Subgroups — C₈₉×#24362 #36402210

Order 22784.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#449×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2431	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#135×C₈₉	—	2	4	no	—
19	C₂×#135×C₈₉	—	2	4	no	—
20	C₂×#135×C₈₉	—	2	4	no	—
21	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
33	#464×C₈₉	—	2	4	no	—
34	#460×C₈₉	—	2	4	no	—
35	#449×C₈₉	—	2	4	no	—
36	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#392×C₈₉	—	2	1	no	—
48	#392×C₈₉	—	2	1	no	—
49	#391×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	—	2	1	no	—
51	#390×C₈₉	—	2	1	no	—
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#390×C₈₉	C₂²	1	1	yes	characteristic
54	#390×C₈₉	C₂²	1	1	yes	characteristic
55	#386×C₈₉	—	2	1	no	—
56	#386×C₈₉	—	2	1	no	—
57	#380×C₈₉	—	2	1	no	—
58	#380×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
60	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
61	#340×C₈₉	C₂²	1	1	yes	characteristic
62	#340×C₈₉	C₂²	1	1	yes	characteristic
63	#336×C₈₉	C₂²	1	1	yes	characteristic
64	#336×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×#41×C₈₉	—	2	2	no	—
66	C₂×#41×C₈₉	—	2	2	no	—
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	2	2	no	—
70	C₂×#41×C₈₉	—	2	2	no	—
71	C₂×#41×C₈₉	—	2	2	no	—
72	C₂×#41×C₈₉	—	4	1	no	—
73	C₂×#41×C₈₉	—	4	1	no	—
74	C₂×#41×C₈₉	—	4	1	no	—
75	C₂×#41×C₈₉	—	4	1	no	—
76	C₂×#41×C₈₉	D₄	1	4	yes	complemented
77	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₈₉	—	2	1	no	—
80	C₂²×D₄×C₈₉	—	2	1	no	—
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	—	2	1	no	—
83	C₂²×D₄×C₈₉	—	2	1	no	—
84	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	—	2	1	no	—
88	C₂³×C₄×C₈₉	—	2	1	no	—
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	#135×C₈₉	—	2	32	no	—
91	C₂×Q₁₆×C₈₉	—	2	2	no	—
92	C₂×Q₁₆×C₈₉	—	2	2	no	—
93	C₂×Q₁₆×C₈₉	D₄	1	4	yes	complemented
94	C₂×SD₁₆×C₈₉	—	2	2	no	—
95	C₂×SD₁₆×C₈₉	—	2	2	no	—
96	C₂×SD₁₆×C₈₉	—	2	2	no	—
97	C₂×SD₁₆×C₈₉	—	2	2	no	—
98	C₂×SD₁₆×C₈₉	—	2	2	no	—
99	C₂×SD₁₆×C₈₉	—	2	2	no	—
100	C₂×SD₁₆×C₈₉	—	2	2	no	—
101	C₂×SD₁₆×C₈₉	—	2	2	no	—
102	C₂×SD₁₆×C₈₉	D₄	1	4	yes	complemented
103	C₂×D₈×C₈₉	—	2	2	no	—
104	C₂×D₈×C₈₉	—	2	2	no	—
105	C₂×D₈×C₈₉	—	2	2	no	—
106	C₂×D₈×C₈₉	—	2	2	no	—
107	C₂×D₈×C₈₉	—	4	1	no	—
108	C₂×D₈×C₈₉	—	4	1	no	—
109	C₂²×C₈×C₈₉	—	2	2	no	—
110	C₂²×C₈×C₈₉	—	2	2	no	—
111	C₂²×C₈×C₈₉	—	2	2	no	—
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	#127×C₈₉	—	2	2	no	—
117	#127×C₈₉	—	4	1	no	—
118	#124×C₈₉	—	2	2	no	—
119	#124×C₈₉	—	4	1	no	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	—	2	2	no	—
122	C₄×Q₈×C₈₉	—	2	2	no	—
