Subgroups — C₈₉×#35260 #36413108

Order 22784.

2526 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2847	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2628	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2625	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2624	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2620	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2481	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2479	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2477	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2474	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2472	C₂	1	2	yes	maximal, complemented
16	C₈₉×#2470	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2449	C₂	1	2	yes	maximal, complemented
18	C₈₉×#2418	C₂	1	2	yes	maximal, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2314	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
25	#542×C₈₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
28	C₂×#124×C₈₉	C₂²	1	2	yes	—
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#123×C₈₉	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#120×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#117×C₈₉	—	2	8	no	—
44	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
52	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
53	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
58	#400×C₈₉	C₂²	1	2	yes	complemented
59	#400×C₈₉	C₂²	1	2	yes	complemented
60	#399×C₈₉	C₂²	1	2	yes	—
61	#399×C₈₉	C₂²	1	2	yes	complemented
62	#398×C₈₉	C₂²	1	2	yes	complemented
63	#397×C₈₉	C₂²	1	2	yes	—
64	#397×C₈₉	C₂²	1	2	yes	—
65	#397×C₈₉	C₂²	1	2	yes	complemented
66	#396×C₈₉	C₂²	1	2	yes	complemented
67	#396×C₈₉	C₂²	1	2	yes	complemented
68	#395×C₈₉	C₂²	1	2	yes	complemented
69	#394×C₈₉	C₂²	1	2	yes	—
70	#394×C₈₉	C₂²	1	2	yes	—
71	#394×C₈₉	C₂²	1	2	yes	—
72	#394×C₈₉	C₂²	1	2	yes	—
73	#393×C₈₉	C₂²	1	2	yes	—
74	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	#391×C₈₉	C₂²	1	2	yes	complemented
77	#390×C₈₉	C₂²	1	2	yes	—
78	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
82	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	#389×C₈₉	C₂²	1	2	yes	complemented
84	#389×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	#389×C₈₉	C₂²	1	2	yes	complemented
86	#388×C₈₉	C₂²	1	2	yes	—
87	#388×C₈₉	C₂²	1	2	yes	—
88	#388×C₈₉	C₂²	1	2	yes	—
89	#388×C₈₉	C₂²	1	2	yes	—
90	#388×C₈₉	C₂²	1	2	yes	complemented
91	#388×C₈₉	C₂²	1	2	yes	complemented
92	#388×C₈₉	C₂²	1	2	yes	complemented
93	#388×C₈₉	C₂²	1	2	yes	complemented
94	#387×C₈₉	C₂²	1	2	yes	complemented
95	#387×C₈₉	C₂²	1	2	yes	complemented
96	#387×C₈₉	C₂²	1	2	yes	complemented
97	#387×C₈₉	C₂²	1	2	yes	complemented
98	#386×C₈₉	C₂²	1	2	yes	—
99	#386×C₈₉	C₂²	1	2	yes	—
100	#386×C₈₉	C₂²	1	2	yes	—
101	#386×C₈₉	C₂²	1	2	yes	—
102	#386×C₈₉	C₂²	1	2	yes	—
103	#386×C₈₉	C₂²	1	2	yes	—
104	#386×C₈₉	C₂²	1	2	yes	—
105	#385×C₈₉	C₂²	1	2	yes	—
106	#385×C₈₉	C₂²	1	2	yes	—
107	#385×C₈₉	C₂²	1	2	yes	—
108	#385×C₈₉	C₂²	1	2	yes	—
109	#385×C₈₉	C₂²	1	2	yes	complemented
110	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
111	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
112	#380×C₈₉	C₂²	1	1	yes	characteristic
113	#380×C₈₉	C₂²	1	1	yes	characteristic
114	#380×C₈₉	C₂²	1	1	yes	characteristic
115	#380×C₈₉	C₂²	1	1	yes	characteristic
116	#380×C₈₉	C₂²	1	1	yes	characteristic
117	#380×C₈₉	C₂²	1	1	yes	characteristic
118	#380×C₈₉	C₂²	1	2	yes	—
119	#379×C₈₉	C₂²	1	2	yes	—
120	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
124	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
125	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	—	2	4	no	—
133	C₂³×C₄×C₈₉	—	2	4	no	—
134	C₂³×C₄×C₈₉	—	2	4	no	—
135	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
146	C₄⋊Q₈×C₈₉	—	2	4	no	—
147	#126×C₈₉	—	2	8	no	—
148	#124×C₈₉	—	2	8	no	—
149	#124×C₈₉	—	2	4	no	—
150	#123×C₈₉	—	2	8	no	—
151	C₂²⋊Q₈×C₈₉	—	2	4	no	—
152	C₂²⋊Q₈×C₈₉	—	2	4	no	—
153	C₂²⋊Q₈×C₈₉	—	2	4	no	—
154	C₂²⋊Q₈×C₈₉	—	2	8	no	—
155	C₂²⋊Q₈×C₈₉	—	4	4	no	—
156	#121×C₈₉	—	2	4	no	—
157	#121×C₈₉	—	2	4	no	—
158	#121×C₈₉	—	2	4	no	—
159	#120×C₈₉	—	4	4	no	—
160	C₄×Q₈×C₈₉	—	2	4	no	—
161	C₄×D₄×C₈₉	—	2	4	no	—
162	C₄×D₄×C₈₉	—	4	4	no	—
163	#117×C₈₉	—	2	4	no	—
164	#117×C₈₉	—	2	4	no	—
165	#117×C₈₉	—	2	4	no	—
166	#117×C₈₉	—	2	4	no	—
167	#117×C₈₉	—	2	4	no	—
168	#117×C₈₉	—	2	4	no	—
169	#117×C₈₉	—	2	4	no	—
170	#117×C₈₉	D₄	1	8	yes	complemented
171	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
