₄×C₈₉	—	4	2	no	—
384	C₄×C₈₉	—	4	2	no	—
385	C₄×C₈₉	—	4	8	no	—
386	C₄×C₈₉	C₂×#120	1	4	yes	—
387	C₄×C₈₉	C₂×#120	1	4	yes	—
388	#35251	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
389	C₂×C₈₉	—	2	4	no	—
390	C₂×C₈₉	—	2	4	no	—
391	C₂×C₈₉	—	4	2	no	—
392	C₂×C₈₉	—	4	8	no	—
393	C₂×C₈₉	—	8	2	no	—
394	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
395	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
396	C₂×C₈₉	#3449	1	1	yes	characteristic
397	C₂×C₈₉	#3488	1	2	yes	—
398	C₂×C₈₉	#3489	1	2	yes	—
399	C₂³×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
400	C₂×#537	C₂×C₈₉	1	2	yes	complemented
401	C₂×#525	C₂×C₈₉	1	1	yes	characteristic, complemented
402	#2848	C₂×C₈₉	1	2	yes	complemented
403	#2847	C₂×C₈₉	1	2	yes	complemented
404	#2616	C₂×C₈₉	1	2	yes	complemented
405	#2615	C₂×C₈₉	1	2	yes	complemented
406	#2430	C₂×C₈₉	1	4	yes	complemented
407	#2410	C₂×C₈₉	1	4	yes	complemented
408	#2409	C₂×C₈₉	1	2	yes	complemented
409	#2408	C₂×C₈₉	1	2	yes	complemented
410	#2407	C₂×C₈₉	1	4	yes	complemented
411	#2311	C₂×C₈₉	1	2	yes	complemented
412	C₂×#380	C₂×C₈₉	1	1	yes	characteristic, complemented
413	C₈₉	#35251	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²×#41	—	2	16	no	—
415	C₂²×#41	—	2	8	no	—
416	C₂²×#41	C₂²×C₈₉	1	2	yes	—
417	C₂²×#41	C₂²×C₈₉	1	2	yes	—
418	C₂²×#41	C₂²×C₈₉	1	2	yes	—
419	C₂²×#41	C₂²×C₈₉	1	2	yes	—
420	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
421	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
422	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
424	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
425	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
426	#537	—	2	16	no	—
427	#525	—	2	8	no	—
428	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
429	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
431	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
432	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
433	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
435	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic, complemented
436	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
437	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
438	C₂×#120	C₂²×C₈₉	1	2	yes	—
439	C₂×#120	C₂²×C₈₉	1	4	yes	—
440	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
441	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
442	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
443	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
444	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
445	#395	C₂²×C₈₉	1	4	yes	complemented
446	#394	C₂²×C₈₉	1	8	yes	complemented
447	#394	C₂²×C₈₉	1	4	yes	complemented
448	#393	C₂²×C₈₉	1	4	yes	complemented
449	#392	C₂²×C₈₉	1	8	yes	complemented
450	#392	C₂²×C₈₉	1	4	yes	complemented
451	#391	C₂²×C₈₉	1	4	yes	complemented
452	#390	C₂²×C₈₉	1	4	yes	complemented
453	#386	C₂²×C₈₉	1	4	yes	—
454	#386	C₂²×C₈₉	1	8	yes	complemented
455	#386	C₂²×C₈₉	1	8	yes	complemented
456	#385	C₂²×C₈₉	1	4	yes	—
457	#385	C₂²×C₈₉	1	8	yes	complemented
458	#380	C₂²×C₈₉	1	2	yes	—
459	#380	C₂²×C₈₉	1	2	yes	—
460	#380	C₂²×C₈₉	1	4	yes	complemented
461	#380	C₂²×C₈₉	1	4	yes	complemented
462	#380	C₂²×C₈₉	1	2	yes	complemented
463	#380	C₂²×C₈₉	1	2	yes	complemented
464	#379	C₂²×C₈₉	1	4	yes	—
465	C₂×#95	C₂²×C₈₉	1	2	yes	complemented
466	C₂⁵	C₂³×C₈₉	1	2	yes	—
467	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
468	C₂×#41	—	2	128	no	—
469	C₂×#41	—	2	8	no	—
470	C₂×#41	—	2	8	no	—
471	C₂×#41	—	2	16	no	—
472	C₂×#41	—	2	8	no	—
473	C₂×#41	—	2	16	no	—
474	C₂×#41	—	2	8	no	—
475	C₂×#41	—	2	8	no	—
476	C₂×#41	—	2	8	no	—
477	C₂×#41	—	2	8	no	—
478	C₂×#41	—	2	4	no	—
479	C₂×#41	—	2	8	no	—
480	C₂×#41	D₄×C₈₉	1	16	yes	complemented
481	C₂²×Q₈	—	2	8	no	—
