Subgroups — C₈₉×#61959 #36439807

Order 22784.

2178 conjugacy classes of subgroups.

The subgroup lattice has 956 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×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3397	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3366	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3325	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3310	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3272	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3264	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3251	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3217	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3115	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3038	C₂	1	2	yes	maximal, complemented
16	C₂×#459×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2989	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	4	yes	complemented
20	C₂²×D₈×C₈₉	C₂²	1	2	yes	complemented
21	#556×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	#555×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	#554×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#553×C₈₉	—	2	1	no	—
25	#552×C₈₉	—	2	1	no	—
26	#552×C₈₉	C₂²	1	2	yes	complemented
27	#551×C₈₉	—	2	2	no	—
28	#550×C₈₉	—	2	1	no	—
29	#550×C₈₉	C₂²	1	2	yes	complemented
30	#547×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#546×C₈₉	C₂²	1	2	yes	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	complemented
36	#535×C₈₉	—	2	1	no	—
37	#535×C₈₉	—	2	2	no	—
38	#533×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	#532×C₈₉	C₂²	1	2	yes	complemented
41	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
43	#529×C₈₉	—	2	2	no	—
44	#529×C₈₉	C₂²	1	2	yes	complemented
45	#525×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
47	C₄×#41×C₈₉	C₂²	1	2	yes	complemented
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#117×C₈₉	—	2	1	no	—
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	4	yes	complemented
55	#480×C₈₉	C₂²	1	2	yes	complemented
56	#478×C₈₉	C₂²	1	4	yes	complemented
57	#476×C₈₉	C₂²	1	2	yes	complemented
58	#475×C₈₉	C₂²	1	2	yes	complemented
59	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#474×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#469×C₈₉	C₂²	1	4	yes	complemented
62	#468×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	2	yes	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	#459×C₈₉	C₂²	1	2	yes	complemented
71	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	#459×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	#459×C₈₉	C₂²	1	4	yes	complemented
74	#459×C₈₉	C₂²	1	2	yes	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	4	yes	complemented
80	#447×C₈₉	C₂²	1	4	yes	complemented
81	#447×C₈₉	C₂²	1	2	yes	complemented
82	#446×C₈₉	C₂²	1	2	yes	complemented
83	#442×C₈₉	C₂²	1	4	yes	complemented
84	#440×C₈₉	C₂²	1	4	yes	complemented
85	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
86	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
87	#436×C₈₉	C₂²	1	2	yes	complemented
88	#435×C₈₉	C₂²	1	4	yes	complemented
89	#432×C₈₉	C₂²	1	2	yes	complemented
90	#431×C₈₉	C₂²	1	1	yes	characteristic, complemented
91	#423×C₈₉	C₂²	1	2	yes	complemented
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
93	#418×C₈₉	C₂²	1	4	yes	complemented
94	C₂×#102×C₈₉	C₂²	1	2	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	D₄	1	1	yes	characteristic
100	C₂×#41×C₈₉	C₂³	1	2	yes	—
101	C₂²×D₄×C₈₉	—	2	4	no	—
102	C₂²×D₄×C₈₉	—	2	2	no	—
103	C₂²×D₄×C₈₉	—	2	1	no	—
104	C₂²×D₄×C₈₉	—	2	2	no	—
105	C₂²×D₄×C₈₉	—	2	1	no	—
106	C₂²×D₄×C₈₉	—	2	2	no	—
107	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
