Subgroups — C₈₉×#61954 #36439802

Order 22784.

1868 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3394	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3364	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3302	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3301	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3285	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3284	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3248	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3245	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3212	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3107	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3035	C₂	1	2	yes	maximal, complemented
16	C₂×#462×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₈₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₉	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
20	#559×C₈₉	—	2	1	no	—
21	#559×C₈₉	C₂²	1	1	yes	characteristic
22	#557×C₈₉	C₂²	1	1	yes	characteristic
23	#556×C₈₉	—	2	1	no	—
24	#556×C₈₉	C₂²	1	2	yes	—
25	#556×C₈₉	C₂²	1	1	yes	characteristic
26	#555×C₈₉	—	2	1	no	—
27	#554×C₈₉	—	2	1	no	—
28	#553×C₈₉	—	2	2	no	—
29	#553×C₈₉	—	2	2	no	—
30	#553×C₈₉	C₂²	1	2	yes	—
31	#550×C₈₉	C₂²	1	1	yes	characteristic
32	#548×C₈₉	C₂²	1	2	yes	—
33	#548×C₈₉	C₂²	1	4	yes	—
34	#547×C₈₉	C₂²	1	2	yes	—
35	#542×C₈₉	—	2	2	no	—
36	#537×C₈₉	—	2	1	no	—
37	#533×C₈₉	C₂²	1	2	yes	—
38	#532×C₈₉	—	2	1	no	—
39	#532×C₈₉	C₂²	1	2	yes	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#532×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	#529×C₈₉	—	2	2	no	—
44	#529×C₈₉	C₂²	1	2	yes	—
45	#520×C₈₉	—	2	1	no	—
46	C₄×#41×C₈₉	—	2	1	no	—
47	C₄×#41×C₈₉	C₂²	1	2	yes	—
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
50	#495×C₈₉	C₂²	1	4	yes	—
51	#492×C₈₉	C₂²	1	2	yes	—
52	#488×C₈₉	C₂²	1	4	yes	—
53	#487×C₈₉	C₂²	1	2	yes	—
54	#485×C₈₉	C₂²	1	4	yes	—
55	#481×C₈₉	C₂²	1	2	yes	—
56	#479×C₈₉	C₂²	1	4	yes	—
57	#475×C₈₉	C₂²	1	1	yes	characteristic
58	#475×C₈₉	C₂²	1	1	yes	characteristic
59	#474×C₈₉	C₂²	1	2	yes	—
60	#474×C₈₉	C₂²	1	2	yes	—
61	#467×C₈₉	C₂²	1	4	yes	—
62	#466×C₈₉	C₂²	1	4	yes	—
63	#465×C₈₉	C₂²	1	4	yes	—
64	#464×C₈₉	C₂²	1	4	yes	—
65	#464×C₈₉	C₂²	1	4	yes	—
66	#463×C₈₉	C₂²	1	4	yes	—
67	#462×C₈₉	C₂²	1	2	yes	—
68	#462×C₈₉	C₂²	1	2	yes	—
69	#462×C₈₉	C₂²	1	2	yes	—
70	#462×C₈₉	C₂²	1	2	yes	—
71	#461×C₈₉	C₂²	1	2	yes	—
72	#461×C₈₉	C₂²	1	2	yes	—
73	#460×C₈₉	C₂²	1	1	yes	characteristic
74	#460×C₈₉	C₂²	1	1	yes	characteristic
75	#459×C₈₉	C₂²	1	2	yes	—
76	#459×C₈₉	C₂²	1	2	yes	—
77	#452×C₈₉	C₂²	1	4	yes	—
78	#452×C₈₉	C₂²	1	4	yes	—
79	#449×C₈₉	C₂²	1	4	yes	—
80	#448×C₈₉	C₂²	1	2	yes	—
81	#448×C₈₉	C₂²	1	4	yes	—
82	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
86	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
87	C₈×D₄×C₈₉	C₂²	1	2	yes	—
88	C₈×D₄×C₈₉	C₂²	1	4	yes	—
89	#431×C₈₉	C₂²	1	1	yes	characteristic
90	#431×C₈₉	C₂²	1	2	yes	—
91	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
