Subgroups — C₈₉×#36679 #36414527

Order 22784.

1506 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2841	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2839	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2838	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2833	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2831	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2827	C₂	1	2	yes	maximal
9	C₈₉×#2817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2814	C₂	1	2	yes	maximal
11	C₈₉×#2402	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2401	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2401	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2399	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2398	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2396	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2395	C₂	1	1	yes	maximal, characteristic
18	C₄×C₂²⋊Q₈×C₈₉	C₂	1	2	yes	maximal, complemented
19	C₄×#123×C₈₉	C₂	1	1	yes	maximal, characteristic
20	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
27	#401×C₈₉	C₂²	1	2	yes	—
28	#401×C₈₉	C₂²	1	2	yes	—
29	#400×C₈₉	C₂²	1	2	yes	—
30	#400×C₈₉	C₂²	1	2	yes	—
31	#400×C₈₉	C₂²	1	2	yes	—
32	#400×C₈₉	C₂²	1	2	yes	—
33	#400×C₈₉	C₂²	1	2	yes	—
34	#400×C₈₉	C₂²	1	2	yes	—
35	#400×C₈₉	C₂²	1	2	yes	—
36	#400×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#400×C₈₉	C₂²	1	1	yes	characteristic
42	#399×C₈₉	C₂²	1	2	yes	—
43	#399×C₈₉	C₂²	1	1	yes	characteristic
44	#398×C₈₉	C₂²	1	2	yes	—
45	#398×C₈₉	C₂²	1	2	yes	—
46	#398×C₈₉	C₂²	1	2	yes	—
47	#398×C₈₉	C₂²	1	2	yes	—
48	#398×C₈₉	C₂²	1	2	yes	—
49	#398×C₈₉	C₂²	1	2	yes	—
50	#398×C₈₉	C₂²	1	2	yes	—
51	#398×C₈₉	C₂²	1	1	yes	characteristic
52	#398×C₈₉	C₂²	1	2	yes	—
53	#398×C₈₉	C₂²	1	2	yes	—
54	#398×C₈₉	C₂²	1	2	yes	—
55	#397×C₈₉	C₂²	1	2	yes	—
56	#397×C₈₉	C₂²	1	2	yes	—
57	#397×C₈₉	C₂²	1	2	yes	—
58	#397×C₈₉	C₂²	1	2	yes	—
59	#397×C₈₉	C₂²	1	1	yes	characteristic
60	#397×C₈₉	C₂²	1	1	yes	characteristic
61	#397×C₈₉	C₂²	1	2	yes	—
62	#397×C₈₉	C₂²	1	2	yes	—
63	#397×C₈₉	C₂²	1	1	yes	characteristic
64	#397×C₈₉	C₂²	1	2	yes	—
65	#396×C₈₉	C₂²	1	2	yes	—
66	#396×C₈₉	C₂²	1	2	yes	—
67	#396×C₈₉	C₂²	1	2	yes	—
68	#396×C₈₉	C₂²	1	2	yes	—
69	#395×C₈₉	C₂²	1	2	yes	—
70	#395×C₈₉	C₂²	1	2	yes	—
71	#395×C₈₉	C₂²	1	2	yes	—
72	#395×C₈₉	C₂²	1	2	yes	—
73	#395×C₈₉	C₂²	1	2	yes	—
74	#394×C₈₉	C₂²	1	2	yes	—
75	#394×C₈₉	C₂²	1	2	yes	—
76	#393×C₈₉	C₂²	1	2	yes	—
77	#393×C₈₉	C₂²	1	1	yes	characteristic
78	#393×C₈₉	C₂²	1	1	yes	characteristic
79	#391×C₈₉	C₂²	1	2	yes	—
80	#389×C₈₉	C₂²	1	2	yes	—
81	#388×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	2	yes	—
85	#386×C₈₉	C₂²	1	1	yes	characteristic
86	#385×C₈₉	C₂²	1	1	yes	characteristic
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	2	yes	—
89	#381×C₈₉	C₂²	1	1	yes	characteristic
90	#380×C₈₉	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
105	#376×C₈₉	C₂²	1	1	yes	characteristic
