Subgroups — C₈₉×#35220 #36413068

Order 22784.

2128 conjugacy classes of subgroups.

The subgroup lattice has 1050 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	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2861	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2860	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2664	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2662	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2560	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2558	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2556	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2554	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2550	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2545	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2540	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2492	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2490	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2429	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2426	C₂	1	1	yes	maximal, characteristic, complemented
19	C₈₉×#2324	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈₉×#2323	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₈₉×#2293	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#542×C₈₉	—	2	8	no	—
25	#541×C₈₉	—	2	8	no	—
26	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#126×C₈₉	C₂²	1	2	yes	—
29	C₂×#126×C₈₉	C₂²	1	2	yes	—
30	C₂×#126×C₈₉	C₂²	1	2	yes	—
31	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#125×C₈₉	C₂²	1	2	yes	—
33	C₂×#125×C₈₉	C₂²	1	2	yes	—
34	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#124×C₈₉	C₂²	1	2	yes	—
36	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#123×C₈₉	C₂²	1	2	yes	—
38	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
39	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
53	#400×C₈₉	C₂²	1	2	yes	—
54	#399×C₈₉	C₂²	1	2	yes	—
55	#398×C₈₉	C₂²	1	2	yes	—
56	#398×C₈₉	C₂²	1	2	yes	—
57	#398×C₈₉	C₂²	1	2	yes	—
58	#397×C₈₉	C₂²	1	2	yes	—
59	#396×C₈₉	C₂²	1	2	yes	—
60	#396×C₈₉	C₂²	1	2	yes	—
61	#396×C₈₉	C₂²	1	2	yes	—
62	#396×C₈₉	C₂²	1	2	yes	—
63	#395×C₈₉	C₂²	1	2	yes	—
64	#394×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	#392×C₈₉	C₂²	1	2	yes	—
69	#391×C₈₉	C₂²	1	2	yes	—
70	#391×C₈₉	C₂²	1	2	yes	—
71	#391×C₈₉	C₂²	1	1	yes	characteristic
72	#391×C₈₉	C₂²	1	1	yes	characteristic
73	#390×C₈₉	C₂²	1	1	yes	characteristic
74	#390×C₈₉	C₂²	1	2	yes	—
75	#390×C₈₉	C₂²	1	2	yes	—
76	#390×C₈₉	C₂²	1	2	yes	—
77	#390×C₈₉	C₂²	1	1	yes	characteristic
78	#390×C₈₉	C₂²	1	2	yes	—
79	#390×C₈₉	C₂²	1	2	yes	—
80	#390×C₈₉	C₂²	1	1	yes	characteristic
81	#390×C₈₉	C₂²	1	1	yes	characteristic
82	#389×C₈₉	C₂²	1	2	yes	—
83	#389×C₈₉	C₂²	1	1	yes	characteristic
84	#389×C₈₉	C₂²	1	1	yes	characteristic
85	#389×C₈₉	C₂²	1	1	yes	characteristic
86	#389×C₈₉	C₂²	1	2	yes	—
87	#389×C₈₉	C₂²	1	2	yes	—
88	#389×C₈₉	C₂²	1	1	yes	characteristic
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	2	yes	—
93	#388×C₈₉	C₂²	1	2	yes	—
94	#388×C₈₉	C₂²	1	1	yes	characteristic
95	#388×C₈₉	C₂²	1	2	yes	—
96	#388×C₈₉	C₂²	1	2	yes	—
97	#388×C₈₉	C₂²	1	2	yes	—
98	#388×C₈₉	C₂²	1	2	yes	—
99	#388×C₈₉	C₂²	1	1	yes	characteristic
100	#388×C₈₉	C₂²	1	2	yes	—
101	#388×C₈₉	C₂²	1	2	yes	—
102	#388×C₈₉	C₂²	1	2	yes	—
103	#388×C₈₉	C₂²	1	2	yes	—