92	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
93	#416×C₈₉	C₂²	1	4	yes	—
94	C₂×#103×C₈₉	C₂²	1	2	yes	—
95	C₂×#41×C₈₉	—	2	1	no	—
96	C₂×#41×C₈₉	—	2	1	no	—
97	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
98	C₂×#41×C₈₉	C₂³	1	2	yes	—
99	C₂×#41×C₈₉	C₂³	1	4	yes	—
100	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
102	#135×C₈₉	—	4	8	no	—
103	C₂×Q₁₆×C₈₉	—	4	4	no	—
104	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×D₈×C₈₉	C₂³	1	4	yes	—
111	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
112	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
113	C₄⋊Q₈×C₈₉	—	2	1	no	—
114	C₄⋊Q₈×C₈₉	—	2	1	no	—
115	C₄⋊Q₈×C₈₉	—	2	1	no	—
116	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
117	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
118	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
120	#127×C₈₉	—	2	1	no	—
121	#127×C₈₉	C₂³	1	1	yes	characteristic
122	#127×C₈₉	C₂³	1	1	yes	characteristic
123	#126×C₈₉	—	2	2	no	—
124	#126×C₈₉	—	2	4	no	—
125	#126×C₈₉	—	2	2	no	—
126	#126×C₈₉	—	2	2	no	—
127	#125×C₈₉	—	2	2	no	—
128	#125×C₈₉	—	2	2	no	—
129	#125×C₈₉	C₂³	1	2	yes	—
130	#124×C₈₉	—	2	1	no	—
131	#124×C₈₉	—	2	1	no	—
132	#124×C₈₉	—	2	2	no	—
133	#124×C₈₉	—	2	4	no	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	—	2	1	no	—
136	#124×C₈₉	C₂³	1	4	yes	—
137	#124×C₈₉	C₂³	1	2	yes	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	2	no	—
141	#123×C₈₉	—	2	4	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	2	no	—
145	C₂²⋊Q₈×C₈₉	—	2	4	no	—
146	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
148	#121×C₈₉	—	2	2	no	—
149	#121×C₈₉	—	2	2	no	—
150	#121×C₈₉	—	2	2	no	—
151	#121×C₈₉	—	2	4	no	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	1	no	—
154	#121×C₈₉	—	2	1	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	C₂³	1	2	yes	—
158	#121×C₈₉	C₂³	1	2	yes	—
159	#121×C₈₉	C₂³	1	2	yes	—
160	C₄×Q₈×C₈₉	—	2	1	no	—
161	C₄×Q₈×C₈₉	—	2	1	no	—
162	C₄×Q₈×C₈₉	—	2	1	no	—
163	C₄×Q₈×C₈₉	—	2	1	no	—
164	C₄×Q₈×C₈₉	—	2	2	no	—
165	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
166	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₈₉	—	2	2	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	2	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	1	no	—
178	C₄×D₄×C₈₉	—	2	2	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	4	no	—
181	C₄×D₄×C₈₉	—	2	2	no	—
182	C₄×D₄×C₈₉	—	2	1	no	—
183	C₄×D₄×C₈₉	—	2	2	no	—
184	C₄×D₄×C₈₉	—	2	1	no	—
185	C₄×D₄×C₈₉	D₄	1	2	yes	—
186	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	2	yes	—
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	C₄×D₄×C₈₉	C₂³	1	2	yes	—
190	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₈₉	C₂³	1	2	yes	—
192	#117×C₈₉	—	2	2	no	—
193	#117×C₈₉	—	2	2	no	—
194	#117×C₈₉	—	2	2	no	—
195	#117×C₈₉	—	2	2	no	—
196	#117×C₈₉	D₄	1	1	yes	characteristic
197	#117×C₈₉	D₄	1	2	yes	—
198	#117×C₈₉	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
200	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₈₉	—	2	1	no	—