482	C₂²×Q₈	—	2	4	no	—
483	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
485	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
486	C₂²×D₄	—	2	8	no	—
487	C₂²×D₄	—	2	8	no	—
488	C₂²×D₄	—	2	16	no	—
489	C₂²×D₄	—	2	4	no	—
490	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
491	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
492	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
494	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
495	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
496	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
497	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
498	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
499	C₂³×C₄	—	2	8	no	—
500	C₂³×C₄	—	2	16	no	—
501	C₂³×C₄	—	2	8	no	—
502	C₂³×C₄	D₄×C₈₉	1	8	yes	complemented
503	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
504	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
505	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
506	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
510	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
513	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
514	#123	—	2	8	no	—
515	C₂²⋊Q₈	—	2	16	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	—	2	4	no	—
518	C₂²⋊Q₈	—	2	16	no	—
519	#121	—	2	16	no	—
520	#121	—	2	32	no	—
521	#121	—	2	4	no	—
522	#121	—	2	4	no	—
523	#121	—	2	16	no	—
524	#120	—	2	8	no	—
525	#120	—	4	8	no	—
526	C₄×D₄	—	2	8	no	—
527	C₄×D₄	—	2	8	no	—
528	#117	—	2	4	no	—
529	C₂×C₄⋊C₄	—	2	8	no	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
537	C₂×C₂²⋊C₄	—	4	4	no	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
549	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
550	#95	C₂³×C₈₉	1	4	yes	—
551	#95	C₂³×C₈₉	1	4	yes	—
552	#95	C₂³×C₈₉	1	8	yes	—
553	#95	C₂³×C₈₉	1	8	yes	—
554	C₂⁴	—	2	8	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	4	no	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	—	2	2	no	—
559	C₂⁴	—	2	4	no	—
560	C₂⁴	—	2	4	no	—
561	C₂⁴	—	4	2	no	—
562	C₂⁴	—	4	4	no	—
563	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
564	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
565	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
566	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
567	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
568	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
569	#41	—	2	64	no	—
570	#41	—	2	64	no	—
571	#41	—	2	64	no	—
572	#41	—	2	64	no	—
573	#41	—	4	16	no	—
574	C₂×Q₈	—	2	32	no	—
575	C₂×Q₈	—	2	8	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	4	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	C₂×D₄×C₈₉	1	8	yes	—
582	C₂×D₄	—	2	64	no	—
583	C₂×D₄	—	2	32	no	—
584	C₂×D₄	—	2	8	no	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	8	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	16	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	8	no	—
604	C₂×D₄	—	4	8	no	—
605	C₂×D₄	C₂×D₄×C₈₉	1	16	yes	—
606	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
607	C₂²×C₄	—	2	64	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	8	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	32	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	8	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	8	no	—
616	C₂²×C₄	—	2	8	no	—
617	C₂²×C₄	—	2	4	no	—
618	C₂²×C₄	—	2	8	no	—
619	C₂²×C₄	—	2	8	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	8	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	4	4	no	—
625	C₂²×C₄	—	4	4	no	—
626	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
627	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
628	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
629	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	—