104	#388×C₈₉	C₂²	1	1	yes	characteristic
105	#388×C₈₉	C₂²	1	1	yes	characteristic
106	#387×C₈₉	C₂²	1	2	yes	—
107	#386×C₈₉	C₂²	1	2	yes	—
108	#385×C₈₉	C₂²	1	2	yes	—
109	#382×C₈₉	C₂²	1	1	yes	characteristic
110	#380×C₈₉	C₂²	1	1	yes	characteristic
111	#380×C₈₉	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₄³×C₈₉	C₂²	1	1	yes	characteristic
124	C₄³×C₈₉	C₂²	1	2	yes	—
125	C₂²×Q₈×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	1	yes	characteristic
129	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
130	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₈₉	—	2	4	no	—
136	C₄⋊Q₈×C₈₉	—	2	4	no	—
137	#126×C₈₉	—	2	8	no	—
138	#126×C₈₉	—	2	8	no	—
139	#126×C₈₉	—	2	8	no	—
140	#125×C₈₉	—	2	4	no	—
141	#125×C₈₉	—	2	8	no	—
142	#125×C₈₉	—	2	8	no	—
143	#124×C₈₉	—	2	4	no	—
144	#124×C₈₉	—	2	8	no	—
145	#124×C₈₉	—	2	4	no	—
146	#123×C₈₉	—	2	8	no	—
147	C₂²⋊Q₈×C₈₉	—	2	4	no	—
148	C₂²⋊Q₈×C₈₉	—	2	4	no	—
149	C₂²⋊Q₈×C₈₉	—	2	4	no	—
150	C₂²⋊Q₈×C₈₉	—	2	8	no	—
151	C₂²⋊Q₈×C₈₉	—	2	4	no	—
152	#121×C₈₉	—	2	4	no	—
153	#121×C₈₉	—	2	4	no	—
154	C₄×Q₈×C₈₉	—	2	4	no	—
155	C₄×Q₈×C₈₉	—	2	4	no	—
156	C₄×Q₈×C₈₉	—	2	4	no	—
157	C₄×Q₈×C₈₉	D₄	1	8	yes	complemented
158	C₄×D₄×C₈₉	—	2	4	no	—
159	C₄×D₄×C₈₉	—	2	4	no	—
160	#117×C₈₉	—	2	4	no	—
161	#117×C₈₉	—	2	4	no	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
187	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
197	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
219	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
220	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
221	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
227	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
228	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
229	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
231	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
232	#95×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
241	#95×C₈₉	C₂³	1	2	yes	—
242	#95×C₈₉	C₂³	1	2	yes	—
243	#95×C₈₉	C₂³	1	1	yes	characteristic
244	#95×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
254	C₂×Q₈×C₈₉	—	2	2	no	—
255	C₂×Q₈×C₈₉	—	2	4	no	—
256	C₂×Q₈×C₈₉	—	2	2	no	—
257	C₂×Q₈×C₈₉	—	2	2	no	—
258	C₂×Q₈×C₈₉	—	2	2	no	—
259	C₂×Q₈×C₈₉	—	2	2	no	—
260	C₂×Q₈×C₈₉	—	4	2	no	—
261	C₂×Q₈×C₈₉	—	4	2	no	—
262	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
263	C₂×D₄×C₈₉	—	2	2	no	—
264	C₂×D₄×C₈₉	—	2	4	no	—
265	C₂×D₄×C₈₉	—	2	2	no	—
266	C₂×D₄×C₈₉	—	2	2	no	—
267	C₂×D₄×C₈₉	—	2	2	no	—
268	C₂×D₄×C₈₉	—	2	4	no	—
269	C₂×D₄×C₈₉	—	4	1	no	—
270	C₂×D₄×C₈₉	—	4	1	no	—
271	C₂×D₄×C₈₉	—	4	2	no	—
272	C₂×D₄×C₈₉	—	4	2	no	—
273	C₂×D₄×C₈₉	—	4	2	no	—
274	C₂×D₄×C₈₉	—	4	2	no	—
275	C₂²×C₄×C₈₉	—	2	2	no	—
276	C₂²×C₄×C₈₉	—	2	2	no	—
277	C₂²×C₄×C₈₉	—	2	2	no	—
278	C₂²×C₄×C₈₉	—	2	2	no	—
279	C₂²×C₄×C₈₉	—	2	2	no	—
280	C₂²×C₄×C₈₉	—	2	2	no	—
281	C₂²×C₄×C₈₉	—	2	4	no	—
282	C₂²×C₄×C₈₉	—	4	2	no	—
283	C₂²×C₄×C₈₉	—	4	2	no	—
284	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₈₉	—	2	2	no	—
305	C₄⋊C₄×C₈₉	—	2	2	no	—
306	C₄⋊C₄×C₈₉	—	2	2	no	—
307	C₄⋊C₄×C₈₉	—	2	2	no	—
308	C₄⋊C₄×C₈₉	—	2	2	no	—
309	C₄⋊C₄×C₈₉	—	2	2	no	—
310	C₄⋊C₄×C₈₉	—	2	4	no	—
311	C₄⋊C₄×C₈₉	—	2	4	no	—
312	C₄⋊C₄×C₈₉	—	2	4	no	—
313	C₄⋊C₄×C₈₉	—	2	4	no	—
314	C₄⋊C₄×C₈₉	—	2	4	no	—
315	C₄⋊C₄×C₈₉	—	2	4	no	—
316	C₄⋊C₄×C₈₉	—	2	4	no	—
317	C₄⋊C₄×C₈₉	—	2	4	no	—
318	C₄⋊C₄×C₈₉	—	2	4	no	—
