Subgroups — C₈₉×#35243 #36413091

Order 22784.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1076 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×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2852	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2850	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2637	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2632	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2465	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2458	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2449	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2443	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2436	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2423	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2416	C₂	1	1	yes	maximal, characteristic
18	C₈₉×#2409	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2326	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₈₉×#2320	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	C₈₉×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	#542×C₈₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#126×C₈₉	C₂²	1	2	yes	—
28	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₈₉	C₂²	1	2	yes	—
30	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#123×C₈₉	C₂²	1	2	yes	—
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	—
36	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#121×C₈₉	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
40	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
49	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
50	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
54	#399×C₈₉	C₂²	1	2	yes	—
55	#399×C₈₉	C₂²	1	2	yes	—
56	#398×C₈₉	C₂²	1	2	yes	—
57	#398×C₈₉	C₂²	1	2	yes	—
58	#398×C₈₉	C₂²	1	2	yes	—
59	#397×C₈₉	C₂²	1	2	yes	—
60	#396×C₈₉	C₂²	1	2	yes	—
61	#396×C₈₉	C₂²	1	2	yes	—
62	#395×C₈₉	C₂²	1	2	yes	—
63	#395×C₈₉	C₂²	1	2	yes	—
64	#395×C₈₉	C₂²	1	2	yes	—
65	#394×C₈₉	C₂²	1	2	yes	—
66	#394×C₈₉	C₂²	1	2	yes	—
67	#393×C₈₉	C₂²	1	2	yes	—
68	#393×C₈₉	C₂²	1	2	yes	—
69	#393×C₈₉	C₂²	1	2	yes	—
70	#391×C₈₉	C₂²	1	1	yes	characteristic
71	#391×C₈₉	C₂²	1	1	yes	characteristic
72	#391×C₈₉	C₂²	1	1	yes	characteristic
73	#391×C₈₉	C₂²	1	1	yes	characteristic
74	#391×C₈₉	C₂²	1	2	yes	—
75	#390×C₈₉	C₂²	1	1	yes	characteristic
76	#390×C₈₉	C₂²	1	1	yes	characteristic
77	#390×C₈₉	C₂²	1	2	yes	—
78	#389×C₈₉	C₂²	1	1	yes	characteristic
79	#389×C₈₉	C₂²	1	1	yes	characteristic
80	#389×C₈₉	C₂²	1	1	yes	characteristic
81	#389×C₈₉	C₂²	1	1	yes	characteristic
82	#389×C₈₉	C₂²	1	2	yes	—
83	#388×C₈₉	C₂²	1	2	yes	—
84	#388×C₈₉	C₂²	1	2	yes	—
85	#388×C₈₉	C₂²	1	2	yes	—
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	—
91	#388×C₈₉	C₂²	1	2	yes	—
92	#388×C₈₉	C₂²	1	1	yes	characteristic
93	#388×C₈₉	C₂²	1	1	yes	characteristic
94	#387×C₈₉	C₂²	1	2	yes	—
95	#387×C₈₉	C₂²	1	2	yes	—
96	#387×C₈₉	C₂²	1	2	yes	—
97	#387×C₈₉	C₂²	1	2	yes	—
98	#387×C₈₉	C₂²	1	2	yes	—
99	#387×C₈₉	C₂²	1	1	yes	characteristic
100	#387×C₈₉	C₂²	1	1	yes	characteristic
101	#386×C₈₉	C₂²	1	2	yes	—
102	#386×C₈₉	C₂²	1	1	yes	characteristic
103	#386×C₈₉	C₂²	1	2	yes	—
104	#386×C₈₉	C₂²	1	2	yes	—
105	#386×C₈₉	C₂²	1	2	yes	—
106	#386×C₈₉	C₂²	1	2	yes	—
107	#386×C₈₉	C₂²	1	1	yes	characteristic
108	#385×C₈₉	C₂²	1	2	yes	—
109	#385×C₈₉	C₂²	1	2	yes	—
110	#385×C₈₉	C₂²	1	1	yes	characteristic
111	#385×C₈₉	C₂²	1	2	yes	—
112	#385×C₈₉	C₂²	1	2	yes	—
113	#385×C₈₉	C₂²	1	1	yes	characteristic
