Subgroups — C₈₉×#61998 #36439846

Order 22784.

1840 conjugacy classes of subgroups.

The subgroup lattice has 886 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×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3393	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3364	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3330	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3327	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3277	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3276	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3254	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3252	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3212	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3106	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3104	C₂	1	2	yes	maximal, complemented
15	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3037	C₂	1	2	yes	maximal, complemented
17	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#137×C₈₉	C₂²	1	4	yes	—
19	C₂×#137×C₈₉	C₂²	1	2	yes	—
20	#557×C₈₉	C₂²	1	1	yes	characteristic
21	#556×C₈₉	—	2	1	no	—
22	#556×C₈₉	C₂²	1	2	yes	—
23	#556×C₈₉	C₂²	1	1	yes	characteristic
24	#555×C₈₉	—	2	1	no	—
25	#554×C₈₉	—	2	1	no	—
26	#553×C₈₉	—	2	2	no	—
27	#552×C₈₉	—	2	2	no	—
28	#552×C₈₉	C₂²	1	2	yes	—
29	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	#548×C₈₉	C₂²	1	4	yes	—
31	#548×C₈₉	C₂²	1	2	yes	—
32	#547×C₈₉	—	2	1	no	—
33	#547×C₈₉	C₂²	1	2	yes	—
34	#547×C₈₉	C₂²	1	1	yes	characteristic
35	#542×C₈₉	—	2	2	no	—
36	#537×C₈₉	—	2	1	no	—
37	#533×C₈₉	—	2	1	no	—
38	#533×C₈₉	C₂²	1	2	yes	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#532×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic
48	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
50	#495×C₈₉	C₂²	1	4	yes	—
51	#494×C₈₉	C₂²	1	2	yes	—
52	#488×C₈₉	C₂²	1	4	yes	—
53	#487×C₈₉	C₂²	1	2	yes	—
54	#484×C₈₉	C₂²	1	4	yes	—
55	#482×C₈₉	C₂²	1	2	yes	—
56	#479×C₈₉	C₂²	1	4	yes	—
57	#477×C₈₉	C₂²	1	1	yes	characteristic
58	#477×C₈₉	C₂²	1	2	yes	—
59	#476×C₈₉	C₂²	1	1	yes	characteristic
60	#474×C₈₉	C₂²	1	2	yes	—
61	#470×C₈₉	C₂²	1	4	yes	—
62	#468×C₈₉	C₂²	1	4	yes	—
63	#468×C₈₉	C₂²	1	4	yes	—
64	#464×C₈₉	C₂²	1	4	yes	—
65	#464×C₈₉	C₂²	1	4	yes	—
66	#464×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	#461×C₈₉	C₂²	1	2	yes	—
74	#460×C₈₉	C₂²	1	1	yes	characteristic
75	#460×C₈₉	C₂²	1	2	yes	—
76	#459×C₈₉	C₂²	1	1	yes	characteristic
77	#452×C₈₉	C₂²	1	4	yes	—
78	#451×C₈₉	C₂²	1	4	yes	—
79	#451×C₈₉	C₂²	1	4	yes	—
80	#449×C₈₉	C₂²	1	4	yes	—
81	#449×C₈₉	C₂²	1	2	yes	—
82	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
83	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
84	C₄×Q₁₆×C₈₉	C₂²	1	4	yes	—
85	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
86	C₄×D₈×C₈₉	C₂²	1	2	yes	—
87	#436×C₈₉	C₂²	1	4	yes	—
88	#436×C₈₉	C₂²	1	2	yes	—
89	#431×C₈₉	C₂²	1	2	yes	—
90	#431×C₈₉	C₂²	1	1	yes	characteristic
91	#423×C₈₉	C₂²	1	2	yes	—
92	#423×C₈₉	C₂²	1	1	yes	characteristic
93	#419×C₈₉	C₂²	1	2	yes	—
94	#417×C₈₉	C₂²	1	4	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	1	yes	characteristic
99	C₂×#41×C₈₉	C₂³	1	4	yes	—
100	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
101	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
102	#137×C₈₉	—	4	8	no	—
103	#137×C₈₉	—	4	4	no	—
104	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
105	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
106	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