123	C₄×Q₈×C₈₉	—	2	2	no	—
124	C₄×Q₈×C₈₉	—	4	1	no	—
125	C₄×Q₈×C₈₉	—	4	1	no	—
126	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
137	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
143	C₂×C₄²×C₈₉	—	2	1	no	—
144	C₂×C₄²×C₈₉	—	2	1	no	—
145	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
147	C₄⋊C₈×C₈₉	—	2	2	no	—
148	C₄⋊C₈×C₈₉	—	2	2	no	—
149	#103×C₈₉	—	2	2	no	—
150	#103×C₈₉	—	2	2	no	—
151	#103×C₈₉	—	4	1	no	—
152	#102×C₈₉	—	2	2	no	—
153	#102×C₈₉	—	2	2	no	—
154	#102×C₈₉	—	2	2	no	—
155	#102×C₈₉	—	2	2	no	—
156	#102×C₈₉	—	4	1	no	—
157	C₂²⋊C₈×C₈₉	—	2	2	no	—
158	#95×C₈₉	—	2	1	no	—
159	#95×C₈₉	—	2	1	no	—
160	#95×C₈₉	—	2	1	no	—
161	#95×C₈₉	D₄	1	1	yes	characteristic
162	#95×C₈₉	D₄	1	1	yes	characteristic
163	C₂⁴×C₈₉	—	2	1	no	—
164	C₂⁴×C₈₉	—	2	1	no	—
165	C₂⁴×C₈₉	—	2	1	no	—
166	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
167	#41×C₈₉	—	2	8	no	—
168	#41×C₈₉	—	2	8	no	—
169	#41×C₈₉	—	4	4	no	—
170	#41×C₈₉	—	4	4	no	—
171	#41×C₈₉	—	4	4	no	—
172	#41×C₈₉	—	4	4	no	—
173	#41×C₈₉	—	4	4	no	—
174	#41×C₈₉	—	4	4	no	—
175	C₂×Q₈×C₈₉	—	2	1	no	—
176	C₂×Q₈×C₈₉	—	2	1	no	—
177	C₂×Q₈×C₈₉	—	2	1	no	—
178	C₂×Q₈×C₈₉	—	2	1	no	—
179	C₂×Q₈×C₈₉	—	2	1	no	—
180	C₂×Q₈×C₈₉	—	2	1	no	—
181	C₂×Q₈×C₈₉	—	2	1	no	—
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
186	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	1	no	—
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	C₂×D₄×C₈₉	—	2	1	no	—
195	C₂×D₄×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	1	no	—
199	C₂×D₄×C₈₉	—	2	1	no	—
200	C₂×D₄×C₈₉	—	2	1	no	—
201	C₂×D₄×C₈₉	—	2	1	no	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	4	2	no	—
205	C₂×D₄×C₈₉	—	4	2	no	—
206	C₂×D₄×C₈₉	—	4	2	no	—
207	C₂×D₄×C₈₉	—	4	2	no	—
208	C₂×D₄×C₈₉	—	4	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	2	no	—
213	C₂×D₄×C₈₉	—	4	2	no	—
214	C₂×D₄×C₈₉	—	8	1	no	—
215	C₂×D₄×C₈₉	—	8	1	no	—
216	C₂×D₄×C₈₉	—	8	1	no	—
217	C₂×D₄×C₈₉	—	8	1	no	—
218	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
219	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₈₉	—	2	1	no	—
221	C₂²×C₄×C₈₉	—	2	1	no	—
222	C₂²×C₄×C₈₉	—	2	1	no	—
223	C₂²×C₄×C₈₉	—	2	1	no	—
224	C₂²×C₄×C₈₉	—	2	1	no	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	1	no	—
228	C₂²×C₄×C₈₉	—	2	1	no	—
229	C₂²×C₄×C₈₉	—	2	1	no	—
230	C₂²×C₄×C₈₉	—	4	2	no	—
231	C₂²×C₄×C₈₉	—	4	2	no	—
232	C₂²×C₄×C₈₉	—	4	2	no	—
233	C₂²×C₄×C₈₉	—	4	2	no	—
234	C₂²×C₄×C₈₉	—	4	2	no	—
235	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₈₉	#41	1	2	yes	—
242	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	Q₁₆×C₈₉	—	2	8	no	—
244	SD₁₆×C₈₉	—	2	8	no	—
245	SD₁₆×C₈₉	—	2	8	no	—
