Subgroups — C₈₉×#36752 #36414600

Order 22784.

1570 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2851	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2805	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2802	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2792	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2791	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2791	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2755	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2734	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2713	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2659	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2646	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2569	C₂	1	2	yes	maximal
14	C₈₉×#2440	C₂	1	2	yes	maximal
15	C₈₉×#2438	C₂	1	2	yes	maximal
16	C₈₉×#2438	C₂	1	2	yes	maximal
17	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2313	C₂	1	1	yes	maximal, characteristic
19	C₂×#387×C₈₉	C₂	1	1	yes	maximal, characteristic
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×#117×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
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	#398×C₈₉	C₂²	1	2	yes	—
36	#398×C₈₉	C₂²	1	2	yes	—
37	#398×C₈₉	C₂²	1	2	yes	—
38	#398×C₈₉	C₂²	1	2	yes	—
39	#398×C₈₉	C₂²	1	2	yes	—
40	#398×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#398×C₈₉	C₂²	1	2	yes	—
46	#398×C₈₉	C₂²	1	2	yes	—
47	#395×C₈₉	C₂²	1	2	yes	—
48	#395×C₈₉	C₂²	1	2	yes	—
49	#395×C₈₉	C₂²	1	2	yes	—
50	#395×C₈₉	C₂²	1	2	yes	—
51	#395×C₈₉	C₂²	1	2	yes	—
52	#395×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	2	yes	—
54	#391×C₈₉	C₂²	1	2	yes	—
55	#391×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	1	yes	characteristic
61	#389×C₈₉	C₂²	1	1	yes	characteristic
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	2	yes	—
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	2	yes	—
66	#389×C₈₉	C₂²	1	2	yes	—
67	#389×C₈₉	C₂²	1	2	yes	—
68	#389×C₈₉	C₂²	1	2	yes	—
69	#387×C₈₉	C₂²	1	2	yes	—
70	#387×C₈₉	C₂²	1	2	yes	—
71	#387×C₈₉	C₂²	1	2	yes	—
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	2	yes	—
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	2	yes	—
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	2	yes	—
81	#387×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	#387×C₈₉	C₂²	1	2	yes	—
86	#387×C₈₉	C₂²	1	2	yes	—
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	2	yes	—
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	2	yes	—
91	#384×C₈₉	C₂²	1	1	yes	characteristic
92	#384×C₈₉	C₂²	1	2	yes	—
93	#382×C₈₉	C₂²	1	1	yes	characteristic
94	#381×C₈₉	C₂²	1	2	yes	—
95	#380×C₈₉	C₂²	1	1	yes	characteristic
96	#380×C₈₉	C₂²	1	1	yes	characteristic
97	#380×C₈₉	C₂²	1	2	yes	—
98	#380×C₈₉	C₂²	1	2	yes	—
99	#380×C₈₉	C₂²	1	2	yes	—
100	#380×C₈₉	C₂²	1	1	yes	characteristic
101	#380×C₈₉	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
103	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
104	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
105	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
106	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
108	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
109	C₂³×C₄×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	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₈₉	—	4	2	no	—
117	C₄⋊Q₈×C₈₉	—	4	4	no	—
118	#125×C₈₉	—	4	2	no	—
119	C₂²⋊Q₈×C₈₉	—	4	4	no	—
120	C₂²⋊Q₈×C₈₉	—	4	4	no	—