109	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
110	C₂³×C₄×C₈₉	—	2	1	no	—
111	AGL(1,ℤ/8)×C₈₉	—	4	8	no	—
112	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
114	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
115	C₂×D₈×C₈₉	—	4	4	no	—
116	C₂×D₈×C₈₉	C₂³	1	2	yes	—
117	C₂×D₈×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	4	yes	—
121	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	#127×C₈₉	—	2	1	no	—
126	#127×C₈₉	—	2	1	no	—
127	#127×C₈₉	—	2	2	no	—
128	#127×C₈₉	—	2	2	no	—
129	#127×C₈₉	C₂³	1	2	yes	—
130	#127×C₈₉	C₂³	1	1	yes	characteristic
131	#127×C₈₉	C₂³	1	2	yes	—
132	#127×C₈₉	C₂³	1	4	yes	—
133	#126×C₈₉	—	2	2	no	—
134	#126×C₈₉	—	2	2	no	—
135	#126×C₈₉	—	2	2	no	—
136	#125×C₈₉	—	2	2	no	—
137	#125×C₈₉	—	2	1	no	—
138	#125×C₈₉	C₂³	1	2	yes	—
139	#124×C₈₉	—	2	2	no	—
140	#124×C₈₉	—	2	1	no	—
141	#124×C₈₉	—	2	2	no	—
142	#124×C₈₉	C₂³	1	2	yes	—
143	#123×C₈₉	—	2	2	no	—
144	#123×C₈₉	—	2	2	no	—
145	#123×C₈₉	—	2	2	no	—
146	#123×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	1	no	—
148	C₂²⋊Q₈×C₈₉	—	2	1	no	—
149	C₂²⋊Q₈×C₈₉	—	2	1	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
153	#121×C₈₉	—	2	1	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	1	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	2	no	—
158	#121×C₈₉	—	2	4	no	—
159	#121×C₈₉	—	2	4	no	—
160	#121×C₈₉	—	2	2	no	—
161	#121×C₈₉	—	2	2	no	—
162	#121×C₈₉	C₂³	1	2	yes	—
163	#121×C₈₉	C₂³	1	2	yes	—
164	#121×C₈₉	C₂³	1	4	yes	—
165	#120×C₈₉	—	2	2	no	—
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	D₄	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
173	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	2	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	1	no	—
179	C₄×D₄×C₈₉	—	2	1	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	D₄	1	2	yes	—
182	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₈₉	C₂³	1	2	yes	—
186	C₄×D₄×C₈₉	C₂³	1	4	yes	—
187	C₄×D₄×C₈₉	C₂³	1	2	yes	—
188	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₈₉	C₂³	1	2	yes	—
191	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
192	#117×C₈₉	—	2	1	no	—
193	#117×C₈₉	—	2	1	no	—
194	#117×C₈₉	—	2	1	no	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	—	2	2	no	—
197	#117×C₈₉	—	2	2	no	—
198	#117×C₈₉	D₄	1	1	yes	characteristic
199	#117×C₈₉	D₄	1	2	yes	—
200	#117×C₈₉	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
206	C₂×C₄²×C₈₉	—	2	2	no	—
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	2	yes	—
210	#107×C₈₉	C₂³	1	2	yes	—
211	#106×C₈₉	C₂³	1	4	yes	—
212	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
216	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
217	#103×C₈₉	C₂³	1	4	yes	—
218	#102×C₈₉	C₂³	1	4	yes	—
219	#102×C₈₉	C₂³	1	4	yes	—
220	#102×C₈₉	C₂³	1	2	yes	—
221	#102×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	4	yes	—
223	#102×C₈₉	C₂³	1	2	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	1	no	—
232	C₂⁴×C₈₉	—	2	4	no	—
233	C₂⁴×C₈₉	—	2	2	no	—
234	#41×C₈₉	—	2	4	no	—
235	#41×C₈₉	—	2	4	no	—
236	#41×C₈₉	—	4	2	no	—
237	#41×C₈₉	—	4	8	no	—
238	#41×C₈₉	—	4	8	no	—
239	#41×C₈₉	—	4	4	no	—
240	C₂×Q₈×C₈₉	—	2	1	no	—
241	C₂×Q₈×C₈₉	—	2	1	no	—
242	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	2	4	no	—
247	C₂×D₄×C₈₉	—	2	2	no	—
248	C₂×D₄×C₈₉	—	2	2	no	—
249	C₂×D₄×C₈₉	—	2	1	no	—
250	C₂×D₄×C₈₉	—	2	1	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	4	no	—
253	C₂×D₄×C₈₉	—	2	2	no	—
254	C₂×D₄×C₈₉	—	2	1	no	—
255	C₂×D₄×C₈₉	—	2	2	no	—
256	C₂×D₄×C₈₉	—	2	4	no	—
257	C₂×D₄×C₈₉	—	2	2	no	—
258	C₂×D₄×C₈₉	—	2	4	no	—
259	C₂×D₄×C₈₉	—	2	2	no	—
260	C₂×D₄×C₈₉	—	4	1	no	—
261	C₂×D₄×C₈₉	—	4	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	8	no	—
