Subgroups — C₈₉×#36553 #36414401

Order 22784.

1834 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2855	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2588	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2587	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2585	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2574	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2511	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2505	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2492	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2450	C₂	1	2	yes	maximal
13	C₈₉×#2440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2417	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2369	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2360	C₂	1	1	yes	maximal, characteristic, complemented
18	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
20	C₈₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#123×C₈₉	C₂	1	2	yes	maximal
22	C₄×#123×C₈₉	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#123×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
37	#400×C₈₉	C₂²	1	2	yes	—
38	#400×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	2	yes	—
40	#400×C₈₉	C₂²	1	2	yes	—
41	#398×C₈₉	C₂²	1	2	yes	—
42	#398×C₈₉	C₂²	1	2	yes	—
43	#398×C₈₉	C₂²	1	2	yes	—
44	#398×C₈₉	C₂²	1	2	yes	—
45	#396×C₈₉	C₂²	1	2	yes	—
46	#396×C₈₉	C₂²	1	2	yes	—
47	#395×C₈₉	C₂²	1	2	yes	—
48	#393×C₈₉	C₂²	1	2	yes	—
49	#391×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	1	yes	characteristic
53	#391×C₈₉	C₂²	1	1	yes	characteristic
54	#391×C₈₉	C₂²	1	1	yes	characteristic
55	#391×C₈₉	C₂²	1	1	yes	characteristic
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	1	yes	characteristic
62	#389×C₈₉	C₂²	1	1	yes	characteristic
63	#389×C₈₉	C₂²	1	1	yes	characteristic
64	#389×C₈₉	C₂²	1	1	yes	characteristic
65	#389×C₈₉	C₂²	1	1	yes	characteristic
66	#389×C₈₉	C₂²	1	1	yes	characteristic
67	#388×C₈₉	C₂²	1	1	yes	characteristic
68	#388×C₈₉	C₂²	1	2	yes	—
69	#388×C₈₉	C₂²	1	1	yes	characteristic
70	#388×C₈₉	C₂²	1	2	yes	—
71	#387×C₈₉	C₂²	1	1	yes	characteristic
72	#387×C₈₉	C₂²	1	2	yes	—
73	#387×C₈₉	C₂²	1	1	yes	characteristic
74	#387×C₈₉	C₂²	1	2	yes	—
75	#387×C₈₉	C₂²	1	2	yes	—
76	#387×C₈₉	C₂²	1	2	yes	—
77	#387×C₈₉	C₂²	1	2	yes	—
78	#387×C₈₉	C₂²	1	2	yes	—
79	#387×C₈₉	C₂²	1	2	yes	—
80	#387×C₈₉	C₂²	1	2	yes	—
81	#387×C₈₉	C₂²	1	2	yes	—
82	#387×C₈₉	C₂²	1	2	yes	—
83	#387×C₈₉	C₂²	1	2	yes	—
84	#387×C₈₉	C₂²	1	2	yes	—
85	#386×C₈₉	C₂²	1	2	yes	—
86	#386×C₈₉	C₂²	1	1	yes	characteristic
87	#385×C₈₉	C₂²	1	2	yes	—
88	#385×C₈₉	C₂²	1	1	yes	characteristic
89	#385×C₈₉	C₂²	1	2	yes	—
90	#385×C₈₉	C₂²	1	2	yes	—
91	#385×C₈₉	C₂²	1	2	yes	—
92	#385×C₈₉	C₂²	1	2	yes	—
93	#385×C₈₉	C₂²	1	2	yes	—
94	#384×C₈₉	C₂²	1	1	yes	characteristic
95	#384×C₈₉	C₂²	1	1	yes	characteristic
96	#382×C₈₉	C₂²	1	2	yes	—
97	#381×C₈₉	C₂²	1	2	yes	—
98	#381×C₈₉	C₂²	1	1	yes	characteristic
99	#380×C₈₉	C₂²	1	2	yes	—
100	#380×C₈₉	C₂²	1	1	yes	characteristic
101	#380×C₈₉	C₂²	1	2	yes	—