246	SD₁₆×C₈₉	—	4	4	no	—
247	D₈×C₈₉	—	2	8	no	—
248	D₈×C₈₉	—	4	4	no	—
249	C₂×C₈×C₈₉	—	2	8	no	—
250	C₂×C₈×C₈₉	—	2	1	no	—
251	C₂×C₈×C₈₉	—	2	1	no	—
252	C₂×C₈×C₈₉	—	2	1	no	—
253	C₂×C₈×C₈₉	—	2	1	no	—
254	C₂×C₈×C₈₉	—	2	1	no	—
255	C₂×C₈×C₈₉	—	2	1	no	—
256	C₂×C₈×C₈₉	—	2	1	no	—
257	C₂×C₈×C₈₉	—	2	1	no	—
258	C₂×C₈×C₈₉	—	2	1	no	—
259	C₂×C₈×C₈₉	—	2	1	no	—
260	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
262	C₄⋊C₄×C₈₉	—	2	1	no	—
263	C₄⋊C₄×C₈₉	—	2	1	no	—
264	C₄⋊C₄×C₈₉	—	2	1	no	—
265	C₄⋊C₄×C₈₉	—	2	1	no	—
266	C₄⋊C₄×C₈₉	—	2	1	no	—
267	C₄⋊C₄×C₈₉	—	2	1	no	—
268	C₄⋊C₄×C₈₉	—	4	2	no	—
269	C₄⋊C₄×C₈₉	—	4	2	no	—
270	C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂²⋊C₄×C₈₉	—	4	1	no	—
272	C₂²⋊C₄×C₈₉	—	4	2	no	—
273	C₂²⋊C₄×C₈₉	—	4	2	no	—
274	C₂²⋊C₄×C₈₉	—	4	2	no	—
275	C₂²⋊C₄×C₈₉	—	4	2	no	—
276	C₂²⋊C₄×C₈₉	—	4	2	no	—
277	C₂²⋊C₄×C₈₉	—	8	1	no	—
278	C₂²⋊C₄×C₈₉	—	8	1	no	—
279	C₂²⋊C₄×C₈₉	—	8	1	no	—
280	C₂²⋊C₄×C₈₉	—	8	1	no	—
281	C₂²⋊C₄×C₈₉	—	8	1	no	—
282	C₄²×C₈₉	—	2	1	no	—
283	C₄²×C₈₉	—	2	1	no	—
284	C₄²×C₈₉	—	2	1	no	—
285	C₄²×C₈₉	—	2	1	no	—
286	C₄²×C₈₉	—	4	2	no	—
287	C₄²×C₈₉	—	4	2	no	—
288	C₂³×C₈₉	—	2	1	no	—
289	C₂³×C₈₉	—	2	1	no	—
290	C₂³×C₈₉	—	2	1	no	—
291	C₂³×C₈₉	—	2	1	no	—
292	C₂³×C₈₉	—	2	1	no	—
293	C₂³×C₈₉	—	2	1	no	—
294	C₂³×C₈₉	—	2	2	no	—
295	C₂³×C₈₉	—	2	2	no	—
296	C₂³×C₈₉	—	4	1	no	—
297	C₂³×C₈₉	—	4	1	no	—
298	C₂³×C₈₉	—	4	1	no	—
299	C₂³×C₈₉	—	4	1	no	—
300	C₂³×C₈₉	—	4	1	no	—
301	C₂³×C₈₉	—	4	1	no	—
302	C₂³×C₈₉	—	4	1	no	—
303	C₂³×C₈₉	—	4	1	no	—
304	C₂³×C₈₉	—	4	1	no	—
305	C₂³×C₈₉	—	4	1	no	—
306	C₂³×C₈₉	—	4	1	no	—
307	C₂³×C₈₉	—	4	1	no	—
308	C₂³×C₈₉	—	4	1	no	—
309	C₂³×C₈₉	—	4	1	no	—
310	C₂³×C₈₉	—	4	1	no	—
311	C₂³×C₈₉	—	4	1	no	—
312	C₂³×C₈₉	—	4	1	no	—
313	C₂³×C₈₉	—	4	1	no	—
314	C₂³×C₈₉	—	4	1	no	—
315	C₂³×C₈₉	#121	1	2	yes	—
316	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₈₉	—	2	2	no	—
318	Q₈×C₈₉	—	2	2	no	—
319	Q₈×C₈₉	—	2	2	no	—
320	Q₈×C₈₉	—	2	2	no	—
321	Q₈×C₈₉	—	2	2	no	—
322	Q₈×C₈₉	—	4	1	no	—
323	Q₈×C₈₉	—	4	1	no	—
324	Q₈×C₈₉	#120	1	4	yes	—
325	D₄×C₈₉	—	2	2	no	—
326	D₄×C₈₉	—	2	2	no	—
327	D₄×C₈₉	—	2	2	no	—
328	D₄×C₈₉	—	2	2	no	—
329	D₄×C₈₉	—	4	8	no	—
330	D₄×C₈₉	—	4	8	no	—
331	D₄×C₈₉	—	4	1	no	—
332	D₄×C₈₉	—	4	1	no	—
333	D₄×C₈₉	—	4	1	no	—
334	D₄×C₈₉	—	4	1	no	—
335	D₄×C₈₉	—	4	1	no	—
336	D₄×C₈₉	—	4	1	no	—
337	D₄×C₈₉	—	4	1	no	—
338	D₄×C₈₉	—	4	1	no	—
339	D₄×C₈₉	—	8	4	no	—
340	D₄×C₈₉	—	8	4	no	—
341	D₄×C₈₉	—	8	4	no	—
342	C₂×C₄×C₈₉	—	2	2	no	—
343	C₂×C₄×C₈₉	—	2	1	no	—
344	C₂×C₄×C₈₉	—	2	2	no	—
345	C₂×C₄×C₈₉	—	2	2	no	—
346	C₂×C₄×C₈₉	—	2	1	no	—
347	C₂×C₄×C₈₉	—	2	1	no	—
348	C₂×C₄×C₈₉	—	2	1	no	—
349	C₂×C₄×C₈₉	—	2	2	no	—
350	C₂×C₄×C₈₉	—	2	2	no	—