319	C₄⋊C₄×C₈₉	—	2	2	no	—
320	C₄⋊C₄×C₈₉	—	2	4	no	—
321	C₄⋊C₄×C₈₉	—	2	4	no	—
322	C₄⋊C₄×C₈₉	—	2	2	no	—
323	C₄⋊C₄×C₈₉	—	2	4	no	—
324	C₄⋊C₄×C₈₉	—	4	1	no	—
325	C₄⋊C₄×C₈₉	—	4	2	no	—
326	C₄⋊C₄×C₈₉	—	4	1	no	—
327	C₄⋊C₄×C₈₉	—	4	2	no	—
328	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
329	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
330	C₄⋊C₄×C₈₉	#41	1	4	yes	—
331	C₂²⋊C₄×C₈₉	—	2	2	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	2	no	—
335	C₂²⋊C₄×C₈₉	—	2	4	no	—
336	C₂²⋊C₄×C₈₉	—	2	4	no	—
337	C₂²⋊C₄×C₈₉	—	2	4	no	—
338	C₂²⋊C₄×C₈₉	—	2	4	no	—
339	C₂²⋊C₄×C₈₉	—	2	4	no	—
340	C₂²⋊C₄×C₈₉	—	2	4	no	—
341	C₂²⋊C₄×C₈₉	—	2	4	no	—
342	C₂²⋊C₄×C₈₉	—	2	2	no	—
343	C₂²⋊C₄×C₈₉	—	2	2	no	—
344	C₂²⋊C₄×C₈₉	—	2	4	no	—
345	C₂²⋊C₄×C₈₉	—	2	4	no	—
346	C₂²⋊C₄×C₈₉	—	2	4	no	—
347	C₂²⋊C₄×C₈₉	—	2	4	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	—	4	2	no	—
352	C₂²⋊C₄×C₈₉	—	4	2	no	—
353	C₂²⋊C₄×C₈₉	—	4	2	no	—
354	C₂²⋊C₄×C₈₉	—	4	2	no	—
355	C₂²⋊C₄×C₈₉	—	4	1	no	—
356	C₂²⋊C₄×C₈₉	—	4	2	no	—
357	C₂²⋊C₄×C₈₉	—	4	1	no	—
358	C₄²×C₈₉	—	2	2	no	—
359	C₄²×C₈₉	—	2	2	no	—
360	C₄²×C₈₉	—	2	4	no	—
361	C₄²×C₈₉	—	2	4	no	—
362	C₄²×C₈₉	—	2	2	no	—
363	C₄²×C₈₉	—	2	4	no	—
364	C₄²×C₈₉	—	2	2	no	—
365	C₄²×C₈₉	—	4	1	no	—
366	C₄²×C₈₉	—	4	2	no	—
367	C₄²×C₈₉	—	4	1	no	—
368	C₄²×C₈₉	—	4	2	no	—
369	C₄²×C₈₉	—	4	1	no	—
370	C₄²×C₈₉	—	4	2	no	—
371	C₄²×C₈₉	C₂×D₄	1	4	yes	—
372	C₄²×C₈₉	C₂×D₄	1	8	yes	—
373	C₄²×C₈₉	#41	1	4	yes	—
374	C₂³×C₈₉	—	2	1	no	—
375	C₂³×C₈₉	—	2	1	no	—
376	C₂³×C₈₉	—	2	2	no	—
377	C₂³×C₈₉	—	2	1	no	—
378	C₂³×C₈₉	—	2	2	no	—
379	C₂³×C₈₉	—	2	1	no	—
380	C₂³×C₈₉	—	2	1	no	—
381	C₂³×C₈₉	—	2	2	no	—
382	C₂³×C₈₉	—	2	1	no	—
383	C₂³×C₈₉	—	2	2	no	—
384	C₂³×C₈₉	—	2	1	no	—
385	C₂³×C₈₉	—	2	1	no	—
386	C₂³×C₈₉	—	2	1	no	—
387	C₂³×C₈₉	—	2	1	no	—
388	C₂³×C₈₉	—	2	2	no	—
389	C₂³×C₈₉	—	2	2	no	—
390	C₂³×C₈₉	—	2	1	no	—
391	C₂³×C₈₉	—	2	1	no	—
392	C₂³×C₈₉	—	2	2	no	—
393	C₂³×C₈₉	—	2	1	no	—
394	C₂³×C₈₉	—	2	1	no	—
395	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
396	Q₈×C₈₉	—	2	8	no	—
397	Q₈×C₈₉	—	4	4	no	—
398	Q₈×C₈₉	—	8	4	no	—
399	D₄×C₈₉	—	4	4	no	—
400	D₄×C₈₉	—	4	4	no	—
401	D₄×C₈₉	—	8	4	no	—
402	D₄×C₈₉	—	8	4	no	—
403	C₂×C₄×C₈₉	—	2	1	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	1	no	—
408	C₂×C₄×C₈₉	—	2	1	no	—
409	C₂×C₄×C₈₉	—	2	1	no	—
410	C₂×C₄×C₈₉	—	2	1	no	—
411	C₂×C₄×C₈₉	—	2	1	no	—
412	C₂×C₄×C₈₉	—	2	1	no	—
413	C₂×C₄×C₈₉	—	2	2	no	—
414	C₂×C₄×C₈₉	—	2	2	no	—
415	C₂×C₄×C₈₉	—	2	1	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	1	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	2	no	—
425	C₂×C₄×C₈₉	—	2	1	no	—
426	C₂×C₄×C₈₉	—	2	2	no	—
427	C₂×C₄×C₈₉	—	2	1	no	—
428	C₂×C₄×C₈₉	—	2	2	no	—
429	C₂×C₄×C₈₉	—	2	1	no	—
430	C₂×C₄×C₈₉	—	2	1	no	—
431	C₂×C₄×C₈₉	—	2	2	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	2	no	—
438	C₂×C₄×C₈₉	—	2	1	no	—
439	C₂×C₄×C₈₉	—	2	2	no	—
440	C₂×C₄×C₈₉	—	2	2	no	—
441	C₂×C₄×C₈₉	—	2	1	no	—
442	C₂×C₄×C₈₉	—	2	1	no	—
443	C₂×C₄×C₈₉	—	2	2	no	—
444	C₂×C₄×C₈₉	—	2	1	no	—
445	C₂×C₄×C₈₉	—	2	1	no	—
446	C₂×C₄×C₈₉	—	2	1	no	—
447	C₂×C₄×C₈₉	—	2	2	no	—
448	C₂×C₄×C₈₉	—	2	1	no	—
449	C₂×C₄×C₈₉	—	2	1	no	—
450	C₂×C₄×C₈₉	—	2	2	no	—
451	C₂×C₄×C₈₉	—	2	1	no	—
452	C₂×C₄×C₈₉	—	4	4	no	—
453	C₂×C₄×C₈₉	—	4	4	no	—
454	C₂×C₄×C₈₉	—	8	4	no	—
455	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
458	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