106	#376×C₈₉	C₂²	1	2	yes	—
107	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
114	#123×C₈₉	—	2	4	no	—
115	C₂²⋊Q₈×C₈₉	—	2	8	no	—
116	C₄×Q₈×C₈₉	—	4	4	no	—
117	C₄×Q₈×C₈₉	—	4	2	no	—
118	C₄×D₄×C₈₉	—	4	2	no	—
119	#117×C₈₉	—	4	2	no	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₄²×C₈₉	—	4	2	no	—
159	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	1	yes	characteristic
168	#95×C₈₉	C₂³	1	1	yes	characteristic
169	#95×C₈₉	C₂³	1	2	yes	—
170	#95×C₈₉	C₂³	1	2	yes	—
171	#95×C₈₉	C₂³	1	2	yes	—
172	#95×C₈₉	C₂³	1	2	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
174	#95×C₈₉	C₂³	1	2	yes	—
175	#95×C₈₉	C₂³	1	2	yes	—
176	#95×C₈₉	C₂³	1	2	yes	—
177	#95×C₈₉	C₂³	1	2	yes	—
178	#95×C₈₉	C₂³	1	2	yes	—
179	#95×C₈₉	C₂³	1	2	yes	—
180	#95×C₈₉	C₂³	1	2	yes	—
181	#95×C₈₉	C₂³	1	2	yes	—
182	#95×C₈₉	C₂³	1	2	yes	—
183	#95×C₈₉	C₂³	1	1	yes	characteristic
184	#95×C₈₉	C₂³	1	1	yes	characteristic
185	#95×C₈₉	C₂³	1	2	yes	—
186	#95×C₈₉	C₂³	1	2	yes	—
187	#95×C₈₉	C₂³	1	2	yes	—
188	#95×C₈₉	C₂³	1	2	yes	—
189	#95×C₈₉	C₂³	1	2	yes	—
190	#95×C₈₉	C₂³	1	2	yes	—
191	#95×C₈₉	C₂³	1	2	yes	—
192	#95×C₈₉	C₂³	1	2	yes	—
193	#95×C₈₉	C₂³	1	2	yes	—
194	#95×C₈₉	C₂³	1	2	yes	—
195	#95×C₈₉	C₂³	1	2	yes	—
196	#95×C₈₉	C₂³	1	2	yes	—
197	#95×C₈₉	C₂³	1	2	yes	—
198	#95×C₈₉	C₂³	1	2	yes	—
199	#95×C₈₉	C₂³	1	2	yes	—
200	#95×C₈₉	C₂³	1	2	yes	—
201	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
203	C₂×Q₈×C₈₉	—	2	4	no	—
204	C₂×Q₈×C₈₉	—	4	2	no	—
205	C₂×Q₈×C₈₉	—	4	1	no	—
206	C₂×Q₈×C₈₉	—	4	2	no	—
207	C₂×Q₈×C₈₉	—	4	2	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	4	1	no	—
210	C₂×D₄×C₈₉	—	4	1	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	2	no	—
213	C₂²×C₄×C₈₉	—	2	4	no	—
214	C₂²×C₄×C₈₉	—	2	4	no	—
215	C₂²×C₄×C₈₉	—	4	1	no	—
216	C₂²×C₄×C₈₉	—	4	1	no	—
217	C₂²×C₄×C₈₉	—	4	1	no	—
218	C₂²×C₄×C₈₉	—	4	2	no	—
219	C₂²×C₄×C₈₉	#41	1	4	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	4	2	no	—
242	C₄⋊C₄×C₈₉	—	4	2	no	—
243	C₄⋊C₄×C₈₉	—	4	2	no	—
244	C₄⋊C₄×C₈₉	—	4	2	no	—
245	C₄⋊C₄×C₈₉	—	4	2	no	—
246	C₄⋊C₄×C₈₉	—	4	2	no	—
247	C₄⋊C₄×C₈₉	—	4	2	no	—
248	C₄⋊C₄×C₈₉	—	4	2	no	—
249	C₄⋊C₄×C₈₉	—	4	2	no	—
250	C₄⋊C₄×C₈₉	—	4	2	no	—
251	C₄⋊C₄×C₈₉	—	4	2	no	—
252	C₄⋊C₄×C₈₉	—	4	2	no	—
253	C₄⋊C₄×C₈₉	—	4	1	no	—
254	C₄⋊C₄×C₈₉	—	4	1	no	—
255	C₄⋊C₄×C₈₉	—	4	1	no	—
256	C₄⋊C₄×C₈₉	—	4	2	no	—
257	C₄⋊C₄×C₈₉	—	4	2	no	—
258	C₄⋊C₄×C₈₉	—	4	2	no	—
259	C₄⋊C₄×C₈₉	—	4	1	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	2	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	4	2	no	—
266	C₂²⋊C₄×C₈₉	—	4	2	no	—
267	C₂²⋊C₄×C₈₉	—	4	2	no	—
268	C₂²⋊C₄×C₈₉	—	4	2	no	—
269	C₂²⋊C₄×C₈₉	—	4	1	no	—
270	C₂²⋊C₄×C₈₉	—	4	2	no	—
271	C₂²⋊C₄×C₈₉	—	4	2	no	—
272	C₂²⋊C₄×C₈₉	—	4	2	no	—
273	C₂²⋊C₄×C₈₉	—	4	1	no	—
274	C₂²⋊C₄×C₈₉	—	4	1	no	—
275	C₄²×C₈₉	—	2	4	no	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	2	2	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	—	2	4	no	—
280	C₄²×C₈₉	—	2	4	no	—
