Subgroups — C₈₉×#61983 #36439831

Order 22784.

2164 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3397	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3368	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3310	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3294	C₂	1	2	yes	maximal, complemented
7	D₄×SD₁₆×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3265	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3247	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3217	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3112	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#460×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2990	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×H(5,𝔽₂)×C₈₉	—	2	1	no	—
19	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	complemented
20	C₂²×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
21	#557×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	#556×C₈₉	—	2	1	no	—
23	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#552×C₈₉	—	2	2	no	—
25	#552×C₈₉	C₂²	1	2	yes	complemented
26	#550×C₈₉	—	2	1	no	—
27	#550×C₈₉	C₂²	1	2	yes	—
28	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#548×C₈₉	C₂²	1	2	yes	complemented
30	#547×C₈₉	—	2	1	no	—
31	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	D₄²×C₈₉	—	2	1	no	—
33	D₄²×C₈₉	—	2	2	no	—
34	D₄²×C₈₉	C₂²	1	4	yes	—
35	D₄²×C₈₉	C₂²	1	2	yes	—
36	#535×C₈₉	—	2	2	no	—
37	#535×C₈₉	—	2	1	no	—
38	#533×C₈₉	—	2	1	no	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#532×C₈₉	C₂²	1	2	yes	—
42	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#127×C₈₉	C₂²	1	2	yes	—
44	#529×C₈₉	—	2	2	no	—
45	#529×C₈₉	C₂²	1	2	yes	complemented
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
50	#496×C₈₉	C₂²	1	4	yes	complemented
51	#492×C₈₉	C₂²	1	2	yes	complemented
52	#490×C₈₉	C₂²	1	4	yes	complemented
53	#486×C₈₉	C₂²	1	2	yes	complemented
54	#482×C₈₉	C₂²	1	2	yes	complemented
55	#480×C₈₉	C₂²	1	4	yes	complemented
56	#478×C₈₉	C₂²	1	4	yes	complemented
57	#477×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#477×C₈₉	C₂²	1	2	yes	complemented
59	#476×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#474×C₈₉	C₂²	1	2	yes	complemented
61	#468×C₈₉	C₂²	1	4	yes	complemented
62	#466×C₈₉	C₂²	1	4	yes	complemented
63	#465×C₈₉	C₂²	1	4	yes	complemented
64	#463×C₈₉	C₂²	1	4	yes	complemented
65	#461×C₈₉	C₂²	1	2	yes	complemented
66	#460×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	#460×C₈₉	C₂²	1	4	yes	complemented
68	#460×C₈₉	C₂²	1	2	yes	complemented
69	#460×C₈₉	C₂²	1	2	yes	complemented
70	#460×C₈₉	C₂²	1	2	yes	complemented
71	#460×C₈₉	C₂²	1	4	yes	complemented
72	#460×C₈₉	C₂²	1	2	yes	complemented
73	#460×C₈₉	C₂²	1	2	yes	complemented
74	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	#459×C₈₉	C₂²	1	2	yes	complemented
76	#459×C₈₉	C₂²	1	2	yes	complemented
77	#450×C₈₉	C₂²	1	4	yes	complemented
78	#450×C₈₉	C₂²	1	4	yes	complemented
79	#449×C₈₉	C₂²	1	2	yes	complemented
80	#448×C₈₉	C₂²	1	4	yes	complemented
81	#447×C₈₉	C₂²	1	4	yes	complemented
82	#446×C₈₉	C₂²	1	2	yes	complemented
83	#440×C₈₉	C₂²	1	4	yes	complemented
84	#440×C₈₉	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
86	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
87	#435×C₈₉	C₂²	1	4	yes	complemented
88	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
89	#432×C₈₉	C₂²	1	2	yes	complemented
90	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#423×C₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
93	#418×C₈₉	C₂²	1	2	yes	complemented
94	C₂×#102×C₈₉	C₂²	1	4	yes	complemented
95	H(5,𝔽₂)×C₈₉	—	4	8	no	—
96	C₂×#41×C₈₉	—	2	2	no	—
97	C₂×#41×C₈₉	—	2	1	no	—
98	C₂×#41×C₈₉	—	2	2	no	—
99	C₂×#41×C₈₉	—	2	1	no	—
100	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
101	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₈₉	—	2	4	no	—
104	C₂²×D₄×C₈₉	—	2	2	no	—