459	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
461	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
462	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
463	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
464	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
465	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
466	C₂²×C₈₉	—	4	1	no	—
467	C₂²×C₈₉	—	4	1	no	—
468	C₂²×C₈₉	—	4	2	no	—
469	C₂²×C₈₉	—	4	1	no	—
470	C₂²×C₈₉	—	4	1	no	—
471	C₂²×C₈₉	—	4	2	no	—
472	C₂²×C₈₉	—	4	2	no	—
473	C₂²×C₈₉	—	4	1	no	—
474	C₂²×C₈₉	—	4	1	no	—
475	C₂²×C₈₉	—	4	1	no	—
476	C₂²×C₈₉	—	4	1	no	—
477	C₂²×C₈₉	—	4	2	no	—
478	C₂²×C₈₉	—	4	2	no	—
479	C₂²×C₈₉	—	4	1	no	—
480	C₂²×C₈₉	—	4	1	no	—
481	C₂²×C₈₉	—	4	1	no	—
482	C₂²×C₈₉	—	4	2	no	—
483	C₂²×C₈₉	—	4	1	no	—
484	C₂²×C₈₉	—	4	1	no	—
485	C₂²×C₈₉	—	4	2	no	—
486	C₂²×C₈₉	—	4	1	no	—
487	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
488	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
489	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂²×C₈₉	#585	1	1	yes	characteristic
492	C₂²×C₈₉	#585	1	1	yes	characteristic
493	C₂²×C₈₉	#585	1	1	yes	characteristic
494	C₄×C₈₉	—	2	4	no	—
495	C₄×C₈₉	—	2	2	no	—
496	C₄×C₈₉	—	2	2	no	—
497	C₄×C₈₉	—	2	2	no	—
498	C₄×C₈₉	—	2	2	no	—
499	C₄×C₈₉	—	2	4	no	—
500	C₄×C₈₉	—	2	2	no	—
501	C₄×C₈₉	—	2	4	no	—
502	C₄×C₈₉	—	4	1	no	—
503	C₄×C₈₉	—	4	1	no	—
504	C₄×C₈₉	—	4	2	no	—
505	C₄×C₈₉	—	4	2	no	—
506	C₄×C₈₉	—	4	1	no	—
507	C₄×C₈₉	—	4	1	no	—
508	C₄×C₈₉	—	4	2	no	—
509	C₄×C₈₉	—	4	1	no	—
510	C₄×C₈₉	—	4	2	no	—
511	C₄×C₈₉	—	4	1	no	—
512	C₄×C₈₉	—	4	1	no	—
513	C₄×C₈₉	#532	1	4	yes	—
514	#35220	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
515	C₂×C₈₉	—	8	1	no	—
516	C₂×C₈₉	—	8	1	no	—
517	C₂×C₈₉	—	8	2	no	—
518	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
519	C₂×C₈₉	#3455	1	1	yes	characteristic
520	C₂×C₈₉	#3461	1	1	yes	characteristic
521	C₂×C₈₉	#3497	1	1	yes	characteristic
522	C₂×C₈₉	#3500	1	1	yes	characteristic
523	C₂×C₈₉	#3516	1	1	yes	characteristic
524	C₂×C₈₉	#3521	1	1	yes	characteristic
525	C₂×#542	C₂×C₈₉	1	1	yes	characteristic, complemented
526	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
527	#2861	C₂×C₈₉	1	2	yes	complemented
528	#2860	C₂×C₈₉	1	2	yes	complemented
529	#2664	C₂×C₈₉	1	2	yes	complemented
530	#2662	C₂×C₈₉	1	2	yes	complemented
531	#2560	C₂×C₈₉	1	2	yes	complemented
532	#2558	C₂×C₈₉	1	2	yes	complemented
533	#2556	C₂×C₈₉	1	2	yes	complemented
534	#2554	C₂×C₈₉	1	2	yes	complemented
535	#2550	C₂×C₈₉	1	1	yes	characteristic, complemented
536	#2545	C₂×C₈₉	1	1	yes	characteristic, complemented
537	#2540	C₂×C₈₉	1	1	yes	characteristic
538	#2536	C₂×C₈₉	1	1	yes	characteristic, complemented
539	#2492	C₂×C₈₉	1	1	yes	characteristic, complemented
540	#2490	C₂×C₈₉	1	1	yes	characteristic, complemented
541	#2429	C₂×C₈₉	1	1	yes	characteristic, complemented
542	#2426	C₂×C₈₉	1	1	yes	characteristic, complemented
543	#2324	C₂×C₈₉	1	1	yes	characteristic, complemented
544	#2323	C₂×C₈₉	1	1	yes	characteristic, complemented
545	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
546	#2293	C₂×C₈₉	1	1	yes	characteristic, complemented
547	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
548	C₈₉	#35220	1	1	yes	characteristic, direct product factor, Sylow
549	#542	—	2	8	no	—
550	#541	—	2	8	no	—