281	C₄²×C₈₉	—	2	4	no	—
282	C₄²×C₈₉	—	4	2	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	—	2	1	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	2	no	—
290	C₂³×C₈₉	—	2	2	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	C₂×#41	1	2	yes	—
293	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
294	Q₈×C₈₉	—	4	8	no	—
295	Q₈×C₈₉	—	4	4	no	—
296	D₄×C₈₉	—	4	4	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	1	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	2	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	2	2	no	—
331	C₂×C₄×C₈₉	—	2	2	no	—
332	C₂×C₄×C₈₉	—	2	2	no	—
333	C₂×C₄×C₈₉	—	2	2	no	—
334	C₂×C₄×C₈₉	—	2	2	no	—
335	C₂×C₄×C₈₉	—	2	2	no	—
336	C₂×C₄×C₈₉	—	2	2	no	—
337	C₂×C₄×C₈₉	—	2	1	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	2	no	—
340	C₂×C₄×C₈₉	—	2	2	no	—
341	C₂×C₄×C₈₉	—	4	4	no	—
342	C₂×C₄×C₈₉	—	4	4	no	—
343	C₂×C₄×C₈₉	—	4	4	no	—
344	C₂×C₄×C₈₉	—	4	4	no	—
345	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
346	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
348	C₂²×C₈₉	—	2	2	no	—
349	C₂²×C₈₉	—	2	4	no	—
350	C₂²×C₈₉	—	4	1	no	—
351	C₂²×C₈₉	—	4	1	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	1	no	—
354	C₂²×C₈₉	—	4	2	no	—
355	C₂²×C₈₉	—	4	1	no	—
356	C₂²×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
359	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
360	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
361	C₂²×C₈₉	#585	1	1	yes	characteristic
362	C₂²×C₈₉	#585	1	2	yes	—
363	C₄×C₈₉	—	2	4	no	—
364	C₄×C₈₉	—	4	1	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	2	no	—
368	C₄×C₈₉	—	4	2	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	1	no	—
371	C₄×C₈₉	—	4	1	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	2	no	—
374	C₄×C₈₉	—	4	1	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	#563	1	4	yes	—
380	#36679	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₈₉	—	4	2	no	—
382	C₂×C₈₉	—	8	1	no	—
383	C₂×C₈₉	#3459	1	1	yes	characteristic
384	C₂×C₈₉	#3461	1	2	yes	—
385	C₂×C₈₉	C₂×#563	1	1	yes	characteristic
386	C₂×C₈₉	#3529	1	1	yes	characteristic
387	C₂×C₈₉	#3531	1	2	yes	—
388	#2841	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2839	C₂×C₈₉	1	2	yes	complemented
390	#2838	C₂×C₈₉	1	2	yes	complemented
391	#2835	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#2834	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#2833	C₂×C₈₉	1	2	yes	complemented
394	#2831	C₂×C₈₉	1	2	yes	complemented
395	#2827	C₂×C₈₉	1	2	yes	—
396	#2817	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2814	C₂×C₈₉	1	2	yes	—
398	#2402	C₂×C₈₉	1	2	yes	complemented
399	#2401	C₂×C₈₉	1	2	yes	complemented
400	#2401	C₂×C₈₉	1	2	yes	complemented
401	#2399	C₂×C₈₉	1	2	yes	complemented
402	#2398	C₂×C₈₉	1	1	yes	characteristic
403	#2396	C₂×C₈₉	1	2	yes	complemented
404	#2395	C₂×C₈₉	1	1	yes	characteristic
405	C₄×C₂²⋊Q₈	C₂×C₈₉	1	2	yes	complemented