102	#380×C₈₉	C₂²	1	1	yes	characteristic
103	#380×C₈₉	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
105	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×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	1	yes	characteristic
115	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
122	C₂×#95×C₈₉	C₂²	1	2	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
125	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
128	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
129	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₈₉	—	2	4	no	—
134	#123×C₈₉	Q₈	1	8	yes	complemented
135	C₂²⋊Q₈×C₈₉	—	2	4	no	—
136	C₂²⋊Q₈×C₈₉	—	2	4	no	—
137	C₂²⋊Q₈×C₈₉	—	4	4	no	—
138	C₄×Q₈×C₈₉	—	2	4	no	—
139	C₄×D₄×C₈₉	—	2	4	no	—
140	C₄×D₄×C₈₉	—	4	4	no	—
141	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
142	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
143	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	—	2	4	no	—
187	C₂×C₄²×C₈₉	—	4	4	no	—
188	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
190	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
197	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
198	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
200	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
202	#95×C₈₉	C₂³	1	2	yes	—
203	#95×C₈₉	C₂³	1	2	yes	—
204	#95×C₈₉	C₂³	1	2	yes	—
205	#95×C₈₉	C₂³	1	2	yes	—
206	#95×C₈₉	C₂³	1	1	yes	characteristic
207	#95×C₈₉	C₂³	1	2	yes	—
208	#95×C₈₉	C₂³	1	2	yes	—
209	#95×C₈₉	C₂³	1	1	yes	characteristic
210	#95×C₈₉	C₂³	1	1	yes	characteristic
211	#95×C₈₉	C₂³	1	1	yes	characteristic
212	#95×C₈₉	C₂³	1	2	yes	—
213	#95×C₈₉	C₂³	1	2	yes	—
214	#95×C₈₉	C₂³	1	1	yes	characteristic
215	#95×C₈₉	C₂³	1	2	yes	—
216	#95×C₈₉	C₂³	1	1	yes	characteristic
217	#95×C₈₉	C₂³	1	2	yes	—
218	#95×C₈₉	C₂³	1	2	yes	—
219	#95×C₈₉	C₂³	1	1	yes	characteristic
220	#95×C₈₉	C₂³	1	2	yes	—
221	#95×C₈₉	C₂³	1	2	yes	—
222	#95×C₈₉	C₂³	1	1	yes	characteristic
223	#95×C₈₉	C₂³	1	2	yes	—
224	#95×C₈₉	C₂³	1	1	yes	characteristic
225	#95×C₈₉	C₂³	1	2	yes	—
226	#95×C₈₉	C₂³	1	2	yes	—
227	#95×C₈₉	C₂³	1	1	yes	characteristic
228	#95×C₈₉	C₂³	1	2	yes	—
229	#95×C₈₉	C₂³	1	2	yes	—
230	#95×C₈₉	C₂³	1	2	yes	—
231	#95×C₈₉	C₂³	1	2	yes	—
232	#95×C₈₉	C₂³	1	2	yes	—
233	#95×C₈₉	C₂³	1	2	yes	—
234	#95×C₈₉	C₂³	1	2	yes	—
235	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₈₉	—	2	2	no	—
238	C₂×Q₈×C₈₉	—	2	2	no	—
239	C₂×Q₈×C₈₉	—	2	2	no	—
240	C₂×Q₈×C₈₉	—	2	4	no	—
241	C₂×Q₈×C₈₉	—	4	2	no	—
242	C₂×Q₈×C₈₉	—	4	2	no	—
243	C₂×D₄×C₈₉	—	2	2	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₈₉	—	2	2	no	—
247	C₂²×C₄×C₈₉	—	2	2	no	—
248	C₂²×C₄×C₈₉	—	2	2	no	—
249	C₂²×C₄×C₈₉	—	2	2	no	—
250	C₂²×C₄×C₈₉	—	2	2	no	—
251	C₂²×C₄×C₈₉	—	2	4	no	—
252	C₂²×C₄×C₈₉	—	2	4	no	—
253	C₂²×C₄×C₈₉	—	2	4	no	—
254	C₂²×C₄×C₈₉	—	2	4	no	—
255	C₂²×C₄×C₈₉	—	2	2	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	4	no	—
259	C₂²×C₄×C₈₉	—	4	2	no	—
260	C₂²×C₄×C₈₉	—	4	2	no	—
261	C₂²×C₄×C₈₉	—	4	1	no	—
262	C₂²×C₄×C₈₉	—	4	1	no	—
263	C₂²×C₄×C₈₉	—	4	2	no	—
264	C₂²×C₄×C₈₉	—	4	2	no	—
