Subgroups — C₈₉×#11189 #36389037

Order 22784.

1210 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#340×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#340×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#336×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
15	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
16	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#102×C₈₉	—	2	2	no	—
18	C₂×#102×C₈₉	—	2	2	no	—
19	C₂×#102×C₈₉	—	2	2	no	—
20	C₂×#102×C₈₉	—	2	2	no	—
21	C₂×#102×C₈₉	—	2	2	no	—
22	C₂×#102×C₈₉	C₄	1	4	yes	complemented
23	#390×C₈₉	—	2	2	no	—
24	#390×C₈₉	—	2	2	no	—
25	C₂×#95×C₈₉	—	2	1	no	—
26	C₂×#95×C₈₉	—	2	1	no	—
27	#340×C₈₉	—	2	2	no	—
28	#340×C₈₉	—	2	2	no	—
29	#336×C₈₉	—	2	2	no	—
30	C₂⁵×C₈₉	—	2	1	no	—
31	C₂²×D₄×C₈₉	—	2	1	no	—
32	C₂²×D₄×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	—	2	1	no	—
34	C₂²×D₄×C₈₉	—	2	1	no	—
35	C₂²×D₄×C₈₉	—	2	1	no	—
36	C₂²×D₄×C₈₉	—	2	1	no	—
37	C₂²×D₄×C₈₉	—	2	1	no	—
38	C₂²×D₄×C₈₉	—	2	1	no	—
39	C₂²×D₄×C₈₉	—	2	1	no	—
40	C₂²×D₄×C₈₉	—	2	1	no	—
41	C₂²×D₄×C₈₉	—	2	1	no	—
42	C₂²×D₄×C₈₉	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₈₉	D₄	1	2	yes	—
44	C₂²×D₄×C₈₉	D₄	1	2	yes	—
45	C₂³×C₄×C₈₉	—	2	1	no	—
46	C₂³×C₄×C₈₉	—	2	1	no	—
47	C₂³×C₄×C₈₉	—	2	1	no	—
48	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₈₉	—	2	1	no	—
52	C₂²×C₈×C₈₉	—	2	1	no	—
53	C₂²×C₈×C₈₉	—	2	1	no	—
54	C₂²×C₈×C₈₉	—	2	1	no	—
55	C₂²×C₈×C₈₉	—	2	1	no	—
56	C₂²×C₈×C₈₉	—	2	1	no	—
57	C₂²×C₈×C₈₉	—	2	1	no	—
58	C₂²×C₈×C₈₉	—	2	1	no	—
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂²×C₈×C₈₉	—	2	1	no	—
63	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₈₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
83	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
86	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
87	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
88	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
89	C₂×C₄²×C₈₉	—	2	1	no	—
90	C₂×C₄²×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	—	2	1	no	—
94	C₂×C₄²×C₈₉	—	2	1	no	—
95	#102×C₈₉	—	2	8	no	—
96	#102×C₈₉	—	2	8	no	—
97	#95×C₈₉	—	4	2	no	—
98	#95×C₈₉	—	4	2	no	—
99	C₂⁴×C₈₉	—	2	2	no	—
100	C₂⁴×C₈₉	—	2	2	no	—
101	C₂⁴×C₈₉	—	2	2	no	—
102	C₂⁴×C₈₉	—	4	1	no	—
103	C₂⁴×C₈₉	—	4	1	no	—
104	C₂⁴×C₈₉	—	4	1	no	—
105	C₂⁴×C₈₉	—	4	1	no	—
106	C₂⁴×C₈₉	—	4	1	no	—
107	C₂⁴×C₈₉	—	4	1	no	—
108	C₂⁴×C₈₉	—	4	1	no	—
109	C₂⁴×C₈₉	—	4	1	no	—
110	C₂⁴×C₈₉	—	4	1	no	—
111	C₂⁴×C₈₉	—	4	1	no	—
112	C₂⁴×C₈₉	—	4	1	no	—
113	C₂⁴×C₈₉	—	4	1	no	—
114	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₈₉	—	2	2	no	—
116	C₂×D₄×C₈₉	—	2	2	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	2	no	—
121	C₂×D₄×C₈₉	—	2	2	no	—
122	C₂×D₄×C₈₉	—	2	2	no	—
123	C₂×D₄×C₈₉	—	2	2	no	—
124	C₂×D₄×C₈₉	—	2	2	no	—
125	C₂×D₄×C₈₉	—	2	2	no	—
126	C₂×D₄×C₈₉	—	2	2	no	—
127	C₂×D₄×C₈₉	—	2	2	no	—