266	C₂×D₄×C₈₉	—	4	16	no	—
267	C₂×D₄×C₈₉	—	4	8	no	—
268	C₂×D₄×C₈₉	—	4	4	no	—
269	C₂×D₄×C₈₉	—	8	2	no	—
270	C₂×D₄×C₈₉	—	8	4	no	—
271	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
272	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
274	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	—	2	1	no	—
278	C₂²×C₄×C₈₉	—	2	1	no	—
279	C₂²×C₄×C₈₉	—	2	2	no	—
280	C₂²×C₄×C₈₉	—	2	1	no	—
281	C₂²×C₄×C₈₉	—	2	1	no	—
282	C₂²×C₄×C₈₉	—	2	1	no	—
283	C₂²×C₄×C₈₉	—	2	4	no	—
284	C₂²×C₄×C₈₉	—	2	2	no	—
285	C₂²×C₄×C₈₉	—	2	2	no	—
286	C₂²×C₄×C₈₉	—	4	4	no	—
287	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
293	SD₁₆×C₈₉	—	4	4	no	—
294	SD₁₆×C₈₉	—	4	4	no	—
295	SD₁₆×C₈₉	—	4	4	no	—
296	D₈×C₈₉	—	2	8	no	—
297	D₈×C₈₉	—	2	4	no	—
298	D₈×C₈₉	—	4	4	no	—
299	D₈×C₈₉	—	4	2	no	—
300	M₁₆×C₈₉	—	4	4	no	—
301	C₂×C₈×C₈₉	—	4	2	no	—
302	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
303	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
304	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₈₉	—	2	1	no	—
306	C₄⋊C₄×C₈₉	—	2	1	no	—
307	C₄⋊C₄×C₈₉	—	2	2	no	—
308	C₄⋊C₄×C₈₉	—	2	2	no	—
309	C₄⋊C₄×C₈₉	—	2	1	no	—
310	C₄⋊C₄×C₈₉	—	2	2	no	—
311	C₄⋊C₄×C₈₉	—	2	2	no	—
312	C₄⋊C₄×C₈₉	—	2	1	no	—
313	C₄⋊C₄×C₈₉	—	2	2	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	1	yes	characteristic
318	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
319	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
321	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
327	C₂²⋊C₄×C₈₉	—	2	1	no	—
328	C₂²⋊C₄×C₈₉	—	2	2	no	—
329	C₂²⋊C₄×C₈₉	—	2	2	no	—
330	C₂²⋊C₄×C₈₉	—	2	1	no	—
331	C₂²⋊C₄×C₈₉	—	2	1	no	—
332	C₂²⋊C₄×C₈₉	—	2	1	no	—
333	C₂²⋊C₄×C₈₉	—	2	2	no	—
334	C₂²⋊C₄×C₈₉	—	2	4	no	—
335	C₂²⋊C₄×C₈₉	—	2	2	no	—
336	C₂²⋊C₄×C₈₉	—	2	2	no	—
337	C₂²⋊C₄×C₈₉	—	2	4	no	—
338	C₂²⋊C₄×C₈₉	—	2	2	no	—
339	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
342	C₄²×C₈₉	—	2	2	no	—
343	C₄²×C₈₉	—	2	2	no	—
344	C₄²×C₈₉	—	2	2	no	—
345	C₄²×C₈₉	C₂×D₄	1	2	yes	—
346	C₄²×C₈₉	C₂×D₄	1	2	yes	—
347	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
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	1	no	—
354	C₂³×C₈₉	—	2	4	no	—
355	C₂³×C₈₉	—	2	2	no	—
356	C₂³×C₈₉	—	4	2	no	—
357	C₂³×C₈₉	—	4	8	no	—
358	C₂³×C₈₉	—	4	2	no	—
359	C₂³×C₈₉	—	4	4	no	—
360	C₂³×C₈₉	—	8	1	no	—
361	C₂³×C₈₉	—	8	2	no	—
362	C₂³×C₈₉	—	8	4	no	—
363	C₂³×C₈₉	—	8	2	no	—
364	C₂³×C₈₉	—	8	4	no	—
365	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
366	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₈₉	—	2	2	no	—
368	Q₈×C₈₉	—	2	2	no	—
369	Q₈×C₈₉	—	2	2	no	—
370	Q₈×C₈₉	—	4	2	no	—
371	Q₈×C₈₉	—	8	1	no	—
372	D₄×C₈₉	—	2	4	no	—
373	D₄×C₈₉	—	2	2	no	—
374	D₄×C₈₉	—	2	4	no	—
375	D₄×C₈₉	—	2	2	no	—
376	D₄×C₈₉	—	2	1	no	—
377	D₄×C₈₉	—	2	1	no	—
378	D₄×C₈₉	—	2	1	no	—
379	D₄×C₈₉	—	2	2	no	—
380	D₄×C₈₉	—	2	4	no	—
381	D₄×C₈₉	—	4	2	no	—
382	D₄×C₈₉	—	4	8	no	—
383	D₄×C₈₉	—	4	2	no	—
384	D₄×C₈₉	—	4	4	no	—
385	D₄×C₈₉	—	4	4	no	—
386	D₄×C₈₉	—	4	8	no	—
387	D₄×C₈₉	—	4	4	no	—
388	D₄×C₈₉	—	4	2	no	—
389	D₄×C₈₉	—	4	4	no	—
390	D₄×C₈₉	—	4	4	no	—
391	D₄×C₈₉	—	8	4	no	—
392	D₄×C₈₉	—	8	2	no	—
393	D₄×C₈₉	—	8	4	no	—
394	D₄×C₈₉	—	8	2	no	—
395	D₄×C₈₉	—	8	2	no	—
396	D₄×C₈₉	H(5,𝔽₂)	1	2	yes	complemented
397	C₂×C₄×C₈₉	—	2	4	no	—
398	C₂×C₄×C₈₉	—	2	1	no	—
399	C₂×C₄×C₈₉	—	2	2	no	—
400	C₂×C₄×C₈₉	—	2	1	no	—
401	C₂×C₄×C₈₉	—	2	2	no	—
402	C₂×C₄×C₈₉	—	2	1	no	—
403	C₂×C₄×C₈₉	—	2	2	no	—
404	C₂×C₄×C₈₉	—	2	2	no	—
405	C₂×C₄×C₈₉	—	2	2	no	—
406	C₂×C₄×C₈₉	—	2	1	no	—
407	C₂×C₄×C₈₉	—	4	2	no	—
408	C₂×C₄×C₈₉	—	4	1	no	—
409	C₂×C₄×C₈₉	—	4	4	no	—
410	C₂×C₄×C₈₉	—	4	8	no	—
411	C₂×C₄×C₈₉	—	4	2	no	—
412	C₂×C₄×C₈₉	—	4	2	no	—
413	C₂×C₄×C₈₉	—	4	2	no	—
414	C₂×C₄×C₈₉	—	4	2	no	—