551	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
552	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
553	C₂×#126	C₂²×C₈₉	1	2	yes	—
554	C₂×#126	C₂²×C₈₉	1	2	yes	—
555	C₂×#126	C₂²×C₈₉	1	2	yes	—
556	C₂×#125	C₂²×C₈₉	1	2	yes	—
557	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
558	C₂×#125	C₂²×C₈₉	1	2	yes	—
559	C₂×#124	C₂²×C₈₉	1	2	yes	—
560	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
561	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
562	C₂×#123	C₂²×C₈₉	1	2	yes	—
563	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
564	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
565	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
566	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
567	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
568	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
569	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
570	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
571	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
572	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
573	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
575	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
576	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
577	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
578	#400	C₂²×C₈₉	1	2	yes	—
579	#399	C₂²×C₈₉	1	2	yes	—
580	#398	C₂²×C₈₉	1	2	yes	—
581	#398	C₂²×C₈₉	1	2	yes	—
582	#398	C₂²×C₈₉	1	2	yes	—
583	#397	C₂²×C₈₉	1	2	yes	—
584	#396	C₂²×C₈₉	1	2	yes	—
585	#396	C₂²×C₈₉	1	2	yes	—
586	#396	C₂²×C₈₉	1	2	yes	—
587	#396	C₂²×C₈₉	1	2	yes	—
588	#395	C₂²×C₈₉	1	2	yes	—
589	#394	C₂²×C₈₉	1	2	yes	—
590	#394	C₂²×C₈₉	1	2	yes	—
591	#394	C₂²×C₈₉	1	2	yes	—
592	#393	C₂²×C₈₉	1	2	yes	—
593	#392	C₂²×C₈₉	1	2	yes	—
594	#391	C₂²×C₈₉	1	2	yes	—
595	#391	C₂²×C₈₉	1	1	yes	characteristic
596	#391	C₂²×C₈₉	1	2	yes	—
597	#391	C₂²×C₈₉	1	1	yes	characteristic
598	#390	C₂²×C₈₉	1	2	yes	—
599	#390	C₂²×C₈₉	1	2	yes	—
600	#390	C₂²×C₈₉	1	1	yes	characteristic
601	#390	C₂²×C₈₉	1	2	yes	—
602	#390	C₂²×C₈₉	1	2	yes	—
603	#390	C₂²×C₈₉	1	2	yes	—
604	#390	C₂²×C₈₉	1	1	yes	characteristic
605	#390	C₂²×C₈₉	1	1	yes	characteristic
606	#390	C₂²×C₈₉	1	1	yes	characteristic
607	#389	C₂²×C₈₉	1	2	yes	—
608	#389	C₂²×C₈₉	1	1	yes	characteristic
609	#389	C₂²×C₈₉	1	1	yes	characteristic
610	#389	C₂²×C₈₉	1	2	yes	—
611	#389	C₂²×C₈₉	1	2	yes	—
612	#389	C₂²×C₈₉	1	1	yes	characteristic
613	#389	C₂²×C₈₉	1	1	yes	characteristic
614	#388	C₂²×C₈₉	1	1	yes	characteristic
615	#388	C₂²×C₈₉	1	2	yes	—
616	#388	C₂²×C₈₉	1	2	yes	—
617	#388	C₂²×C₈₉	1	2	yes	—
618	#388	C₂²×C₈₉	1	2	yes	—
619	#388	C₂²×C₈₉	1	2	yes	—
620	#388	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	1	yes	characteristic
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	2	yes	—
630	#388	C₂²×C₈₉	1	1	yes	characteristic
631	#387	C₂²×C₈₉	1	2	yes	—
632	#386	C₂²×C₈₉	1	2	yes	—
633	#385	C₂²×C₈₉	1	2	yes	—
634	#382	C₂²×C₈₉	1	1	yes	characteristic
635	#380	C₂²×C₈₉	1	1	yes	characteristic
636	#380	C₂²×C₈₉	1	1	yes	characteristic
637	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
638	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
639	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
640	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
641	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