205	C₂×C₄²×C₈₉	—	2	2	no	—
206	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
208	#107×C₈₉	C₂³	1	4	yes	—
209	#106×C₈₉	C₂³	1	2	yes	—
210	#106×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₈×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	1	yes	characteristic
216	#103×C₈₉	C₂³	1	4	yes	—
217	#103×C₈₉	C₂³	1	4	yes	—
218	#103×C₈₉	C₂³	1	4	yes	—
219	#103×C₈₉	C₂³	1	2	yes	—
220	#103×C₈₉	C₂³	1	2	yes	—
221	#103×C₈₉	C₂³	1	4	yes	—
222	#102×C₈₉	C₂³	1	2	yes	—
223	#102×C₈₉	C₂³	1	4	yes	—
224	#102×C₈₉	C₂³	1	2	yes	—
225	#102×C₈₉	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
228	C₄×C₈×C₈₉	C₂³	1	2	yes	—
229	C₄×C₈×C₈₉	C₂³	1	4	yes	—
230	#41×C₈₉	—	2	4	no	—
231	#41×C₈₉	—	2	4	no	—
232	#41×C₈₉	—	4	2	no	—
233	#41×C₈₉	—	4	4	no	—
234	#41×C₈₉	—	4	4	no	—
235	#41×C₈₉	—	4	4	no	—
236	#41×C₈₉	—	4	4	no	—
237	C₂×Q₈×C₈₉	—	2	1	no	—
238	C₂×Q₈×C₈₉	—	2	1	no	—
239	C₂×Q₈×C₈₉	—	2	1	no	—
240	C₂×Q₈×C₈₉	—	2	2	no	—
241	C₂×Q₈×C₈₉	—	2	2	no	—
242	C₂×Q₈×C₈₉	—	4	1	no	—
243	C₂×Q₈×C₈₉	—	4	2	no	—
244	C₂×Q₈×C₈₉	—	4	2	no	—
245	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
247	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₈₉	—	2	2	no	—
250	C₂×D₄×C₈₉	—	2	2	no	—
251	C₂×D₄×C₈₉	—	2	2	no	—
252	C₂×D₄×C₈₉	—	2	2	no	—
253	C₂×D₄×C₈₉	—	2	4	no	—
254	C₂×D₄×C₈₉	—	2	1	no	—
255	C₂×D₄×C₈₉	—	2	1	no	—
256	C₂×D₄×C₈₉	—	2	1	no	—
257	C₂×D₄×C₈₉	—	2	1	no	—
258	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
261	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	2	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	2	no	—
267	C₂²×C₄×C₈₉	—	2	2	no	—
268	C₂²×C₄×C₈₉	—	2	2	no	—
269	C₂²×C₄×C₈₉	—	2	4	no	—
270	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
276	Q₁₆×C₈₉	—	2	8	no	—
277	Q₁₆×C₈₉	—	4	4	no	—
278	SD₁₆×C₈₉	—	2	4	no	—
279	SD₁₆×C₈₉	—	4	4	no	—
280	SD₁₆×C₈₉	—	4	2	no	—
281	SD₁₆×C₈₉	—	4	4	no	—
282	D₈×C₈₉	—	4	4	no	—
283	C₂×C₈×C₈₉	—	4	2	no	—
284	C₂×C₈×C₈₉	—	4	4	no	—
285	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
286	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
287	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	1	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	4	no	—
293	C₄⋊C₄×C₈₉	—	2	1	no	—
294	C₄⋊C₄×C₈₉	—	2	1	no	—
295	C₄⋊C₄×C₈₉	—	2	1	no	—
296	C₄⋊C₄×C₈₉	—	2	2	no	—
297	C₄⋊C₄×C₈₉	—	2	1	no	—
298	C₄⋊C₄×C₈₉	—	2	1	no	—
299	C₄⋊C₄×C₈₉	—	2	2	no	—
300	C₄⋊C₄×C₈₉	—	2	2	no	—
301	C₄⋊C₄×C₈₉	—	2	2	no	—
302	C₄⋊C₄×C₈₉	—	2	1	no	—
303	C₄⋊C₄×C₈₉	—	2	2	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
306	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
307	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
308	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
311	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	2	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	2	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	2	no	—
320	C₂²⋊C₄×C₈₉	—	2	2	no	—
321	C₂²⋊C₄×C₈₉	—	2	4	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	2	no	—