105	C₂²×D₄×C₈₉	—	2	2	no	—
106	C₂²×D₄×C₈₉	—	2	1	no	—
107	C₂²×D₄×C₈₉	—	2	2	no	—
108	C₂²×D₄×C₈₉	—	2	1	no	—
109	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
110	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
111	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
112	C₂×SD₁₆×C₈₉	—	4	8	no	—
113	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
118	C₂×D₈×C₈₉	C₂³	1	2	yes	—
119	C₂×D₈×C₈₉	C₂³	1	4	yes	—
120	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
122	C₄⋊Q₈×C₈₉	—	2	1	no	—
123	C₄⋊Q₈×C₈₉	—	2	1	no	—
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
127	#127×C₈₉	—	2	1	no	—
128	#127×C₈₉	—	2	2	no	—
129	#127×C₈₉	—	2	1	no	—
130	#127×C₈₉	—	2	2	no	—
131	#127×C₈₉	C₂³	1	1	yes	characteristic
132	#127×C₈₉	C₂³	1	2	yes	—
133	#127×C₈₉	C₂³	1	2	yes	—
134	#127×C₈₉	C₂³	1	4	yes	—
135	#126×C₈₉	—	2	2	no	—
136	#126×C₈₉	—	2	2	no	—
137	#126×C₈₉	—	2	2	no	—
138	#125×C₈₉	—	2	2	no	—
139	#125×C₈₉	—	2	2	no	—
140	#125×C₈₉	—	2	1	no	—
141	#125×C₈₉	C₂³	1	2	yes	—
142	#124×C₈₉	—	2	2	no	—
143	#124×C₈₉	—	2	1	no	—
144	#124×C₈₉	—	2	2	no	—
145	#124×C₈₉	C₂³	1	2	yes	—
146	#123×C₈₉	—	2	2	no	—
147	#123×C₈₉	—	2	2	no	—
148	#123×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	—	2	1	no	—
150	C₂²⋊Q₈×C₈₉	—	2	1	no	—
151	C₂²⋊Q₈×C₈₉	—	2	1	no	—
152	C₂²⋊Q₈×C₈₉	—	2	2	no	—
153	C₂²⋊Q₈×C₈₉	—	2	2	no	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	1	no	—
159	#121×C₈₉	—	2	2	no	—
160	#121×C₈₉	—	2	4	no	—
161	#121×C₈₉	—	2	4	no	—
162	#121×C₈₉	—	2	2	no	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	#121×C₈₉	C₂³	1	4	yes	—
165	#121×C₈₉	C₂³	1	2	yes	—
166	#120×C₈₉	—	2	4	no	—
167	#120×C₈₉	—	2	4	no	—
168	#120×C₈₉	—	2	4	no	—
169	C₄×Q₈×C₈₉	—	2	1	no	—
170	C₄×Q₈×C₈₉	—	2	2	no	—
171	C₄×Q₈×C₈₉	—	2	2	no	—
172	C₄×Q₈×C₈₉	—	2	1	no	—
173	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
174	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
176	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
177	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
178	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
179	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₈₉	—	2	1	no	—
181	C₄×D₄×C₈₉	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	1	no	—
183	C₄×D₄×C₈₉	—	2	1	no	—
184	C₄×D₄×C₈₉	—	2	2	no	—
185	C₄×D₄×C₈₉	—	2	1	no	—
186	C₄×D₄×C₈₉	—	2	2	no	—
187	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
188	C₄×D₄×C₈₉	D₄	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₈₉	C₂³	1	2	yes	—
191	C₄×D₄×C₈₉	C₂³	1	4	yes	—
192	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₈₉	C₂³	1	2	yes	—
195	#117×C₈₉	—	2	1	no	—
196	#117×C₈₉	—	2	1	no	—
197	#117×C₈₉	—	2	2	no	—
198	#117×C₈₉	—	2	1	no	—
199	#117×C₈₉	—	2	2	no	—
200	#117×C₈₉	D₄	1	2	yes	—
201	#117×C₈₉	D₄	1	1	yes	characteristic
202	#117×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
204	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
205	C₂×C₄²×C₈₉	—	2	2	no	—
206	C₂×C₄²×C₈₉	—	2	1	no	—
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
209	#107×C₈₉	C₂³	1	2	yes	—
210	#107×C₈₉	C₂³	1	4	yes	—
211	#106×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
215	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
217	#103×C₈₉	C₂³	1	2	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	2	yes	—
220	#102×C₈₉	C₂³	1	4	yes	—
221	#102×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	2	yes	—
226	#102×C₈₉	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
228	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
229	#97×C₈₉	C₂³	1	4	yes	—
230	C₄×C₈×C₈₉	C₂³	1	2	yes	—
231	C₂⁴×C₈₉	—	2	2	no	—
232	C₂⁴×C₈₉	—	2	4	no	—
233	#41×C₈₉	—	2	4	no	—
234	#41×C₈₉	—	2	2	no	—
235	#41×C₈₉	—	4	1	no	—
236	#41×C₈₉	—	4	8	no	—
237	#41×C₈₉	—	4	4	no	—
238	#41×C₈₉	—	4	8	no	—
239	#41×C₈₉	—	4	4	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	2	1	no	—
242	C₂×Q₈×C₈₉	—	2	1	no	—
243	C₂×Q₈×C₈₉	—	2	4	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₈₉	—	2	1	no	—