630	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
631	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
632	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
633	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
634	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
637	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
642	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
643	C₄⋊C₄	—	2	8	no	—
644	C₄⋊C₄	—	2	8	no	—
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	2	2	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	16	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	16	no	—
654	C₂²⋊C₄	—	2	8	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	16	no	—
658	C₂²⋊C₄	—	4	4	no	—
659	C₂²⋊C₄	—	4	8	no	—
660	C₂²⋊C₄	—	4	8	no	—
661	C₄²	—	2	4	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	16	no	—
668	C₂³	—	2	8	no	—
669	C₂³	—	2	8	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	4	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	4	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	4	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	2	4	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	4	4	no	—
686	C₂³	—	4	8	no	—
687	C₂³	—	4	16	no	—
688	C₂³	—	4	8	no	—
689	C₂³	—	4	16	no	—
690	C₂³	—	4	8	no	—
691	C₂³	—	4	8	no	—
692	C₂³	C₂²×D₄×C₈₉	1	8	yes	—
693	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
694	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
695	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
696	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
697	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
698	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
699	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
700	Q₈	—	2	16	no	—
701	Q₈	—	2	16	no	—
702	Q₈	—	4	4	no	—
703	D₄	—	2	32	no	—
704	D₄	—	2	16	no	—
705	D₄	—	2	32	no	—
706	D₄	—	2	16	no	—
707	D₄	—	4	8	no	—
708	D₄	—	4	8	no	—
709	D₄	—	4	8	no	—
710	D₄	—	4	4	no	—
711	D₄	—	8	16	no	—
712	C₂×C₄	—	2	16	no	—
713	C₂×C₄	—	2	32	no	—
714	C₂×C₄	—	2	8	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	8	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	8	no	—
722	C₂×C₄	—	2	32	no	—
723	C₂×C₄	—	2	8	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	8	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	4	no	—
729	C₂×C₄	—	2	8	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	4	no	—
733	C₂×C₄	—	2	8	no	—
734	C₂×C₄	—	4	8	no	—
735	C₂×C₄	—	8	8	no	—
736	C₂×C₄	#120×C₈₉	1	16	yes	complemented
737	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
738	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
739	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
741	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
742	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
743	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	4	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	4	no	—
751	C₂²	—	2	4	no	—
752	C₂²	—	2	8	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	8	no	—
757	C₂²	—	2	8	no	—
758	C₂²	—	4	16	no	—
759	C₂²	—	4	32	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	4	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	4	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	4	no	—
770	C₂²	—	4	4	no	—
771	C₂²	C₂×#120×C₈₉	1	4	yes	—
772	C₂²	#537×C₈₉	1	4	yes	complemented
773	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
774	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
775	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
776	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
777	C₂²	#585×C₈₉	1	2	yes	—
778	C₄	—	2	2	no	—
779	C₄	—	2	8	no	—
780	C₄	—	2	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	—	4	8	no	—