406	C₄×#123	C₂×C₈₉	1	1	yes	characteristic
407	C₈₉	#36679	1	1	yes	characteristic, direct product factor, Sylow
408	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
410	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
411	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
412	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
415	#401	C₂²×C₈₉	1	2	yes	—
416	#401	C₂²×C₈₉	1	2	yes	—
417	#400	C₂²×C₈₉	1	2	yes	—
418	#400	C₂²×C₈₉	1	2	yes	—
419	#400	C₂²×C₈₉	1	2	yes	—
420	#400	C₂²×C₈₉	1	2	yes	—
421	#400	C₂²×C₈₉	1	2	yes	—
422	#400	C₂²×C₈₉	1	2	yes	—
423	#400	C₂²×C₈₉	1	2	yes	—
424	#400	C₂²×C₈₉	1	2	yes	—
425	#400	C₂²×C₈₉	1	2	yes	—
426	#400	C₂²×C₈₉	1	2	yes	—
427	#400	C₂²×C₈₉	1	2	yes	—
428	#400	C₂²×C₈₉	1	2	yes	—
429	#400	C₂²×C₈₉	1	1	yes	characteristic
430	#399	C₂²×C₈₉	1	2	yes	—
431	#399	C₂²×C₈₉	1	1	yes	characteristic
432	#398	C₂²×C₈₉	1	2	yes	—
433	#398	C₂²×C₈₉	1	2	yes	—
434	#398	C₂²×C₈₉	1	2	yes	—
435	#398	C₂²×C₈₉	1	2	yes	—
436	#398	C₂²×C₈₉	1	1	yes	characteristic
437	#398	C₂²×C₈₉	1	2	yes	—
438	#398	C₂²×C₈₉	1	2	yes	—
439	#398	C₂²×C₈₉	1	2	yes	—
440	#398	C₂²×C₈₉	1	2	yes	—
441	#398	C₂²×C₈₉	1	2	yes	—
442	#398	C₂²×C₈₉	1	2	yes	—
443	#397	C₂²×C₈₉	1	2	yes	—
444	#397	C₂²×C₈₉	1	1	yes	characteristic
445	#397	C₂²×C₈₉	1	1	yes	characteristic
446	#397	C₂²×C₈₉	1	2	yes	—
447	#397	C₂²×C₈₉	1	2	yes	—
448	#397	C₂²×C₈₉	1	1	yes	characteristic
449	#397	C₂²×C₈₉	1	2	yes	—
450	#397	C₂²×C₈₉	1	2	yes	—
451	#397	C₂²×C₈₉	1	2	yes	—
452	#397	C₂²×C₈₉	1	2	yes	—
453	#396	C₂²×C₈₉	1	2	yes	—
454	#396	C₂²×C₈₉	1	2	yes	—
455	#396	C₂²×C₈₉	1	2	yes	—
456	#396	C₂²×C₈₉	1	2	yes	—
457	#395	C₂²×C₈₉	1	2	yes	—
458	#395	C₂²×C₈₉	1	2	yes	—
459	#395	C₂²×C₈₉	1	2	yes	—
460	#395	C₂²×C₈₉	1	2	yes	—
461	#395	C₂²×C₈₉	1	2	yes	—
462	#394	C₂²×C₈₉	1	2	yes	—
463	#394	C₂²×C₈₉	1	2	yes	—
464	#393	C₂²×C₈₉	1	2	yes	—
465	#393	C₂²×C₈₉	1	1	yes	characteristic
466	#393	C₂²×C₈₉	1	1	yes	characteristic
467	#391	C₂²×C₈₉	1	2	yes	—
468	#389	C₂²×C₈₉	1	2	yes	—
469	#388	C₂²×C₈₉	1	2	yes	—
470	#387	C₂²×C₈₉	1	2	yes	—
471	#387	C₂²×C₈₉	1	2	yes	—
472	#387	C₂²×C₈₉	1	2	yes	—
473	#386	C₂²×C₈₉	1	1	yes	characteristic
474	#385	C₂²×C₈₉	1	2	yes	—
475	#385	C₂²×C₈₉	1	2	yes	—
476	#385	C₂²×C₈₉	1	1	yes	characteristic
477	#381	C₂²×C₈₉	1	1	yes	characteristic
478	#380	C₂²×C₈₉	1	2	yes	—
479	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
480	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
481	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
482	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
483	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
484	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
485	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
486	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
487	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
488	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
489	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