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	2	no	—
251	C₂×D₄×C₈₉	—	2	4	no	—
252	C₂×D₄×C₈₉	—	2	1	no	—
253	C₂×D₄×C₈₉	—	2	2	no	—
254	C₂×D₄×C₈₉	—	2	4	no	—
255	C₂×D₄×C₈₉	—	2	2	no	—
256	C₂×D₄×C₈₉	—	2	1	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	—	2	2	no	—
259	C₂×D₄×C₈₉	—	2	4	no	—
260	C₂×D₄×C₈₉	—	2	4	no	—
261	C₂×D₄×C₈₉	—	2	2	no	—
262	C₂×D₄×C₈₉	—	4	4	no	—
263	C₂×D₄×C₈₉	—	4	2	no	—
264	C₂×D₄×C₈₉	—	4	4	no	—
265	C₂×D₄×C₈₉	—	4	2	no	—
266	C₂×D₄×C₈₉	—	4	8	no	—
267	C₂×D₄×C₈₉	—	4	4	no	—
268	C₂×D₄×C₈₉	—	4	16	no	—
269	C₂×D₄×C₈₉	—	4	8	no	—
270	C₂×D₄×C₈₉	—	8	4	no	—
271	C₂×D₄×C₈₉	—	8	2	no	—
272	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
275	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
276	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	—	2	2	no	—
278	C₂²×C₄×C₈₉	—	2	2	no	—
279	C₂²×C₄×C₈₉	—	2	1	no	—
280	C₂²×C₄×C₈₉	—	2	1	no	—
281	C₂²×C₄×C₈₉	—	2	1	no	—
282	C₂²×C₄×C₈₉	—	2	4	no	—
283	C₂²×C₄×C₈₉	—	2	2	no	—
284	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
290	SD₁₆×C₈₉	—	2	4	no	—
291	SD₁₆×C₈₉	—	2	8	no	—
292	SD₁₆×C₈₉	—	4	4	no	—
293	SD₁₆×C₈₉	—	4	4	no	—
294	SD₁₆×C₈₉	—	4	4	no	—
295	D₈×C₈₉	—	4	2	no	—
296	D₈×C₈₉	—	4	4	no	—
297	M₁₆×C₈₉	—	4	2	no	—
298	C₂×C₈×C₈₉	—	4	4	no	—
299	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
300	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
301	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₈₉	—	2	1	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
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	1	no	—
308	C₄⋊C₄×C₈₉	—	2	2	no	—
309	C₄⋊C₄×C₈₉	—	2	2	no	—
310	C₄⋊C₄×C₈₉	—	2	1	no	—
311	C₄⋊C₄×C₈₉	—	2	1	no	—
312	C₄⋊C₄×C₈₉	—	2	2	no	—
313	C₄⋊C₄×C₈₉	—	2	1	no	—
314	C₄⋊C₄×C₈₉	—	2	2	no	—
315	C₄⋊C₄×C₈₉	—	2	1	no	—
316	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
318	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
321	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	—	2	1	no	—
327	C₂²⋊C₄×C₈₉	—	2	2	no	—
328	C₂²⋊C₄×C₈₉	—	2	1	no	—
329	C₂²⋊C₄×C₈₉	—	2	1	no	—
330	C₂²⋊C₄×C₈₉	—	2	2	no	—
331	C₂²⋊C₄×C₈₉	—	2	2	no	—
332	C₂²⋊C₄×C₈₉	—	2	2	no	—
333	C₂²⋊C₄×C₈₉	—	2	4	no	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	2	no	—
336	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
337	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
338	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
339	C₄²×C₈₉	—	2	1	no	—
340	C₄²×C₈₉	—	2	1	no	—
341	C₄²×C₈₉	—	2	2	no	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	1	no	—
344	C₄²×C₈₉	—	2	2	no	—
345	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₈₉	C₂×D₄	1	2	yes	—
348	C₄²×C₈₉	C₂×D₄	1	2	yes	—
349	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₄²×C₈₉	C₂⁴	1	2	yes	—
351	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂³×C₈₉	—	2	1	no	—
353	C₂³×C₈₉	—	2	4	no	—
354	C₂³×C₈₉	—	2	2	no	—
355	C₂³×C₈₉	—	4	4	no	—
356	C₂³×C₈₉	—	4	8	no	—
357	C₂³×C₈₉	—	8	4	no	—
358	C₂³×C₈₉	—	8	2	no	—
359	C₂³×C₈₉	—	8	4	no	—
360	C₂³×C₈₉	—	8	2	no	—
361	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
362	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
363	Q₈×C₈₉	—	2	2	no	—
364	Q₈×C₈₉	—	2	1	no	—
365	Q₈×C₈₉	—	2	2	no	—
366	Q₈×C₈₉	—	2	2	no	—
367	Q₈×C₈₉	—	4	4	no	—
368	Q₈×C₈₉	—	4	2	no	—
369	Q₈×C₈₉	—	4	2	no	—
370	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	complemented
371	D₄×C₈₉	—	2	4	no	—
372	D₄×C₈₉	—	2	1	no	—
373	D₄×C₈₉	—	2	4	no	—
374	D₄×C₈₉	—	2	2	no	—
375	D₄×C₈₉	—	2	1	no	—
376	D₄×C₈₉	—	2	2	no	—
377	D₄×C₈₉	—	2	4	no	—
378	D₄×C₈₉	—	4	2	no	—
379	D₄×C₈₉	—	4	4	no	—
380	D₄×C₈₉	—	4	2	no	—
381	D₄×C₈₉	—	4	8	no	—
382	D₄×C₈₉	—	4	4	no	—
383	D₄×C₈₉	—	4	8	no	—
384	D₄×C₈₉	—	4	4	no	—
385	D₄×C₈₉	—	4	4	no	—
386	D₄×C₈₉	—	4	2	no	—
387	D₄×C₈₉	—	4	4	no	—
388	D₄×C₈₉	—	8	2	no	—
389	D₄×C₈₉	—	8	4	no	—
390	D₄×C₈₉	—	8	4	no	—
391	D₄×C₈₉	—	8	2	no	—
392	D₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