128	C₂×D₄×C₈₉	—	2	2	no	—
129	C₂×D₄×C₈₉	—	2	2	no	—
130	C₂×D₄×C₈₉	—	4	1	no	—
131	C₂×D₄×C₈₉	—	4	1	no	—
132	C₂×D₄×C₈₉	—	4	1	no	—
133	C₂×D₄×C₈₉	—	4	1	no	—
134	C₂×D₄×C₈₉	—	4	1	no	—
135	C₂×D₄×C₈₉	—	4	1	no	—
136	C₂×D₄×C₈₉	—	4	1	no	—
137	C₂×D₄×C₈₉	—	4	1	no	—
138	C₂×D₄×C₈₉	—	4	1	no	—
139	C₂×D₄×C₈₉	—	4	1	no	—
140	C₂×D₄×C₈₉	—	4	1	no	—
141	C₂×D₄×C₈₉	—	4	1	no	—
142	C₂×D₄×C₈₉	C₂²⋊C₄	1	4	yes	—
143	C₂²×C₄×C₈₉	—	2	1	no	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	1	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	1	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	1	no	—
155	C₂²×C₄×C₈₉	—	2	2	no	—
156	C₂²×C₄×C₈₉	—	2	2	no	—
157	C₂²×C₄×C₈₉	—	2	2	no	—
158	C₂²×C₄×C₈₉	—	4	1	no	—
159	C₂²×C₄×C₈₉	—	4	1	no	—
160	C₂²×C₄×C₈₉	—	4	1	no	—
161	C₂²×C₄×C₈₉	—	4	1	no	—
162	C₂²×C₄×C₈₉	—	4	1	no	—
163	C₂²×C₄×C₈₉	—	4	1	no	—
164	C₂²×C₄×C₈₉	—	4	1	no	—
165	C₂²×C₄×C₈₉	—	4	1	no	—
166	C₂²×C₄×C₈₉	—	4	1	no	—
167	C₂²×C₄×C₈₉	—	4	1	no	—
168	C₂²×C₄×C₈₉	—	4	1	no	—
169	C₂²×C₄×C₈₉	—	4	1	no	—
170	C₂²×C₄×C₈₉	—	4	1	no	—
171	C₂²×C₄×C₈₉	—	4	1	no	—
172	C₂²×C₄×C₈₉	—	4	1	no	—
173	C₂²×C₄×C₈₉	—	4	1	no	—
174	C₂²×C₄×C₈₉	—	4	1	no	—
175	C₂²×C₄×C₈₉	—	4	1	no	—
176	C₂²×C₄×C₈₉	D₈	1	2	yes	—
177	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
178	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
192	C₂×C₈×C₈₉	—	2	2	no	—
193	C₂×C₈×C₈₉	—	2	2	no	—
194	C₂×C₈×C₈₉	—	2	2	no	—
195	C₂×C₈×C₈₉	—	2	2	no	—
196	C₂×C₈×C₈₉	—	2	2	no	—
197	C₂×C₈×C₈₉	—	2	2	no	—
198	C₂×C₈×C₈₉	—	4	1	no	—
199	C₂×C₈×C₈₉	—	4	1	no	—
200	C₂×C₈×C₈₉	—	4	1	no	—
201	C₂×C₈×C₈₉	—	4	1	no	—
202	C₂×C₈×C₈₉	—	4	1	no	—
203	C₂×C₈×C₈₉	—	4	1	no	—
204	C₂×C₈×C₈₉	—	4	1	no	—
205	C₂×C₈×C₈₉	—	4	1	no	—
206	C₄⋊C₄×C₈₉	—	2	2	no	—
207	C₄⋊C₄×C₈₉	—	2	2	no	—
208	C₄⋊C₄×C₈₉	—	2	2	no	—
209	C₄⋊C₄×C₈₉	—	2	2	no	—
210	C₄⋊C₄×C₈₉	—	2	2	no	—
211	C₄⋊C₄×C₈₉	—	2	2	no	—
212	C₄⋊C₄×C₈₉	—	4	1	no	—
213	C₄⋊C₄×C₈₉	—	4	1	no	—
214	C₄⋊C₄×C₈₉	—	4	1	no	—
215	C₄⋊C₄×C₈₉	—	4	1	no	—
216	C₄⋊C₄×C₈₉	—	4	1	no	—
217	C₄⋊C₄×C₈₉	—	4	1	no	—
218	C₂²⋊C₄×C₈₉	—	4	8	no	—
219	C₂²⋊C₄×C₈₉	—	4	8	no	—
220	C₄²×C₈₉	—	4	1	no	—
221	C₄²×C₈₉	—	4	1	no	—
222	C₄²×C₈₉	—	4	1	no	—
223	C₄²×C₈₉	—	4	1	no	—
224	C₂³×C₈₉	—	2	4	no	—
225	C₂³×C₈₉	—	4	2	no	—
226	C₂³×C₈₉	—	4	2	no	—
227	C₂³×C₈₉	—	4	2	no	—
228	C₂³×C₈₉	—	4	2	no	—
229	C₂³×C₈₉	—	4	2	no	—
230	C₂³×C₈₉	—	4	2	no	—
231	C₂³×C₈₉	—	4	2	no	—
232	C₂³×C₈₉	—	4	2	no	—
233	C₂³×C₈₉	—	4	2	no	—
234	C₂³×C₈₉	—	4	2	no	—
235	C₂³×C₈₉	—	4	2	no	—
236	C₂³×C₈₉	—	4	2	no	—
237	C₂³×C₈₉	—	4	2	no	—
238	C₂³×C₈₉	—	4	2	no	—
239	C₂³×C₈₉	—	4	2	no	—
240	C₂³×C₈₉	—	4	2	no	—
241	C₂³×C₈₉	—	4	2	no	—
242	C₂³×C₈₉	—	4	2	no	—
243	C₂³×C₈₉	—	8	1	no	—
244	C₂³×C₈₉	—	8	1	no	—
245	C₂³×C₈₉	—	8	1	no	—
246	C₂³×C₈₉	—	8	1	no	—
247	C₂³×C₈₉	—	8	1	no	—
248	C₂³×C₈₉	—	8	1	no	—
249	C₂³×C₈₉	—	8	1	no	—
250	C₂³×C₈₉	—	8	1	no	—
251	C₂³×C₈₉	—	8	1	no	—
252	C₂³×C₈₉	—	8	1	no	—
253	C₂³×C₈₉	—	8	1	no	—
254	C₂³×C₈₉	—	8	1	no	—