199	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₈₉	—	2	4	no	—
228	C₂×C₄²×C₈₉	—	2	4	no	—
229	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
230	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
235	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
236	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
237	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
238	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
239	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
240	#95×C₈₉	C₂³	1	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	2	yes	—
243	#95×C₈₉	C₂³	1	2	yes	—
244	#95×C₈₉	C₂³	1	2	yes	—
245	#95×C₈₉	C₂³	1	2	yes	—
246	#95×C₈₉	C₂³	1	2	yes	—
247	#95×C₈₉	C₂³	1	2	yes	—
248	#95×C₈₉	C₂³	1	2	yes	—
249	#95×C₈₉	C₂³	1	2	yes	—
250	#95×C₈₉	C₂³	1	2	yes	—
251	#95×C₈₉	C₂³	1	2	yes	—
252	#95×C₈₉	C₂³	1	2	yes	—
253	#95×C₈₉	C₂³	1	2	yes	—
254	#95×C₈₉	C₂³	1	2	yes	—
255	#95×C₈₉	C₂³	1	2	yes	—
256	#95×C₈₉	C₂³	1	2	yes	—
257	#95×C₈₉	C₂³	1	2	yes	—
258	C₂⁴×C₈₉	—	2	2	no	—
259	C₂⁴×C₈₉	—	2	2	no	—
260	C₂⁴×C₈₉	—	2	2	no	—
261	C₂⁴×C₈₉	—	2	2	no	—
262	C₂⁴×C₈₉	—	2	2	no	—
263	C₂⁴×C₈₉	—	4	1	no	—
264	C₂⁴×C₈₉	—	4	1	no	—
265	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
266	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
267	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂×Q₈×C₈₉	—	2	2	no	—
270	C₂×Q₈×C₈₉	—	2	4	no	—
271	C₂×Q₈×C₈₉	—	2	2	no	—
272	C₂×Q₈×C₈₉	—	2	2	no	—
273	C₂×Q₈×C₈₉	—	4	2	no	—
274	C₂×Q₈×C₈₉	—	4	2	no	—
275	C₂×D₄×C₈₉	—	2	4	no	—
276	C₂×D₄×C₈₉	—	2	4	no	—
277	C₂×D₄×C₈₉	—	2	4	no	—
278	C₂×D₄×C₈₉	—	2	4	no	—
279	C₂×D₄×C₈₉	—	2	4	no	—
280	C₂×D₄×C₈₉	—	2	2	no	—
281	C₂×D₄×C₈₉	—	2	2	no	—
282	C₂×D₄×C₈₉	—	2	2	no	—
283	C₂×D₄×C₈₉	—	4	2	no	—
284	C₂×D₄×C₈₉	—	4	2	no	—
285	C₂×D₄×C₈₉	—	4	2	no	—
286	C₂×D₄×C₈₉	—	4	2	no	—
287	C₂²×C₄×C₈₉	—	2	32	no	—
288	C₂²×C₄×C₈₉	—	2	2	no	—
289	C₂²×C₄×C₈₉	—	2	2	no	—
290	C₂²×C₄×C₈₉	—	2	2	no	—
291	C₂²×C₄×C₈₉	—	2	2	no	—
292	C₂²×C₄×C₈₉	—	2	2	no	—
293	C₂²×C₄×C₈₉	—	2	2	no	—
294	C₂²×C₄×C₈₉	—	2	2	no	—
295	C₂²×C₄×C₈₉	—	2	2	no	—
296	C₂²×C₄×C₈₉	—	2	2	no	—
297	C₂²×C₄×C₈₉	—	2	2	no	—
298	C₂²×C₄×C₈₉	—	2	2	no	—
299	C₂²×C₄×C₈₉	—	2	2	no	—
300	C₂²×C₄×C₈₉	—	2	2	no	—
301	C₂²×C₄×C₈₉	—	2	2	no	—
302	C₂²×C₄×C₈₉	—	2	2	no	—
303	C₂²×C₄×C₈₉	—	2	2	no	—
304	C₂²×C₄×C₈₉	—	2	2	no	—
305	C₂²×C₄×C₈₉	—	2	2	no	—
306	C₂²×C₄×C₈₉	—	2	2	no	—
307	C₂²×C₄×C₈₉	—	2	2	no	—
308	C₂²×C₄×C₈₉	—	2	2	no	—
309	C₂²×C₄×C₈₉	—	2	2	no	—
310	C₂²×C₄×C₈₉	—	2	2	no	—
311	C₂²×C₄×C₈₉	—	2	4	no	—
312	C₂²×C₄×C₈₉	—	4	1	no	—
313	C₂²×C₄×C₈₉	—	4	1	no	—
314	C₂²×C₄×C₈₉	—	4	1	no	—
315	C₂²×C₄×C₈₉	—	4	1	no	—
316	C₂²×C₄×C₈₉	—	4	2	no	—
317	C₂²×C₄×C₈₉	—	4	2	no	—
318	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
319	C₂²×C₄×C₈₉	#41	1	4	yes	—
320	C₂²×C₄×C₈₉	#41	1	4	yes	—
321	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
322	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
325	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
328	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
329	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
340	C₄⋊C₄×C₈₉	—	2	2	no	—
341	C₄⋊C₄×C₈₉	—	2	2	no	—
342	C₄⋊C₄×C₈₉	—	2	2	no	—
343	C₄⋊C₄×C₈₉	—	2	2	no	—
344	C₄⋊C₄×C₈₉	—	2	2	no	—
345	C₄⋊C₄×C₈₉	—	2	2	no	—
346	C₄⋊C₄×C₈₉	—	2	2	no	—
347	C₄⋊C₄×C₈₉	—	2	2	no	—
348	C₄⋊C₄×C₈₉	—	2	4	no	—
349	C₄⋊C₄×C₈₉	—	2	4	no	—
350	C₄⋊C₄×C₈₉	—	2	4	no	—
351	C₄⋊C₄×C₈₉	—	2	2	no	—
352	C₄⋊C₄×C₈₉	—	2	2	no	—
353	C₄⋊C₄×C₈₉	—	2	2	no	—
354	C₄⋊C₄×C₈₉	—	2	2	no	—
355	C₄⋊C₄×C₈₉	—	2	4	no	—
356	C₄⋊C₄×C₈₉	—	2	4	no	—
357	C₄⋊C₄×C₈₉	—	4	2	no	—
358	C₄⋊C₄×C₈₉	—	4	2	no	—
359	C₄⋊C₄×C₈₉	—	4	2	no	—
360	C₄⋊C₄×C₈₉	—	4	2	no	—
361	C₄⋊C₄×C₈₉	—	4	2	no	—
362	C₄⋊C₄×C₈₉	—	4	2	no	—
363	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
364	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
365	C₂²⋊C₄×C₈₉	—	2	2	no	—
366	C₂²⋊C₄×C₈₉	—	2	2	no	—
367	C₂²⋊C₄×C₈₉	—	2	4	no	—
368	C₂²⋊C₄×C₈₉	—	2	4	no	—
369	C₂²⋊C₄×C₈₉	—	2	4	no	—
370	C₂²⋊C₄×C₈₉	—	2	4	no	—
371	C₂²⋊C₄×C₈₉	—	2	4	no	—
372	C₂²⋊C₄×C₈₉	—	2	2	no	—
373	C₂²⋊C₄×C₈₉	—	2	2	no	—
374	C₂²⋊C₄×C₈₉	—	2	2	no	—
375	C₂²⋊C₄×C₈₉	—	2	2	no	—
376	C₂²⋊C₄×C₈₉	—	2	4	no	—
377	C₂²⋊C₄×C₈₉	—	2	4	no	—
378	C₂²⋊C₄×C₈₉	—	2	4	no	—
379	C₂²⋊C₄×C₈₉	—	2	4	no	—
380	C₂²⋊C₄×C₈₉	—	2	4	no	—
381	C₂²⋊C₄×C₈₉	—	2	4	no	—
382	C₂²⋊C₄×C₈₉	—	4	2	no	—
383	C₂²⋊C₄×C₈₉	—	4	2	no	—
384	C₂²⋊C₄×C₈₉	—	4	2	no	—
385	C₂²⋊C₄×C₈₉	—	4	2	no	—
386	C₂²⋊C₄×C₈₉	—	4	2	no	—
387	C₂²⋊C₄×C₈₉	—	4	2	no	—
388	C₂²⋊C₄×C₈₉	—	4	2	no	—
389	C₂²⋊C₄×C₈₉	—	4	2	no	—
390	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