642	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
643	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
645	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
646	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
647	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
648	C₄³	C₂²×C₈₉	1	2	yes	—
649	C₄³	C₂²×C₈₉	1	1	yes	characteristic
650	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
651	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
653	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
654	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
656	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
657	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
658	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
660	C₄⋊Q₈	—	2	4	no	—
661	C₄⋊Q₈	—	2	4	no	—
662	#126	—	2	8	no	—
663	#126	—	2	8	no	—
664	#126	—	2	8	no	—
665	#125	—	2	4	no	—
666	#125	—	2	8	no	—
667	#125	—	2	8	no	—
668	#124	—	2	4	no	—
669	#124	—	2	8	no	—
670	#124	—	2	4	no	—
671	#123	—	2	8	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	C₂²⋊Q₈	—	2	4	no	—
674	C₂²⋊Q₈	—	2	4	no	—
675	C₂²⋊Q₈	—	2	8	no	—
676	C₂²⋊Q₈	—	2	4	no	—
677	#121	—	2	4	no	—
678	#121	—	2	4	no	—
679	C₄×Q₈	—	2	4	no	—
680	C₄×Q₈	—	2	4	no	—
681	C₄×Q₈	—	2	4	no	—
682	C₄×Q₈	D₄×C₈₉	1	8	yes	complemented
683	C₄×D₄	—	2	4	no	—
684	C₄×D₄	—	2	4	no	—
685	#117	—	2	4	no	—
686	#117	—	2	4	no	—
687	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
688	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
689	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
695	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
701	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
705	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
707	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
715	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
716	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
720	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
721	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
726	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
727	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
741	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
744	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
746	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
747	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
751	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
753	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
754	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
756	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
757	#95	C₂³×C₈₉	1	2	yes	—
758	#95	C₂³×C₈₉	1	2	yes	—
759	#95	C₂³×C₈₉	1	1	yes	characteristic
760	#95	C₂³×C₈₉	1	1	yes	characteristic
761	#95	C₂³×C₈₉	1	2	yes	—
762	#95	C₂³×C₈₉	1	1	yes	characteristic
763	#95	C₂³×C₈₉	1	1	yes	characteristic
764	#95	C₂³×C₈₉	1	2	yes	—
765	#95	C₂³×C₈₉	1	2	yes	—
766	#95	C₂³×C₈₉	1	2	yes	—
767	#95	C₂³×C₈₉	1	2	yes	—
768	#95	C₂³×C₈₉	1	1	yes	characteristic
769	#95	C₂³×C₈₉	1	1	yes	characteristic
770	#95	C₂³×C₈₉	1	2	yes	—
771	#95	C₂³×C₈₉	1	2	yes	—
772	#95	C₂³×C₈₉	1	2	yes	—
773	#95	C₂³×C₈₉	1	2	yes	—
774	#95	C₂³×C₈₉	1	2	yes	—
775	#95	C₂³×C₈₉	1	2	yes	—
776	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