114	#384×C₈₉	C₂²	1	1	yes	characteristic
115	#383×C₈₉	C₂²	1	2	yes	—
116	#382×C₈₉	C₂²	1	2	yes	—
117	#380×C₈₉	C₂²	1	1	yes	characteristic
118	#380×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
124	#376×C₈₉	C₂²	1	1	yes	characteristic
125	C₂²×Q₈×C₈₉	—	2	4	no	—
126	C₂²×Q₈×C₈₉	—	2	4	no	—
127	C₂²×Q₈×C₈₉	—	2	4	no	—
128	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
129	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
132	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
134	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
136	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
139	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
141	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
143	C₄⋊Q₈×C₈₉	—	2	4	no	—
144	#126×C₈₉	—	2	8	no	—
145	#124×C₈₉	—	2	4	no	—
146	#124×C₈₉	—	2	4	no	—
147	#124×C₈₉	—	2	8	no	—
148	#123×C₈₉	—	2	8	no	—
149	C₂²⋊Q₈×C₈₉	—	2	4	no	—
150	C₂²⋊Q₈×C₈₉	—	2	4	no	—
151	C₂²⋊Q₈×C₈₉	—	2	8	no	—
152	C₂²⋊Q₈×C₈₉	—	4	4	no	—
153	#121×C₈₉	—	2	4	no	—
154	#121×C₈₉	—	2	4	no	—
155	#121×C₈₉	—	4	4	no	—
156	C₄×Q₈×C₈₉	—	2	4	no	—
157	C₄×Q₈×C₈₉	—	2	4	no	—
158	C₄×Q₈×C₈₉	—	2	8	no	—
159	C₄×Q₈×C₈₉	—	2	4	no	—
160	C₄×Q₈×C₈₉	—	2	8	no	—
161	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
162	C₄×D₄×C₈₉	—	2	4	no	—
163	C₄×D₄×C₈₉	—	2	4	no	—
164	C₄×D₄×C₈₉	—	4	4	no	—
165	#117×C₈₉	—	2	4	no	—
166	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
167	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
184	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
208	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₂×C₄²×C₈₉	—	2	4	no	—
216	C₂×C₄²×C₈₉	—	2	8	no	—
217	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
223	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
225	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
226	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	1	yes	characteristic
230	#95×C₈₉	C₂³	1	1	yes	characteristic
231	#95×C₈₉	C₂³	1	1	yes	characteristic
232	#95×C₈₉	C₂³	1	1	yes	characteristic
233	#95×C₈₉	C₂³	1	2	yes	—
234	#95×C₈₉	C₂³	1	1	yes	characteristic
235	#95×C₈₉	C₂³	1	1	yes	characteristic
236	#95×C₈₉	C₂³	1	2	yes	—
237	#95×C₈₉	C₂³	1	1	yes	characteristic
238	#95×C₈₉	C₂³	1	1	yes	characteristic
239	#95×C₈₉	C₂³	1	2	yes	—
240	#95×C₈₉	C₂³	1	1	yes	characteristic
241	#95×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
256	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×Q₈×C₈₉	—	2	32	no	—
258	C₂×Q₈×C₈₉	—	2	4	no	—
259	C₂×Q₈×C₈₉	—	2	2	no	—
260	C₂×Q₈×C₈₉	—	2	4	no	—
261	C₂×Q₈×C₈₉	—	2	4	no	—
262	C₂×Q₈×C₈₉	—	2	4	no	—
263	C₂×Q₈×C₈₉	—	2	2	no	—
264	C₂×Q₈×C₈₉	—	2	2	no	—
265	C₂×Q₈×C₈₉	—	2	2	no	—
266	C₂×Q₈×C₈₉	—	4	2	no	—
267	C₂×Q₈×C₈₉	—	4	2	no	—
268	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
269	C₂×Q₈×C₈₉	#41	1	4	yes	—
270	C₂×D₄×C₈₉	—	2	2	no	—
271	C₂×D₄×C₈₉	—	2	4	no	—
272	C₂×D₄×C₈₉	—	2	4	no	—
273	C₂×D₄×C₈₉	—	2	2	no	—
274	C₂×D₄×C₈₉	—	2	2	no	—
275	C₂×D₄×C₈₉	—	2	4	no	—
276	C₂×D₄×C₈₉	—	2	2	no	—
277	C₂×D₄×C₈₉	—	2	4	no	—
278	C₂×D₄×C₈₉	—	2	2	no	—
279	C₂×D₄×C₈₉	—	2	2	no	—
280	C₂×D₄×C₈₉	—	4	2	no	—
281	C₂×D₄×C₈₉	—	4	2	no	—
282	C₂²×C₄×C₈₉	—	2	4	no	—
283	C₂²×C₄×C₈₉	—	2	2	no	—
284	C₂²×C₄×C₈₉	—	2	2	no	—
285	C₂²×C₄×C₈₉	—	2	4	no	—
286	C₂²×C₄×C₈₉	—	2	2	no	—
287	C₂²×C₄×C₈₉	—	2	4	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	4	no	—
292	C₂²×C₄×C₈₉	—	2	2	no	—
293	C₂²×C₄×C₈₉	—	2	4	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	4	no	—
298	C₂²×C₄×C₈₉	—	4	1	no	—
299	C₂²×C₄×C₈₉	—	4	2	no	—
300	C₂²×C₄×C₈₉	—	4	2	no	—