324	C₂²⋊C₄×C₈₉	—	2	2	no	—
325	C₂²⋊C₄×C₈₉	—	2	2	no	—
326	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
329	C₄²×C₈₉	—	2	1	no	—
330	C₄²×C₈₉	—	2	1	no	—
331	C₄²×C₈₉	—	2	2	no	—
332	C₄²×C₈₉	—	2	2	no	—
333	C₄²×C₈₉	—	2	1	no	—
334	C₄²×C₈₉	—	2	1	no	—
335	C₄²×C₈₉	—	2	4	no	—
336	C₄²×C₈₉	C₂×D₄	1	2	yes	—
337	C₄²×C₈₉	C₂×D₄	1	2	yes	—
338	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
341	C₄²×C₈₉	C₂⁴	1	2	yes	—
342	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
343	C₂³×C₈₉	—	2	2	no	—
344	C₂³×C₈₉	—	2	2	no	—
345	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
346	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
347	Q₈×C₈₉	—	2	2	no	—
348	Q₈×C₈₉	—	2	1	no	—
349	Q₈×C₈₉	—	2	4	no	—
350	Q₈×C₈₉	—	2	1	no	—
351	Q₈×C₈₉	—	2	1	no	—
352	Q₈×C₈₉	—	2	4	no	—
353	Q₈×C₈₉	—	4	2	no	—
354	Q₈×C₈₉	—	4	2	no	—
355	Q₈×C₈₉	—	4	2	no	—
356	Q₈×C₈₉	—	8	2	no	—
357	Q₈×C₈₉	H(5,𝔽₂)	1	2	yes	—
358	D₄×C₈₉	—	2	4	no	—
359	D₄×C₈₉	—	2	2	no	—
360	D₄×C₈₉	—	2	2	no	—
361	D₄×C₈₉	—	2	2	no	—
362	D₄×C₈₉	—	2	2	no	—
363	D₄×C₈₉	—	2	2	no	—
364	D₄×C₈₉	—	4	4	no	—
365	D₄×C₈₉	—	4	2	no	—
366	D₄×C₈₉	—	4	4	no	—
367	D₄×C₈₉	—	4	4	no	—
368	D₄×C₈₉	—	4	2	no	—
369	D₄×C₈₉	—	4	2	no	—
370	D₄×C₈₉	—	8	1	no	—
371	D₄×C₈₉	—	8	2	no	—
372	D₄×C₈₉	—	8	4	no	—
373	C₂×C₄×C₈₉	—	2	1	no	—
374	C₂×C₄×C₈₉	—	2	4	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	2	no	—
377	C₂×C₄×C₈₉	—	2	1	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	1	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	2	1	no	—
384	C₂×C₄×C₈₉	—	2	4	no	—
385	C₂×C₄×C₈₉	—	4	2	no	—
386	C₂×C₄×C₈₉	—	4	1	no	—
387	C₂×C₄×C₈₉	—	4	4	no	—
388	C₂×C₄×C₈₉	—	4	2	no	—
389	C₂×C₄×C₈₉	—	4	4	no	—
390	C₂×C₄×C₈₉	—	4	4	no	—
391	C₂×C₄×C₈₉	—	8	2	no	—
392	C₂×C₄×C₈₉	—	8	4	no	—
393	C₂×C₄×C₈₉	—	8	1	no	—
394	C₂×C₄×C₈₉	—	8	2	no	—
395	C₂×C₄×C₈₉	#135	1	4	yes	complemented
396	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
405	C₈×C₈₉	—	2	4	no	—
406	C₈×C₈₉	—	2	2	no	—
407	C₈×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	1	no	—
409	C₂²×C₈₉	—	2	1	no	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	2	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	4	2	no	—
414	C₂²×C₈₉	—	4	2	no	—
415	C₂²×C₈₉	—	4	2	no	—
416	C₂²×C₈₉	—	4	2	no	—
417	C₂²×C₈₉	—	4	2	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	C₂×#135	1	2	yes	—
420	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₈₉	—	2	1	no	—
422	C₄×C₈₉	—	2	2	no	—
423	C₄×C₈₉	—	2	1	no	—
424	C₄×C₈₉	—	2	2	no	—
425	C₄×C₈₉	—	2	1	no	—
426	C₄×C₈₉	—	2	2	no	—
427	C₄×C₈₉	—	2	2	no	—
428	C₄×C₈₉	—	4	1	no	—
429	C₄×C₈₉	—	4	1	no	—
430	C₄×C₈₉	—	4	1	no	—
431	C₄×C₈₉	—	4	4	no	—
432	C₄×C₈₉	—	4	2	no	—
433	C₄×C₈₉	—	4	2	no	—
434	C₄×C₈₉	C₂×#135	1	2	yes	—
435	C₄×C₈₉	C₂×#135	1	2	yes	—
436	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₄×C₈₉	#585	1	1	yes	characteristic
438	#61954	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂×C₈₉	—	2	2	no	—
440	C₂×C₈₉	—	4	2	no	—
441	C₂×C₈₉	—	8	2	no	—
442	C₂×C₈₉	—	8	2	no	—