391	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
392	C₄²×C₈₉	—	2	2	no	—
393	C₄²×C₈₉	—	2	2	no	—
394	C₄²×C₈₉	—	2	2	no	—
395	C₄²×C₈₉	—	2	2	no	—
396	C₄²×C₈₉	—	2	2	no	—
397	C₄²×C₈₉	—	2	2	no	—
398	C₄²×C₈₉	—	2	4	no	—
399	C₄²×C₈₉	—	4	2	no	—
400	C₄²×C₈₉	—	4	2	no	—
401	C₄²×C₈₉	C₂×D₄	1	4	yes	—
402	C₄²×C₈₉	C₂×D₄	1	4	yes	—
403	C₂³×C₈₉	—	2	1	no	—
404	C₂³×C₈₉	—	2	1	no	—
405	C₂³×C₈₉	—	2	1	no	—
406	C₂³×C₈₉	—	2	1	no	—
407	C₂³×C₈₉	—	2	8	no	—
408	C₂³×C₈₉	—	2	1	no	—
409	C₂³×C₈₉	—	2	1	no	—
410	C₂³×C₈₉	—	2	1	no	—
411	C₂³×C₈₉	—	2	1	no	—
412	C₂³×C₈₉	—	2	1	no	—
413	C₂³×C₈₉	—	2	1	no	—
414	C₂³×C₈₉	—	2	1	no	—
415	C₂³×C₈₉	—	2	1	no	—
416	C₂³×C₈₉	—	2	1	no	—
417	C₂³×C₈₉	—	2	1	no	—
418	C₂³×C₈₉	—	2	1	no	—
419	C₂³×C₈₉	—	2	1	no	—
420	C₂³×C₈₉	—	2	2	no	—
421	C₂³×C₈₉	—	2	2	no	—
422	C₂³×C₈₉	—	2	2	no	—
423	C₂³×C₈₉	—	2	2	no	—
424	C₂³×C₈₉	—	2	2	no	—
425	C₂³×C₈₉	—	2	2	no	—
426	C₂³×C₈₉	—	2	2	no	—
427	C₂³×C₈₉	—	4	4	no	—
428	C₂³×C₈₉	—	4	4	no	—
429	C₂³×C₈₉	—	4	4	no	—
430	C₂³×C₈₉	—	4	4	no	—
431	C₂³×C₈₉	—	4	4	no	—
432	C₂³×C₈₉	—	4	4	no	—
433	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
434	C₂³×C₈₉	C₂×#41	1	2	yes	—
435	C₂³×C₈₉	C₂×#41	1	2	yes	—
436	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
437	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
438	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
439	Q₈×C₈₉	—	4	4	no	—
440	Q₈×C₈₉	—	8	4	no	—
441	D₄×C₈₉	—	4	8	no	—
442	D₄×C₈₉	—	4	4	no	—
443	D₄×C₈₉	—	8	4	no	—
444	D₄×C₈₉	—	8	4	no	—
445	C₂×C₄×C₈₉	—	2	8	no	—
446	C₂×C₄×C₈₉	—	2	8	no	—
447	C₂×C₄×C₈₉	—	2	8	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	1	no	—
450	C₂×C₄×C₈₉	—	2	1	no	—
451	C₂×C₄×C₈₉	—	2	1	no	—
452	C₂×C₄×C₈₉	—	2	1	no	—
453	C₂×C₄×C₈₉	—	2	1	no	—
454	C₂×C₄×C₈₉	—	2	1	no	—
455	C₂×C₄×C₈₉	—	2	1	no	—
456	C₂×C₄×C₈₉	—	2	1	no	—
457	C₂×C₄×C₈₉	—	2	1	no	—
458	C₂×C₄×C₈₉	—	2	1	no	—
459	C₂×C₄×C₈₉	—	2	1	no	—
460	C₂×C₄×C₈₉	—	2	1	no	—
461	C₂×C₄×C₈₉	—	2	1	no	—
462	C₂×C₄×C₈₉	—	2	8	no	—
463	C₂×C₄×C₈₉	—	2	8	no	—
464	C₂×C₄×C₈₉	—	2	8	no	—
465	C₂×C₄×C₈₉	—	2	1	no	—
466	C₂×C₄×C₈₉	—	2	1	no	—
467	C₂×C₄×C₈₉	—	2	1	no	—
468	C₂×C₄×C₈₉	—	2	1	no	—
469	C₂×C₄×C₈₉	—	2	2	no	—
470	C₂×C₄×C₈₉	—	2	2	no	—
471	C₂×C₄×C₈₉	—	2	2	no	—
472	C₂×C₄×C₈₉	—	2	2	no	—
473	C₂×C₄×C₈₉	—	2	2	no	—
474	C₂×C₄×C₈₉	—	2	2	no	—
475	C₂×C₄×C₈₉	—	2	2	no	—
476	C₂×C₄×C₈₉	—	2	2	no	—
477	C₂×C₄×C₈₉	—	2	2	no	—
478	C₂×C₄×C₈₉	—	2	2	no	—
479	C₂×C₄×C₈₉	—	2	2	no	—
480	C₂×C₄×C₈₉	—	2	2	no	—
481	C₂×C₄×C₈₉	—	2	2	no	—
482	C₂×C₄×C₈₉	—	2	2	no	—
483	C₂×C₄×C₈₉	—	2	1	no	—
484	C₂×C₄×C₈₉	—	2	1	no	—
485	C₂×C₄×C₈₉	—	2	1	no	—
486	C₂×C₄×C₈₉	—	2	1	no	—
487	C₂×C₄×C₈₉	—	2	2	no	—
488	C₂×C₄×C₈₉	—	2	2	no	—
489	C₂×C₄×C₈₉	—	2	2	no	—
490	C₂×C₄×C₈₉	—	2	2	no	—
491	C₂×C₄×C₈₉	—	2	2	no	—
492	C₂×C₄×C₈₉	—	2	1	no	—
493	C₂×C₄×C₈₉	—	2	1	no	—
494	C₂×C₄×C₈₉	—	2	1	no	—
495	C₂×C₄×C₈₉	—	2	2	no	—
496	C₂×C₄×C₈₉	—	2	1	no	—
497	C₂×C₄×C₈₉	—	2	2	no	—
498	C₂×C₄×C₈₉	—	4	4	no	—
499	C₂×C₄×C₈₉	—	4	4	no	—
500	C₂×C₄×C₈₉	—	4	4	no	—
501	C₂×C₄×C₈₉	—	4	4	no	—
502	C₂×C₄×C₈₉	—	8	4	no	—
503	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
510	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
511	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
512	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
513	C₂²×C₈₉	—	2	2	no	—
514	C₂²×C₈₉	—	2	2	no	—
515	C₂²×C₈₉	—	2	2	no	—
516	C₂²×C₈₉	—	2	2	no	—
517	C₂²×C₈₉	—	2	2	no	—
518	C₂²×C₈₉	—	2	2	no	—
519	C₂²×C₈₉	—	2	2	no	—
520	C₂²×C₈₉	—	2	2	no	—
521	C₂²×C₈₉	—	2	2	no	—
522	C₂²×C₈₉	—	2	2	no	—
523	C₂²×C₈₉	—	2	2	no	—
524	C₂²×C₈₉	—	2	2	no	—
525	C₂²×C₈₉	—	4	16	no	—
526	C₂²×C₈₉	—	4	1	no	—
527	C₂²×C₈₉	—	4	1	no	—
528	C₂²×C₈₉	—	4	1	no	—
529	C₂²×C₈₉	—	4	1	no	—
530	C₂²×C₈₉	—	4	1	no	—
531	C₂²×C₈₉	—	4	1	no	—
532	C₂²×C₈₉	—	4	1	no	—
533	C₂²×C₈₉	—	4	1	no	—
534	C₂²×C₈₉	—	4	2	no	—
535	C₂²×C₈₉	—	4	2	no	—
536	C₂²×C₈₉	—	4	2	no	—
537	C₂²×C₈₉	—	4	2	no	—
538	C₂²×C₈₉	—	4	2	no	—
539	C₂²×C₈₉	—	4	2	no	—
540	C₂²×C₈₉	—	4	2	no	—
541	C₂²×C₈₉	#542	1	4	yes	complemented
542	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
543	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₂²×C₈₉	#585	1	1	yes	characteristic
548	C₂²×C₈₉	#585	1	1	yes	characteristic
549	C₄×C₈₉	—	2	2	no	—
550	C₄×C₈₉	—	2	2	no	—
551	C₄×C₈₉	—	2	2	no	—
552	C₄×C₈₉	—	2	2	no	—
553	C₄×C₈₉	—	2	2	no	—
554	C₄×C₈₉	—	2	2	no	—
555	C₄×C₈₉	—	2	2	no	—
556	C₄×C₈₉	—	4	2	no	—
557	C₄×C₈₉	—	4	2	no	—
558	C₄×C₈₉	—	4	2	no	—
559	C₄×C₈₉	—	4	1	no	—
560	C₄×C₈₉	—	4	1	no	—
561	C₄×C₈₉	—	4	2	no	—
562	C₄×C₈₉	—	4	2	no	—
563	C₄×C₈₉	—	4	1	no	—
564	C₄×C₈₉	—	4	1	no	—
565	C₄×C₈₉	—	4	2	no	—