255	C₂³×C₈₉	—	8	1	no	—
256	C₂³×C₈₉	—	8	1	no	—
257	C₂³×C₈₉	—	8	1	no	—
258	C₂³×C₈₉	—	8	1	no	—
259	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
260	C₂³×C₈₉	#120	1	1	yes	characteristic
261	C₂³×C₈₉	#121	1	1	yes	characteristic
262	C₂³×C₈₉	#121	1	1	yes	characteristic
263	C₂³×C₈₉	#121	1	1	yes	characteristic
264	C₂³×C₈₉	#123	1	1	yes	characteristic
265	C₂³×C₈₉	#124	1	1	yes	characteristic
266	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
267	C₂³×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
268	C₂³×C₈₉	#135	1	1	yes	characteristic
269	C₂³×C₈₉	#135	1	1	yes	characteristic
270	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₂³×C₈₉	#137	1	1	yes	characteristic
274	D₄×C₈₉	—	2	4	no	—
275	D₄×C₈₉	—	2	4	no	—
276	D₄×C₈₉	—	4	2	no	—
277	D₄×C₈₉	—	4	2	no	—
278	D₄×C₈₉	—	4	2	no	—
279	D₄×C₈₉	—	4	2	no	—
280	D₄×C₈₉	—	4	2	no	—
281	D₄×C₈₉	—	4	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	2	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	4	1	no	—
289	C₂×C₄×C₈₉	—	4	1	no	—
290	C₂×C₄×C₈₉	—	4	1	no	—
291	C₂×C₄×C₈₉	—	4	1	no	—
292	C₂×C₄×C₈₉	—	4	1	no	—
293	C₂×C₄×C₈₉	—	4	1	no	—
294	C₂×C₄×C₈₉	—	4	1	no	—
295	C₂×C₄×C₈₉	—	4	1	no	—
296	C₂×C₄×C₈₉	—	4	2	no	—
297	C₂×C₄×C₈₉	—	4	2	no	—
298	C₂×C₄×C₈₉	—	4	2	no	—
299	C₂×C₄×C₈₉	—	4	2	no	—
300	C₂×C₄×C₈₉	—	4	2	no	—
301	C₂×C₄×C₈₉	—	4	2	no	—
302	C₂×C₄×C₈₉	—	4	2	no	—
303	C₂×C₄×C₈₉	—	4	2	no	—
304	C₂×C₄×C₈₉	—	4	2	no	—
305	C₂×C₄×C₈₉	—	8	1	no	—
306	C₂×C₄×C₈₉	—	8	1	no	—
307	C₂×C₄×C₈₉	—	8	1	no	—
308	C₂×C₄×C₈₉	—	8	1	no	—
309	C₂×C₄×C₈₉	—	8	1	no	—
310	C₂×C₄×C₈₉	—	8	1	no	—
311	C₂×C₄×C₈₉	—	8	1	no	—
312	C₂×C₄×C₈₉	—	8	1	no	—
313	C₂×C₄×C₈₉	—	8	1	no	—
314	C₂×C₄×C₈₉	—	8	1	no	—
315	C₂×C₄×C₈₉	—	8	1	no	—
316	C₂×C₄×C₈₉	—	8	1	no	—
317	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
319	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
320	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
321	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
322	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
323	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
324	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
325	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
326	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
327	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
328	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
329	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
330	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
331	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
332	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
333	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
334	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
335	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
336	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