351	C₂×C₄×C₈₉	—	2	2	no	—
352	C₂×C₄×C₈₉	—	2	2	no	—
353	C₂×C₄×C₈₉	—	2	1	no	—
354	C₂×C₄×C₈₉	—	2	1	no	—
355	C₂×C₄×C₈₉	—	2	1	no	—
356	C₂×C₄×C₈₉	—	2	2	no	—
357	C₂×C₄×C₈₉	—	2	1	no	—
358	C₂×C₄×C₈₉	—	2	1	no	—
359	C₂×C₄×C₈₉	—	2	1	no	—
360	C₂×C₄×C₈₉	—	2	1	no	—
361	C₂×C₄×C₈₉	—	2	1	no	—
362	C₂×C₄×C₈₉	—	2	1	no	—
363	C₂×C₄×C₈₉	—	4	8	no	—
364	C₂×C₄×C₈₉	—	4	8	no	—
365	C₂×C₄×C₈₉	—	4	1	no	—
366	C₂×C₄×C₈₉	—	4	1	no	—
367	C₂×C₄×C₈₉	—	4	1	no	—
368	C₂×C₄×C₈₉	—	4	1	no	—
369	C₂×C₄×C₈₉	—	4	1	no	—
370	C₂×C₄×C₈₉	—	4	1	no	—
371	C₂×C₄×C₈₉	—	4	1	no	—
372	C₂×C₄×C₈₉	—	4	1	no	—
373	C₂×C₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	4	1	no	—
375	C₂×C₄×C₈₉	—	4	1	no	—
376	C₂×C₄×C₈₉	#121	1	2	yes	—
377	C₂×C₄×C₈₉	#135	1	2	yes	complemented
378	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
383	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
384	C₈×C₈₉	—	2	2	no	—
385	C₈×C₈₉	—	2	2	no	—
386	C₈×C₈₉	—	4	1	no	—
387	C₈×C₈₉	—	4	1	no	—
388	C₂²×C₈₉	—	2	2	no	—
389	C₂²×C₈₉	—	2	2	no	—
390	C₂²×C₈₉	—	2	2	no	—
391	C₂²×C₈₉	—	4	1	no	—
392	C₂²×C₈₉	—	4	1	no	—
393	C₂²×C₈₉	—	4	1	no	—
394	C₂²×C₈₉	—	4	1	no	—
395	C₂²×C₈₉	—	4	2	no	—
396	C₂²×C₈₉	—	4	2	no	—
397	C₂²×C₈₉	—	4	2	no	—
398	C₂²×C₈₉	—	4	2	no	—
399	C₂²×C₈₉	—	4	2	no	—
400	C₂²×C₈₉	—	4	2	no	—
401	C₂²×C₈₉	—	8	1	no	—
402	C₂²×C₈₉	—	8	1	no	—
403	C₂²×C₈₉	—	8	1	no	—
404	C₂²×C₈₉	—	8	1	no	—
405	C₂²×C₈₉	—	8	1	no	—
406	C₂²×C₈₉	—	8	1	no	—
407	C₂²×C₈₉	—	8	1	no	—
408	C₂²×C₈₉	—	8	1	no	—
409	C₂²×C₈₉	—	8	1	no	—
410	C₂²×C₈₉	—	8	1	no	—
411	C₂²×C₈₉	—	8	1	no	—
412	C₂²×C₈₉	—	8	1	no	—
413	C₂²×C₈₉	—	8	1	no	—
414	C₂²×C₈₉	—	8	1	no	—
415	C₂²×C₈₉	—	8	1	no	—
416	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
417	C₂²×C₈₉	D₄²	1	1	yes	characteristic
418	C₂²×C₈₉	D₄²	1	1	yes	characteristic
419	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
420	C₂²×C₈₉	#575	1	1	yes	characteristic
421	C₂²×C₈₉	#576	1	1	yes	characteristic
422	C₂²×C₈₉	#577	1	1	yes	characteristic
423	C₄×C₈₉	—	2	2	no	—
424	C₄×C₈₉	—	2	4	no	—
425	C₄×C₈₉	—	2	2	no	—
426	C₄×C₈₉	—	4	2	no	—
427	C₄×C₈₉	—	4	1	no	—
428	C₄×C₈₉	—	4	1	no	—
429	C₄×C₈₉	—	4	1	no	—
430	C₄×C₈₉	—	8	1	no	—
431	C₄×C₈₉	—	8	1	no	—
432	C₄×C₈₉	—	8	1	no	—
433	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
434	C₄×C₈₉	#534	1	1	yes	characteristic
435	C₄×C₈₉	#546	1	1	yes	characteristic
436	C₄×C₈₉	#546	1	1	yes	characteristic
437	#24362	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂×C₈₉	—	4	2	no	—
439	C₂×C₈₉	—	8	2	no	—
440	C₂×C₈₉	—	8	2	no	—
441	C₂×C₈₉	—	16	1	no	—
442	C₂×C₈₉	#2410	1	1	yes	characteristic
443	C₂×C₈₉	#3035	1	1	yes	characteristic
444	C₂×C₈₉	#3045	1	1	yes	characteristic
445	C₂×C₈₉	#3268	1	1	yes	characteristic