265	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
266	C₂²×C₄×C₈₉	#41	1	4	yes	—
267	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
288	C₄⋊C₄×C₈₉	—	2	4	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	4	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	4	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	4	no	—
298	C₄⋊C₄×C₈₉	—	2	4	no	—
299	C₄⋊C₄×C₈₉	—	2	4	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	4	1	no	—
302	C₄⋊C₄×C₈₉	—	4	1	no	—
303	C₄⋊C₄×C₈₉	—	4	2	no	—
304	C₄⋊C₄×C₈₉	—	4	2	no	—
305	C₄⋊C₄×C₈₉	—	4	2	no	—
306	C₄⋊C₄×C₈₉	—	4	2	no	—
307	C₄⋊C₄×C₈₉	—	4	2	no	—
308	C₄⋊C₄×C₈₉	—	4	2	no	—
309	C₄⋊C₄×C₈₉	—	4	2	no	—
310	C₄⋊C₄×C₈₉	—	4	2	no	—
311	C₄⋊C₄×C₈₉	—	4	2	no	—
312	C₄⋊C₄×C₈₉	—	4	2	no	—
313	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
314	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
315	C₄⋊C₄×C₈₉	#41	1	4	yes	—
316	C₄⋊C₄×C₈₉	#41	1	4	yes	—
317	C₂²⋊C₄×C₈₉	—	2	2	no	—
318	C₂²⋊C₄×C₈₉	—	2	4	no	—
319	C₂²⋊C₄×C₈₉	—	2	4	no	—
320	C₂²⋊C₄×C₈₉	—	2	2	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	—	2	4	no	—
323	C₂²⋊C₄×C₈₉	—	4	2	no	—
324	C₂²⋊C₄×C₈₉	—	4	1	no	—
325	C₂²⋊C₄×C₈₉	—	4	1	no	—
326	C₂²⋊C₄×C₈₉	—	4	2	no	—
327	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
328	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
329	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
330	C₄²×C₈₉	—	2	2	no	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	2	2	no	—
333	C₄²×C₈₉	—	2	2	no	—
334	C₄²×C₈₉	—	2	2	no	—
335	C₄²×C₈₉	—	2	2	no	—
336	C₄²×C₈₉	—	2	4	no	—
337	C₄²×C₈₉	—	2	2	no	—
338	C₄²×C₈₉	—	4	2	no	—
339	C₄²×C₈₉	—	4	2	no	—
340	C₄²×C₈₉	—	4	2	no	—
341	C₄²×C₈₉	—	4	2	no	—
342	C₄²×C₈₉	—	4	2	no	—
343	C₄²×C₈₉	—	4	2	no	—
344	C₂³×C₈₉	—	2	1	no	—
345	C₂³×C₈₉	—	2	1	no	—
346	C₂³×C₈₉	—	2	1	no	—
347	C₂³×C₈₉	—	2	1	no	—
348	C₂³×C₈₉	—	2	1	no	—
349	C₂³×C₈₉	—	2	1	no	—
350	C₂³×C₈₉	—	2	1	no	—
351	C₂³×C₈₉	—	2	1	no	—
352	C₂³×C₈₉	—	2	1	no	—
353	C₂³×C₈₉	—	2	1	no	—
354	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
355	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
356	C₂³×C₈₉	C₂×#41	1	2	yes	—
357	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
358	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
359	Q₈×C₈₉	—	4	4	no	—
360	Q₈×C₈₉	—	8	4	no	—
361	D₄×C₈₉	—	2	8	no	—
362	C₂×C₄×C₈₉	—	2	8	no	—
363	C₂×C₄×C₈₉	—	2	1	no	—
364	C₂×C₄×C₈₉	—	2	1	no	—
365	C₂×C₄×C₈₉	—	2	1	no	—
366	C₂×C₄×C₈₉	—	2	1	no	—
367	C₂×C₄×C₈₉	—	2	1	no	—
368	C₂×C₄×C₈₉	—	2	1	no	—
369	C₂×C₄×C₈₉	—	2	1	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	1	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	8	no	—
380	C₂×C₄×C₈₉	—	2	1	no	—
381	C₂×C₄×C₈₉	—	2	1	no	—
382	C₂×C₄×C₈₉	—	2	1	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	1	no	—
386	C₂×C₄×C₈₉	—	2	2	no	—
387	C₂×C₄×C₈₉	—	2	1	no	—
388	C₂×C₄×C₈₉	—	2	2	no	—
389	C₂×C₄×C₈₉	—	2	2	no	—
390	C₂×C₄×C₈₉	—	2	1	no	—
391	C₂×C₄×C₈₉	—	2	1	no	—
392	C₂×C₄×C₈₉	—	2	2	no	—
393	C₂×C₄×C₈₉	—	2	2	no	—
394	C₂×C₄×C₈₉	—	2	2	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	2	no	—