121	#117×C₈₉	—	4	4	no	—
122	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
123	C₂×C₄⋊C₄×C₈₉	Q₈	1	8	yes	complemented
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	1	yes	characteristic
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	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	1	yes	characteristic
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	—	4	2	no	—
163	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
166	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄²×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	2	yes	—
184	#95×C₈₉	C₂³	1	2	yes	—
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	#95×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
204	C₂×Q₈×C₈₉	—	2	4	no	—
205	C₂×Q₈×C₈₉	—	4	2	no	—
206	C₂×Q₈×C₈₉	—	4	2	no	—
207	C₂×Q₈×C₈₉	—	4	2	no	—
208	C₂×Q₈×C₈₉	—	4	2	no	—
209	C₂×Q₈×C₈₉	—	4	2	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	2	no	—
212	C₂²×C₄×C₈₉	—	2	2	no	—
213	C₂²×C₄×C₈₉	—	2	2	no	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	4	1	no	—
219	C₂²×C₄×C₈₉	—	4	1	no	—
220	C₂²×C₄×C₈₉	—	4	1	no	—
221	C₂²×C₄×C₈₉	—	4	1	no	—
222	C₂²×C₄×C₈₉	—	4	1	no	—
223	C₂²×C₄×C₈₉	—	4	1	no	—
224	C₂²×C₄×C₈₉	—	4	1	no	—
225	C₂²×C₄×C₈₉	—	4	1	no	—
226	C₂²×C₄×C₈₉	—	4	1	no	—
227	C₂²×C₄×C₈₉	—	4	1	no	—
228	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
229	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
230	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	4	2	no	—
254	C₄⋊C₄×C₈₉	—	4	2	no	—
255	C₄⋊C₄×C₈₉	—	4	1	no	—
256	C₄⋊C₄×C₈₉	—	4	1	no	—
257	C₄⋊C₄×C₈₉	—	4	1	no	—
258	C₄⋊C₄×C₈₉	—	4	1	no	—
259	C₄⋊C₄×C₈₉	—	4	2	no	—
260	C₄⋊C₄×C₈₉	—	4	2	no	—
261	C₄⋊C₄×C₈₉	—	4	2	no	—
262	C₄⋊C₄×C₈₉	—	4	2	no	—
263	C₄⋊C₄×C₈₉	—	4	2	no	—
264	C₄⋊C₄×C₈₉	—	4	2	no	—
265	C₄⋊C₄×C₈₉	—	4	2	no	—
266	C₄⋊C₄×C₈₉	—	4	2	no	—
267	C₄⋊C₄×C₈₉	—	4	2	no	—
268	C₄⋊C₄×C₈₉	—	4	2	no	—
269	C₄⋊C₄×C₈₉	—	4	2	no	—
270	C₄⋊C₄×C₈₉	—	4	2	no	—
271	C₄⋊C₄×C₈₉	—	4	2	no	—
272	C₄⋊C₄×C₈₉	—	4	2	no	—
273	C₄⋊C₄×C₈₉	—	4	1	no	—
274	C₄⋊C₄×C₈₉	—	4	1	no	—
275	C₄⋊C₄×C₈₉	—	4	2	no	—
276	C₄⋊C₄×C₈₉	—	4	1	no	—
277	C₄⋊C₄×C₈₉	—	4	2	no	—
278	C₄⋊C₄×C₈₉	—	4	1	no	—
279	C₄⋊C₄×C₈₉	—	4	2	no	—
280	C₄⋊C₄×C₈₉	—	4	2	no	—
281	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
282	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
283	C₂²⋊C₄×C₈₉	—	2	4	no	—
284	C₂²⋊C₄×C₈₉	—	2	4	no	—
285	C₂²⋊C₄×C₈₉	—	2	4	no	—
286	C₂²⋊C₄×C₈₉	—	2	4	no	—
287	C₄²×C₈₉	—	2	2	no	—
288	C₄²×C₈₉	—	2	2	no	—
289	C₄²×C₈₉	—	4	1	no	—
290	C₄²×C₈₉	—	4	1	no	—
291	C₄²×C₈₉	—	4	2	no	—
292	C₄²×C₈₉	—	4	2	no	—
293	C₄²×C₈₉	—	4	2	no	—
294	C₄²×C₈₉	—	4	2	no	—
295	C₂³×C₈₉	—	2	1	no	—
296	C₂³×C₈₉	—	2	1	no	—
297	C₂³×C₈₉	—	2	1	no	—
298	C₂³×C₈₉	—	2	1	no	—
299	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
300	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
301	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
302	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
303	Q₈×C₈₉	—	8	4	no	—
304	Q₈×C₈₉	—	8	4	no	—
305	C₂×C₄×C₈₉	—	2	8	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	1	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	1	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	2	1	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	1	no	—
319	C₂×C₄×C₈₉	—	2	1	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	1	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	2	no	—
338	C₂×C₄×C₈₉	—	2	2	no	—
339	C₂×C₄×C₈₉	—	2	1	no	—
340	C₂×C₄×C₈₉	—	2	1	no	—