415	C₂×C₄×C₈₉	—	4	2	no	—
416	C₂×C₄×C₈₉	—	4	4	no	—
417	C₂×C₄×C₈₉	—	8	2	no	—
418	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
419	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
428	C₈×C₈₉	—	2	4	no	—
429	C₈×C₈₉	—	2	2	no	—
430	C₈×C₈₉	—	2	2	no	—
431	C₂²×C₈₉	—	2	1	no	—
432	C₂²×C₈₉	—	2	1	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	—	4	1	no	—
438	C₂²×C₈₉	—	4	1	no	—
439	C₂²×C₈₉	—	4	4	no	—
440	C₂²×C₈₉	—	4	2	no	—
441	C₂²×C₈₉	—	4	1	no	—
442	C₂²×C₈₉	—	4	1	no	—
443	C₂²×C₈₉	—	4	4	no	—
444	C₂²×C₈₉	—	4	2	no	—
445	C₂²×C₈₉	—	4	1	no	—
446	C₂²×C₈₉	—	4	4	no	—
447	C₂²×C₈₉	—	4	2	no	—
448	C₂²×C₈₉	—	8	4	no	—
449	C₂²×C₈₉	—	16	4	no	—
450	C₂²×C₈₉	—	16	8	no	—
451	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
452	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₈₉	—	2	1	no	—
454	C₄×C₈₉	—	2	2	no	—
455	C₄×C₈₉	—	2	1	no	—
456	C₄×C₈₉	—	2	2	no	—
457	C₄×C₈₉	—	2	1	no	—
458	C₄×C₈₉	—	2	2	no	—
459	C₄×C₈₉	—	4	2	no	—
460	C₄×C₈₉	—	4	2	no	—
461	C₄×C₈₉	—	4	1	no	—
462	C₄×C₈₉	—	4	1	no	—
463	C₄×C₈₉	—	4	2	no	—
464	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
465	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
466	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₄×C₈₉	#585	1	1	yes	characteristic
468	#61959	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
469	C₂×C₈₉	—	2	2	no	—
470	C₂×C₈₉	—	4	2	no	—
471	C₂×C₈₉	—	4	2	no	—
472	C₂×C₈₉	—	8	1	no	—
473	C₂×C₈₉	—	8	4	no	—
474	C₂×C₈₉	—	8	2	no	—
475	C₂×C₈₉	#3488	1	1	yes	characteristic
476	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂×C₈₉	#3585	1	1	yes	characteristic
478	#3498	C₂×C₈₉	1	1	yes	characteristic, complemented
479	#3475	C₂×C₈₉	1	1	yes	characteristic, complemented
480	#3397	C₂×C₈₉	1	2	yes	complemented
481	#3366	C₂×C₈₉	1	2	yes	complemented
482	#3325	C₂×C₈₉	1	2	yes	complemented
483	#3310	C₂×C₈₉	1	4	yes	complemented
484	#3272	C₂×C₈₉	1	2	yes	complemented
485	#3264	C₂×C₈₉	1	4	yes	complemented
486	#3251	C₂×C₈₉	1	2	yes	complemented
487	#3246	C₂×C₈₉	1	1	yes	characteristic, complemented
488	#3217	C₂×C₈₉	1	2	yes	complemented
489	#3208	C₂×C₈₉	1	1	yes	characteristic, complemented
490	#3115	C₂×C₈₉	1	2	yes	complemented
491	#3100	C₂×C₈₉	1	1	yes	characteristic, complemented
492	#3038	C₂×C₈₉	1	2	yes	complemented
493	C₂×#459	C₂×C₈₉	1	1	yes	characteristic, complemented
494	#2989	C₂×C₈₉	1	1	yes	characteristic, complemented
495	C₈₉	#61959	1	1	yes	characteristic, direct product factor, Sylow
496	C₂×H(5,𝔽₂)	—	2	1	no	—
497	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	complemented
498	C₂²×D₈	C₂²×C₈₉	1	2	yes	complemented
499	#556	C₂²×C₈₉	1	1	yes	characteristic, complemented
500	#555	C₂²×C₈₉	1	1	yes	characteristic, complemented
501	#554	C₂²×C₈₉	1	1	yes	characteristic, complemented
502	#553	—	2	1	no	—
503	#552	—	2	1	no	—
504	#552	C₂²×C₈₉	1	2	yes	complemented
505	#551	—	2	2	no	—
506	#550	—	2	1	no	—
507	#550	C₂²×C₈₉	1	2	yes	complemented
508	#547	C₂²×C₈₉	1	1	yes	characteristic, complemented
509	#546	C₂²×C₈₉	1	2	yes	complemented
510	D₄²	—	2	1	no	—
511	D₄²	—	2	2	no	—
512	D₄²	C₂²×C₈₉	1	4	yes	—
513	D₄²	C₂²×C₈₉	1	2	yes	complemented
514	#535	—	2	1	no	—
515	#535	—	2	2	no	—
516	#533	C₂²×C₈₉	1	1	yes	characteristic, complemented
517	#532	C₂²×C₈₉	1	1	yes	characteristic
518	#532	C₂²×C₈₉	1	2	yes	complemented
519	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
520	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
521	#529	—	2	2	no	—
522	#529	C₂²×C₈₉	1	2	yes	complemented
523	#525	—	2	1	no	—
524	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
525	C₄×#41	C₂²×C₈₉	1	2	yes	complemented
526	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
527	C₂×#117	—	2	1	no	—