566	C₄×C₈₉	—	4	2	no	—
567	C₄×C₈₉	#525	1	4	yes	—
568	#35260	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
569	C₂×C₈₉	—	2	4	no	—
570	C₂×C₈₉	—	4	2	no	—
571	C₂×C₈₉	—	4	2	no	—
572	C₂×C₈₉	—	8	2	no	—
573	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
574	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
575	C₂×C₈₉	#3455	1	1	yes	characteristic
576	C₂×C₈₉	#3488	1	1	yes	characteristic
577	C₂×C₈₉	#3489	1	1	yes	characteristic
578	C₂×C₈₉	#3494	1	1	yes	characteristic
579	C₂×C₈₉	#3495	1	1	yes	characteristic
580	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
581	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
582	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
583	#2850	C₂×C₈₉	1	1	yes	characteristic, complemented
584	#2848	C₂×C₈₉	1	1	yes	characteristic, complemented
585	#2847	C₂×C₈₉	1	1	yes	characteristic
586	#2628	C₂×C₈₉	1	1	yes	characteristic, complemented
587	#2625	C₂×C₈₉	1	1	yes	characteristic, complemented
588	#2624	C₂×C₈₉	1	1	yes	characteristic, complemented
589	#2620	C₂×C₈₉	1	1	yes	characteristic, complemented
590	#2481	C₂×C₈₉	1	2	yes	complemented
591	#2479	C₂×C₈₉	1	2	yes	complemented
592	#2477	C₂×C₈₉	1	2	yes	complemented
593	#2474	C₂×C₈₉	1	2	yes	complemented
594	#2472	C₂×C₈₉	1	2	yes	complemented
595	#2470	C₂×C₈₉	1	2	yes	complemented
596	#2449	C₂×C₈₉	1	2	yes	complemented
597	#2418	C₂×C₈₉	1	2	yes	complemented
598	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
599	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
600	#2314	C₂×C₈₉	1	1	yes	characteristic, complemented
601	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
602	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
603	C₈₉	#35260	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
605	#542	—	2	8	no	—
606	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
607	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
608	C₂×#124	C₂²×C₈₉	1	2	yes	—
609	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
610	C₂×#123	C₂²×C₈₉	1	2	yes	—
611	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
612	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
613	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
614	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
615	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
616	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
617	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
618	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
619	C₂×#120	C₂²×C₈₉	1	2	yes	—
620	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
621	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
622	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
623	C₂×#117	—	2	8	no	—
624	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
625	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
626	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
627	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
628	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
629	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
630	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
631	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
632	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
633	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
634	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
635	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
636	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
637	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
638	#400	C₂²×C₈₉	1	2	yes	complemented
639	#400	C₂²×C₈₉	1	2	yes	complemented
640	#399	C₂²×C₈₉	1	2	yes	—
641	#399	C₂²×C₈₉	1	2	yes	complemented
642	#398	C₂²×C₈₉	1	2	yes	complemented
643	#397	C₂²×C₈₉	1	2	yes	—
644	#397	C₂²×C₈₉	1	2	yes	—
645	#397	C₂²×C₈₉	1	2	yes	complemented
646	#396	C₂²×C₈₉	1	2	yes	complemented
647	#396	C₂²×C₈₉	1	2	yes	complemented
648	#395	C₂²×C₈₉	1	2	yes	complemented
649	#394	C₂²×C₈₉	1	2	yes	—
650	#394	C₂²×C₈₉	1	2	yes	—
651	#394	C₂²×C₈₉	1	2	yes	—
652	#394	C₂²×C₈₉	1	2	yes	—
653	#393	C₂²×C₈₉	1	2	yes	—
654	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
655	#391	C₂²×C₈₉	1	2	yes	complemented
656	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
657	#390	C₂²×C₈₉	1	2	yes	—
658	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
659	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
660	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