341	C₂×C₄×C₈₉	—	2	2	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	2	no	—
344	C₂×C₄×C₈₉	—	2	2	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	2	2	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	2	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	2	no	—
354	C₂×C₄×C₈₉	—	4	4	no	—
355	C₂×C₄×C₈₉	—	4	4	no	—
356	C₂×C₄×C₈₉	—	4	4	no	—
357	C₂×C₄×C₈₉	—	4	4	no	—
358	C₂×C₄×C₈₉	—	8	2	no	—
359	C₂×C₄×C₈₉	—	8	2	no	—
360	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
361	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
362	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
363	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
364	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
365	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	2	no	—
368	C₂²×C₈₉	—	2	2	no	—
369	C₂²×C₈₉	—	2	2	no	—
370	C₂²×C₈₉	—	2	2	no	—
371	C₂²×C₈₉	—	2	2	no	—
372	C₂²×C₈₉	#544	1	4	yes	—
373	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
374	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
378	C₂²×C₈₉	#585	1	1	yes	characteristic
379	C₂²×C₈₉	#585	1	1	yes	characteristic
380	C₄×C₈₉	—	2	4	no	—
381	C₄×C₈₉	—	2	2	no	—
382	C₄×C₈₉	—	2	2	no	—
383	C₄×C₈₉	—	2	4	no	—
384	C₄×C₈₉	—	2	2	no	—
385	C₄×C₈₉	—	2	2	no	—
386	C₄×C₈₉	—	4	1	no	—
387	C₄×C₈₉	—	4	2	no	—
388	C₄×C₈₉	—	4	2	no	—
389	C₄×C₈₉	—	4	2	no	—
390	C₄×C₈₉	—	4	2	no	—
391	C₄×C₈₉	—	4	2	no	—
392	C₄×C₈₉	—	4	1	no	—
393	C₄×C₈₉	—	4	2	no	—
394	C₄×C₈₉	—	4	2	no	—
395	C₄×C₈₉	—	4	2	no	—
396	C₄×C₈₉	—	4	2	no	—
397	C₄×C₈₉	—	4	2	no	—
398	#36752	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂×C₈₉	—	2	4	no	—
400	C₂×C₈₉	C₂×#544	1	1	yes	characteristic
401	C₂×C₈₉	#3501	1	1	yes	characteristic
402	C₂×C₈₉	#3502	1	1	yes	characteristic
403	C₂×C₈₉	#3534	1	1	yes	characteristic
404	C₂×C₈₉	#3538	1	1	yes	characteristic
405	C₂×C₈₉	#3559	1	1	yes	characteristic
406	C₂×C₈₉	#3564	1	1	yes	characteristic
407	#2857	C₂×C₈₉	1	1	yes	characteristic
408	#2851	C₂×C₈₉	1	1	yes	characteristic
409	#2805	C₂×C₈₉	1	2	yes	complemented
410	#2802	C₂×C₈₉	1	2	yes	complemented
411	#2792	C₂×C₈₉	1	2	yes	complemented
412	#2791	C₂×C₈₉	1	2	yes	complemented
413	#2791	C₂×C₈₉	1	2	yes	complemented
414	#2755	C₂×C₈₉	1	2	yes	complemented
415	#2734	C₂×C₈₉	1	2	yes	complemented
416	#2713	C₂×C₈₉	1	2	yes	complemented
417	#2659	C₂×C₈₉	1	1	yes	characteristic
418	#2646	C₂×C₈₉	1	1	yes	characteristic
419	#2569	C₂×C₈₉	1	2	yes	—
420	#2440	C₂×C₈₉	1	2	yes	—
421	#2438	C₂×C₈₉	1	2	yes	—
422	#2438	C₂×C₈₉	1	2	yes	—
423	#2316	C₂×C₈₉	1	1	yes	characteristic
424	#2313	C₂×C₈₉	1	1	yes	characteristic
425	C₂×#387	C₂×C₈₉	1	1	yes	characteristic
426	C₈₉	#36752	1	1	yes	characteristic, direct product factor, Sylow
427	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
429	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
430	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
431	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
432	C₂×#117	C₂²×C₈₉	1	2	yes	—
433	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
435	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
436	#400	C₂²×C₈₉	1	2	yes	—
437	#400	C₂²×C₈₉	1	2	yes	—
438	#400	C₂²×C₈₉	1	2	yes	—
439	#400	C₂²×C₈₉	1	2	yes	—
440	#400	C₂²×C₈₉	1	2	yes	—
441	#400	C₂²×C₈₉	1	2	yes	—
442	#398	C₂²×C₈₉	1	2	yes	—
443	#398	C₂²×C₈₉	1	2	yes	—
444	#398	C₂²×C₈₉	1	2	yes	—
445	#398	C₂²×C₈₉	1	2	yes	—
446	#398	C₂²×C₈₉	1	2	yes	—
447	#398	C₂²×C₈₉	1	2	yes	—
448	#398	C₂²×C₈₉	1	2	yes	—
449	#398	C₂²×C₈₉	1	2	yes	—
450	#398	C₂²×C₈₉	1	2	yes	—