110	C₂×D₈×C₈₉	C₂³	1	2	yes	—
111	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
112	C₂×M₁₆×C₈₉	C₂³	1	2	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	—	2	1	no	—
117	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
120	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₄⋊Q₈×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	—	2	1	no	—
130	#125×C₈₉	—	2	2	no	—
131	#125×C₈₉	C₂³	1	2	yes	—
132	#124×C₈₉	—	2	2	no	—
133	#124×C₈₉	—	2	4	no	—
134	#124×C₈₉	—	2	1	no	—
135	#124×C₈₉	C₂³	1	4	yes	—
136	#124×C₈₉	C₂³	1	2	yes	—
137	#123×C₈₉	—	2	2	no	—
138	#123×C₈₉	—	2	2	no	—
139	#123×C₈₉	—	2	2	no	—
140	#123×C₈₉	—	2	4	no	—
141	C₂²⋊Q₈×C₈₉	—	2	1	no	—
142	C₂²⋊Q₈×C₈₉	—	2	2	no	—
143	C₂²⋊Q₈×C₈₉	—	2	2	no	—
144	C₂²⋊Q₈×C₈₉	—	2	1	no	—
145	C₂²⋊Q₈×C₈₉	—	2	1	no	—
146	C₂²⋊Q₈×C₈₉	—	2	2	no	—
147	C₂²⋊Q₈×C₈₉	—	2	4	no	—
148	C₂²⋊Q₈×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
152	#121×C₈₉	—	2	2	no	—
153	#121×C₈₉	—	2	2	no	—
154	#121×C₈₉	—	2	4	no	—
155	#121×C₈₉	—	2	2	no	—
156	#121×C₈₉	—	2	1	no	—
157	#121×C₈₉	—	2	2	no	—
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	2	no	—
162	C₄×Q₈×C₈₉	—	2	2	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	2	yes	—
168	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
169	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
170	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
172	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
173	C₄×D₄×C₈₉	—	2	1	no	—
174	C₄×D₄×C₈₉	—	2	2	no	—
175	C₄×D₄×C₈₉	—	2	1	no	—
176	C₄×D₄×C₈₉	—	2	1	no	—
177	C₄×D₄×C₈₉	—	2	2	no	—
178	C₄×D₄×C₈₉	—	2	4	no	—
179	C₄×D₄×C₈₉	—	2	2	no	—
180	C₄×D₄×C₈₉	—	2	2	no	—
181	C₄×D₄×C₈₉	—	2	1	no	—
182	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
183	C₄×D₄×C₈₉	D₄	1	2	yes	—
184	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₈₉	C₂³	1	2	yes	—
186	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₈₉	C₂³	1	2	yes	—
189	#117×C₈₉	—	2	1	no	—
190	#117×C₈₉	—	2	2	no	—
191	#117×C₈₉	—	2	1	no	—
192	#117×C₈₉	—	2	2	no	—
193	#117×C₈₉	—	2	2	no	—
194	#117×C₈₉	—	2	1	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	1	yes	characteristic
199	C₂×C₄⋊C₄×C₈₉	—	2	2	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	2	yes	—
204	C₂×C₄²×C₈₉	—	2	2	no	—
205	C₂×C₄²×C₈₉	—	2	1	no	—
206	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
207	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
208	#107×C₈₉	C₂³	1	2	yes	—
209	#107×C₈₉	C₂³	1	4	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	4	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	2	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	2	no	—
231	#41×C₈₉	—	4	2	no	—
232	#41×C₈₉	—	4	1	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	2	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	4	no	—
242	C₂×Q₈×C₈₉	—	4	2	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	2	yes	—
248	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×D₄×C₈₉	—	2	2	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	1	no	—
254	C₂×D₄×C₈₉	—	2	1	no	—
255	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
257	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	2	no	—
261	C₂²×C₄×C₈₉	—	2	2	no	—
262	C₂²×C₄×C₈₉	—	2	1	no	—
263	C₂²×C₄×C₈₉	—	2	1	no	—
264	C₂²×C₄×C₈₉	—	2	1	no	—
265	C₂²×C₄×C₈₉	—	2	2	no	—
266	C₂²×C₄×C₈₉	—	2	4	no	—
267	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
268	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	Q₁₆×C₈₉	—	2	8	no	—
274	Q₁₆×C₈₉	—	4	4	no	—
275	Q₁₆×C₈₉	—	4	4	no	—