661	#389	C₂²×C₈₉	1	2	yes	complemented
662	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
663	#389	C₂²×C₈₉	1	2	yes	complemented
664	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
665	#389	C₂²×C₈₉	1	1	yes	characteristic, complemented
666	#388	C₂²×C₈₉	1	2	yes	—
667	#388	C₂²×C₈₉	1	2	yes	—
668	#388	C₂²×C₈₉	1	2	yes	—
669	#388	C₂²×C₈₉	1	2	yes	—
670	#388	C₂²×C₈₉	1	2	yes	complemented
671	#388	C₂²×C₈₉	1	2	yes	complemented
672	#388	C₂²×C₈₉	1	2	yes	complemented
673	#388	C₂²×C₈₉	1	2	yes	complemented
674	#387	C₂²×C₈₉	1	2	yes	complemented
675	#387	C₂²×C₈₉	1	2	yes	complemented
676	#387	C₂²×C₈₉	1	2	yes	complemented
677	#387	C₂²×C₈₉	1	2	yes	complemented
678	#386	C₂²×C₈₉	1	2	yes	—
679	#386	C₂²×C₈₉	1	2	yes	—
680	#386	C₂²×C₈₉	1	2	yes	—
681	#386	C₂²×C₈₉	1	2	yes	—
682	#386	C₂²×C₈₉	1	2	yes	—
683	#386	C₂²×C₈₉	1	2	yes	—
684	#386	C₂²×C₈₉	1	2	yes	—
685	#385	C₂²×C₈₉	1	2	yes	—
686	#385	C₂²×C₈₉	1	2	yes	—
687	#385	C₂²×C₈₉	1	2	yes	—
688	#385	C₂²×C₈₉	1	2	yes	—
689	#385	C₂²×C₈₉	1	2	yes	complemented
690	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
691	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
692	#380	C₂²×C₈₉	1	1	yes	characteristic
693	#380	C₂²×C₈₉	1	1	yes	characteristic
694	#380	C₂²×C₈₉	1	1	yes	characteristic
695	#380	C₂²×C₈₉	1	1	yes	characteristic
696	#380	C₂²×C₈₉	1	1	yes	characteristic
697	#380	C₂²×C₈₉	1	1	yes	characteristic
698	#380	C₂²×C₈₉	1	2	yes	—
699	#379	C₂²×C₈₉	1	2	yes	—
700	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
701	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
702	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
703	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
704	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
705	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
706	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
707	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
708	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
709	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
710	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
711	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
712	C₂³×C₄	—	2	4	no	—
713	C₂³×C₄	—	2	4	no	—
714	C₂³×C₄	—	2	4	no	—
715	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
716	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
717	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
718	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
719	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
720	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
721	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
722	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
723	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
724	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
725	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
726	C₄⋊Q₈	—	2	4	no	—
727	#126	—	2	8	no	—
728	#124	—	2	8	no	—
729	#124	—	2	4	no	—
730	#123	—	2	8	no	—
731	C₂²⋊Q₈	—	2	4	no	—
732	C₂²⋊Q₈	—	2	4	no	—
733	C₂²⋊Q₈	—	2	4	no	—
734	C₂²⋊Q₈	—	2	8	no	—
735	C₂²⋊Q₈	—	4	4	no	—
736	#121	—	2	4	no	—
737	#121	—	2	4	no	—
738	#121	—	2	4	no	—
739	#120	—	4	4	no	—
740	C₄×Q₈	—	2	4	no	—
741	C₄×D₄	—	2	4	no	—
742	C₄×D₄	—	4	4	no	—
743	#117	—	2	4	no	—
744	#117	—	2	4	no	—
745	#117	—	2	4	no	—
746	#117	—	2	4	no	—
747	#117	—	2	4	no	—
748	#117	—	2	4	no	—
749	#117	—	2	4	no	—
750	#117	D₄×C₈₉	1	8	yes	complemented
751	C₂×C₄⋊C₄	—	2	4	no	—
752	C₂×C₄⋊C₄	—	2	4	no	—
753	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
754	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
755	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
761	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
762	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
763	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
764	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
765	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
766	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
767	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
768	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
769	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
770	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
771	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
773	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
774	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
775	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