451	#398	C₂²×C₈₉	1	2	yes	—
452	#398	C₂²×C₈₉	1	2	yes	—
453	#398	C₂²×C₈₉	1	2	yes	—
454	#395	C₂²×C₈₉	1	2	yes	—
455	#395	C₂²×C₈₉	1	2	yes	—
456	#395	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	#391	C₂²×C₈₉	1	2	yes	—
461	#391	C₂²×C₈₉	1	2	yes	—
462	#391	C₂²×C₈₉	1	2	yes	—
463	#389	C₂²×C₈₉	1	2	yes	—
464	#389	C₂²×C₈₉	1	2	yes	—
465	#389	C₂²×C₈₉	1	2	yes	—
466	#389	C₂²×C₈₉	1	2	yes	—
467	#389	C₂²×C₈₉	1	1	yes	characteristic
468	#389	C₂²×C₈₉	1	1	yes	characteristic
469	#389	C₂²×C₈₉	1	1	yes	characteristic
470	#389	C₂²×C₈₉	1	2	yes	—
471	#389	C₂²×C₈₉	1	1	yes	characteristic
472	#389	C₂²×C₈₉	1	2	yes	—
473	#389	C₂²×C₈₉	1	2	yes	—
474	#389	C₂²×C₈₉	1	2	yes	—
475	#389	C₂²×C₈₉	1	2	yes	—
476	#387	C₂²×C₈₉	1	2	yes	—
477	#387	C₂²×C₈₉	1	2	yes	—
478	#387	C₂²×C₈₉	1	2	yes	—
479	#387	C₂²×C₈₉	1	2	yes	—
480	#387	C₂²×C₈₉	1	2	yes	—
481	#387	C₂²×C₈₉	1	2	yes	—
482	#387	C₂²×C₈₉	1	2	yes	—
483	#387	C₂²×C₈₉	1	2	yes	—
484	#387	C₂²×C₈₉	1	2	yes	—
485	#387	C₂²×C₈₉	1	2	yes	—
486	#387	C₂²×C₈₉	1	2	yes	—
487	#387	C₂²×C₈₉	1	2	yes	—
488	#387	C₂²×C₈₉	1	2	yes	—
489	#387	C₂²×C₈₉	1	2	yes	—
490	#387	C₂²×C₈₉	1	2	yes	—
491	#387	C₂²×C₈₉	1	2	yes	—
492	#387	C₂²×C₈₉	1	2	yes	—
493	#387	C₂²×C₈₉	1	2	yes	—
494	#385	C₂²×C₈₉	1	2	yes	—
495	#385	C₂²×C₈₉	1	2	yes	—
496	#385	C₂²×C₈₉	1	2	yes	—
497	#385	C₂²×C₈₉	1	2	yes	—
498	#384	C₂²×C₈₉	1	1	yes	characteristic
499	#384	C₂²×C₈₉	1	2	yes	—
500	#382	C₂²×C₈₉	1	1	yes	characteristic
501	#381	C₂²×C₈₉	1	2	yes	—
502	#380	C₂²×C₈₉	1	1	yes	characteristic
503	#380	C₂²×C₈₉	1	1	yes	characteristic
504	#380	C₂²×C₈₉	1	2	yes	—
505	#380	C₂²×C₈₉	1	2	yes	—
506	#380	C₂²×C₈₉	1	2	yes	—
507	#380	C₂²×C₈₉	1	1	yes	characteristic
508	#380	C₂²×C₈₉	1	1	yes	characteristic
509	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
510	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
513	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
515	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
516	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
523	C₄⋊Q₈	—	4	2	no	—
524	C₄⋊Q₈	—	4	4	no	—
525	#125	—	4	2	no	—
526	C₂²⋊Q₈	—	4	4	no	—
527	C₂²⋊Q₈	—	4	4	no	—
528	#117	—	4	4	no	—
529	C₂×C₄⋊C₄	—	4	2	no	—
530	C₂×C₄⋊C₄	Q₈×C₈₉	1	8	yes	complemented
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
569	C₂×C₄²	—	4	2	no	—
570	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
573	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
574	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
575	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
576	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
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	#95	C₂³×C₈₉	1	2	yes	—
590	#95	C₂³×C₈₉	1	2	yes	—
591	#95	C₂³×C₈₉	1	2	yes	—
592	#95	C₂³×C₈₉	1	2	yes	—
593	#95	C₂³×C₈₉	1	2	yes	—
594	#95	C₂³×C₈₉	1	2	yes	—
595	#95	C₂³×C₈₉	1	2	yes	—
596	#95	C₂³×C₈₉	1	2	yes	—
597	#95	C₂³×C₈₉	1	2	yes	—
598	#95	C₂³×C₈₉	1	2	yes	—
599	#95	C₂³×C₈₉	1	2	yes	—
600	#95	C₂³×C₈₉	1	2	yes	—
601	#95	C₂³×C₈₉	1	2	yes	—
602	#95	C₂³×C₈₉	1	2	yes	—
603	#95	C₂³×C₈₉	1	2	yes	—
604	#95	C₂³×C₈₉	1	2	yes	—
605	#95	C₂³×C₈₉	1	2	yes	—
606	#95	C₂³×C₈₉	1	2	yes	—
607	#95	C₂³×C₈₉	1	2	yes	—
608	#95	C₂³×C₈₉	1	2	yes	—
609	#95	C₂³×C₈₉	1	2	yes	—
610	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	4	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	4	1	no	—
626	C₂²×C₄	—	4	1	no	—
627	C₂²×C₄	—	4	1	no	—
628	C₂²×C₄	—	4	1	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	1	no	—
632	C₂²×C₄	—	4	1	no	—
633	C₂²×C₄	—	4	1	no	—