443	C₂×C₈₉	#3488	1	1	yes	characteristic
444	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
445	C₂×C₈₉	#3586	1	1	yes	characteristic
446	#3511	C₂×C₈₉	1	1	yes	characteristic, complemented
447	#3480	C₂×C₈₉	1	1	yes	characteristic, complemented
448	#3394	C₂×C₈₉	1	2	yes	complemented
449	#3364	C₂×C₈₉	1	2	yes	complemented
450	#3302	C₂×C₈₉	1	2	yes	complemented
451	#3301	C₂×C₈₉	1	4	yes	complemented
452	#3285	C₂×C₈₉	1	4	yes	complemented
453	#3284	C₂×C₈₉	1	2	yes	complemented
454	#3248	C₂×C₈₉	1	2	yes	complemented
455	#3245	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#3212	C₂×C₈₉	1	2	yes	complemented
457	#3206	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#3107	C₂×C₈₉	1	2	yes	complemented
459	#3103	C₂×C₈₉	1	1	yes	characteristic, complemented
460	#3035	C₂×C₈₉	1	2	yes	complemented
461	C₂×#462	C₂×C₈₉	1	1	yes	characteristic, complemented
462	#2988	C₂×C₈₉	1	1	yes	characteristic, complemented
463	C₈₉	#61954	1	1	yes	characteristic, direct product factor, Sylow
464	C₂×#135	C₂²×C₈₉	1	4	yes	—
465	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
466	#559	—	2	1	no	—
467	#559	C₂²×C₈₉	1	1	yes	characteristic
468	#557	C₂²×C₈₉	1	1	yes	characteristic
469	#556	—	2	1	no	—
470	#556	C₂²×C₈₉	1	2	yes	—
471	#556	C₂²×C₈₉	1	1	yes	characteristic
472	#555	—	2	1	no	—
473	#554	—	2	1	no	—
474	#553	—	2	2	no	—
475	#553	—	2	2	no	—
476	#553	C₂²×C₈₉	1	2	yes	—
477	#550	C₂²×C₈₉	1	1	yes	characteristic
478	#548	C₂²×C₈₉	1	2	yes	—
479	#548	C₂²×C₈₉	1	4	yes	—
480	#547	C₂²×C₈₉	1	2	yes	—
481	#542	—	2	2	no	—
482	#537	—	2	1	no	—
483	#533	C₂²×C₈₉	1	2	yes	—
484	#532	—	2	1	no	—
485	#532	C₂²×C₈₉	1	2	yes	—
486	#532	C₂²×C₈₉	1	1	yes	characteristic
487	#532	C₂²×C₈₉	1	1	yes	characteristic
488	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
489	#529	—	2	2	no	—
490	#529	C₂²×C₈₉	1	2	yes	—
491	#520	—	2	1	no	—
492	C₄×#41	—	2	1	no	—
493	C₄×#41	C₂²×C₈₉	1	2	yes	—
494	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
496	#495	C₂²×C₈₉	1	4	yes	—
497	#492	C₂²×C₈₉	1	2	yes	—
498	#488	C₂²×C₈₉	1	4	yes	—
499	#487	C₂²×C₈₉	1	2	yes	—
500	#485	C₂²×C₈₉	1	4	yes	—
501	#481	C₂²×C₈₉	1	2	yes	—
502	#479	C₂²×C₈₉	1	4	yes	—
503	#475	C₂²×C₈₉	1	1	yes	characteristic
504	#475	C₂²×C₈₉	1	1	yes	characteristic
505	#474	C₂²×C₈₉	1	2	yes	—
506	#474	C₂²×C₈₉	1	2	yes	—
507	#467	C₂²×C₈₉	1	4	yes	—
508	#466	C₂²×C₈₉	1	4	yes	—
509	#465	C₂²×C₈₉	1	4	yes	—
510	#464	C₂²×C₈₉	1	4	yes	—
511	#464	C₂²×C₈₉	1	4	yes	—
512	#463	C₂²×C₈₉	1	4	yes	—
513	#462	C₂²×C₈₉	1	2	yes	—
514	#462	C₂²×C₈₉	1	2	yes	—
515	#462	C₂²×C₈₉	1	2	yes	—
516	#462	C₂²×C₈₉	1	2	yes	—
517	#461	C₂²×C₈₉	1	2	yes	—
518	#461	C₂²×C₈₉	1	2	yes	—
519	#460	C₂²×C₈₉	1	1	yes	characteristic
520	#460	C₂²×C₈₉	1	1	yes	characteristic
521	#459	C₂²×C₈₉	1	2	yes	—
522	#459	C₂²×C₈₉	1	2	yes	—
523	#452	C₂²×C₈₉	1	4	yes	—
524	#452	C₂²×C₈₉	1	4	yes	—
525	#449	C₂²×C₈₉	1	4	yes	—
526	#448	C₂²×C₈₉	1	2	yes	—
527	#448	C₂²×C₈₉	1	4	yes	—
528	C₈×Q₈	C₂²×C₈₉	1	2	yes	—
529	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