776	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
777	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
778	C₂×C₂²⋊C₄	—	2	4	no	—
779	C₂×C₂²⋊C₄	—	2	4	no	—
780	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
781	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
782	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
783	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
784	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
785	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
786	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
795	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
796	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
797	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
798	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
799	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
800	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
801	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
802	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
803	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
804	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
805	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
806	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
807	C₂×C₄²	—	2	4	no	—
808	C₂×C₄²	—	2	4	no	—
809	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
810	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
811	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
812	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
813	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
815	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
816	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
817	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
818	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
819	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
820	#95	C₂³×C₈₉	1	2	yes	—
821	#95	C₂³×C₈₉	1	2	yes	—
822	#95	C₂³×C₈₉	1	2	yes	—
823	#95	C₂³×C₈₉	1	2	yes	—
824	#95	C₂³×C₈₉	1	2	yes	—
825	#95	C₂³×C₈₉	1	2	yes	—
826	#95	C₂³×C₈₉	1	2	yes	—
827	#95	C₂³×C₈₉	1	2	yes	—
828	#95	C₂³×C₈₉	1	2	yes	—
829	#95	C₂³×C₈₉	1	2	yes	—
830	#95	C₂³×C₈₉	1	2	yes	—
831	#95	C₂³×C₈₉	1	2	yes	—
832	#95	C₂³×C₈₉	1	2	yes	—
833	#95	C₂³×C₈₉	1	2	yes	—
834	#95	C₂³×C₈₉	1	2	yes	—
835	#95	C₂³×C₈₉	1	2	yes	—
836	#95	C₂³×C₈₉	1	2	yes	—
837	#95	C₂³×C₈₉	1	2	yes	—
838	C₂⁴	—	2	2	no	—
839	C₂⁴	—	2	2	no	—
840	C₂⁴	—	2	2	no	—
841	C₂⁴	—	2	2	no	—
842	C₂⁴	—	2	2	no	—
843	C₂⁴	—	4	1	no	—
844	C₂⁴	—	4	1	no	—
845	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
846	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
848	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	4	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	2	no	—
855	C₂×D₄	—	2	4	no	—
856	C₂×D₄	—	2	4	no	—
857	C₂×D₄	—	2	4	no	—
858	C₂×D₄	—	2	4	no	—
859	C₂×D₄	—	2	4	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	4	2	no	—
864	C₂×D₄	—	4	2	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂²×C₄	—	2	32	no	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	—	2	2	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	2	4	no	—
892	C₂²×C₄	—	4	1	no	—
893	C₂²×C₄	—	4	1	no	—
894	C₂²×C₄	—	4	1	no	—
895	C₂²×C₄	—	4	1	no	—
896	C₂²×C₄	—	4	2	no	—
897	C₂²×C₄	—	4	2	no	—
898	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
899	C₂²×C₄	#41×C₈₉	1	4	yes	—
900	C₂²×C₄	#41×C₈₉	1	4	yes	—
901	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
902	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
904	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
905	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
907	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
910	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
911	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
912	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
913	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
914	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
915	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
919	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	4	no	—
929	C₄⋊C₄	—	2	4	no	—
930	C₄⋊C₄	—	2	4	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	4	no	—
936	C₄⋊C₄	—	2	4	no	—
937	C₄⋊C₄	—	4	2	no	—
938	C₄⋊C₄	—	4	2	no	—
939	C₄⋊C₄	—	4	2	no	—
940	C₄⋊C₄	—	4	2	no	—
941	C₄⋊C₄	—	4	2	no	—
942	C₄⋊C₄	—	4	2	no	—
943	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