528	#496	C₂²×C₈₉	1	4	yes	complemented
529	#492	C₂²×C₈₉	1	2	yes	complemented
530	#490	C₂²×C₈₉	1	4	yes	complemented
531	#486	C₂²×C₈₉	1	2	yes	complemented
532	#482	C₂²×C₈₉	1	4	yes	complemented
533	#480	C₂²×C₈₉	1	2	yes	complemented
534	#478	C₂²×C₈₉	1	4	yes	complemented
535	#476	C₂²×C₈₉	1	2	yes	complemented
536	#475	C₂²×C₈₉	1	2	yes	complemented
537	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
538	#474	C₂²×C₈₉	1	1	yes	characteristic, complemented
539	#469	C₂²×C₈₉	1	4	yes	complemented
540	#468	C₂²×C₈₉	1	4	yes	complemented
541	#465	C₂²×C₈₉	1	4	yes	complemented
542	#463	C₂²×C₈₉	1	4	yes	complemented
543	#461	C₂²×C₈₉	1	2	yes	complemented
544	#460	C₂²×C₈₉	1	2	yes	complemented
545	#460	C₂²×C₈₉	1	4	yes	complemented
546	#460	C₂²×C₈₉	1	2	yes	complemented
547	#460	C₂²×C₈₉	1	2	yes	complemented
548	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
549	#459	C₂²×C₈₉	1	1	yes	characteristic, complemented
550	#459	C₂²×C₈₉	1	4	yes	complemented
551	#459	C₂²×C₈₉	1	2	yes	complemented
552	#459	C₂²×C₈₉	1	2	yes	complemented
553	#459	C₂²×C₈₉	1	2	yes	complemented
554	#459	C₂²×C₈₉	1	2	yes	complemented
555	#450	C₂²×C₈₉	1	4	yes	complemented
556	#450	C₂²×C₈₉	1	4	yes	complemented
557	#449	C₂²×C₈₉	1	4	yes	complemented
558	#447	C₂²×C₈₉	1	2	yes	complemented
559	#447	C₂²×C₈₉	1	4	yes	complemented
560	#446	C₂²×C₈₉	1	2	yes	complemented
561	#442	C₂²×C₈₉	1	4	yes	complemented
562	#440	C₂²×C₈₉	1	4	yes	complemented
563	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
564	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
565	#436	C₂²×C₈₉	1	2	yes	complemented
566	#435	C₂²×C₈₉	1	4	yes	complemented
567	#432	C₂²×C₈₉	1	2	yes	complemented
568	#431	C₂²×C₈₉	1	1	yes	characteristic, complemented
569	#423	C₂²×C₈₉	1	2	yes	complemented
570	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
571	#418	C₂²×C₈₉	1	4	yes	complemented
572	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
573	H(5,𝔽₂)	—	4	8	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	2	1	no	—
576	C₂×#41	—	2	2	no	—
577	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
578	C₂×#41	C₂³×C₈₉	1	2	yes	—
579	C₂²×D₄	—	2	4	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
587	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
588	C₂³×C₄	—	2	1	no	—
589	AGL(1,ℤ/8)	—	4	8	no	—
590	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
592	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
593	C₂×D₈	—	4	4	no	—
594	C₂×D₈	C₂³×C₈₉	1	4	yes	—
595	C₂×D₈	C₂³×C₈₉	1	2	yes	—
596	C₂×D₈	C₂³×C₈₉	1	4	yes	—
597	C₂×D₈	C₂³×C₈₉	1	2	yes	—
598	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
599	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
602	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
603	#127	—	2	1	no	—
604	#127	—	2	1	no	—
605	#127	—	2	2	no	—
606	#127	—	2	2	no	—
607	#127	C₂³×C₈₉	1	2	yes	—
608	#127	C₂³×C₈₉	1	2	yes	—
609	#127	C₂³×C₈₉	1	1	yes	characteristic
610	#127	C₂³×C₈₉	1	4	yes	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#125	—	2	2	no	—
615	#125	—	2	1	no	—
616	#125	C₂³×C₈₉	1	2	yes	—
617	#124	—	2	2	no	—
618	#124	—	2	1	no	—
619	#124	—	2	2	no	—
620	#124	C₂³×C₈₉	1	2	yes	—
621	#123	—	2	2	no	—
622	#123	—	2	2	no	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	C₂²⋊Q₈	—	2	1	no	—
626	C₂²⋊Q₈	—	2	1	no	—
627	C₂²⋊Q₈	—	2	1	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
630	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
631	#121	—	2	1	no	—
632	#121	—	2	1	no	—
633	#121	—	2	1	no	—
634	#121	—	2	2	no	—
635	#121	—	2	2	no	—
636	#121	—	2	4	no	—
637	#121	—	2	4	no	—
638	#121	—	2	2	no	—
639	#121	—	2	2	no	—
640	#121	C₂³×C₈₉	1	2	yes	—
641	#121	C₂³×C₈₉	1	2	yes	—
642	#121	C₂³×C₈₉	1	4	yes	—