397	C₂×C₄×C₈₉	—	2	2	no	—
398	C₂×C₄×C₈₉	—	2	2	no	—
399	C₂×C₄×C₈₉	—	2	1	no	—
400	C₂×C₄×C₈₉	—	2	2	no	—
401	C₂×C₄×C₈₉	—	2	1	no	—
402	C₂×C₄×C₈₉	—	2	2	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	1	no	—
405	C₂×C₄×C₈₉	—	2	1	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	2	2	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	2	no	—
416	C₂×C₄×C₈₉	—	4	8	no	—
417	C₂×C₄×C₈₉	—	4	8	no	—
418	C₂×C₄×C₈₉	—	4	4	no	—
419	C₂×C₄×C₈₉	—	4	4	no	—
420	C₂×C₄×C₈₉	—	8	4	no	—
421	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
422	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
423	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
424	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
425	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
426	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
427	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
428	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
429	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
430	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
431	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
432	C₂²×C₈₉	—	2	2	no	—
433	C₂²×C₈₉	—	2	2	no	—
434	C₂²×C₈₉	—	2	2	no	—
435	C₂²×C₈₉	—	2	2	no	—
436	C₂²×C₈₉	—	2	2	no	—
437	C₂²×C₈₉	—	2	2	no	—
438	C₂²×C₈₉	—	2	2	no	—
439	C₂²×C₈₉	—	2	2	no	—
440	C₂²×C₈₉	—	2	2	no	—
441	C₂²×C₈₉	—	4	1	no	—
442	C₂²×C₈₉	—	4	1	no	—
443	C₂²×C₈₉	—	4	1	no	—
444	C₂²×C₈₉	—	4	1	no	—
445	C₂²×C₈₉	#554	1	4	yes	—
446	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
447	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₈₉	#585	1	1	yes	characteristic
452	C₂²×C₈₉	#585	1	1	yes	characteristic
453	C₄×C₈₉	—	2	2	no	—
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	2	2	no	—
456	C₄×C₈₉	—	2	2	no	—
457	C₄×C₈₉	—	2	2	no	—
458	C₄×C₈₉	—	2	2	no	—
459	C₄×C₈₉	—	2	4	no	—
460	C₄×C₈₉	—	2	4	no	—
461	C₄×C₈₉	—	4	1	no	—
462	C₄×C₈₉	—	4	2	no	—
463	C₄×C₈₉	—	4	1	no	—
464	C₄×C₈₉	—	4	2	no	—
465	C₄×C₈₉	—	4	1	no	—
466	C₄×C₈₉	—	4	1	no	—
467	C₄×C₈₉	—	4	1	no	—
468	C₄×C₈₉	—	4	2	no	—
469	C₄×C₈₉	—	4	2	no	—
470	C₄×C₈₉	—	4	2	no	—
471	C₄×C₈₉	—	4	2	no	—
472	C₄×C₈₉	—	4	1	no	—
473	C₄×C₈₉	#529	1	4	yes	—
474	#36553	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
475	C₂×C₈₉	—	2	4	no	—
476	C₂×C₈₉	—	4	2	no	—
477	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
478	C₂×C₈₉	C₂×#554	1	1	yes	characteristic
479	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
480	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
481	C₂×C₈₉	#3493	1	1	yes	characteristic
482	C₂×C₈₉	#3513	1	1	yes	characteristic
483	C₂×C₈₉	#3513	1	1	yes	characteristic
484	#2855	C₂×C₈₉	1	1	yes	characteristic, complemented
485	#2855	C₂×C₈₉	1	2	yes	complemented
486	#2588	C₂×C₈₉	1	2	yes	complemented
487	#2587	C₂×C₈₉	1	2	yes	complemented
488	#2585	C₂×C₈₉	1	2	yes	complemented
489	#2574	C₂×C₈₉	1	2	yes	complemented
490	#2511	C₂×C₈₉	1	1	yes	characteristic, complemented
491	#2507	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#2505	C₂×C₈₉	1	2	yes	complemented