393	C₂×C₄×C₈₉	—	2	4	no	—
394	C₂×C₄×C₈₉	—	2	1	no	—
395	C₂×C₄×C₈₉	—	2	2	no	—
396	C₂×C₄×C₈₉	—	2	4	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	1	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	2	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	4	no	—
409	C₂×C₄×C₈₉	—	4	8	no	—
410	C₂×C₄×C₈₉	—	4	4	no	—
411	C₂×C₄×C₈₉	—	4	4	no	—
412	C₂×C₄×C₈₉	—	4	2	no	—
413	C₂×C₄×C₈₉	—	4	2	no	—
414	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
418	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
423	C₈×C₈₉	—	2	2	no	—
424	C₈×C₈₉	—	2	4	no	—
425	C₈×C₈₉	—	2	2	no	—
426	C₂²×C₈₉	—	2	2	no	—
427	C₂²×C₈₉	—	2	2	no	—
428	C₂²×C₈₉	—	2	1	no	—
429	C₂²×C₈₉	—	2	1	no	—
430	C₂²×C₈₉	—	2	1	no	—
431	C₂²×C₈₉	—	4	1	no	—
432	C₂²×C₈₉	—	4	4	no	—
433	C₂²×C₈₉	—	4	2	no	—
434	C₂²×C₈₉	—	4	4	no	—
435	C₂²×C₈₉	—	4	2	no	—
436	C₂²×C₈₉	—	4	1	no	—
437	C₂²×C₈₉	—	4	1	no	—
438	C₂²×C₈₉	—	4	2	no	—
439	C₂²×C₈₉	—	4	4	no	—
440	C₂²×C₈₉	—	16	8	no	—
441	C₂²×C₈₉	—	16	4	no	—
442	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
443	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
444	C₄×C₈₉	—	2	1	no	—
445	C₄×C₈₉	—	2	2	no	—
446	C₄×C₈₉	—	2	2	no	—
447	C₄×C₈₉	—	2	1	no	—
448	C₄×C₈₉	—	2	2	no	—
449	C₄×C₈₉	—	2	2	no	—
450	C₄×C₈₉	—	2	1	no	—
451	C₄×C₈₉	—	4	2	no	—
452	C₄×C₈₉	—	4	1	no	—
453	C₄×C₈₉	—	4	2	no	—
454	C₄×C₈₉	—	4	2	no	—
455	C₄×C₈₉	—	4	1	no	—
456	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
457	C₄×C₈₉	#577	1	2	yes	—
458	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₄×C₈₉	#585	1	1	yes	characteristic
460	#61983	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₈₉	—	2	4	no	—
462	C₂×C₈₉	—	4	1	no	—
463	C₂×C₈₉	—	8	1	no	—
464	C₂×C₈₉	—	8	2	no	—
465	C₂×C₈₉	—	8	4	no	—
466	C₂×C₈₉	#3488	1	1	yes	characteristic
467	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
468	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
469	#3498	C₂×C₈₉	1	1	yes	characteristic, complemented
470	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
471	#3397	C₂×C₈₉	1	2	yes	complemented
472	#3368	C₂×C₈₉	1	2	yes	complemented
473	#3310	C₂×C₈₉	1	4	yes	complemented
474	#3294	C₂×C₈₉	1	2	yes	complemented
475	D₄×SD₁₆	C₂×C₈₉	1	2	yes	complemented
476	#3265	C₂×C₈₉	1	4	yes	complemented
477	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
478	#3247	C₂×C₈₉	1	2	yes	complemented
479	#3217	C₂×C₈₉	1	2	yes	complemented
480	#3208	C₂×C₈₉	1	1	yes	characteristic, complemented
481	#3112	C₂×C₈₉	1	2	yes	complemented
482	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
483	#3038	C₂×C₈₉	1	1	yes	characteristic, complemented
484	C₂×#460	C₂×C₈₉	1	2	yes	complemented
485	#2990	C₂×C₈₉	1	1	yes	characteristic, complemented
486	C₈₉	#61983	1	1	yes	characteristic, direct product factor, Sylow
487	C₂×H(5,𝔽₂)	—	2	1	no	—
488	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	complemented
489	C₂²×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
490	#557	C₂²×C₈₉	1	1	yes	characteristic, complemented
491	#556	—	2	1	no	—
492	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
493	#552	—	2	2	no	—
494	#552	C₂²×C₈₉	1	2	yes	complemented
495	#550	—	2	1	no	—
496	#550	C₂²×C₈₉	1	2	yes	—
497	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
498	#548	C₂²×C₈₉	1	2	yes	complemented
499	#547	—	2	1	no	—
500	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	D₄²	—	2	1	no	—
502	D₄²	—	2	2	no	—
503	D₄²	C₂²×C₈₉	1	4	yes	—
504	D₄²	C₂²×C₈₉	1	2	yes	—
505	#535	—	2	2	no	—
506	#535	—	2	1	no	—
507	#533	—	2	1	no	—
508	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	#532	C₂²×C₈₉	1	1	yes	characteristic
510	#532	C₂²×C₈₉	1	2	yes	—
511	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
512	C₂×#127	C₂²×C₈₉	1	2	yes	—
513	#529	—	2	2	no	—
514	#529	C₂²×C₈₉	1	2	yes	complemented
515	C₄×#41	—	2	1	no	—
516	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
517	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