337	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
338	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
339	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
340	C₂×C₄×C₈₉	#124	1	1	yes	characteristic
341	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
342	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
343	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
344	C₂×C₄×C₈₉	#126	1	1	yes	characteristic
345	C₈×C₈₉	—	4	2	no	—
346	C₈×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	—	4	4	no	—
348	C₂²×C₈₉	—	4	4	no	—
349	C₂²×C₈₉	—	4	4	no	—
350	C₂²×C₈₉	—	8	2	no	—
351	C₂²×C₈₉	—	8	2	no	—
352	C₂²×C₈₉	—	8	2	no	—
353	C₂²×C₈₉	—	8	2	no	—
354	C₂²×C₈₉	—	8	2	no	—
355	C₂²×C₈₉	—	8	2	no	—
356	C₂²×C₈₉	—	8	2	no	—
357	C₂²×C₈₉	—	8	2	no	—
358	C₂²×C₈₉	—	8	2	no	—
359	C₂²×C₈₉	—	8	2	no	—
360	C₂²×C₈₉	—	8	2	no	—
361	C₂²×C₈₉	—	8	2	no	—
362	C₂²×C₈₉	#386	1	1	yes	characteristic
363	C₂²×C₈₉	#388	1	1	yes	characteristic
364	C₂²×C₈₉	#388	1	1	yes	characteristic
365	C₂²×C₈₉	#394	1	1	yes	characteristic
366	C₂²×C₈₉	#394	1	1	yes	characteristic
367	C₂²×C₈₉	#394	1	1	yes	characteristic
368	C₂²×C₈₉	#397	1	1	yes	characteristic
369	C₂²×C₈₉	C₄×D₈	1	1	yes	characteristic
370	C₂²×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
371	C₂²×C₈₉	#440	1	1	yes	characteristic
372	C₂²×C₈₉	#442	1	1	yes	characteristic
373	C₂²×C₈₉	#447	1	1	yes	characteristic
374	C₂²×C₈₉	#449	1	1	yes	characteristic
375	C₂²×C₈₉	#450	1	1	yes	characteristic
376	C₂²×C₈₉	#452	1	1	yes	characteristic
377	C₂²×C₈₉	#459	1	1	yes	characteristic
378	C₂²×C₈₉	#459	1	1	yes	characteristic
379	C₂²×C₈₉	#460	1	1	yes	characteristic
380	C₂²×C₈₉	#461	1	1	yes	characteristic
381	C₂²×C₈₉	#463	1	1	yes	characteristic
382	C₂²×C₈₉	#463	1	1	yes	characteristic
383	C₂²×C₈₉	#463	1	1	yes	characteristic
384	C₂²×C₈₉	#464	1	1	yes	characteristic
385	C₂²×C₈₉	#465	1	1	yes	characteristic
386	C₂²×C₈₉	#466	1	1	yes	characteristic
387	C₂²×C₈₉	#468	1	1	yes	characteristic
388	C₂²×C₈₉	#469	1	1	yes	characteristic
389	C₂²×C₈₉	#480	1	1	yes	characteristic
390	C₂²×C₈₉	#481	1	1	yes	characteristic
391	C₂²×C₈₉	#482	1	1	yes	characteristic
392	C₂²×C₈₉	#482	1	1	yes	characteristic
393	C₂²×C₈₉	#486	1	1	yes	characteristic
394	C₂²×C₈₉	#488	1	1	yes	characteristic
395	C₂²×C₈₉	#489	1	1	yes	characteristic
396	C₂²×C₈₉	#490	1	1	yes	characteristic
397	C₄×C₈₉	—	4	2	no	—
398	C₄×C₈₉	—	4	2	no	—
399	C₄×C₈₉	—	8	2	no	—
400	C₄×C₈₉	—	8	2	no	—
401	C₄×C₈₉	—	8	2	no	—
402	C₄×C₈₉	#381	1	1	yes	characteristic
403	C₄×C₈₉	#386	1	1	yes	characteristic
404	C₄×C₈₉	#388	1	1	yes	characteristic
405	C₄×C₈₉	#388	1	1	yes	characteristic
406	C₄×C₈₉	#394	1	1	yes	characteristic
407	C₄×C₈₉	#397	1	1	yes	characteristic
408	C₄×C₈₉	#397	1	1	yes	characteristic
409	C₄×C₈₉	#397	1	1	yes	characteristic
410	#11189	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂×C₈₉	—	8	4	no	—