530	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
531	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
532	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
533	C₈×D₄	C₂²×C₈₉	1	2	yes	—
534	C₈×D₄	C₂²×C₈₉	1	4	yes	—
535	#431	C₂²×C₈₉	1	1	yes	characteristic
536	#431	C₂²×C₈₉	1	2	yes	—
537	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
538	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
539	#416	C₂²×C₈₉	1	4	yes	—
540	C₂×#103	C₂²×C₈₉	1	2	yes	—
541	C₂×#41	—	2	1	no	—
542	C₂×#41	—	2	1	no	—
543	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
544	C₂×#41	C₂³×C₈₉	1	2	yes	—
545	C₂×#41	C₂³×C₈₉	1	4	yes	—
546	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
548	#135	—	4	8	no	—
549	C₂×Q₁₆	—	4	4	no	—
550	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
551	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
552	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
553	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
555	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
556	C₂×D₈	C₂³×C₈₉	1	4	yes	—
557	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
558	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
563	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
564	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
566	#127	—	2	1	no	—
567	#127	C₂³×C₈₉	1	1	yes	characteristic
568	#127	C₂³×C₈₉	1	1	yes	characteristic
569	#126	—	2	2	no	—
570	#126	—	2	4	no	—
571	#126	—	2	2	no	—
572	#126	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	—	2	2	no	—
575	#125	C₂³×C₈₉	1	2	yes	—
576	#124	—	2	1	no	—
577	#124	—	2	1	no	—
578	#124	—	2	2	no	—
579	#124	—	2	4	no	—
580	#124	—	2	1	no	—
581	#124	—	2	1	no	—
582	#124	C₂³×C₈₉	1	2	yes	—
583	#124	C₂³×C₈₉	1	4	yes	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	4	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	4	no	—
592	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	4	no	—
598	#121	—	2	2	no	—
599	#121	—	2	1	no	—
600	#121	—	2	1	no	—
601	#121	—	2	2	no	—
602	#121	—	2	2	no	—
603	#121	C₂³×C₈₉	1	2	yes	—
604	#121	C₂³×C₈₉	1	2	yes	—
605	#121	C₂³×C₈₉	1	2	yes	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	1	no	—
608	C₄×Q₈	—	2	1	no	—
609	C₄×Q₈	—	2	1	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
613	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
615	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
617	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
618	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	1	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	4	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	D₄×C₈₉	1	2	yes	—
632	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₈₉	1	2	yes	—
634	C₄×D₄	C₂³×C₈₉	1	2	yes	—
635	C₄×D₄	C₂³×C₈₉	1	2	yes	—
636	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₈₉	1	2	yes	—
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	2	no	—
642	#117	D₄×C₈₉	1	1	yes	characteristic
643	#117	D₄×C₈₉	1	2	yes	—