518	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
519	#496	C₂²×C₈₉	1	4	yes	complemented
520	#492	C₂²×C₈₉	1	2	yes	complemented
521	#490	C₂²×C₈₉	1	4	yes	complemented
522	#486	C₂²×C₈₉	1	2	yes	complemented
523	#482	C₂²×C₈₉	1	2	yes	complemented
524	#480	C₂²×C₈₉	1	4	yes	complemented
525	#478	C₂²×C₈₉	1	4	yes	complemented
526	#477	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	#477	C₂²×C₈₉	1	2	yes	complemented
528	#476	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	#474	C₂²×C₈₉	1	2	yes	complemented
530	#468	C₂²×C₈₉	1	4	yes	complemented
531	#466	C₂²×C₈₉	1	4	yes	complemented
532	#465	C₂²×C₈₉	1	4	yes	complemented
533	#463	C₂²×C₈₉	1	4	yes	complemented
534	#461	C₂²×C₈₉	1	2	yes	complemented
535	#460	C₂²×C₈₉	1	1	yes	characteristic, complemented
536	#460	C₂²×C₈₉	1	2	yes	complemented
537	#460	C₂²×C₈₉	1	2	yes	complemented
538	#460	C₂²×C₈₉	1	4	yes	complemented
539	#460	C₂²×C₈₉	1	2	yes	complemented
540	#460	C₂²×C₈₉	1	4	yes	complemented
541	#460	C₂²×C₈₉	1	2	yes	complemented
542	#460	C₂²×C₈₉	1	2	yes	complemented
543	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
544	#459	C₂²×C₈₉	1	2	yes	complemented
545	#459	C₂²×C₈₉	1	2	yes	complemented
546	#450	C₂²×C₈₉	1	4	yes	complemented
547	#450	C₂²×C₈₉	1	4	yes	complemented
548	#449	C₂²×C₈₉	1	2	yes	complemented
549	#448	C₂²×C₈₉	1	4	yes	complemented
550	#447	C₂²×C₈₉	1	4	yes	complemented
551	#446	C₂²×C₈₉	1	2	yes	complemented
552	#440	C₂²×C₈₉	1	4	yes	complemented
553	#440	C₂²×C₈₉	1	4	yes	complemented
554	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
555	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
556	#435	C₂²×C₈₉	1	4	yes	complemented
557	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
558	#432	C₂²×C₈₉	1	2	yes	complemented
559	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
560	#423	C₂²×C₈₉	1	1	yes	characteristic, complemented
561	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
562	#418	C₂²×C₈₉	1	2	yes	complemented
563	C₂×#102	C₂²×C₈₉	1	4	yes	complemented
564	H(5,𝔽₂)	—	4	8	no	—
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	2	no	—
568	C₂×#41	—	2	1	no	—
569	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
570	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
572	C₂²×D₄	—	2	4	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	2	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
579	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
580	AGL(1,ℤ/8)	—	4	4	no	—
581	C₂×SD₁₆	—	4	8	no	—
582	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
586	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
587	C₂×D₈	C₂³×C₈₉	1	4	yes	—
588	C₂×D₈	C₂³×C₈₉	1	2	yes	—
589	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
590	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
591	C₄⋊Q₈	—	2	1	no	—
592	C₄⋊Q₈	—	2	1	no	—
593	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
594	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
595	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
596	#127	—	2	1	no	—
597	#127	—	2	2	no	—
598	#127	—	2	1	no	—
599	#127	—	2	2	no	—
600	#127	C₂³×C₈₉	1	2	yes	—
601	#127	C₂³×C₈₉	1	1	yes	characteristic
602	#127	C₂³×C₈₉	1	2	yes	—
603	#127	C₂³×C₈₉	1	4	yes	—
604	#126	—	2	2	no	—
605	#126	—	2	2	no	—
606	#126	—	2	2	no	—
607	#125	—	2	2	no	—
608	#125	—	2	2	no	—
609	#125	—	2	1	no	—
610	#125	C₂³×C₈₉	1	2	yes	—
611	#124	—	2	2	no	—
612	#124	—	2	1	no	—
613	#124	—	2	2	no	—
614	#124	C₂³×C₈₉	1	2	yes	—
615	#123	—	2	2	no	—
616	#123	—	2	2	no	—
617	#123	—	2	2	no	—
618	C₂²⋊Q₈	—	2	1	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	1	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
624	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	—	2	1	no	—
628	#121	—	2	2	no	—
629	#121	—	2	4	no	—
630	#121	—	2	4	no	—
631	#121	—	2	2	no	—
632	#121	C₂³×C₈₉	1	2	yes	—
633	#121	C₂³×C₈₉	1	4	yes	—
634	#121	C₂³×C₈₉	1	2	yes	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	#120	—	2	4	no	—