412	C₂×C₈₉	#1440	1	1	yes	characteristic
413	C₂×C₈₉	#1877	1	1	yes	characteristic
414	C₂×C₈₉	#1879	1	1	yes	characteristic
415	C₂×C₈₉	#1925	1	1	yes	characteristic
416	C₂×C₈₉	#1926	1	1	yes	characteristic
417	C₂×C₈₉	#1934	1	1	yes	characteristic
418	C₂×C₈₉	#1936	1	1	yes	characteristic
419	C₂×C₈₉	#2033	1	1	yes	characteristic
420	C₂×C₈₉	#2034	1	1	yes	characteristic
421	C₂×C₈₉	#2041	1	1	yes	characteristic
422	C₂×C₈₉	#2042	1	1	yes	characteristic
423	C₂×C₈₉	#2054	1	1	yes	characteristic
424	C₂×C₈₉	#2055	1	1	yes	characteristic
425	C₂×C₈₉	#2071	1	1	yes	characteristic
426	C₂×C₈₉	#2073	1	1	yes	characteristic
427	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic
428	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic
429	C₂×#390	C₂×C₈₉	1	1	yes	characteristic
430	C₂×#340	C₂×C₈₉	1	1	yes	characteristic, complemented
431	C₂×#340	C₂×C₈₉	1	1	yes	characteristic, complemented
432	C₂×#336	C₂×C₈₉	1	1	yes	characteristic, complemented
433	C₄⋊#95	C₂×C₈₉	1	1	yes	characteristic, complemented
434	C₈₉	#11189	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
436	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
437	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	—	2	1	no	—
442	C₂²×C₂²⋊C₄	—	2	1	no	—
443	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
444	C₂×#102	—	2	2	no	—
445	C₂×#102	—	2	2	no	—
446	C₂×#102	—	2	2	no	—
447	C₂×#102	—	2	2	no	—
448	C₂×#102	—	2	2	no	—
449	C₂×#102	C₄×C₈₉	1	4	yes	complemented
450	#390	—	2	2	no	—
451	#390	—	2	2	no	—
452	C₂×#95	—	2	1	no	—
453	C₂×#95	—	2	1	no	—
454	#340	—	2	2	no	—
455	#340	—	2	2	no	—
456	#336	—	2	2	no	—
457	C₂⁵	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	1	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	1	no	—
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	—	2	1	no	—
467	C₂²×D₄	—	2	1	no	—
468	C₂²×D₄	—	2	1	no	—
469	C₂²×D₄	C₂×C₄×C₈₉	1	2	yes	—
470	C₂²×D₄	D₄×C₈₉	1	2	yes	—
471	C₂²×D₄	D₄×C₈₉	1	2	yes	—
472	C₂³×C₄	—	2	1	no	—
473	C₂³×C₄	—	2	1	no	—
474	C₂³×C₄	—	2	1	no	—
475	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
476	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×C₈	—	2	1	no	—
479	C₂²×C₈	—	2	1	no	—
480	C₂²×C₈	—	2	1	no	—
481	C₂²×C₈	—	2	1	no	—
482	C₂²×C₈	—	2	1	no	—
483	C₂²×C₈	—	2	1	no	—
484	C₂²×C₈	—	2	1	no	—
485	C₂²×C₈	—	2	1	no	—
486	C₂²×C₈	—	2	1	no	—
487	C₂²×C₈	—	2	1	no	—
488	C₂²×C₈	—	2	1	no	—
489	C₂²×C₈	—	2	1	no	—
490	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
491	C₂²×C₈	D₄×C₈₉	1	2	yes	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	1	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
508	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	—	2	4	no	—
512	C₂×C₂²⋊C₄	—	4	2	no	—
513	C₂×C₂²⋊C₄	—	4	2	no	—
514	C₂×C₂²⋊C₄	—	4	2	no	—
515	C₂×C₂²⋊C₄	—	4	2	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂×C₄²	—	2	1	no	—
520	C₂×C₄²	—	2	1	no	—
521	C₂×C₄²	—	2	1	no	—