777	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
778	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
779	C₂×Q₈	—	2	2	no	—
780	C₂×Q₈	—	2	4	no	—
781	C₂×Q₈	—	2	2	no	—
782	C₂×Q₈	—	2	2	no	—
783	C₂×Q₈	—	2	2	no	—
784	C₂×Q₈	—	2	2	no	—
785	C₂×Q₈	—	4	2	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	4	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	2	no	—
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	4	1	no	—
795	C₂×D₄	—	4	1	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	2	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
810	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
811	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
823	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
824	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	4	no	—
836	C₄⋊C₄	—	2	4	no	—
837	C₄⋊C₄	—	2	4	no	—
838	C₄⋊C₄	—	2	4	no	—
839	C₄⋊C₄	—	2	4	no	—
840	C₄⋊C₄	—	2	4	no	—
841	C₄⋊C₄	—	2	4	no	—
842	C₄⋊C₄	—	2	4	no	—
843	C₄⋊C₄	—	2	4	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	4	no	—
846	C₄⋊C₄	—	2	4	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	4	1	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	1	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
854	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
855	C₄⋊C₄	#41×C₈₉	1	4	yes	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	2	4	no	—
862	C₂²⋊C₄	—	2	4	no	—
863	C₂²⋊C₄	—	2	4	no	—
864	C₂²⋊C₄	—	2	4	no	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	4	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	2	no	—
880	C₂²⋊C₄	—	4	1	no	—
881	C₂²⋊C₄	—	4	2	no	—
882	C₂²⋊C₄	—	4	1	no	—
883	C₄²	—	2	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	4	no	—
886	C₄²	—	2	4	no	—
887	C₄²	—	2	2	no	—
888	C₄²	—	2	4	no	—
889	C₄²	—	2	2	no	—
890	C₄²	—	4	1	no	—
891	C₄²	—	4	2	no	—
892	C₄²	—	4	1	no	—
893	C₄²	—	4	2	no	—
894	C₄²	—	4	1	no	—
895	C₄²	—	4	2	no	—
896	C₄²	C₂×D₄×C₈₉	1	4	yes	—
897	C₄²	C₂×D₄×C₈₉	1	8	yes	—
898	C₄²	#41×C₈₉	1	4	yes	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	1	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	1	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	2	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	1	no	—
910	C₂³	—	2	1	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	2	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
921	Q₈	—	2	8	no	—
922	Q₈	—	4	4	no	—
923	Q₈	—	8	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	4	no	—
926	D₄	—	8	4	no	—
927	D₄	—	8	4	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	1	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	2	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	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	4	4	no	—
978	C₂×C₄	—	4	4	no	—
979	C₂×C₄	—	8	4	no	—
980	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
981	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
982	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
983	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
984	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
985	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
986	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
987	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
988	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
989	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