301	C₂²×C₄×C₈₉	—	4	2	no	—
302	C₂²×C₄×C₈₉	#41	1	4	yes	—
303	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₈₉	—	2	4	no	—
324	C₄⋊C₄×C₈₉	—	2	4	no	—
325	C₄⋊C₄×C₈₉	—	2	4	no	—
326	C₄⋊C₄×C₈₉	—	2	4	no	—
327	C₄⋊C₄×C₈₉	—	2	2	no	—
328	C₄⋊C₄×C₈₉	—	2	2	no	—
329	C₄⋊C₄×C₈₉	—	2	2	no	—
330	C₄⋊C₄×C₈₉	—	2	2	no	—
331	C₄⋊C₄×C₈₉	—	2	4	no	—
332	C₄⋊C₄×C₈₉	—	2	4	no	—
333	C₄⋊C₄×C₈₉	—	2	2	no	—
334	C₄⋊C₄×C₈₉	—	2	2	no	—
335	C₄⋊C₄×C₈₉	—	2	2	no	—
336	C₄⋊C₄×C₈₉	—	2	4	no	—
337	C₄⋊C₄×C₈₉	—	2	2	no	—
338	C₄⋊C₄×C₈₉	—	4	1	no	—
339	C₄⋊C₄×C₈₉	—	4	2	no	—
340	C₄⋊C₄×C₈₉	—	4	2	no	—
341	C₄⋊C₄×C₈₉	—	4	2	no	—
342	C₄⋊C₄×C₈₉	—	4	2	no	—
343	C₄⋊C₄×C₈₉	—	4	2	no	—
344	C₄⋊C₄×C₈₉	—	4	2	no	—
345	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
346	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
347	C₂²⋊C₄×C₈₉	—	2	2	no	—
348	C₂²⋊C₄×C₈₉	—	2	4	no	—
349	C₂²⋊C₄×C₈₉	—	2	2	no	—
350	C₂²⋊C₄×C₈₉	—	2	2	no	—
351	C₂²⋊C₄×C₈₉	—	2	2	no	—
352	C₂²⋊C₄×C₈₉	—	2	2	no	—
353	C₂²⋊C₄×C₈₉	—	2	4	no	—
354	C₂²⋊C₄×C₈₉	—	2	4	no	—
355	C₂²⋊C₄×C₈₉	—	2	4	no	—
356	C₂²⋊C₄×C₈₉	—	2	4	no	—
357	C₂²⋊C₄×C₈₉	—	2	4	no	—
358	C₂²⋊C₄×C₈₉	—	2	2	no	—
359	C₂²⋊C₄×C₈₉	—	2	4	no	—
360	C₂²⋊C₄×C₈₉	—	2	4	no	—
361	C₂²⋊C₄×C₈₉	—	2	4	no	—
362	C₂²⋊C₄×C₈₉	—	2	4	no	—
363	C₂²⋊C₄×C₈₉	—	2	4	no	—
364	C₂²⋊C₄×C₈₉	—	2	2	no	—
365	C₂²⋊C₄×C₈₉	—	4	2	no	—
366	C₂²⋊C₄×C₈₉	—	4	1	no	—
367	C₂²⋊C₄×C₈₉	—	4	2	no	—
368	C₂²⋊C₄×C₈₉	—	4	2	no	—
369	C₂²⋊C₄×C₈₉	—	4	2	no	—
370	C₄²×C₈₉	—	2	2	no	—
371	C₄²×C₈₉	—	2	4	no	—
372	C₄²×C₈₉	—	2	4	no	—
373	C₄²×C₈₉	—	2	2	no	—
374	C₄²×C₈₉	—	2	2	no	—
375	C₄²×C₈₉	—	2	4	no	—
376	C₄²×C₈₉	—	2	2	no	—
377	C₄²×C₈₉	—	2	2	no	—
378	C₄²×C₈₉	—	2	2	no	—
379	C₄²×C₈₉	—	4	2	no	—
380	C₄²×C₈₉	C₂×D₄	1	4	yes	—
381	C₄²×C₈₉	C₂×D₄	1	8	yes	—
382	C₂³×C₈₉	—	2	1	no	—
383	C₂³×C₈₉	—	2	1	no	—
384	C₂³×C₈₉	—	2	1	no	—
385	C₂³×C₈₉	—	2	1	no	—
386	C₂³×C₈₉	—	2	1	no	—
387	C₂³×C₈₉	—	2	2	no	—
388	C₂³×C₈₉	—	2	1	no	—
389	C₂³×C₈₉	—	2	2	no	—
390	C₂³×C₈₉	—	2	1	no	—
391	C₂³×C₈₉	—	2	2	no	—
392	C₂³×C₈₉	—	2	2	no	—
393	C₂³×C₈₉	—	2	1	no	—
394	C₂³×C₈₉	—	2	1	no	—
395	C₂³×C₈₉	—	2	2	no	—
396	C₂³×C₈₉	—	2	1	no	—
397	C₂³×C₈₉	—	2	2	no	—
398	C₂³×C₈₉	—	2	2	no	—
399	C₂³×C₈₉	—	2	1	no	—
400	C₂³×C₈₉	C₂×#41	1	2	yes	—
401	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
402	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
403	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
404	Q₈×C₈₉	—	2	16	no	—
405	Q₈×C₈₉	—	2	8	no	—
406	Q₈×C₈₉	—	2	8	no	—
407	Q₈×C₈₉	—	8	4	no	—
408	D₄×C₈₉	—	4	4	no	—
409	D₄×C₈₉	—	4	8	no	—
410	D₄×C₈₉	—	4	4	no	—
411	D₄×C₈₉	—	8	4	no	—
412	C₂×C₄×C₈₉	—	2	8	no	—
413	C₂×C₄×C₈₉	—	2	16	no	—
414	C₂×C₄×C₈₉	—	2	1	no	—
415	C₂×C₄×C₈₉	—	2	2	no	—
416	C₂×C₄×C₈₉	—	2	1	no	—
417	C₂×C₄×C₈₉	—	2	2	no	—
418	C₂×C₄×C₈₉	—	2	2	no	—
419	C₂×C₄×C₈₉	—	2	2	no	—
420	C₂×C₄×C₈₉	—	2	1	no	—
421	C₂×C₄×C₈₉	—	2	1	no	—
422	C₂×C₄×C₈₉	—	2	2	no	—
423	C₂×C₄×C₈₉	—	2	1	no	—
424	C₂×C₄×C₈₉	—	2	1	no	—
425	C₂×C₄×C₈₉	—	2	1	no	—
426	C₂×C₄×C₈₉	—	2	1	no	—
427	C₂×C₄×C₈₉	—	2	2	no	—
428	C₂×C₄×C₈₉	—	2	8	no	—
429	C₂×C₄×C₈₉	—	2	2	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	1	no	—
432	C₂×C₄×C₈₉	—	2	1	no	—
433	C₂×C₄×C₈₉	—	2	1	no	—
434	C₂×C₄×C₈₉	—	2	2	no	—
435	C₂×C₄×C₈₉	—	2	1	no	—
436	C₂×C₄×C₈₉	—	2	1	no	—
437	C₂×C₄×C₈₉	—	2	1	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	1	no	—
441	C₂×C₄×C₈₉	—	2	2	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	2	no	—
445	C₂×C₄×C₈₉	—	2	1	no	—
446	C₂×C₄×C₈₉	—	2	2	no	—
447	C₂×C₄×C₈₉	—	2	1	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	2	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	2	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	2	no	—