522	#102	—	2	8	no	—
523	#102	—	2	8	no	—
524	#95	—	4	2	no	—
525	#95	—	4	2	no	—
526	C₂⁴	—	2	2	no	—
527	C₂⁴	—	2	2	no	—
528	C₂⁴	—	2	2	no	—
529	C₂⁴	—	4	1	no	—
530	C₂⁴	—	4	1	no	—
531	C₂⁴	—	4	1	no	—
532	C₂⁴	—	4	1	no	—
533	C₂⁴	—	4	1	no	—
534	C₂⁴	—	4	1	no	—
535	C₂⁴	—	4	1	no	—
536	C₂⁴	—	4	1	no	—
537	C₂⁴	—	4	1	no	—
538	C₂⁴	—	4	1	no	—
539	C₂⁴	—	4	1	no	—
540	C₂⁴	—	4	1	no	—
541	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	4	1	no	—
558	C₂×D₄	—	4	1	no	—
559	C₂×D₄	—	4	1	no	—
560	C₂×D₄	—	4	1	no	—
561	C₂×D₄	—	4	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	C₂²⋊C₄×C₈₉	1	4	yes	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	—	4	1	no	—
595	C₂²×C₄	—	4	1	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	1	no	—
603	C₂²×C₄	D₈×C₈₉	1	2	yes	—
604	C₂²×C₄	SD₁₆×C₈₉	1	2	yes	—
605	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
611	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
615	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
617	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
618	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	2	no	—
625	C₂×C₈	—	4	1	no	—
626	C₂×C₈	—	4	1	no	—
627	C₂×C₈	—	4	1	no	—
628	C₂×C₈	—	4	1	no	—
629	C₂×C₈	—	4	1	no	—
630	C₂×C₈	—	4	1	no	—
631	C₂×C₈	—	4	1	no	—
632	C₂×C₈	—	4	1	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	2	no	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	4	1	no	—
640	C₄⋊C₄	—	4	1	no	—
641	C₄⋊C₄	—	4	1	no	—
642	C₄⋊C₄	—	4	1	no	—
643	C₄⋊C₄	—	4	1	no	—
644	C₄⋊C₄	—	4	1	no	—
645	C₂²⋊C₄	—	4	8	no	—
646	C₂²⋊C₄	—	4	8	no	—
647	C₄²	—	4	1	no	—
648	C₄²	—	4	1	no	—
649	C₄²	—	4	1	no	—
650	C₄²	—	4	1	no	—
651	C₂³	—	2	4	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	4	2	no	—
655	C₂³	—	4	2	no	—
656	C₂³	—	4	2	no	—
657	C₂³	—	4	2	no	—
658	C₂³	—	4	2	no	—
659	C₂³	—	4	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	4	2	no	—
668	C₂³	—	4	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	8	1	no	—
671	C₂³	—	8	1	no	—
672	C₂³	—	8	1	no	—
673	C₂³	—	8	1	no	—
674	C₂³	—	8	1	no	—
675	C₂³	—	8	1	no	—
676	C₂³	—	8	1	no	—
677	C₂³	—	8	1	no	—
678	C₂³	—	8	1	no	—
679	C₂³	—	8	1	no	—
680	C₂³	—	8	1	no	—
681	C₂³	—	8	1	no	—
682	C₂³	—	8	1	no	—
683	C₂³	—	8	1	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	C₄×D₄×C₈₉	1	1	yes	characteristic
687	C₂³	#120×C₈₉	1	1	yes	characteristic
688	C₂³	#121×C₈₉	1	1	yes	characteristic
689	C₂³	#121×C₈₉	1	1	yes	characteristic
690	C₂³	#121×C₈₉	1	1	yes	characteristic
691	C₂³	#123×C₈₉	1	1	yes	characteristic
692	C₂³	#124×C₈₉	1	1	yes	characteristic
693	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
694	C₂³	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
695	C₂³	#135×C₈₉	1	1	yes	characteristic
696	C₂³	#135×C₈₉	1	1	yes	characteristic
697	C₂³	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
698	C₂³	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