643	#120	—	2	2	no	—
644	#120	—	2	4	no	—
645	#120	—	2	4	no	—
646	#120	—	2	4	no	—
647	C₄×Q₈	—	2	1	no	—
648	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
649	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
650	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
651	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	2	no	—
654	C₄×D₄	—	2	2	no	—
655	C₄×D₄	—	2	1	no	—
656	C₄×D₄	—	2	1	no	—
657	C₄×D₄	—	2	1	no	—
658	C₄×D₄	—	2	2	no	—
659	C₄×D₄	D₄×C₈₉	1	2	yes	—
660	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
662	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
663	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
665	C₄×D₄	C₂³×C₈₉	1	2	yes	—
666	C₄×D₄	C₂³×C₈₉	1	2	yes	—
667	C₄×D₄	C₂³×C₈₉	1	4	yes	—
668	C₄×D₄	C₂³×C₈₉	1	2	yes	—
669	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
670	#117	—	2	1	no	—
671	#117	—	2	1	no	—
672	#117	—	2	1	no	—
673	#117	—	2	2	no	—
674	#117	—	2	2	no	—
675	#117	—	2	2	no	—
676	#117	D₄×C₈₉	1	1	yes	characteristic
677	#117	D₄×C₈₉	1	2	yes	—
678	#117	C₂³×C₈₉	1	2	yes	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	—	2	1	no	—
681	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	—	2	1	no	—
683	C₂×C₂²⋊C₄	—	2	2	no	—
684	C₂×C₄²	—	2	2	no	—
685	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
687	#107	C₂³×C₈₉	1	2	yes	—
688	#107	C₂³×C₈₉	1	2	yes	—
689	#106	C₂³×C₈₉	1	4	yes	—
690	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
691	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
692	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
693	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
694	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
695	#103	C₂³×C₈₉	1	4	yes	—
696	#102	C₂³×C₈₉	1	4	yes	—
697	#102	C₂³×C₈₉	1	4	yes	—
698	#102	C₂³×C₈₉	1	2	yes	—
699	#102	C₂³×C₈₉	1	4	yes	—
700	#102	C₂³×C₈₉	1	4	yes	—
701	#102	C₂³×C₈₉	1	2	yes	—
702	#102	C₂³×C₈₉	1	2	yes	—
703	#102	C₂³×C₈₉	1	2	yes	—
704	#102	C₂³×C₈₉	1	4	yes	—
705	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
706	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
707	#97	C₂³×C₈₉	1	4	yes	—
708	C₄×C₈	C₂³×C₈₉	1	2	yes	—
709	C₂⁴	—	2	1	no	—
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	2	2	no	—
712	#41	—	2	4	no	—
713	#41	—	2	4	no	—
714	#41	—	4	2	no	—
715	#41	—	4	8	no	—
716	#41	—	4	8	no	—
717	#41	—	4	4	no	—
718	C₂×Q₈	—	2	1	no	—
719	C₂×Q₈	—	2	1	no	—
720	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
721	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	1	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	4	1	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	4	no	—
741	C₂×D₄	—	4	2	no	—
742	C₂×D₄	—	4	4	no	—
743	C₂×D₄	—	4	8	no	—
744	C₂×D₄	—	4	16	no	—
745	C₂×D₄	—	4	8	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	—	8	2	no	—
748	C₂×D₄	—	8	4	no	—
749	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
750	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
751	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
752	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
753	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
754	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
766	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	SD₁₆	—	4	4	no	—
774	D₈	—	2	8	no	—
775	D₈	—	2	4	no	—
776	D₈	—	4	4	no	—
777	D₈	—	4	2	no	—
778	M₁₆	—	4	4	no	—
779	C₂×C₈	—	4	2	no	—
780	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
781	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
782	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
795	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
797	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