459	C₂×C₄×C₈₉	—	2	1	no	—
460	C₂×C₄×C₈₉	—	2	1	no	—
461	C₂×C₄×C₈₉	—	2	2	no	—
462	C₂×C₄×C₈₉	—	2	1	no	—
463	C₂×C₄×C₈₉	—	2	2	no	—
464	C₂×C₄×C₈₉	—	2	1	no	—
465	C₂×C₄×C₈₉	—	4	4	no	—
466	C₂×C₄×C₈₉	—	4	8	no	—
467	C₂×C₄×C₈₉	—	4	4	no	—
468	C₂×C₄×C₈₉	—	8	4	no	—
469	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
471	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
473	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
475	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
476	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
477	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
478	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
479	C₂²×C₈₉	—	2	2	no	—
480	C₂²×C₈₉	—	2	2	no	—
481	C₂²×C₈₉	—	2	2	no	—
482	C₂²×C₈₉	—	2	2	no	—
483	C₂²×C₈₉	—	2	2	no	—
484	C₂²×C₈₉	—	2	2	no	—
485	C₂²×C₈₉	—	4	1	no	—
486	C₂²×C₈₉	—	4	2	no	—
487	C₂²×C₈₉	—	4	1	no	—
488	C₂²×C₈₉	—	4	2	no	—
489	C₂²×C₈₉	—	4	1	no	—
490	C₂²×C₈₉	—	4	2	no	—
491	C₂²×C₈₉	—	4	1	no	—
492	C₂²×C₈₉	—	4	2	no	—
493	C₂²×C₈₉	—	4	2	no	—
494	C₂²×C₈₉	—	4	1	no	—
495	C₂²×C₈₉	—	4	1	no	—
496	C₂²×C₈₉	—	4	2	no	—
497	C₂²×C₈₉	—	4	1	no	—
498	C₂²×C₈₉	—	4	2	no	—
499	C₂²×C₈₉	#542	1	4	yes	complemented
500	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
501	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
502	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
503	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
505	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
506	C₂²×C₈₉	#585	1	1	yes	characteristic
507	C₄×C₈₉	—	2	4	no	—
508	C₄×C₈₉	—	2	4	no	—
509	C₄×C₈₉	—	2	2	no	—
510	C₄×C₈₉	—	2	2	no	—
511	C₄×C₈₉	—	2	2	no	—
512	C₄×C₈₉	—	2	2	no	—
513	C₄×C₈₉	—	2	4	no	—
514	C₄×C₈₉	—	4	1	no	—
515	C₄×C₈₉	—	4	1	no	—
516	C₄×C₈₉	—	4	2	no	—
517	C₄×C₈₉	—	4	1	no	—
518	C₄×C₈₉	—	4	1	no	—
519	C₄×C₈₉	—	4	1	no	—
520	C₄×C₈₉	—	4	2	no	—
521	C₄×C₈₉	—	4	2	no	—
522	C₄×C₈₉	—	4	1	no	—
523	C₄×C₈₉	—	4	1	no	—
524	C₄×C₈₉	—	4	1	no	—
525	C₄×C₈₉	—	4	2	no	—
526	C₄×C₈₉	#525	1	4	yes	—
527	#35243	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
528	C₂×C₈₉	—	2	4	no	—
529	C₂×C₈₉	—	8	1	no	—
530	C₂×C₈₉	—	8	2	no	—
531	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
532	C₂×C₈₉	C₂×#542	1	1	yes	characteristic
533	C₂×C₈₉	#3461	1	1	yes	characteristic
534	C₂×C₈₉	#3486	1	1	yes	characteristic
535	C₂×C₈₉	#3488	1	1	yes	characteristic
536	C₂×C₈₉	#3516	1	1	yes	characteristic
537	C₂×C₈₉	#3522	1	1	yes	characteristic
538	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
539	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
540	#2852	C₂×C₈₉	1	2	yes	complemented
541	#2850	C₂×C₈₉	1	2	yes	complemented
542	#2637	C₂×C₈₉	1	2	yes	complemented
543	#2632	C₂×C₈₉	1	2	yes	complemented
544	#2465	C₂×C₈₉	1	2	yes	complemented
545	#2458	C₂×C₈₉	1	2	yes	complemented
546	#2451	C₂×C₈₉	1	1	yes	characteristic, complemented
547	#2449	C₂×C₈₉	1	2	yes	complemented
548	#2448	C₂×C₈₉	1	1	yes	characteristic, complemented
549	#2443	C₂×C₈₉	1	2	yes	complemented
550	#2440	C₂×C₈₉	1	1	yes	characteristic, complemented
551	#2436	C₂×C₈₉	1	1	yes	characteristic, complemented
552	#2426	C₂×C₈₉	1	1	yes	characteristic, complemented
553	#2423	C₂×C₈₉	1	1	yes	characteristic, complemented
554	#2416	C₂×C₈₉	1	1	yes	characteristic
555	#2409	C₂×C₈₉	1	1	yes	characteristic, complemented
556	#2326	C₂×C₈₉	1	1	yes	characteristic, complemented
557	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