699	C₂³	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
700	C₂³	#137×C₈₉	1	1	yes	characteristic
701	D₄	—	2	4	no	—
702	D₄	—	2	4	no	—
703	D₄	—	4	2	no	—
704	D₄	—	4	2	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	4	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	8	1	no	—
733	C₂×C₄	—	8	1	no	—
734	C₂×C₄	—	8	1	no	—
735	C₂×C₄	—	8	1	no	—
736	C₂×C₄	—	8	1	no	—
737	C₂×C₄	—	8	1	no	—
738	C₂×C₄	—	8	1	no	—
739	C₂×C₄	—	8	1	no	—
740	C₂×C₄	—	8	1	no	—
741	C₂×C₄	—	8	1	no	—
742	C₂×C₄	—	8	1	no	—
743	C₂×C₄	—	8	1	no	—
744	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
745	C₂×C₄	#117×C₈₉	1	1	yes	characteristic
746	C₂×C₄	#117×C₈₉	1	1	yes	characteristic
747	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
748	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
749	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
750	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
751	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
752	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
753	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
754	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
755	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
756	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
757	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
758	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
759	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
760	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
761	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
762	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
763	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
764	C₂×C₄	#123×C₈₉	1	1	yes	characteristic
765	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
766	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
767	C₂×C₄	#124×C₈₉	1	1	yes	characteristic
768	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
769	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
770	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
771	C₂×C₄	#126×C₈₉	1	1	yes	characteristic
772	C₈	—	4	2	no	—
773	C₈	—	4	2	no	—
774	C₂²	—	4	4	no	—
775	C₂²	—	4	4	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	8	2	no	—
778	C₂²	—	8	2	no	—
779	C₂²	—	8	2	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	8	2	no	—
782	C₂²	—	8	2	no	—
783	C₂²	—	8	2	no	—
784	C₂²	—	8	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	2	no	—
787	C₂²	—	8	2	no	—
788	C₂²	—	8	2	no	—
789	C₂²	#386×C₈₉	1	1	yes	characteristic
790	C₂²	#388×C₈₉	1	1	yes	characteristic
791	C₂²	#388×C₈₉	1	1	yes	characteristic
792	C₂²	#394×C₈₉	1	1	yes	characteristic
793	C₂²	#394×C₈₉	1	1	yes	characteristic
794	C₂²	#394×C₈₉	1	1	yes	characteristic
795	C₂²	#397×C₈₉	1	1	yes	characteristic
796	C₂²	C₄×D₈×C₈₉	1	1	yes	characteristic