493	#2497	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#2492	C₂×C₈₉	1	1	yes	characteristic, complemented
495	#2450	C₂×C₈₉	1	2	yes	—
496	#2440	C₂×C₈₉	1	1	yes	characteristic, complemented
497	#2417	C₂×C₈₉	1	1	yes	characteristic
498	#2369	C₂×C₈₉	1	1	yes	characteristic, complemented
499	#2360	C₂×C₈₉	1	1	yes	characteristic, complemented
500	#2360	C₂×C₈₉	1	1	yes	characteristic, complemented
501	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
502	D₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
503	#2345	C₂×C₈₉	1	1	yes	characteristic, complemented
504	C₄×#123	C₂×C₈₉	1	1	yes	characteristic
505	C₄×#123	C₂×C₈₉	1	2	yes	—
506	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
507	C₈₉	#36553	1	1	yes	characteristic, direct product factor, Sylow
508	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
509	C₂×#123	C₂²×C₈₉	1	1	yes	characteristic
510	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
511	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
513	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
514	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
516	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
517	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
518	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
519	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
520	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
521	#400	C₂²×C₈₉	1	2	yes	—
522	#400	C₂²×C₈₉	1	2	yes	—
523	#400	C₂²×C₈₉	1	2	yes	—
524	#400	C₂²×C₈₉	1	2	yes	—
525	#398	C₂²×C₈₉	1	2	yes	—
526	#398	C₂²×C₈₉	1	2	yes	—
527	#398	C₂²×C₈₉	1	2	yes	—
528	#398	C₂²×C₈₉	1	2	yes	—
529	#396	C₂²×C₈₉	1	2	yes	—
530	#396	C₂²×C₈₉	1	2	yes	—
531	#395	C₂²×C₈₉	1	2	yes	—
532	#393	C₂²×C₈₉	1	2	yes	—
533	#391	C₂²×C₈₉	1	2	yes	—
534	#391	C₂²×C₈₉	1	2	yes	—
535	#391	C₂²×C₈₉	1	2	yes	—
536	#391	C₂²×C₈₉	1	1	yes	characteristic
537	#391	C₂²×C₈₉	1	1	yes	characteristic
538	#391	C₂²×C₈₉	1	1	yes	characteristic
539	#391	C₂²×C₈₉	1	1	yes	characteristic
540	#389	C₂²×C₈₉	1	2	yes	—
541	#389	C₂²×C₈₉	1	2	yes	—
542	#389	C₂²×C₈₉	1	2	yes	—
543	#389	C₂²×C₈₉	1	2	yes	—
544	#389	C₂²×C₈₉	1	2	yes	—
545	#389	C₂²×C₈₉	1	1	yes	characteristic
546	#389	C₂²×C₈₉	1	1	yes	characteristic
547	#389	C₂²×C₈₉	1	1	yes	characteristic
548	#389	C₂²×C₈₉	1	1	yes	characteristic
549	#389	C₂²×C₈₉	1	1	yes	characteristic
550	#389	C₂²×C₈₉	1	1	yes	characteristic
551	#388	C₂²×C₈₉	1	1	yes	characteristic
552	#388	C₂²×C₈₉	1	2	yes	—
553	#388	C₂²×C₈₉	1	1	yes	characteristic
554	#388	C₂²×C₈₉	1	2	yes	—
555	#387	C₂²×C₈₉	1	2	yes	—
556	#387	C₂²×C₈₉	1	2	yes	—
557	#387	C₂²×C₈₉	1	2	yes	—
558	#387	C₂²×C₈₉	1	1	yes	characteristic
559	#387	C₂²×C₈₉	1	2	yes	—
560	#387	C₂²×C₈₉	1	2	yes	—
561	#387	C₂²×C₈₉	1	2	yes	—
562	#387	C₂²×C₈₉	1	2	yes	—
563	#387	C₂²×C₈₉	1	2	yes	—
564	#387	C₂²×C₈₉	1	2	yes	—
565	#387	C₂²×C₈₉	1	1	yes	characteristic
566	#387	C₂²×C₈₉	1	2	yes	—
567	#387	C₂²×C₈₉	1	2	yes	—
568	#387	C₂²×C₈₉	1	2	yes	—
569	#386	C₂²×C₈₉	1	2	yes	—
570	#386	C₂²×C₈₉	1	1	yes	characteristic
571	#385	C₂²×C₈₉	1	2	yes	—
572	#385	C₂²×C₈₉	1	2	yes	—