558	#2320	C₂×C₈₉	1	1	yes	characteristic, complemented
559	C₄×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
560	#2290	C₂×C₈₉	1	1	yes	characteristic, complemented
561	C₈₉	#35243	1	1	yes	characteristic, direct product factor, Sylow
562	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
563	#542	—	2	8	no	—
564	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
565	C₂×#126	C₂²×C₈₉	1	2	yes	—
566	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
567	C₂×#124	C₂²×C₈₉	1	2	yes	—
568	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
569	C₂×#123	C₂²×C₈₉	1	2	yes	—
570	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
571	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
572	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
573	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
574	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
575	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
576	C₂×#121	C₂²×C₈₉	1	2	yes	—
577	C₂×C₄×Q₈	—	2	8	no	—
578	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
579	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
580	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
581	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
582	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
583	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
584	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
586	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
587	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
588	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
589	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
590	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
591	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
592	#399	C₂²×C₈₉	1	2	yes	—
593	#399	C₂²×C₈₉	1	2	yes	—
594	#398	C₂²×C₈₉	1	2	yes	—
595	#398	C₂²×C₈₉	1	2	yes	—
596	#398	C₂²×C₈₉	1	2	yes	—
597	#397	C₂²×C₈₉	1	2	yes	—
598	#396	C₂²×C₈₉	1	2	yes	—
599	#396	C₂²×C₈₉	1	2	yes	—
600	#395	C₂²×C₈₉	1	2	yes	—
601	#395	C₂²×C₈₉	1	2	yes	—
602	#395	C₂²×C₈₉	1	2	yes	—
603	#394	C₂²×C₈₉	1	2	yes	—
604	#394	C₂²×C₈₉	1	2	yes	—
605	#393	C₂²×C₈₉	1	2	yes	—
606	#393	C₂²×C₈₉	1	2	yes	—
607	#393	C₂²×C₈₉	1	2	yes	—
608	#391	C₂²×C₈₉	1	1	yes	characteristic
609	#391	C₂²×C₈₉	1	1	yes	characteristic
610	#391	C₂²×C₈₉	1	1	yes	characteristic
611	#391	C₂²×C₈₉	1	1	yes	characteristic
612	#391	C₂²×C₈₉	1	2	yes	—
613	#390	C₂²×C₈₉	1	1	yes	characteristic
614	#390	C₂²×C₈₉	1	2	yes	—
615	#390	C₂²×C₈₉	1	1	yes	characteristic
616	#389	C₂²×C₈₉	1	1	yes	characteristic
617	#389	C₂²×C₈₉	1	1	yes	characteristic
618	#389	C₂²×C₈₉	1	1	yes	characteristic
619	#389	C₂²×C₈₉	1	2	yes	—
620	#389	C₂²×C₈₉	1	1	yes	characteristic
621	#388	C₂²×C₈₉	1	2	yes	—
622	#388	C₂²×C₈₉	1	2	yes	—
623	#388	C₂²×C₈₉	1	2	yes	—
624	#388	C₂²×C₈₉	1	2	yes	—
625	#388	C₂²×C₈₉	1	2	yes	—
626	#388	C₂²×C₈₉	1	2	yes	—
627	#388	C₂²×C₈₉	1	2	yes	—
628	#388	C₂²×C₈₉	1	2	yes	—
629	#388	C₂²×C₈₉	1	1	yes	characteristic
630	#388	C₂²×C₈₉	1	2	yes	—
631	#388	C₂²×C₈₉	1	1	yes	characteristic
632	#387	C₂²×C₈₉	1	2	yes	—
633	#387	C₂²×C₈₉	1	2	yes	—
634	#387	C₂²×C₈₉	1	2	yes	—
635	#387	C₂²×C₈₉	1	2	yes	—
636	#387	C₂²×C₈₉	1	2	yes	—
637	#387	C₂²×C₈₉	1	1	yes	characteristic
638	#387	C₂²×C₈₉	1	1	yes	characteristic
639	#386	C₂²×C₈₉	1	1	yes	characteristic
640	#386	C₂²×C₈₉	1	2	yes	—
641	#386	C₂²×C₈₉	1	2	yes	—
642	#386	C₂²×C₈₉	1	2	yes	—
643	#386	C₂²×C₈₉	1	2	yes	—
644	#386	C₂²×C₈₉	1	2	yes	—
645	#386	C₂²×C₈₉	1	1	yes	characteristic