638	C₄×Q₈	—	2	1	no	—
639	C₄×Q₈	—	2	2	no	—
640	C₄×Q₈	—	2	2	no	—
641	C₄×Q₈	—	2	1	no	—
642	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
643	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
644	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
645	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
646	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
647	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
648	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	1	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
657	C₄×D₄	D₄×C₈₉	1	2	yes	—
658	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
660	C₄×D₄	C₂³×C₈₉	1	2	yes	—
661	C₄×D₄	C₂³×C₈₉	1	4	yes	—
662	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₄×D₄	C₂³×C₈₉	1	2	yes	—
664	#117	—	2	1	no	—
665	#117	—	2	1	no	—
666	#117	—	2	2	no	—
667	#117	—	2	1	no	—
668	#117	—	2	2	no	—
669	#117	D₄×C₈₉	1	2	yes	—
670	#117	D₄×C₈₉	1	1	yes	characteristic
671	#117	C₂³×C₈₉	1	1	yes	characteristic
672	C₂×C₄⋊C₄	—	2	2	no	—
673	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
674	C₂×C₄²	—	2	2	no	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
677	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
678	#107	C₂³×C₈₉	1	2	yes	—
679	#107	C₂³×C₈₉	1	4	yes	—
680	#106	C₂³×C₈₉	1	2	yes	—
681	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
682	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
683	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
684	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
685	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
686	#103	C₂³×C₈₉	1	2	yes	—
687	#103	C₂³×C₈₉	1	4	yes	—
688	#102	C₂³×C₈₉	1	2	yes	—
689	#102	C₂³×C₈₉	1	4	yes	—
690	#102	C₂³×C₈₉	1	4	yes	—
691	#102	C₂³×C₈₉	1	4	yes	—
692	#102	C₂³×C₈₉	1	4	yes	—
693	#102	C₂³×C₈₉	1	2	yes	—
694	#102	C₂³×C₈₉	1	2	yes	—
695	#102	C₂³×C₈₉	1	4	yes	—
696	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
697	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
698	#97	C₂³×C₈₉	1	4	yes	—
699	C₄×C₈	C₂³×C₈₉	1	2	yes	—
700	C₂⁴	—	2	2	no	—
701	C₂⁴	—	2	4	no	—
702	#41	—	2	4	no	—
703	#41	—	2	2	no	—
704	#41	—	4	1	no	—
705	#41	—	4	8	no	—
706	#41	—	4	4	no	—
707	#41	—	4	8	no	—
708	#41	—	4	4	no	—
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	1	no	—
711	C₂×Q₈	—	2	1	no	—
712	C₂×Q₈	—	2	4	no	—
713	C₂×Q₈	—	4	2	no	—
714	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
715	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	4	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	4	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	8	no	—
736	C₂×D₄	—	4	4	no	—
737	C₂×D₄	—	4	16	no	—
738	C₂×D₄	—	4	8	no	—
739	C₂×D₄	—	8	4	no	—
740	C₂×D₄	—	8	2	no	—
741	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
743	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
744	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
745	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
755	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
759	SD₁₆	—	2	4	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	4	4	no	—
762	SD₁₆	—	4	4	no	—
763	SD₁₆	—	4	4	no	—
764	D₈	—	4	4	no	—
765	D₈	—	4	2	no	—
766	M₁₆	—	4	2	no	—
767	C₂×C₈	—	4	4	no	—
768	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
769	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
770	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	1	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	2	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
787	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
788	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄×C₈₉	1	2	yes	—
806	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
807	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	2	no	—
814	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
815	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