634	C₂²×C₄	—	4	1	no	—
635	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
636	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
637	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
638	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
639	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
648	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	2	no	—
664	C₄⋊C₄	—	4	2	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	1	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	1	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	2	no	—
686	C₄⋊C₄	—	4	2	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
689	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	4	1	no	—
697	C₄²	—	4	1	no	—
698	C₄²	—	4	2	no	—
699	C₄²	—	4	2	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
707	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
708	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
709	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
710	Q₈	—	8	4	no	—
711	Q₈	—	8	4	no	—
712	C₂×C₄	—	2	8	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	4	4	no	—
763	C₂×C₄	—	4	4	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	8	2	no	—
766	C₂×C₄	—	8	2	no	—
767	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
768	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
769	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
770	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
771	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
772	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	#544×C₈₉	1	4	yes	—
780	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
781	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
782	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
783	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
784	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
785	C₂²	#585×C₈₉	1	1	yes	characteristic
786	C₂²	#585×C₈₉	1	1	yes	characteristic
787	C₄	—	2	4	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	2	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	2	no	—
804	C₄	—	4	2	no	—
805	C₂	—	2	4	no	—
806	C₂	C₂×#544×C₈₉	1	1	yes	characteristic
807	C₂	C₈₉×#3501	1	1	yes	characteristic
808	C₂	C₈₉×#3502	1	1	yes	characteristic
809	C₂	C₈₉×#3534	1	1	yes	characteristic
810	C₂	C₈₉×#3538	1	1	yes	characteristic
811	C₂	C₈₉×#3559	1	1	yes	characteristic
812	C₂	C₈₉×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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
3. C₈₉×#2805	C₂	semidirect
4. C₈₉×#2802	C₂	semidirect
5. C₈₉×#2792	C₂	semidirect
6. C₈₉×#2791	C₂	semidirect
7. C₈₉×#2791	C₂	semidirect
8. C₈₉×#2755	C₂	semidirect
9. C₈₉×#2734	C₂	semidirect
10. C₈₉×#2713	C₂	semidirect
123. C₂×C₄⋊C₄×C₈₉	Q₈	semidirect
398. #36752	C₈₉	direct (N × H)
409. #2805	C₂×C₈₉	semidirect
410. #2802	C₂×C₈₉	semidirect
411. #2792	C₂×C₈₉	semidirect
412. #2791	C₂×C₈₉	semidirect
413. #2791	C₂×C₈₉	semidirect
414. #2755	C₂×C₈₉	semidirect
415. #2734	C₂×C₈₉	semidirect
416. #2713	C₂×C₈₉	semidirect
426. C₈₉	#36752	direct (N × H)
530. C₂×C₄⋊C₄	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2857	2
C₈₉×#2851	2
C₈₉×#2805	2
C₈₉×#2802	2
C₈₉×#2792	2
C₈₉×#2791	2
C₈₉×#2755	2
C₈₉×#2734	2
C₈₉×#2713	2
C₈₉×#2659	2
C₈₉×#2646	2
C₈₉×#2569	2
C₈₉×#2440	2
C₈₉×#2438	2
C₈₉×#2316	2
C₈₉×#2313	2
C₂×#387×C₈₉	2
#36752	89

Subgroups — C89×#36752 #36414600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36752 #36414600