944	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	4	no	—
948	C₂²⋊C₄	—	2	4	no	—
949	C₂²⋊C₄	—	2	4	no	—
950	C₂²⋊C₄	—	2	4	no	—
951	C₂²⋊C₄	—	2	4	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	4	no	—
957	C₂²⋊C₄	—	2	4	no	—
958	C₂²⋊C₄	—	2	4	no	—
959	C₂²⋊C₄	—	2	4	no	—
960	C₂²⋊C₄	—	2	4	no	—
961	C₂²⋊C₄	—	2	4	no	—
962	C₂²⋊C₄	—	4	2	no	—
963	C₂²⋊C₄	—	4	2	no	—
964	C₂²⋊C₄	—	4	2	no	—
965	C₂²⋊C₄	—	4	2	no	—
966	C₂²⋊C₄	—	4	2	no	—
967	C₂²⋊C₄	—	4	2	no	—
968	C₂²⋊C₄	—	4	2	no	—
969	C₂²⋊C₄	—	4	2	no	—
970	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
971	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	4	no	—
979	C₄²	—	4	2	no	—
980	C₄²	—	4	2	no	—
981	C₄²	C₂×D₄×C₈₉	1	4	yes	—
982	C₄²	C₂×D₄×C₈₉	1	4	yes	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	—	2	8	no	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	1	no	—
990	C₂³	—	2	1	no	—
991	C₂³	—	2	1	no	—
992	C₂³	—	2	1	no	—
993	C₂³	—	2	1	no	—
994	C₂³	—	2	1	no	—
995	C₂³	—	2	1	no	—
996	C₂³	—	2	1	no	—
997	C₂³	—	2	1	no	—
998	C₂³	—	2	1	no	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	2	2	no	—
1001	C₂³	—	2	2	no	—
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	2	2	no	—
1005	C₂³	—	2	2	no	—
1006	C₂³	—	2	2	no	—
1007	C₂³	—	4	4	no	—
1008	C₂³	—	4	4	no	—
1009	C₂³	—	4	4	no	—
1010	C₂³	—	4	4	no	—
1011	C₂³	—	4	4	no	—
1012	C₂³	—	4	4	no	—
1013	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
1014	C₂³	C₂×#41×C₈₉	1	2	yes	—
1015	C₂³	C₂×#41×C₈₉	1	2	yes	—
1016	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
1017	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
1018	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
1019	Q₈	—	4	4	no	—
1020	Q₈	—	8	4	no	—
1021	D₄	—	4	8	no	—
1022	D₄	—	4	4	no	—
1023	D₄	—	8	4	no	—
1024	D₄	—	8	4	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	8	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	8	no	—
1043	C₂×C₄	—	2	8	no	—
1044	C₂×C₄	—	2	8	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	1	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	2	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	4	4	no	—
1079	C₂×C₄	—	4	4	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	4	no	—
1082	C₂×C₄	—	8	4	no	—
1083	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1084	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1085	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1086	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1087	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1089	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1090	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1091	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1092	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1093	C₂²	—	2	2	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	2	2	no	—
1098	C₂²	—	2	2	no	—
1099	C₂²	—	2	2	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	2	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	4	16	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	4	2	no	—
1115	C₂²	—	4	2	no	—
1116	C₂²	—	4	2	no	—
1117	C₂²	—	4	2	no	—
1118	C₂²	—	4	2	no	—
1119	C₂²	—	4	2	no	—
1120	C₂²	—	4	2	no	—
1121	C₂²	#542×C₈₉	1	4	yes	complemented
1122	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1123	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1124	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1125	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1126	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1127	C₂²	#585×C₈₉	1	1	yes	characteristic
1128	C₂²	#585×C₈₉	1	1	yes	characteristic
1129	C₄	—	2	2	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	2	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	4	2	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	#525×C₈₉	1	4	yes	—
1148	C₂	—	2	4	no	—
1149	C₂	—	4	2	no	—
1150	C₂	—	4	2	no	—
1151	C₂	—	8	2	no	—
1152	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1153	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
1154	C₂	C₈₉×#3455	1	1	yes	characteristic
1155	C₂	C₈₉×#3488	1	1	yes	characteristic
1156	C₂	C₈₉×#3489	1	1	yes	characteristic
1157	C₂	C₈₉×#3494	1	1	yes	characteristic
1158	C₂	C₈₉×#3495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2847	C₂
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×#542×C₈₉	C₂	semidirect
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#2857	C₂	semidirect
4. C₈₉×#2850	C₂	semidirect
5. C₈₉×#2848	C₂	semidirect
7. C₈₉×#2628	C₂	semidirect
8. C₈₉×#2625	C₂	semidirect