573	#385	C₂²×C₈₉	1	2	yes	—
574	#385	C₂²×C₈₉	1	2	yes	—
575	#385	C₂²×C₈₉	1	2	yes	—
576	#385	C₂²×C₈₉	1	2	yes	—
577	#385	C₂²×C₈₉	1	1	yes	characteristic
578	#384	C₂²×C₈₉	1	1	yes	characteristic
579	#384	C₂²×C₈₉	1	1	yes	characteristic
580	#382	C₂²×C₈₉	1	2	yes	—
581	#381	C₂²×C₈₉	1	2	yes	—
582	#381	C₂²×C₈₉	1	1	yes	characteristic
583	#380	C₂²×C₈₉	1	2	yes	—
584	#380	C₂²×C₈₉	1	1	yes	characteristic
585	#380	C₂²×C₈₉	1	2	yes	—
586	#380	C₂²×C₈₉	1	1	yes	characteristic
587	#380	C₂²×C₈₉	1	1	yes	characteristic
588	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
589	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
590	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
591	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
597	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
598	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
601	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
602	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
603	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
604	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
605	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
606	C₂×#95	C₂²×C₈₉	1	2	yes	—
607	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
609	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
610	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
612	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
613	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
615	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
616	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
617	C₄⋊Q₈	—	2	4	no	—
618	#123	Q₈×C₈₉	1	8	yes	complemented
619	C₂²⋊Q₈	—	2	4	no	—
620	C₂²⋊Q₈	—	2	4	no	—
621	C₂²⋊Q₈	—	4	4	no	—
622	C₄×Q₈	—	2	4	no	—
623	C₄×D₄	—	2	4	no	—
624	C₄×D₄	—	4	4	no	—
625	C₂×C₄⋊C₄	—	2	4	no	—
626	C₂×C₄⋊C₄	—	2	4	no	—
627	C₂×C₄⋊C₄	—	2	4	no	—
628	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
660	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
661	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
667	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
668	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
670	C₂×C₄²	—	2	4	no	—
671	C₂×C₄²	—	4	4	no	—
672	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
673	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
674	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
679	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
681	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
682	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
683	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
684	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
685	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
686	#95	C₂³×C₈₉	1	2	yes	—
687	#95	C₂³×C₈₉	1	2	yes	—
688	#95	C₂³×C₈₉	1	2	yes	—
689	#95	C₂³×C₈₉	1	2	yes	—
690	#95	C₂³×C₈₉	1	1	yes	characteristic
691	#95	C₂³×C₈₉	1	2	yes	—
692	#95	C₂³×C₈₉	1	2	yes	—
693	#95	C₂³×C₈₉	1	1	yes	characteristic
694	#95	C₂³×C₈₉	1	1	yes	characteristic