990	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	2	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	1	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	1	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	1	no	—
1009	C₂²	—	4	1	no	—
1010	C₂²	—	4	2	no	—
1011	C₂²	—	4	1	no	—
1012	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
1013	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1014	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
1015	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
1016	C₂²	#585×C₈₉	1	1	yes	characteristic
1017	C₂²	#585×C₈₉	1	1	yes	characteristic
1018	C₂²	#585×C₈₉	1	1	yes	characteristic
1019	C₄	—	2	4	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	2	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	4	no	—
1027	C₄	—	4	1	no	—
1028	C₄	—	4	1	no	—
1029	C₄	—	4	2	no	—
1030	C₄	—	4	2	no	—
1031	C₄	—	4	1	no	—
1032	C₄	—	4	1	no	—
1033	C₄	—	4	2	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	#532×C₈₉	1	4	yes	—
1039	C₂	—	8	1	no	—
1040	C₂	—	8	1	no	—
1041	C₂	—	8	2	no	—
1042	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
1043	C₂	C₈₉×#3455	1	1	yes	characteristic
1044	C₂	C₈₉×#3461	1	1	yes	characteristic
1045	C₂	C₈₉×#3497	1	1	yes	characteristic
1046	C₂	C₈₉×#3500	1	1	yes	characteristic
1047	C₂	C₈₉×#3516	1	1	yes	characteristic
1048	C₂	C₈₉×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2540	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. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#2861	C₂	semidirect
4. C₈₉×#2860	C₂	semidirect
5. C₈₉×#2664	C₂	semidirect
6. C₈₉×#2662	C₂	semidirect
7. C₈₉×#2560	C₂	semidirect
8. C₈₉×#2558	C₂	semidirect
9. C₈₉×#2556	C₂	semidirect
10. C₈₉×#2554	C₂	semidirect
11. C₈₉×#2550	C₂	semidirect
12. C₈₉×#2545	C₂	semidirect
14. C₈₉×#2536	C₂	semidirect
15. C₈₉×#2492	C₂	semidirect
16. C₈₉×#2490	C₂	semidirect
17. C₈₉×#2429	C₂	semidirect
18. C₈₉×#2426	C₂	semidirect
19. C₈₉×#2324	C₂	semidirect
20. C₈₉×#2323	C₂	semidirect
21. C₄×#124×C₈₉	C₂	semidirect
22. C₈₉×#2293	C₂	semidirect
23. C₄²×Q₈×C₈₉	C₂	semidirect
157. C₄×Q₈×C₈₉	D₄	semidirect
514. #35220	C₈₉	direct (N × H)
525. C₂×#542	C₂×C₈₉	semidirect
526. C₂×#541	C₂×C₈₉	semidirect
527. #2861	C₂×C₈₉	semidirect
528. #2860	C₂×C₈₉	semidirect
529. #2664	C₂×C₈₉	semidirect
530. #2662	C₂×C₈₉	semidirect
531. #2560	C₂×C₈₉	semidirect
532. #2558	C₂×C₈₉	semidirect
533. #2556	C₂×C₈₉	semidirect
534. #2554	C₂×C₈₉	semidirect
535. #2550	C₂×C₈₉	semidirect
536. #2545	C₂×C₈₉	semidirect
538. #2536	C₂×C₈₉	semidirect
539. #2492	C₂×C₈₉	semidirect
540. #2490	C₂×C₈₉	semidirect
541. #2429	C₂×C₈₉	semidirect
542. #2426	C₂×C₈₉	semidirect
543. #2324	C₂×C₈₉	semidirect
544. #2323	C₂×C₈₉	semidirect
545. C₄×#124	C₂×C₈₉	semidirect
546. #2293	C₂×C₈₉	semidirect
547. C₄²×Q₈	C₂×C₈₉	semidirect
548. C₈₉	#35220	direct (N × H)
682. C₄×Q₈	D₄×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
C₂×#541×C₈₉	2
C₈₉×#2861	2
C₈₉×#2860	2
C₈₉×#2664	2
C₈₉×#2662	2
C₈₉×#2560	2
C₈₉×#2558	2
C₈₉×#2556	2
C₈₉×#2554	2
C₈₉×#2550	2
C₈₉×#2545	2
C₈₉×#2540	2
C₈₉×#2536	2
C₈₉×#2492	2
C₈₉×#2490	2
C₈₉×#2429	2
C₈₉×#2426	2
C₈₉×#2324	2
C₈₉×#2323	2
C₄×#124×C₈₉	2
C₈₉×#2293	2
C₄²×Q₈×C₈₉	2
#35220	89

Subgroups — C89×#35220 #36413068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35220 #36413068