490	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
491	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
492	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
493	#376	C₂²×C₈₉	1	1	yes	characteristic
494	#376	C₂²×C₈₉	1	2	yes	—
495	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
496	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
502	#123	—	2	4	no	—
503	C₂²⋊Q₈	—	2	8	no	—
504	C₄×Q₈	—	4	4	no	—
505	C₄×Q₈	—	4	2	no	—
506	C₄×D₄	—	4	2	no	—
507	#117	—	4	2	no	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
546	C₂×C₄²	—	4	2	no	—
547	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
548	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
551	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
553	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
554	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
555	#95	C₂³×C₈₉	1	1	yes	characteristic
556	#95	C₂³×C₈₉	1	1	yes	characteristic
557	#95	C₂³×C₈₉	1	2	yes	—
558	#95	C₂³×C₈₉	1	2	yes	—
559	#95	C₂³×C₈₉	1	2	yes	—
560	#95	C₂³×C₈₉	1	2	yes	—
561	#95	C₂³×C₈₉	1	2	yes	—
562	#95	C₂³×C₈₉	1	2	yes	—
563	#95	C₂³×C₈₉	1	2	yes	—
564	#95	C₂³×C₈₉	1	2	yes	—
565	#95	C₂³×C₈₉	1	2	yes	—
566	#95	C₂³×C₈₉	1	2	yes	—
567	#95	C₂³×C₈₉	1	2	yes	—
568	#95	C₂³×C₈₉	1	2	yes	—
569	#95	C₂³×C₈₉	1	2	yes	—
570	#95	C₂³×C₈₉	1	2	yes	—
571	#95	C₂³×C₈₉	1	1	yes	characteristic
572	#95	C₂³×C₈₉	1	1	yes	characteristic
573	#95	C₂³×C₈₉	1	2	yes	—
574	#95	C₂³×C₈₉	1	2	yes	—
575	#95	C₂³×C₈₉	1	2	yes	—
576	#95	C₂³×C₈₉	1	2	yes	—
577	#95	C₂³×C₈₉	1	2	yes	—
578	#95	C₂³×C₈₉	1	2	yes	—
579	#95	C₂³×C₈₉	1	2	yes	—
580	#95	C₂³×C₈₉	1	2	yes	—
581	#95	C₂³×C₈₉	1	2	yes	—
582	#95	C₂³×C₈₉	1	2	yes	—
583	#95	C₂³×C₈₉	1	2	yes	—
584	#95	C₂³×C₈₉	1	2	yes	—
585	#95	C₂³×C₈₉	1	2	yes	—
586	#95	C₂³×C₈₉	1	2	yes	—
587	#95	C₂³×C₈₉	1	2	yes	—
588	#95	C₂³×C₈₉	1	2	yes	—
589	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
590	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
591	C₂×Q₈	—	2	4	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	1	no	—
594	C₂×Q₈	—	4	2	no	—
595	C₂×Q₈	—	4	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	4	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	4	1	no	—
604	C₂²×C₄	—	4	1	no	—
605	C₂²×C₄	—	4	1	no	—
606	C₂²×C₄	—	4	2	no	—
607	C₂²×C₄	#41×C₈₉	1	4	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
614	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
619	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
623	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	4	1	no	—
630	C₄⋊C₄	—	4	1	no	—
631	C₄⋊C₄	—	4	1	no	—
632	C₄⋊C₄	—	4	2	no	—
633	C₄⋊C₄	—	4	2	no	—
634	C₄⋊C₄	—	4	2	no	—
635	C₄⋊C₄	—	4	1	no	—
636	C₄⋊C₄	—	4	2	no	—
637	C₄⋊C₄	—	4	2	no	—
638	C₄⋊C₄	—	4	2	no	—
639	C₄⋊C₄	—	4	2	no	—
640	C₄⋊C₄	—	4	2	no	—
641	C₄⋊C₄	—	4	2	no	—
642	C₄⋊C₄	—	4	2	no	—
643	C₄⋊C₄	—	4	2	no	—
644	C₄⋊C₄	—	4	2	no	—
645	C₄⋊C₄	—	4	2	no	—
646	C₄⋊C₄	—	4	2	no	—
647	C₄⋊C₄	—	4	2	no	—