446	C₂×C₈₉	#3271	1	1	yes	characteristic
447	C₂×C₈₉	#3282	1	1	yes	characteristic
448	C₂×C₈₉	#3287	1	1	yes	characteristic
449	C₂²×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
450	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
451	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
452	C₂×#449	C₂×C₈₉	1	1	yes	characteristic, complemented
453	#2431	C₂×C₈₉	1	1	yes	characteristic, complemented
454	#2341	C₂×C₈₉	1	1	yes	characteristic, complemented
455	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#2054	C₂×C₈₉	1	1	yes	characteristic, complemented
457	#2012	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#2011	C₂×C₈₉	1	1	yes	characteristic, complemented
459	#1893	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
461	#1878	C₂×C₈₉	1	1	yes	characteristic, complemented
462	#1850	C₂×C₈₉	1	1	yes	characteristic, complemented
463	#1788	C₂×C₈₉	1	1	yes	characteristic, complemented
464	C₈₉	#24362	1	1	yes	characteristic, direct product factor, Sylow
465	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
466	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
467	C₂×#135	—	2	4	no	—
468	C₂×#135	—	2	4	no	—
469	C₂×#135	—	2	4	no	—
470	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
471	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
472	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
473	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
474	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
475	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
476	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
477	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
478	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
479	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
480	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
481	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
482	#464	—	2	4	no	—
483	#460	—	2	4	no	—
484	#449	—	2	4	no	—
485	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
486	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
487	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
488	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
489	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
490	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
491	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
493	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
494	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
496	#392	—	2	1	no	—
497	#392	—	2	1	no	—
498	#391	C₂²×C₈₉	1	1	yes	characteristic
499	#390	—	2	1	no	—