644	#117	C₂³×C₈₉	1	2	yes	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
650	C₂×C₄²	—	2	1	no	—
651	C₂×C₄²	—	2	2	no	—
652	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
654	#107	C₂³×C₈₉	1	4	yes	—
655	#106	C₂³×C₈₉	1	2	yes	—
656	#106	C₂³×C₈₉	1	2	yes	—
657	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
658	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
659	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
660	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
661	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
662	#103	C₂³×C₈₉	1	4	yes	—
663	#103	C₂³×C₈₉	1	4	yes	—
664	#103	C₂³×C₈₉	1	4	yes	—
665	#103	C₂³×C₈₉	1	2	yes	—
666	#103	C₂³×C₈₉	1	2	yes	—
667	#103	C₂³×C₈₉	1	4	yes	—
668	#102	C₂³×C₈₉	1	2	yes	—
669	#102	C₂³×C₈₉	1	4	yes	—
670	#102	C₂³×C₈₉	1	2	yes	—
671	#102	C₂³×C₈₉	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
673	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
674	C₄×C₈	C₂³×C₈₉	1	2	yes	—
675	C₄×C₈	C₂³×C₈₉	1	4	yes	—
676	#41	—	2	4	no	—
677	#41	—	2	4	no	—
678	#41	—	4	2	no	—
679	#41	—	4	4	no	—
680	#41	—	4	4	no	—
681	#41	—	4	4	no	—
682	#41	—	4	4	no	—
683	C₂×Q₈	—	2	1	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	4	1	no	—
689	C₂×Q₈	—	4	2	no	—
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
693	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
694	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
706	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
707	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
717	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
718	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
719	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
720	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
722	Q₁₆	—	2	8	no	—
723	Q₁₆	—	4	4	no	—
724	SD₁₆	—	2	4	no	—
725	SD₁₆	—	4	4	no	—
726	SD₁₆	—	4	4	no	—
727	SD₁₆	—	4	2	no	—
728	D₈	—	4	4	no	—
729	C₂×C₈	—	4	2	no	—
730	C₂×C₈	—	4	4	no	—
731	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
732	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
733	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
752	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
753	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
754	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
757	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
758	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
773	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
774	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	2	no	—
779	C₄²	—	2	1	no	—
780	C₄²	—	2	1	no	—
781	C₄²	—	2	4	no	—
782	C₄²	C₂×D₄×C₈₉	1	2	yes	—
783	C₄²	C₂×D₄×C₈₉	1	2	yes	—
784	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
785	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
786	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
787	C₄²	C₂⁴×C₈₉	1	2	yes	—
788	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