648	C₄⋊C₄	—	4	2	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	4	2	no	—
654	C₂²⋊C₄	—	4	1	no	—
655	C₂²⋊C₄	—	4	1	no	—
656	C₂²⋊C₄	—	4	2	no	—
657	C₂²⋊C₄	—	4	2	no	—
658	C₂²⋊C₄	—	4	2	no	—
659	C₂²⋊C₄	—	4	2	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	2	no	—
662	C₂²⋊C₄	—	4	2	no	—
663	C₄²	—	2	4	no	—
664	C₄²	—	2	4	no	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	—	2	4	no	—
670	C₄²	—	4	2	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	1	no	—
680	C₂³	C₂×#41×C₈₉	1	2	yes	—
681	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
682	Q₈	—	4	8	no	—
683	Q₈	—	4	4	no	—
684	D₄	—	4	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	—	4	4	no	—
732	C₂×C₄	—	4	4	no	—
733	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
734	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
735	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	2	no	—
746	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
747	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
748	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
749	C₂²	#585×C₈₉	1	1	yes	characteristic
750	C₂²	#585×C₈₉	1	2	yes	—
751	C₄	—	2	4	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	1	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	#563×C₈₉	1	4	yes	—
768	C₂	—	4	2	no	—
769	C₂	—	8	1	no	—
770	C₂	C₈₉×#3459	1	1	yes	characteristic
771	C₂	C₈₉×#3461	1	2	yes	—
772	C₂	C₂×#563×C₈₉	1	1	yes	characteristic
773	C₂	C₈₉×#3529	1	1	yes	characteristic
774	C₂	C₈₉×#3531	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂⁵
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2841	C₂	semidirect
2. C₈₉×#2839	C₂	semidirect
3. C₈₉×#2838	C₂	semidirect
4. C₈₉×#2835	C₂	semidirect
5. C₈₉×#2834	C₂	semidirect
6. C₈₉×#2833	C₂	semidirect
7. C₈₉×#2831	C₂	semidirect
9. C₈₉×#2817	C₂	semidirect
11. C₈₉×#2402	C₂	semidirect
12. C₈₉×#2401	C₂	semidirect
13. C₈₉×#2401	C₂	semidirect
14. C₈₉×#2399	C₂	semidirect
16. C₈₉×#2396	C₂	semidirect
18. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
380. #36679	C₈₉	direct (N × H)
388. #2841	C₂×C₈₉	semidirect
389. #2839	C₂×C₈₉	semidirect
390. #2838	C₂×C₈₉	semidirect
391. #2835	C₂×C₈₉	semidirect
392. #2834	C₂×C₈₉	semidirect
393. #2833	C₂×C₈₉	semidirect
394. #2831	C₂×C₈₉	semidirect
396. #2817	C₂×C₈₉	semidirect
398. #2402	C₂×C₈₉	semidirect
399. #2401	C₂×C₈₉	semidirect
400. #2401	C₂×C₈₉	semidirect
401. #2399	C₂×C₈₉	semidirect
403. #2396	C₂×C₈₉	semidirect
405. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
407. C₈₉	#36679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2841	2
C₈₉×#2839	2
C₈₉×#2838	2
C₈₉×#2835	2
C₈₉×#2834	2
C₈₉×#2833	2
C₈₉×#2831	2
C₈₉×#2827	2
C₈₉×#2817	2
C₈₉×#2814	2
C₈₉×#2402	2
C₈₉×#2401	2
C₈₉×#2399	2
C₈₉×#2398	2
C₈₉×#2396	2
C₈₉×#2395	2
C₄×C₂²⋊Q₈×C₈₉	2
C₄×#123×C₈₉	2
#36679	89

Subgroups — C89×#36679 #36414527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36679 #36414527