500	#390	—	2	1	no	—
501	#390	C₂²×C₈₉	1	1	yes	characteristic
502	#390	C₂²×C₈₉	1	1	yes	characteristic
503	#390	C₂²×C₈₉	1	1	yes	characteristic
504	#386	—	2	1	no	—
505	#386	—	2	1	no	—
506	#380	—	2	1	no	—
507	#380	C₂²×C₈₉	1	1	yes	characteristic
508	C₄×C₂²⋊C₄	—	2	1	no	—
509	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
510	#340	C₂²×C₈₉	1	1	yes	characteristic
511	#340	C₂²×C₈₉	1	1	yes	characteristic
512	#336	C₂²×C₈₉	1	1	yes	characteristic
513	#336	C₂²×C₈₉	1	1	yes	characteristic
514	C₂×#41	—	2	2	no	—
515	C₂×#41	—	2	2	no	—
516	C₂×#41	—	2	2	no	—
517	C₂×#41	—	2	2	no	—
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	—	4	1	no	—
522	C₂×#41	—	4	1	no	—
523	C₂×#41	—	4	1	no	—
524	C₂×#41	—	4	1	no	—
525	C₂×#41	D₄×C₈₉	1	4	yes	complemented
526	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
528	C₂²×D₄	—	2	1	no	—
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	—	2	1	no	—
531	C₂²×D₄	—	2	1	no	—
532	C₂²×D₄	—	2	1	no	—
533	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
534	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
536	C₂³×C₄	—	2	1	no	—
537	C₂³×C₄	—	2	1	no	—
538	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
539	#135	—	2	32	no	—
540	C₂×Q₁₆	—	2	2	no	—
541	C₂×Q₁₆	—	2	2	no	—
542	C₂×Q₁₆	D₄×C₈₉	1	4	yes	complemented
543	C₂×SD₁₆	—	2	2	no	—
544	C₂×SD₁₆	—	2	2	no	—
545	C₂×SD₁₆	—	2	2	no	—
546	C₂×SD₁₆	—	2	2	no	—
547	C₂×SD₁₆	—	2	2	no	—
548	C₂×SD₁₆	—	2	2	no	—
549	C₂×SD₁₆	—	2	2	no	—
550	C₂×SD₁₆	—	2	2	no	—
551	C₂×SD₁₆	D₄×C₈₉	1	4	yes	complemented
552	C₂×D₈	—	2	2	no	—
553	C₂×D₈	—	2	2	no	—
554	C₂×D₈	—	2	2	no	—
555	C₂×D₈	—	2	2	no	—
556	C₂×D₈	—	4	1	no	—
557	C₂×D₈	—	4	1	no	—
558	C₂²×C₈	—	2	2	no	—
559	C₂²×C₈	—	2	2	no	—
560	C₂²×C₈	—	2	2	no	—
561	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
563	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
564	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
565	#127	—	2	2	no	—
566	#127	—	4	1	no	—
567	#124	—	2	2	no	—
568	#124	—	4	1	no	—
569	#121	—	2	2	no	—
570	#121	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	2	no	—
573	C₄×Q₈	—	4	1	no	—
574	C₄×Q₈	—	4	1	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	1	no	—
582	C₂×C₂²⋊C₄	—	2	1	no	—
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
596	C₄⋊C₈	—	2	2	no	—
597	C₄⋊C₈	—	2	2	no	—
598	#103	—	2	2	no	—
599	#103	—	2	2	no	—
600	#103	—	4	1	no	—
601	#102	—	2	2	no	—
602	#102	—	2	2	no	—
603	#102	—	2	2	no	—
604	#102	—	2	2	no	—
605	#102	—	4	1	no	—
606	C₂²⋊C₈	—	2	2	no	—
607	#95	—	2	1	no	—
608	#95	—	2	1	no	—
609	#95	—	2	1	no	—
610	#95	D₄×C₈₉	1	1	yes	characteristic
611	#95	D₄×C₈₉	1	1	yes	characteristic