695	#95	C₂³×C₈₉	1	1	yes	characteristic
696	#95	C₂³×C₈₉	1	2	yes	—
697	#95	C₂³×C₈₉	1	2	yes	—
698	#95	C₂³×C₈₉	1	1	yes	characteristic
699	#95	C₂³×C₈₉	1	2	yes	—
700	#95	C₂³×C₈₉	1	1	yes	characteristic
701	#95	C₂³×C₈₉	1	2	yes	—
702	#95	C₂³×C₈₉	1	2	yes	—
703	#95	C₂³×C₈₉	1	1	yes	characteristic
704	#95	C₂³×C₈₉	1	2	yes	—
705	#95	C₂³×C₈₉	1	2	yes	—
706	#95	C₂³×C₈₉	1	1	yes	characteristic
707	#95	C₂³×C₈₉	1	2	yes	—
708	#95	C₂³×C₈₉	1	1	yes	characteristic
709	#95	C₂³×C₈₉	1	2	yes	—
710	#95	C₂³×C₈₉	1	2	yes	—
711	#95	C₂³×C₈₉	1	1	yes	characteristic
712	#95	C₂³×C₈₉	1	2	yes	—
713	#95	C₂³×C₈₉	1	2	yes	—
714	#95	C₂³×C₈₉	1	2	yes	—
715	#95	C₂³×C₈₉	1	2	yes	—
716	#95	C₂³×C₈₉	1	2	yes	—
717	#95	C₂³×C₈₉	1	2	yes	—
718	#95	C₂³×C₈₉	1	2	yes	—
719	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
720	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
721	C₂×Q₈	—	2	2	no	—
722	C₂×Q₈	—	2	2	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	4	no	—
725	C₂×Q₈	—	4	2	no	—
726	C₂×Q₈	—	4	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	4	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	4	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	1	no	—
746	C₂²×C₄	—	4	1	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
750	C₂²×C₄	#41×C₈₉	1	4	yes	—
751	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	—	4	1	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	—	4	2	no	—
797	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
798	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
799	C₄⋊C₄	#41×C₈₉	1	4	yes	—
800	C₄⋊C₄	#41×C₈₉	1	4	yes	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	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	—	4	1	no	—
810	C₂²⋊C₄	—	4	1	no	—
811	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
812	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
813	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	4	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	2	no	—
825	C₄²	—	4	2	no	—
826	C₄²	—	4	2	no	—
827	C₄²	—	4	2	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
839	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
840	C₂³	C₂×#41×C₈₉	1	2	yes	—
841	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
842	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
843	Q₈	—	4	4	no	—
844	Q₈	—	8	4	no	—
845	D₄	—	2	8	no	—
846	C₂×C₄	—	2	8	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	8	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	8	no	—
901	C₂×C₄	—	4	8	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	8	4	no	—
905	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
906	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
907	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
908	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
909	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
910	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
911	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
912	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