646	#385	C₂²×C₈₉	1	2	yes	—
647	#385	C₂²×C₈₉	1	2	yes	—
648	#385	C₂²×C₈₉	1	1	yes	characteristic
649	#385	C₂²×C₈₉	1	2	yes	—
650	#385	C₂²×C₈₉	1	2	yes	—
651	#385	C₂²×C₈₉	1	1	yes	characteristic
652	#384	C₂²×C₈₉	1	1	yes	characteristic
653	#383	C₂²×C₈₉	1	2	yes	—
654	#382	C₂²×C₈₉	1	2	yes	—
655	#380	C₂²×C₈₉	1	1	yes	characteristic
656	#380	C₂²×C₈₉	1	1	yes	characteristic
657	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
658	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
659	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
661	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
662	#376	C₂²×C₈₉	1	1	yes	characteristic
663	C₂²×Q₈	—	2	4	no	—
664	C₂²×Q₈	—	2	4	no	—
665	C₂²×Q₈	—	2	4	no	—
666	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
667	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
668	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
669	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
670	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
671	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
672	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
673	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
674	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
675	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
678	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
679	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
680	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
681	C₄⋊Q₈	—	2	4	no	—
682	#126	—	2	8	no	—
683	#124	—	2	4	no	—
684	#124	—	2	4	no	—
685	#124	—	2	8	no	—
686	#123	—	2	8	no	—
687	C₂²⋊Q₈	—	2	4	no	—
688	C₂²⋊Q₈	—	2	4	no	—
689	C₂²⋊Q₈	—	2	8	no	—
690	C₂²⋊Q₈	—	4	4	no	—
691	#121	—	2	4	no	—
692	#121	—	2	4	no	—
693	#121	—	4	4	no	—
694	C₄×Q₈	—	2	4	no	—
695	C₄×Q₈	—	2	4	no	—
696	C₄×Q₈	—	2	8	no	—
697	C₄×Q₈	—	2	4	no	—
698	C₄×Q₈	—	2	8	no	—
699	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
700	C₄×D₄	—	2	4	no	—
701	C₄×D₄	—	2	4	no	—
702	C₄×D₄	—	4	4	no	—
703	#117	—	2	4	no	—
704	C₂×C₄⋊C₄	—	2	4	no	—
705	C₂×C₄⋊C₄	—	2	8	no	—
706	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
709	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
721	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
727	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
735	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
736	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
743	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
753	C₂×C₄²	—	2	4	no	—
754	C₂×C₄²	—	2	8	no	—
755	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
760	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
762	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
763	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
764	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
765	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
767	#95	C₂³×C₈₉	1	1	yes	characteristic
768	#95	C₂³×C₈₉	1	1	yes	characteristic
769	#95	C₂³×C₈₉	1	1	yes	characteristic
770	#95	C₂³×C₈₉	1	1	yes	characteristic
771	#95	C₂³×C₈₉	1	2	yes	—
772	#95	C₂³×C₈₉	1	1	yes	characteristic
773	#95	C₂³×C₈₉	1	1	yes	characteristic
774	#95	C₂³×C₈₉	1	2	yes	—
775	#95	C₂³×C₈₉	1	1	yes	characteristic
776	#95	C₂³×C₈₉	1	1	yes	characteristic
777	#95	C₂³×C₈₉	1	2	yes	—
778	#95	C₂³×C₈₉	1	1	yes	characteristic
779	#95	C₂³×C₈₉	1	1	yes	characteristic
780	#95	C₂³×C₈₉	1	2	yes	—
781	#95	C₂³×C₈₉	1	2	yes	—
782	#95	C₂³×C₈₉	1	2	yes	—
783	#95	C₂³×C₈₉	1	2	yes	—
784	#95	C₂³×C₈₉	1	2	yes	—