797	C₂²	C₄×SD₁₆×C₈₉	1	1	yes	characteristic
798	C₂²	#440×C₈₉	1	1	yes	characteristic
799	C₂²	#442×C₈₉	1	1	yes	characteristic
800	C₂²	#447×C₈₉	1	1	yes	characteristic
801	C₂²	#449×C₈₉	1	1	yes	characteristic
802	C₂²	#450×C₈₉	1	1	yes	characteristic
803	C₂²	#452×C₈₉	1	1	yes	characteristic
804	C₂²	#459×C₈₉	1	1	yes	characteristic
805	C₂²	#459×C₈₉	1	1	yes	characteristic
806	C₂²	#460×C₈₉	1	1	yes	characteristic
807	C₂²	#461×C₈₉	1	1	yes	characteristic
808	C₂²	#463×C₈₉	1	1	yes	characteristic
809	C₂²	#463×C₈₉	1	1	yes	characteristic
810	C₂²	#463×C₈₉	1	1	yes	characteristic
811	C₂²	#464×C₈₉	1	1	yes	characteristic
812	C₂²	#465×C₈₉	1	1	yes	characteristic
813	C₂²	#466×C₈₉	1	1	yes	characteristic
814	C₂²	#468×C₈₉	1	1	yes	characteristic
815	C₂²	#469×C₈₉	1	1	yes	characteristic
816	C₂²	#480×C₈₉	1	1	yes	characteristic
817	C₂²	#481×C₈₉	1	1	yes	characteristic
818	C₂²	#482×C₈₉	1	1	yes	characteristic
819	C₂²	#482×C₈₉	1	1	yes	characteristic
820	C₂²	#486×C₈₉	1	1	yes	characteristic
821	C₂²	#488×C₈₉	1	1	yes	characteristic
822	C₂²	#489×C₈₉	1	1	yes	characteristic
823	C₂²	#490×C₈₉	1	1	yes	characteristic
824	C₄	—	4	2	no	—
825	C₄	—	4	2	no	—
826	C₄	—	8	2	no	—
827	C₄	—	8	2	no	—
828	C₄	—	8	2	no	—
829	C₄	#381×C₈₉	1	1	yes	characteristic
830	C₄	#386×C₈₉	1	1	yes	characteristic
831	C₄	#388×C₈₉	1	1	yes	characteristic
832	C₄	#388×C₈₉	1	1	yes	characteristic
833	C₄	#394×C₈₉	1	1	yes	characteristic
834	C₄	#397×C₈₉	1	1	yes	characteristic
835	C₄	#397×C₈₉	1	1	yes	characteristic
836	C₄	#397×C₈₉	1	1	yes	characteristic
837	C₂	—	8	4	no	—
838	C₂	C₈₉×#1440	1	1	yes	characteristic
839	C₂	C₈₉×#1877	1	1	yes	characteristic
840	C₂	C₈₉×#1879	1	1	yes	characteristic
841	C₂	C₈₉×#1925	1	1	yes	characteristic
842	C₂	C₈₉×#1926	1	1	yes	characteristic
843	C₂	C₈₉×#1934	1	1	yes	characteristic
844	C₂	C₈₉×#1936	1	1	yes	characteristic
845	C₂	C₈₉×#2033	1	1	yes	characteristic
846	C₂	C₈₉×#2034	1	1	yes	characteristic
847	C₂	C₈₉×#2041	1	1	yes	characteristic
848	C₂	C₈₉×#2042	1	1	yes	characteristic
849	C₂	C₈₉×#2054	1	1	yes	characteristic
850	C₂	C₈₉×#2055	1	1	yes	characteristic
851	C₂	C₈₉×#2071	1	1	yes	characteristic
852	C₂	C₈₉×#2073	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₈₉
Frattini, cosocle	C₂³×C₄	C₂³×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₂×#340×C₈₉	C₂	semidirect
5. C₂×#340×C₈₉	C₂	semidirect
6. C₂×#336×C₈₉	C₂	semidirect
7. C₈₉×C₄⋊#95	C₂	semidirect
22. C₂×#102×C₈₉	C₄	semidirect
410. #11189	C₈₉	direct (N × H)
430. C₂×#340	C₂×C₈₉	semidirect
431. C₂×#340	C₂×C₈₉	semidirect
432. C₂×#336	C₂×C₈₉	semidirect
433. C₄⋊#95	C₂×C₈₉	semidirect
434. C₈₉	#11189	direct (N × H)
449. C₂×#102	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#102×C₈₉	2
C₂×#390×C₈₉	2
C₂×#340×C₈₉	2
C₂×#336×C₈₉	2
C₈₉×C₄⋊#95	2
#11189	89

Subgroups — C89×#11189 #36389037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#11189 #36389037