792	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	1	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	2	1	no	—
797	Q₈	—	2	1	no	—
798	Q₈	—	2	4	no	—
799	Q₈	—	4	2	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	8	2	no	—
803	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	2	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	2	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	1	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	4	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	4	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	2	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	4	4	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	1	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	#135×C₈₉	1	4	yes	complemented
842	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
848	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
849	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
851	C₈	—	2	4	no	—
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	C₂×#135×C₈₉	1	2	yes	—
866	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	4	no	—
880	C₄	C₂×#135×C₈₉	1	2	yes	—
881	C₄	C₂×#135×C₈₉	1	2	yes	—
882	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
883	C₄	#585×C₈₉	1	1	yes	characteristic
884	C₂	—	2	2	no	—
885	C₂	—	4	2	no	—
886	C₂	—	8	2	no	—
887	C₂	—	8	2	no	—
888	C₂	C₈₉×#3488	1	1	yes	characteristic
889	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
890	C₂	C₈₉×#3586	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×#3511	C₂	semidirect
2. C₈₉×#3480	C₂	semidirect
3. C₈₉×#3394	C₂	semidirect
4. C₈₉×#3364	C₂	semidirect
5. C₈₉×#3302	C₂	semidirect
6. C₈₉×#3301	C₂	semidirect
7. C₈₉×#3285	C₂	semidirect
8. C₈₉×#3284	C₂	semidirect
9. C₈₉×#3248	C₂	semidirect
10. C₈₉×#3245	C₂	semidirect
11. C₈₉×#3212	C₂	semidirect
12. C₈₉×#3206	C₂	semidirect
13. C₈₉×#3107	C₂	semidirect
14. C₈₉×#3103	C₂	semidirect
15. C₈₉×#3035	C₂	semidirect
16. C₂×#462×C₈₉	C₂	semidirect
17. C₈₉×#2988	C₂	semidirect
395. C₂×C₄×C₈₉	#135	semidirect
438. #61954	C₈₉	direct (N × H)
446. #3511	C₂×C₈₉	semidirect
447. #3480	C₂×C₈₉	semidirect
448. #3394	C₂×C₈₉	semidirect
449. #3364	C₂×C₈₉	semidirect
450. #3302	C₂×C₈₉	semidirect
451. #3301	C₂×C₈₉	semidirect
452. #3285	C₂×C₈₉	semidirect
453. #3284	C₂×C₈₉	semidirect
454. #3248	C₂×C₈₉	semidirect
455. #3245	C₂×C₈₉	semidirect
456. #3212	C₂×C₈₉	semidirect
457. #3206	C₂×C₈₉	semidirect
458. #3107	C₂×C₈₉	semidirect
459. #3103	C₂×C₈₉	semidirect
460. #3035	C₂×C₈₉	semidirect
461. C₂×#462	C₂×C₈₉	semidirect
462. #2988	C₂×C₈₉	semidirect
463. C₈₉	#61954	direct (N × H)
841. 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
C₈₉×#3511	2
C₈₉×#3480	2
C₈₉×#3394	2
C₈₉×#3364	2
C₈₉×#3302	2
C₈₉×#3301	2
C₈₉×#3285	2
C₈₉×#3284	2
C₈₉×#3248	2
C₈₉×#3245	2
C₈₉×#3212	2
C₈₉×#3206	2
C₈₉×#3107	2
C₈₉×#3103	2
C₈₉×#3035	2
C₂×#462×C₈₉	2
C₈₉×#2988	2
#61954	89

Subgroups — C89×#61954 #36439802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61954 #36439802