816	C₄²	C₂×D₄×C₈₉	1	2	yes	—
817	C₄²	C₂×D₄×C₈₉	1	2	yes	—
818	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
819	C₄²	C₂⁴×C₈₉	1	2	yes	—
820	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
821	C₂³	—	2	1	no	—
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	4	4	no	—
825	C₂³	—	4	8	no	—
826	C₂³	—	8	4	no	—
827	C₂³	—	8	2	no	—
828	C₂³	—	8	4	no	—
829	C₂³	—	8	2	no	—
830	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
831	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	1	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	4	4	no	—
837	Q₈	—	4	2	no	—
838	Q₈	—	4	2	no	—
839	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	complemented
840	D₄	—	2	4	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	1	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	4	no	—
847	D₄	—	4	2	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	2	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	2	no	—
856	D₄	—	4	4	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	4	no	—
859	D₄	—	8	4	no	—
860	D₄	—	8	2	no	—
861	D₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	complemented
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	4	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	8	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	4	2	no	—
883	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
884	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
885	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
886	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
887	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
889	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
891	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
892	C₈	—	2	2	no	—
893	C₈	—	2	4	no	—
894	C₈	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	4	4	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	4	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	4	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	16	8	no	—
910	C₂²	—	16	4	no	—
911	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
912	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
913	C₄	—	2	1	no	—
914	C₄	—	2	2	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	1	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
926	C₄	#577×C₈₉	1	2	yes	—
927	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
928	C₄	#585×C₈₉	1	1	yes	characteristic
929	C₂	—	2	4	no	—
930	C₂	—	4	1	no	—
931	C₂	—	8	1	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	4	no	—
934	C₂	C₈₉×#3488	1	1	yes	characteristic
935	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
936	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3498	C₂	semidirect
2. C₈₉×#3482	C₂	semidirect
3. C₈₉×#3397	C₂	semidirect
4. C₈₉×#3368	C₂	semidirect
5. C₈₉×#3310	C₂	semidirect
6. C₈₉×#3294	C₂	semidirect
7. D₄×SD₁₆×C₈₉	C₂	semidirect
8. C₈₉×#3265	C₂	semidirect
9. C₈₉×#3254	C₂	semidirect
10. C₈₉×#3247	C₂	semidirect
11. C₈₉×#3217	C₂	semidirect
12. C₈₉×#3208	C₂	semidirect
13. C₈₉×#3112	C₂	semidirect
14. C₈₉×#3106	C₂	semidirect
15. C₈₉×#3038	C₂	semidirect
16. C₂×#460×C₈₉	C₂	semidirect
17. C₈₉×#2990	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
20. C₂²×SD₁₆×C₈₉	C₂²	semidirect
21. #557×C₈₉	C₂²	semidirect
23. #556×C₈₉	C₂²	semidirect
25. #552×C₈₉	C₂²	semidirect
28. D₄×Q₈×C₈₉	C₂²	semidirect
29. #548×C₈₉	C₂²	semidirect
31. #547×C₈₉	C₂²	semidirect
39. #533×C₈₉	C₂²	semidirect
45. #529×C₈₉	C₂²	semidirect
48. C₄×#41×C₈₉	C₂²	semidirect
49. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
50. #496×C₈₉	C₂²	semidirect
51. #492×C₈₉	C₂²	semidirect
52. #490×C₈₉	C₂²	semidirect
53. #486×C₈₉	C₂²	semidirect
54. #482×C₈₉	C₂²	semidirect
55. #480×C₈₉	C₂²	semidirect
56. #478×C₈₉	C₂²	semidirect
57. #477×C₈₉	C₂²	semidirect
58. #477×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #474×C₈₉	C₂²	semidirect