801	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	2	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	C₂×D₄×C₈₉	1	2	yes	—
824	C₄²	C₂×D₄×C₈₉	1	2	yes	—
825	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
826	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
827	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
828	C₄²	C₂⁴×C₈₉	1	2	yes	—
829	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	4	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	4	8	no	—
836	C₂³	—	4	2	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	8	1	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	4	no	—
841	C₂³	—	8	2	no	—
842	C₂³	—	8	4	no	—
843	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
844	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
845	Q₈	—	2	2	no	—
846	Q₈	—	2	2	no	—
847	Q₈	—	2	2	no	—
848	Q₈	—	4	2	no	—
849	Q₈	—	8	1	no	—
850	D₄	—	2	4	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	4	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	1	no	—
855	D₄	—	2	1	no	—
856	D₄	—	2	1	no	—
857	D₄	—	2	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	8	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	4	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	8	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	2	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	4	no	—
869	D₄	—	8	4	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	4	no	—
872	D₄	—	8	2	no	—
873	D₄	—	8	2	no	—
874	D₄	H(5,𝔽₂)×C₈₉	1	2	yes	complemented
875	C₂×C₄	—	2	4	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	4	2	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	4	no	—
888	C₂×C₄	—	4	8	no	—
889	C₂×C₄	—	4	2	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	complemented
897	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
905	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
906	C₈	—	2	4	no	—
907	C₈	—	2	2	no	—
908	C₈	—	2	2	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	2	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	4	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	4	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
930	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
931	C₄	—	2	2	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	1	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
943	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
944	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
945	C₄	#585×C₈₉	1	1	yes	characteristic
946	C₂	—	2	2	no	—
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	1	no	—
950	C₂	—	8	4	no	—
951	C₂	—	8	2	no	—
952	C₂	C₈₉×#3488	1	1	yes	characteristic
953	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
954	C₂	C₈₉×#3585	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×#3475	C₂	semidirect
3. C₈₉×#3397	C₂	semidirect
4. C₈₉×#3366	C₂	semidirect
5. C₈₉×#3325	C₂	semidirect
6. C₈₉×#3310	C₂	semidirect
7. C₈₉×#3272	C₂	semidirect
8. C₈₉×#3264	C₂	semidirect
9. C₈₉×#3251	C₂	semidirect
10. C₈₉×#3246	C₂	semidirect
11. C₈₉×#3217	C₂	semidirect
12. C₈₉×#3208	C₂	semidirect
13. C₈₉×#3115	C₂	semidirect
14. C₈₉×#3100	C₂	semidirect
15. C₈₉×#3038	C₂	semidirect
16. C₂×#459×C₈₉	C₂	semidirect
17. C₈₉×#2989	C₂	semidirect
19. C₂×AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
20. C₂²×D₈×C₈₉	C₂²	semidirect
21. #556×C₈₉	C₂²	semidirect
22. #555×C₈₉	C₂²	semidirect
23. #554×C₈₉	C₂²	semidirect
26. #552×C₈₉	C₂²	semidirect
29. #550×C₈₉	C₂²	semidirect
30. #547×C₈₉	C₂²	semidirect
31. #546×C₈₉	C₂²	semidirect
35. D₄²×C₈₉	C₂²	semidirect
38. #533×C₈₉	C₂²	semidirect
40. #532×C₈₉	C₂²	semidirect
42. C₂×#127×C₈₉	C₂²	semidirect
44. #529×C₈₉	C₂²	semidirect