612	C₂⁴	—	2	1	no	—
613	C₂⁴	—	2	1	no	—
614	C₂⁴	—	2	1	no	—
615	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
616	#41	—	2	8	no	—
617	#41	—	2	8	no	—
618	#41	—	4	4	no	—
619	#41	—	4	4	no	—
620	#41	—	4	4	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	1	no	—
632	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
633	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
634	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
635	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	1	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	4	2	no	—
661	C₂×D₄	—	4	2	no	—
662	C₂×D₄	—	4	2	no	—
663	C₂×D₄	—	8	1	no	—
664	C₂×D₄	—	8	1	no	—
665	C₂×D₄	—	8	1	no	—
666	C₂×D₄	—	8	1	no	—
667	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
668	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	2	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
686	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
688	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
689	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
690	C₂²×C₄	#41×C₈₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
692	Q₁₆	—	2	8	no	—
693	SD₁₆	—	2	8	no	—
694	SD₁₆	—	2	8	no	—
695	SD₁₆	—	4	4	no	—
696	D₈	—	2	8	no	—
697	D₈	—	4	4	no	—
698	C₂×C₈	—	2	8	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
710	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	8	1	no	—
727	C₂²⋊C₄	—	8	1	no	—
728	C₂²⋊C₄	—	8	1	no	—
729	C₂²⋊C₄	—	8	1	no	—
730	C₂²⋊C₄	—	8	1	no	—
731	C₄²	—	2	1	no	—
732	C₄²	—	2	1	no	—
733	C₄²	—	2	1	no	—
734	C₄²	—	2	1	no	—
735	C₄²	—	4	2	no	—
736	C₄²	—	4	2	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	4	1	no	—
764	C₂³	#121×C₈₉	1	2	yes	—
765	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
766	Q₈	—	2	2	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	4	1	no	—
772	Q₈	—	4	1	no	—
773	Q₈	#120×C₈₉	1	4	yes	—
774	D₄	—	2	2	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	2	no	—
778	D₄	—	4	8	no	—
779	D₄	—	4	8	no	—
780	D₄	—	4	1	no	—
781	D₄	—	4	1	no	—
782	D₄	—	4	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	8	4	no	—
789	D₄	—	8	4	no	—
790	D₄	—	8	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	#121×C₈₉	1	2	yes	—
826	C₂×C₄	#135×C₈₉	1	2	yes	complemented
827	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
830	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
831	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
832	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	2	no	—
835	C₈	—	4	1	no	—
836	C₈	—	4	1	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	2	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	8	1	no	—