785	C₄	C₂×#120×C₈₉	1	4	yes	—
786	C₄	C₂×#120×C₈₉	1	4	yes	—
787	C₂	—	2	4	no	—
788	C₂	—	2	4	no	—
789	C₂	—	4	2	no	—
790	C₂	—	4	8	no	—
791	C₂	—	8	2	no	—
792	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic
793	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
794	C₂	C₈₉×#3449	1	1	yes	characteristic
795	C₂	C₈₉×#3488	1	2	yes	—
796	C₂	C₈₉×#3489	1	2	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. C₂³×#41×C₈₉	C₂	semidirect
2. C₂×#537×C₈₉	C₂	semidirect
3. C₂×#525×C₈₉	C₂	semidirect
4. C₈₉×#2848	C₂	semidirect
5. C₈₉×#2847	C₂	semidirect
6. C₈₉×#2616	C₂	semidirect
7. C₈₉×#2615	C₂	semidirect
8. C₈₉×#2430	C₂	semidirect
9. C₈₉×#2410	C₂	semidirect
10. C₈₉×#2409	C₂	semidirect
11. C₈₉×#2408	C₂	semidirect
12. C₈₉×#2407	C₂	semidirect
13. C₈₉×#2311	C₂	semidirect
14. C₂×#380×C₈₉	C₂	semidirect
21. C₂²×#41×C₈₉	C₂²	semidirect
29. C₂×#123×C₈₉	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
32. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
35. C₂×#121×C₈₉	C₂²	semidirect
36. C₂×#121×C₈₉	C₂²	semidirect
37. C₂×#121×C₈₉	C₂²	semidirect
38. C₂×#121×C₈₉	C₂²	semidirect
42. C₂×C₄×D₄×C₈₉	C₂²	semidirect
43. C₂×#117×C₈₉	C₂²	semidirect
44. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
46. #395×C₈₉	C₂²	semidirect
47. #394×C₈₉	C₂²	semidirect
48. #394×C₈₉	C₂²	semidirect
49. #393×C₈₉	C₂²	semidirect
50. #392×C₈₉	C₂²	semidirect
51. #392×C₈₉	C₂²	semidirect
52. #391×C₈₉	C₂²	semidirect
53. #390×C₈₉	C₂²	semidirect
55. #386×C₈₉	C₂²	semidirect
56. #386×C₈₉	C₂²	semidirect
58. #385×C₈₉	C₂²	semidirect
61. #380×C₈₉	C₂²	semidirect
62. #380×C₈₉	C₂²	semidirect
63. #380×C₈₉	C₂²	semidirect
64. #380×C₈₉	C₂²	semidirect
66. C₂×#95×C₈₉	C₂²	semidirect
81. C₂×#41×C₈₉	D₄	semidirect
103. C₂³×C₄×C₈₉	D₄	semidirect
337. C₂×C₄×C₈₉	#120	semidirect
373. C₂²×C₈₉	#537	semidirect
388. #35251	C₈₉	direct (N × H)
399. C₂³×#41	C₂×C₈₉	semidirect
400. C₂×#537	C₂×C₈₉	semidirect
401. C₂×#525	C₂×C₈₉	semidirect
402. #2848	C₂×C₈₉	semidirect
403. #2847	C₂×C₈₉	semidirect
404. #2616	C₂×C₈₉	semidirect
405. #2615	C₂×C₈₉	semidirect
406. #2430	C₂×C₈₉	semidirect
407. #2410	C₂×C₈₉	semidirect
408. #2409	C₂×C₈₉	semidirect
409. #2408	C₂×C₈₉	semidirect
410. #2407	C₂×C₈₉	semidirect
411. #2311	C₂×C₈₉	semidirect
412. C₂×#380	C₂×C₈₉	semidirect
413. C₈₉	#35251	direct (N × H)
420. C₂²×#41	C₂²×C₈₉	semidirect
428. C₂×#123	C₂²×C₈₉	semidirect
430. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
431. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
432. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
434. C₂×#121	C₂²×C₈₉	semidirect
435. C₂×#121	C₂²×C₈₉	semidirect
436. C₂×#121	C₂²×C₈₉	semidirect
437. C₂×#121	C₂²×C₈₉	semidirect
441. C₂×C₄×D₄	C₂²×C₈₉	semidirect
442. C₂×#117	C₂²×C₈₉	semidirect
443. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
445. #395	C₂²×C₈₉	semidirect
446. #394	C₂²×C₈₉	semidirect
447. #394	C₂²×C₈₉	semidirect
448. #393	C₂²×C₈₉	semidirect
449. #392	C₂²×C₈₉	semidirect
450. #392	C₂²×C₈₉	semidirect
451. #391	C₂²×C₈₉	semidirect
452. #390	C₂²×C₈₉	semidirect
454. #386	C₂²×C₈₉	semidirect
455. #386	C₂²×C₈₉	semidirect
457. #385	C₂²×C₈₉	semidirect
460. #380	C₂²×C₈₉	semidirect
461. #380	C₂²×C₈₉	semidirect
462. #380	C₂²×C₈₉	semidirect
463. #380	C₂²×C₈₉	semidirect
465. C₂×#95	C₂²×C₈₉	semidirect
480. C₂×#41	D₄×C₈₉	semidirect
502. C₂³×C₄	D₄×C₈₉	semidirect
736. C₂×C₄	#120×C₈₉	semidirect
772. C₂²	#537×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂³×#41×C₈₉	2
C₂×#537×C₈₉	2
C₂×#525×C₈₉	2
C₈₉×#2848	2
C₈₉×#2847	2
C₈₉×#2616	2
C₈₉×#2615	2
C₈₉×#2430	2
C₈₉×#2410	2
C₈₉×#2409	2
C₈₉×#2408	2
C₈₉×#2407	2
C₈₉×#2311	2
C₂×#380×C₈₉	2
#35251	89

Subgroups — C89×#35251 #36413099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35251 #36413099