785	#95	C₂³×C₈₉	1	2	yes	—
786	#95	C₂³×C₈₉	1	2	yes	—
787	#95	C₂³×C₈₉	1	2	yes	—
788	#95	C₂³×C₈₉	1	2	yes	—
789	#95	C₂³×C₈₉	1	2	yes	—
790	#95	C₂³×C₈₉	1	2	yes	—
791	#95	C₂³×C₈₉	1	2	yes	—
792	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
793	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
794	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
795	C₂×Q₈	—	2	32	no	—
796	C₂×Q₈	—	2	4	no	—
797	C₂×Q₈	—	2	2	no	—
798	C₂×Q₈	—	2	4	no	—
799	C₂×Q₈	—	2	4	no	—
800	C₂×Q₈	—	2	4	no	—
801	C₂×Q₈	—	2	2	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	4	2	no	—
805	C₂×Q₈	—	4	2	no	—
806	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
807	C₂×Q₈	#41×C₈₉	1	4	yes	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	4	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	4	no	—
816	C₂×D₄	—	2	2	no	—
817	C₂×D₄	—	2	2	no	—
818	C₂×D₄	—	4	2	no	—
819	C₂×D₄	—	4	2	no	—
820	C₂²×C₄	—	2	4	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	2	no	—
825	C₂²×C₄	—	2	4	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	2	2	no	—
831	C₂²×C₄	—	2	4	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	4	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	—	4	2	no	—
839	C₂²×C₄	—	4	2	no	—
840	C₂²×C₄	#41×C₈₉	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
847	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
856	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
861	C₄⋊C₄	—	2	4	no	—
862	C₄⋊C₄	—	2	4	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	4	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	4	no	—
870	C₄⋊C₄	—	2	4	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	4	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	—	4	2	no	—
878	C₄⋊C₄	—	4	2	no	—
879	C₄⋊C₄	—	4	2	no	—
880	C₄⋊C₄	—	4	2	no	—
881	C₄⋊C₄	—	4	1	no	—
882	C₄⋊C₄	—	4	2	no	—
883	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
884	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	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	—	2	4	no	—
893	C₂²⋊C₄	—	2	4	no	—
894	C₂²⋊C₄	—	2	4	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	4	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₂²⋊C₄	—	4	2	no	—
905	C₂²⋊C₄	—	4	2	no	—
906	C₂²⋊C₄	—	4	2	no	—
907	C₂²⋊C₄	—	4	1	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	2	4	no	—
910	C₄²	—	2	4	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	—	2	4	no	—
914	C₄²	—	2	2	no	—
915	C₄²	—	2	2	no	—
916	C₄²	—	2	2	no	—
917	C₄²	—	4	2	no	—
918	C₄²	C₂×D₄×C₈₉	1	4	yes	—
919	C₄²	C₂×D₄×C₈₉	1	8	yes	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	2	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	1	no	—
938	C₂³	C₂×#41×C₈₉	1	2	yes	—
939	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
940	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
941	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
942	Q₈	—	2	16	no	—
943	Q₈	—	2	8	no	—
944	Q₈	—	2	8	no	—
945	Q₈	—	8	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	8	no	—
948	D₄	—	4	4	no	—
949	D₄	—	8	4	no	—
950	C₂×C₄	—	2	8	no	—
951	C₂×C₄	—	2	16	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	8	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	2	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	2	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	8	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	8	4	no	—
1007	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1008	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