854	C₂²	—	8	1	no	—
855	C₂²	—	8	1	no	—
856	C₂²	—	8	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
866	C₂²	D₄²×C₈₉	1	1	yes	characteristic
867	C₂²	D₄²×C₈₉	1	1	yes	characteristic
868	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
869	C₂²	#575×C₈₉	1	1	yes	characteristic
870	C₂²	#576×C₈₉	1	1	yes	characteristic
871	C₂²	#577×C₈₉	1	1	yes	characteristic
872	C₄	—	2	2	no	—
873	C₄	—	2	4	no	—
874	C₄	—	2	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	8	1	no	—
880	C₄	—	8	1	no	—
881	C₄	—	8	1	no	—
882	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
883	C₄	#534×C₈₉	1	1	yes	characteristic
884	C₄	#546×C₈₉	1	1	yes	characteristic
885	C₄	#546×C₈₉	1	1	yes	characteristic
886	C₂	—	4	2	no	—
887	C₂	—	8	2	no	—
888	C₂	—	8	2	no	—
889	C₂	—	16	1	no	—
890	C₂	C₈₉×#2410	1	1	yes	characteristic
891	C₂	C₈₉×#3035	1	1	yes	characteristic
892	C₂	C₈₉×#3045	1	1	yes	characteristic
893	C₂	C₈₉×#3268	1	1	yes	characteristic
894	C₂	C₈₉×#3271	1	1	yes	characteristic
895	C₂	C₈₉×#3282	1	1	yes	characteristic
896	C₂	C₈₉×#3287	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₈₉	C₂	semidirect
2. C₂×#464×C₈₉	C₂	semidirect
3. C₂×#460×C₈₉	C₂	semidirect
4. C₂×#449×C₈₉	C₂	semidirect
5. C₈₉×#2431	C₂	semidirect
6. C₈₉×#2341	C₂	semidirect
7. C₈₉×#2055	C₂	semidirect
8. C₈₉×#2054	C₂	semidirect
9. C₈₉×#2012	C₂	semidirect
10. C₈₉×#2011	C₂	semidirect
11. C₈₉×#1893	C₂	semidirect
12. C₈₉×#1880	C₂	semidirect
13. C₈₉×#1878	C₂	semidirect
14. C₈₉×#1850	C₂	semidirect
15. C₈₉×#1788	C₂	semidirect
76. C₂×#41×C₈₉	D₄	semidirect
93. C₂×Q₁₆×C₈₉	D₄	semidirect
102. C₂×SD₁₆×C₈₉	D₄	semidirect
377. C₂×C₄×C₈₉	#135	semidirect
437. #24362	C₈₉	direct (N × H)
449. C₂²×#135	C₂×C₈₉	semidirect
450. C₂×#464	C₂×C₈₉	semidirect
451. C₂×#460	C₂×C₈₉	semidirect
452. C₂×#449	C₂×C₈₉	semidirect
453. #2431	C₂×C₈₉	semidirect
454. #2341	C₂×C₈₉	semidirect
455. #2055	C₂×C₈₉	semidirect
456. #2054	C₂×C₈₉	semidirect
457. #2012	C₂×C₈₉	semidirect
458. #2011	C₂×C₈₉	semidirect
459. #1893	C₂×C₈₉	semidirect
460. #1880	C₂×C₈₉	semidirect
461. #1878	C₂×C₈₉	semidirect
462. #1850	C₂×C₈₉	semidirect
463. #1788	C₂×C₈₉	semidirect
464. C₈₉	#24362	direct (N × H)
525. C₂×#41	D₄×C₈₉	semidirect
542. C₂×Q₁₆	D₄×C₈₉	semidirect
551. C₂×SD₁₆	D₄×C₈₉	semidirect
826. C₂×C₄	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₈₉	2
C₂×#464×C₈₉	2
C₂×#460×C₈₉	2
C₂×#449×C₈₉	2
C₈₉×#2431	2
C₈₉×#2341	2
C₈₉×#2055	2
C₈₉×#2054	2
C₈₉×#2012	2
C₈₉×#2011	2
C₈₉×#1893	2
C₈₉×#1880	2
C₈₉×#1878	2
C₈₉×#1850	2
C₈₉×#1788	2
#24362	89

Subgroups — C89×#24362 #36402210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#24362 #36402210