47. C₄×#41×C₈₉	C₂²	semidirect
48. C₂×C₄×D₄×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. #476×C₈₉	C₂²	semidirect
58. #475×C₈₉	C₂²	semidirect
59. #474×C₈₉	C₂²	semidirect
60. #474×C₈₉	C₂²	semidirect
61. #469×C₈₉	C₂²	semidirect
62. #468×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. #459×C₈₉	C₂²	semidirect
71. #459×C₈₉	C₂²	semidirect
72. #459×C₈₉	C₂²	semidirect
73. #459×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. #447×C₈₉	C₂²	semidirect
81. #447×C₈₉	C₂²	semidirect
82. #446×C₈₉	C₂²	semidirect
83. #442×C₈₉	C₂²	semidirect
84. #440×C₈₉	C₂²	semidirect
85. C₄×D₈×C₈₉	C₂²	semidirect
86. C₄×D₈×C₈₉	C₂²	semidirect
87. #436×C₈₉	C₂²	semidirect
88. #435×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
396. D₄×C₈₉	H(5,𝔽₂)	semidirect
418. C₂×C₄×C₈₉	AGL(1,ℤ/8)	semidirect
468. #61959	C₈₉	direct (N × H)
478. #3498	C₂×C₈₉	semidirect
479. #3475	C₂×C₈₉	semidirect
480. #3397	C₂×C₈₉	semidirect
481. #3366	C₂×C₈₉	semidirect
482. #3325	C₂×C₈₉	semidirect
483. #3310	C₂×C₈₉	semidirect
484. #3272	C₂×C₈₉	semidirect
485. #3264	C₂×C₈₉	semidirect
486. #3251	C₂×C₈₉	semidirect
487. #3246	C₂×C₈₉	semidirect
488. #3217	C₂×C₈₉	semidirect
489. #3208	C₂×C₈₉	semidirect
490. #3115	C₂×C₈₉	semidirect
491. #3100	C₂×C₈₉	semidirect
492. #3038	C₂×C₈₉	semidirect
493. C₂×#459	C₂×C₈₉	semidirect
494. #2989	C₂×C₈₉	semidirect
495. C₈₉	#61959	direct (N × H)
497. C₂×AGL(1,ℤ/8)	C₂²×C₈₉	semidirect
498. C₂²×D₈	C₂²×C₈₉	semidirect
499. #556	C₂²×C₈₉	semidirect
500. #555	C₂²×C₈₉	semidirect
501. #554	C₂²×C₈₉	semidirect
504. #552	C₂²×C₈₉	semidirect
507. #550	C₂²×C₈₉	semidirect
508. #547	C₂²×C₈₉	semidirect
509. #546	C₂²×C₈₉	semidirect
513. D₄²	C₂²×C₈₉	semidirect
516. #533	C₂²×C₈₉	semidirect
518. #532	C₂²×C₈₉	semidirect
520. C₂×#127	C₂²×C₈₉	semidirect
522. #529	C₂²×C₈₉	semidirect
525. C₄×#41	C₂²×C₈₉	semidirect
526. C₂×C₄×D₄	C₂²×C₈₉	semidirect
528. #496	C₂²×C₈₉	semidirect
529. #492	C₂²×C₈₉	semidirect
530. #490	C₂²×C₈₉	semidirect
531. #486	C₂²×C₈₉	semidirect
532. #482	C₂²×C₈₉	semidirect
533. #480	C₂²×C₈₉	semidirect
534. #478	C₂²×C₈₉	semidirect
535. #476	C₂²×C₈₉	semidirect
536. #475	C₂²×C₈₉	semidirect
537. #474	C₂²×C₈₉	semidirect
538. #474	C₂²×C₈₉	semidirect
539. #469	C₂²×C₈₉	semidirect
540. #468	C₂²×C₈₉	semidirect
541. #465	C₂²×C₈₉	semidirect
542. #463	C₂²×C₈₉	semidirect
543. #461	C₂²×C₈₉	semidirect
544. #460	C₂²×C₈₉	semidirect
545. #460	C₂²×C₈₉	semidirect
546. #460	C₂²×C₈₉	semidirect
547. #460	C₂²×C₈₉	semidirect
548. #459	C₂²×C₈₉	semidirect
549. #459	C₂²×C₈₉	semidirect
550. #459	C₂²×C₈₉	semidirect
551. #459	C₂²×C₈₉	semidirect
552. #459	C₂²×C₈₉	semidirect
553. #459	C₂²×C₈₉	semidirect
554. #459	C₂²×C₈₉	semidirect
555. #450	C₂²×C₈₉	semidirect
556. #450	C₂²×C₈₉	semidirect
557. #449	C₂²×C₈₉	semidirect
558. #447	C₂²×C₈₉	semidirect
559. #447	C₂²×C₈₉	semidirect
560. #446	C₂²×C₈₉	semidirect
561. #442	C₂²×C₈₉	semidirect
562. #440	C₂²×C₈₉	semidirect
563. C₄×D₈	C₂²×C₈₉	semidirect
564. C₄×D₈	C₂²×C₈₉	semidirect
565. #436	C₂²×C₈₉	semidirect
566. #435	C₂²×C₈₉	semidirect
567. #432	C₂²×C₈₉	semidirect
568. #431	C₂²×C₈₉	semidirect
569. #423	C₂²×C₈₉	semidirect
570. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
571. #418	C₂²×C₈₉	semidirect
572. C₂×#102	C₂²×C₈₉	semidirect
874. D₄	H(5,𝔽₂)×C₈₉	semidirect
896. C₂×C₄	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×#3475	2
C₈₉×#3397	2
C₈₉×#3366	2
C₈₉×#3325	2
C₈₉×#3310	2
C₈₉×#3272	2
C₈₉×#3264	2
C₈₉×#3251	2
C₈₉×#3246	2
C₈₉×#3217	2
C₈₉×#3208	2
C₈₉×#3115	2
C₈₉×#3100	2
C₈₉×#3038	2
C₂×#459×C₈₉	2
C₈₉×#2989	2
#61959	89

Subgroups — C89×#61959 #36439807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61959 #36439807