1009	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1010	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
1011	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
1012	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
1013	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1014	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1015	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
1016	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	2	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	#542×C₈₉	1	4	yes	complemented
1038	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1039	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1040	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1041	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
1042	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1043	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1044	C₂²	#585×C₈₉	1	1	yes	characteristic
1045	C₄	—	2	4	no	—
1046	C₄	—	2	4	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	4	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	2	no	—
1064	C₄	#525×C₈₉	1	4	yes	—
1065	C₂	—	2	4	no	—
1066	C₂	—	8	1	no	—
1067	C₂	—	8	2	no	—
1068	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
1069	C₂	C₂×#542×C₈₉	1	1	yes	characteristic
1070	C₂	C₈₉×#3461	1	1	yes	characteristic
1071	C₂	C₈₉×#3486	1	1	yes	characteristic
1072	C₂	C₈₉×#3488	1	1	yes	characteristic
1073	C₂	C₈₉×#3516	1	1	yes	characteristic
1074	C₂	C₈₉×#3522	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2416	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×C₄×Q₈×C₈₉	C₂	semidirect
3. C₈₉×#2852	C₂	semidirect
4. C₈₉×#2850	C₂	semidirect
5. C₈₉×#2637	C₂	semidirect
6. C₈₉×#2632	C₂	semidirect
7. C₈₉×#2465	C₂	semidirect
8. C₈₉×#2458	C₂	semidirect
9. C₈₉×#2451	C₂	semidirect
10. C₈₉×#2449	C₂	semidirect
11. C₈₉×#2448	C₂	semidirect
12. C₈₉×#2443	C₂	semidirect
13. C₈₉×#2440	C₂	semidirect
14. C₈₉×#2436	C₂	semidirect
15. C₈₉×#2426	C₂	semidirect
16. C₈₉×#2423	C₂	semidirect
18. C₈₉×#2409	C₂	semidirect
19. C₈₉×#2326	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₈₉×#2320	C₂	semidirect
22. C₄×#121×C₈₉	C₂	semidirect
23. C₈₉×#2290	C₂	semidirect
161. C₄×Q₈×C₈₉	D₄	semidirect
499. C₂²×C₈₉	#542	semidirect
527. #35243	C₈₉	direct (N × H)
538. C₂×#542	C₂×C₈₉	semidirect
539. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
540. #2852	C₂×C₈₉	semidirect
541. #2850	C₂×C₈₉	semidirect
542. #2637	C₂×C₈₉	semidirect
543. #2632	C₂×C₈₉	semidirect
544. #2465	C₂×C₈₉	semidirect
545. #2458	C₂×C₈₉	semidirect
546. #2451	C₂×C₈₉	semidirect
547. #2449	C₂×C₈₉	semidirect
548. #2448	C₂×C₈₉	semidirect
549. #2443	C₂×C₈₉	semidirect
550. #2440	C₂×C₈₉	semidirect
551. #2436	C₂×C₈₉	semidirect
552. #2426	C₂×C₈₉	semidirect
553. #2423	C₂×C₈₉	semidirect
555. #2409	C₂×C₈₉	semidirect
556. #2326	C₂×C₈₉	semidirect
557. #2323	C₂×C₈₉	semidirect
558. #2320	C₂×C₈₉	semidirect
559. C₄×#121	C₂×C₈₉	semidirect
560. #2290	C₂×C₈₉	semidirect
561. C₈₉	#35243	direct (N × H)
699. C₄×Q₈	D₄×C₈₉	semidirect
1037. 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×C₄×Q₈×C₈₉	2
C₈₉×#2852	2
C₈₉×#2850	2
C₈₉×#2637	2
C₈₉×#2632	2
C₈₉×#2465	2
C₈₉×#2458	2
C₈₉×#2451	2
C₈₉×#2449	2
C₈₉×#2448	2
C₈₉×#2443	2
C₈₉×#2440	2
C₈₉×#2436	2
C₈₉×#2426	2
C₈₉×#2423	2
C₈₉×#2416	2
C₈₉×#2409	2
C₈₉×#2326	2
C₈₉×#2323	2
C₈₉×#2320	2
C₄×#121×C₈₉	2
C₈₉×#2290	2
#35243	89

Subgroups — C89×#35243 #36413091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35243 #36413091