61. #468×C₈₉	C₂²	semidirect
62. #466×C₈₉	C₂²	semidirect
63. #465×C₈₉	C₂²	semidirect
64. #463×C₈₉	C₂²	semidirect
65. #461×C₈₉	C₂²	semidirect
66. #460×C₈₉	C₂²	semidirect
67. #460×C₈₉	C₂²	semidirect
68. #460×C₈₉	C₂²	semidirect
69. #460×C₈₉	C₂²	semidirect
70. #460×C₈₉	C₂²	semidirect
71. #460×C₈₉	C₂²	semidirect
72. #460×C₈₉	C₂²	semidirect
73. #460×C₈₉	C₂²	semidirect
74. #459×C₈₉	C₂²	semidirect
75. #459×C₈₉	C₂²	semidirect
76. #459×C₈₉	C₂²	semidirect
77. #450×C₈₉	C₂²	semidirect
78. #450×C₈₉	C₂²	semidirect
79. #449×C₈₉	C₂²	semidirect
80. #448×C₈₉	C₂²	semidirect
81. #447×C₈₉	C₂²	semidirect
82. #446×C₈₉	C₂²	semidirect
83. #440×C₈₉	C₂²	semidirect
84. #440×C₈₉	C₂²	semidirect
85. C₄×SD₁₆×C₈₉	C₂²	semidirect
86. C₄×D₈×C₈₉	C₂²	semidirect
87. #435×C₈₉	C₂²	semidirect
88. C₈×D₄×C₈₉	C₂²	semidirect
89. #432×C₈₉	C₂²	semidirect
90. #431×C₈₉	C₂²	semidirect
91. #423×C₈₉	C₂²	semidirect
92. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
93. #418×C₈₉	C₂²	semidirect
94. C₂×#102×C₈₉	C₂²	semidirect
370. Q₈×C₈₉	H(5,𝔽₂)	semidirect
392. D₄×C₈₉	AGL(1,ℤ/8)	semidirect
460. #61983	C₈₉	direct (N × H)
469. #3498	C₂×C₈₉	semidirect
470. #3482	C₂×C₈₉	semidirect
471. #3397	C₂×C₈₉	semidirect
472. #3368	C₂×C₈₉	semidirect
473. #3310	C₂×C₈₉	semidirect
474. #3294	C₂×C₈₉	semidirect
475. D₄×SD₁₆	C₂×C₈₉	semidirect
476. #3265	C₂×C₈₉	semidirect
477. #3254	C₂×C₈₉	semidirect
478. #3247	C₂×C₈₉	semidirect
479. #3217	C₂×C₈₉	semidirect
480. #3208	C₂×C₈₉	semidirect
481. #3112	C₂×C₈₉	semidirect
482. #3106	C₂×C₈₉	semidirect
483. #3038	C₂×C₈₉	semidirect
484. C₂×#460	C₂×C₈₉	semidirect
485. #2990	C₂×C₈₉	semidirect
486. C₈₉	#61983	direct (N × H)
488. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
489. C₂²×SD₁₆	C₂²×C₈₉	semidirect
490. #557	C₂²×C₈₉	semidirect
492. #556	C₂²×C₈₉	semidirect
494. #552	C₂²×C₈₉	semidirect
497. D₄×Q₈	C₂²×C₈₉	semidirect
498. #548	C₂²×C₈₉	semidirect
500. #547	C₂²×C₈₉	semidirect
508. #533	C₂²×C₈₉	semidirect
514. #529	C₂²×C₈₉	semidirect
517. C₄×#41	C₂²×C₈₉	semidirect
518. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
519. #496	C₂²×C₈₉	semidirect
520. #492	C₂²×C₈₉	semidirect
521. #490	C₂²×C₈₉	semidirect
522. #486	C₂²×C₈₉	semidirect
523. #482	C₂²×C₈₉	semidirect
524. #480	C₂²×C₈₉	semidirect
525. #478	C₂²×C₈₉	semidirect
526. #477	C₂²×C₈₉	semidirect
527. #477	C₂²×C₈₉	semidirect
528. #476	C₂²×C₈₉	semidirect
529. #474	C₂²×C₈₉	semidirect
530. #468	C₂²×C₈₉	semidirect
531. #466	C₂²×C₈₉	semidirect
532. #465	C₂²×C₈₉	semidirect
533. #463	C₂²×C₈₉	semidirect
534. #461	C₂²×C₈₉	semidirect
535. #460	C₂²×C₈₉	semidirect
536. #460	C₂²×C₈₉	semidirect
537. #460	C₂²×C₈₉	semidirect
538. #460	C₂²×C₈₉	semidirect
539. #460	C₂²×C₈₉	semidirect
540. #460	C₂²×C₈₉	semidirect
541. #460	C₂²×C₈₉	semidirect
542. #460	C₂²×C₈₉	semidirect
543. #459	C₂²×C₈₉	semidirect
544. #459	C₂²×C₈₉	semidirect
545. #459	C₂²×C₈₉	semidirect
546. #450	C₂²×C₈₉	semidirect
547. #450	C₂²×C₈₉	semidirect
548. #449	C₂²×C₈₉	semidirect
549. #448	C₂²×C₈₉	semidirect
550. #447	C₂²×C₈₉	semidirect
551. #446	C₂²×C₈₉	semidirect
552. #440	C₂²×C₈₉	semidirect
553. #440	C₂²×C₈₉	semidirect
554. C₄×SD₁₆	C₂²×C₈₉	semidirect
555. C₄×D₈	C₂²×C₈₉	semidirect
556. #435	C₂²×C₈₉	semidirect
557. C₈×D₄	C₂²×C₈₉	semidirect
558. #432	C₂²×C₈₉	semidirect
559. #431	C₂²×C₈₉	semidirect
560. #423	C₂²×C₈₉	semidirect
561. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
562. #418	C₂²×C₈₉	semidirect
563. C₂×#102	C₂²×C₈₉	semidirect
839. Q₈	H(5,𝔽₂)×C₈₉	semidirect
861. D₄	AGL(1,ℤ/8)×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3498	2
C₈₉×#3482	2
C₈₉×#3397	2
C₈₉×#3368	2
C₈₉×#3310	2
C₈₉×#3294	2
D₄×SD₁₆×C₈₉	2
C₈₉×#3265	2
C₈₉×#3254	2
C₈₉×#3247	2
C₈₉×#3217	2
C₈₉×#3208	2
C₈₉×#3112	2
C₈₉×#3106	2
C₈₉×#3038	2
C₂×#460×C₈₉	2
C₈₉×#2990	2
#61983	89

Subgroups — C89×#61983 #36439831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61983 #36439831