913	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
914	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
915	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	2	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	2	2	no	—
925	C₂²	—	4	1	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	4	1	no	—
928	C₂²	—	4	1	no	—
929	C₂²	#554×C₈₉	1	4	yes	—
930	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
931	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
932	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
933	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
934	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
935	C₂²	#585×C₈₉	1	1	yes	characteristic
936	C₂²	#585×C₈₉	1	1	yes	characteristic
937	C₄	—	2	2	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	4	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	2	no	—
956	C₄	—	4	1	no	—
957	C₄	#529×C₈₉	1	4	yes	—
958	C₂	—	2	4	no	—
959	C₂	—	4	2	no	—
960	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
961	C₂	C₂×#554×C₈₉	1	1	yes	characteristic
962	C₂	Q₈×#41×C₈₉	1	1	yes	characteristic
963	C₂	Q₈×#41×C₈₉	1	1	yes	characteristic
964	C₂	C₈₉×#3493	1	1	yes	characteristic
965	C₂	C₈₉×#3513	1	1	yes	characteristic
966	C₂	C₈₉×#3513	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
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. C₈₉×#2855	C₂	semidirect
2. C₈₉×#2855	C₂	semidirect
3. C₈₉×#2588	C₂	semidirect
4. C₈₉×#2587	C₂	semidirect
5. C₈₉×#2585	C₂	semidirect
6. C₈₉×#2574	C₂	semidirect
7. C₈₉×#2511	C₂	semidirect
8. C₈₉×#2507	C₂	semidirect
9. C₈₉×#2505	C₂	semidirect
10. C₈₉×#2497	C₂	semidirect
11. C₈₉×#2492	C₂	semidirect
13. C₈₉×#2440	C₂	semidirect
15. C₈₉×#2369	C₂	semidirect
16. C₈₉×#2360	C₂	semidirect
17. C₈₉×#2360	C₂	semidirect
18. C₈₉×#2355	C₂	semidirect
20. C₈₉×#2345	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
134. #123×C₈₉	Q₈	semidirect
474. #36553	C₈₉	direct (N × H)
484. #2855	C₂×C₈₉	semidirect
485. #2855	C₂×C₈₉	semidirect
486. #2588	C₂×C₈₉	semidirect
487. #2587	C₂×C₈₉	semidirect
488. #2585	C₂×C₈₉	semidirect
489. #2574	C₂×C₈₉	semidirect
490. #2511	C₂×C₈₉	semidirect
491. #2507	C₂×C₈₉	semidirect
492. #2505	C₂×C₈₉	semidirect
493. #2497	C₂×C₈₉	semidirect
494. #2492	C₂×C₈₉	semidirect
496. #2440	C₂×C₈₉	semidirect
498. #2369	C₂×C₈₉	semidirect
499. #2360	C₂×C₈₉	semidirect
500. #2360	C₂×C₈₉	semidirect
501. #2355	C₂×C₈₉	semidirect
503. #2345	C₂×C₈₉	semidirect
506. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
507. C₈₉	#36553	direct (N × H)
618. #123	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2855	2
C₈₉×#2588	2
C₈₉×#2587	2
C₈₉×#2585	2
C₈₉×#2574	2
C₈₉×#2511	2
C₈₉×#2507	2
C₈₉×#2505	2
C₈₉×#2497	2
C₈₉×#2492	2
C₈₉×#2450	2
C₈₉×#2440	2
C₈₉×#2417	2
C₈₉×#2369	2
C₈₉×#2360	2
C₈₉×#2355	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#2345	2
C₄×#123×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#36553	89

Subgroups — C89×#36553 #36414401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36553 #36414401