9. C₈₉×#2624	C₂	semidirect
10. C₈₉×#2620	C₂	semidirect
11. C₈₉×#2481	C₂	semidirect
12. C₈₉×#2479	C₂	semidirect
13. C₈₉×#2477	C₂	semidirect
14. C₈₉×#2474	C₂	semidirect
15. C₈₉×#2472	C₂	semidirect
16. C₈₉×#2470	C₂	semidirect
17. C₈₉×#2449	C₂	semidirect
18. C₈₉×#2418	C₂	semidirect
19. C₈₉×#2324	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₈₉×#2314	C₂	semidirect
22. C₄×C₂²⋊Q₈×C₈₉	C₂	semidirect
23. C₄×#121×C₈₉	C₂	semidirect
26. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
27. C₂×#126×C₈₉	C₂²	semidirect
29. C₂×#124×C₈₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
40. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
42. C₂×C₄×D₄×C₈₉	C₂²	semidirect
58. #400×C₈₉	C₂²	semidirect
59. #400×C₈₉	C₂²	semidirect
61. #399×C₈₉	C₂²	semidirect
62. #398×C₈₉	C₂²	semidirect
65. #397×C₈₉	C₂²	semidirect
66. #396×C₈₉	C₂²	semidirect
67. #396×C₈₉	C₂²	semidirect
68. #395×C₈₉	C₂²	semidirect
74. #391×C₈₉	C₂²	semidirect
75. #391×C₈₉	C₂²	semidirect
76. #391×C₈₉	C₂²	semidirect
78. #390×C₈₉	C₂²	semidirect
79. #390×C₈₉	C₂²	semidirect
80. #389×C₈₉	C₂²	semidirect
81. #389×C₈₉	C₂²	semidirect
82. #389×C₈₉	C₂²	semidirect
83. #389×C₈₉	C₂²	semidirect
84. #389×C₈₉	C₂²	semidirect
85. #389×C₈₉	C₂²	semidirect
90. #388×C₈₉	C₂²	semidirect
91. #388×C₈₉	C₂²	semidirect
92. #388×C₈₉	C₂²	semidirect
93. #388×C₈₉	C₂²	semidirect
94. #387×C₈₉	C₂²	semidirect
95. #387×C₈₉	C₂²	semidirect
96. #387×C₈₉	C₂²	semidirect
97. #387×C₈₉	C₂²	semidirect
109. #385×C₈₉	C₂²	semidirect
110. #384×C₈₉	C₂²	semidirect
111. #382×C₈₉	C₂²	semidirect
120. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
121. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
122. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
124. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
170. #117×C₈₉	D₄	semidirect
541. C₂²×C₈₉	#542	semidirect
568. #35260	C₈₉	direct (N × H)
580. C₂×#542	C₂×C₈₉	semidirect
581. C₂²×#117	C₂×C₈₉	semidirect
582. #2857	C₂×C₈₉	semidirect
583. #2850	C₂×C₈₉	semidirect
584. #2848	C₂×C₈₉	semidirect
586. #2628	C₂×C₈₉	semidirect
587. #2625	C₂×C₈₉	semidirect
588. #2624	C₂×C₈₉	semidirect
589. #2620	C₂×C₈₉	semidirect
590. #2481	C₂×C₈₉	semidirect
591. #2479	C₂×C₈₉	semidirect
592. #2477	C₂×C₈₉	semidirect
593. #2474	C₂×C₈₉	semidirect
594. #2472	C₂×C₈₉	semidirect
595. #2470	C₂×C₈₉	semidirect
596. #2449	C₂×C₈₉	semidirect
597. #2418	C₂×C₈₉	semidirect
598. #2324	C₂×C₈₉	semidirect
599. #2323	C₂×C₈₉	semidirect
600. #2314	C₂×C₈₉	semidirect
601. C₄×C₂²⋊Q₈	C₂×C₈₉	semidirect
602. C₄×#121	C₂×C₈₉	semidirect
603. C₈₉	#35260	direct (N × H)
606. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
607. C₂×#126	C₂²×C₈₉	semidirect
609. C₂×#124	C₂²×C₈₉	semidirect
615. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
620. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
622. C₂×C₄×D₄	C₂²×C₈₉	semidirect
638. #400	C₂²×C₈₉	semidirect
639. #400	C₂²×C₈₉	semidirect
641. #399	C₂²×C₈₉	semidirect
642. #398	C₂²×C₈₉	semidirect
645. #397	C₂²×C₈₉	semidirect
646. #396	C₂²×C₈₉	semidirect
647. #396	C₂²×C₈₉	semidirect
648. #395	C₂²×C₈₉	semidirect
654. #391	C₂²×C₈₉	semidirect
655. #391	C₂²×C₈₉	semidirect
656. #391	C₂²×C₈₉	semidirect
658. #390	C₂²×C₈₉	semidirect
659. #390	C₂²×C₈₉	semidirect
660. #389	C₂²×C₈₉	semidirect
661. #389	C₂²×C₈₉	semidirect
662. #389	C₂²×C₈₉	semidirect
663. #389	C₂²×C₈₉	semidirect
664. #389	C₂²×C₈₉	semidirect
665. #389	C₂²×C₈₉	semidirect
670. #388	C₂²×C₈₉	semidirect
671. #388	C₂²×C₈₉	semidirect
672. #388	C₂²×C₈₉	semidirect
673. #388	C₂²×C₈₉	semidirect
674. #387	C₂²×C₈₉	semidirect
675. #387	C₂²×C₈₉	semidirect
676. #387	C₂²×C₈₉	semidirect
677. #387	C₂²×C₈₉	semidirect
689. #385	C₂²×C₈₉	semidirect
690. #384	C₂²×C₈₉	semidirect
691. #382	C₂²×C₈₉	semidirect
700. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
701. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
702. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
704. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
750. #117	D₄×C₈₉	semidirect
1121. C₂²	#542×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2857	2
C₈₉×#2850	2
C₈₉×#2848	2
C₈₉×#2847	2
C₈₉×#2628	2
C₈₉×#2625	2
C₈₉×#2624	2
C₈₉×#2620	2
C₈₉×#2481	2
C₈₉×#2479	2
C₈₉×#2477	2
C₈₉×#2474	2
C₈₉×#2472	2
C₈₉×#2470	2
C₈₉×#2449	2
C₈₉×#2418	2
C₈₉×#2324	2
C₈₉×#2323	2
C₈₉×#2314	2
C₄×C₂²⋊Q₈×C₈₉	2
C₄×#121×C₈₉	2
#35260	89

Subgroups — C89×#35260 #36413108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35260 #36413108