276	SD₁₆×C₈₉	—	2	4	no	—
277	SD₁₆×C₈₉	—	4	4	no	—
278	SD₁₆×C₈₉	—	4	4	no	—
279	D₈×C₈₉	—	4	2	no	—
280	M₁₆×C₈₉	—	4	4	no	—
281	M₁₆×C₈₉	—	4	2	no	—
282	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
283	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
284	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
285	C₄⋊C₄×C₈₉	—	2	1	no	—
286	C₄⋊C₄×C₈₉	—	2	2	no	—
287	C₄⋊C₄×C₈₉	—	2	2	no	—
288	C₄⋊C₄×C₈₉	—	2	2	no	—
289	C₄⋊C₄×C₈₉	—	2	4	no	—
290	C₄⋊C₄×C₈₉	—	2	2	no	—
291	C₄⋊C₄×C₈₉	—	2	2	no	—
292	C₄⋊C₄×C₈₉	—	2	2	no	—
293	C₄⋊C₄×C₈₉	—	2	2	no	—
294	C₄⋊C₄×C₈₉	—	2	2	no	—
295	C₄⋊C₄×C₈₉	—	2	1	no	—
296	C₄⋊C₄×C₈₉	—	2	1	no	—
297	C₄⋊C₄×C₈₉	—	2	2	no	—
298	C₄⋊C₄×C₈₉	—	2	2	no	—
299	C₄⋊C₄×C₈₉	—	2	1	no	—
300	C₄⋊C₄×C₈₉	—	2	1	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	2	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	2	no	—
316	C₂²⋊C₄×C₈₉	—	2	1	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	2	no	—
319	C₂²⋊C₄×C₈₉	—	2	1	no	—
320	C₂²⋊C₄×C₈₉	—	2	1	no	—
321	C₂²⋊C₄×C₈₉	—	2	2	no	—
322	C₂²⋊C₄×C₈₉	—	2	2	no	—
323	C₂²⋊C₄×C₈₉	—	2	4	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	2	no	—
335	C₄²×C₈₉	—	2	4	no	—
336	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₈₉	C₂×D₄	1	2	yes	—
339	C₄²×C₈₉	C₂×D₄	1	2	yes	—
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	1	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	2	no	—
350	Q₈×C₈₉	—	2	4	no	—
351	Q₈×C₈₉	—	2	2	no	—
352	Q₈×C₈₉	—	2	4	no	—
353	Q₈×C₈₉	—	4	4	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	2	no	—
359	D₄×C₈₉	—	2	2	no	—
360	D₄×C₈₉	—	2	1	no	—
361	D₄×C₈₉	—	2	1	no	—
362	D₄×C₈₉	—	2	2	no	—
363	D₄×C₈₉	—	4	2	no	—
364	D₄×C₈₉	—	4	2	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	—	8	4	no	—
370	C₂×C₄×C₈₉	—	2	1	no	—
371	C₂×C₄×C₈₉	—	2	2	no	—
372	C₂×C₄×C₈₉	—	2	4	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	1	no	—
376	C₂×C₄×C₈₉	—	2	1	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	1	no	—
379	C₂×C₄×C₈₉	—	2	1	no	—
380	C₂×C₄×C₈₉	—	2	2	no	—
381	C₂×C₄×C₈₉	—	2	2	no	—
382	C₂×C₄×C₈₉	—	2	2	no	—
383	C₂×C₄×C₈₉	—	2	4	no	—
384	C₂×C₄×C₈₉	—	4	2	no	—
385	C₂×C₄×C₈₉	—	4	2	no	—
386	C₂×C₄×C₈₉	—	4	4	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	2	no	—
391	C₂×C₄×C₈₉	—	8	4	no	—
392	C₂×C₄×C₈₉	—	8	2	no	—
393	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
402	C₈×C₈₉	—	2	2	no	—
403	C₈×C₈₉	—	2	4	no	—
404	C₈×C₈₉	—	2	2	no	—
405	C₂²×C₈₉	—	2	2	no	—
406	C₂²×C₈₉	—	2	1	no	—
407	C₂²×C₈₉	—	2	1	no	—
408	C₂²×C₈₉	—	2	2	no	—
409	C₂²×C₈₉	—	2	2	no	—
410	C₂²×C₈₉	—	2	1	no	—
411	C₂²×C₈₉	—	4	1	no	—
412	C₂²×C₈₉	—	4	2	no	—
413	C₂²×C₈₉	—	4	2	no	—
414	C₂²×C₈₉	—	4	1	no	—
415	C₂²×C₈₉	—	4	1	no	—
416	C₂²×C₈₉	—	4	2	no	—
417	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₈₉	—	2	1	no	—
419	C₄×C₈₉	—	2	2	no	—
420	C₄×C₈₉	—	2	2	no	—
421	C₄×C₈₉	—	2	1	no	—
422	C₄×C₈₉	—	2	2	no	—
423	C₄×C₈₉	—	2	2	no	—
424	C₄×C₈₉	—	2	1	no	—
425	C₄×C₈₉	—	4	2	no	—
426	C₄×C₈₉	—	4	4	no	—
427	C₄×C₈₉	—	4	1	no	—
428	C₄×C₈₉	—	4	2	no	—
429	C₄×C₈₉	—	4	2	no	—
430	C₄×C₈₉	—	4	1	no	—
431	C₄×C₈₉	#575	1	2	yes	—
432	C₄×C₈₉	#578	1	2	yes	—
433	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₄×C₈₉	#585	1	1	yes	characteristic
435	#61998	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
436	C₂×C₈₉	—	4	2	no	—
437	C₂×C₈₉	—	4	1	no	—
438	C₂×C₈₉	—	8	1	no	—
439	C₂×C₈₉	—	8	2	no	—
440	C₂×C₈₉	#3488	1	1	yes	characteristic
441	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
442	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
443	#3511	C₂×C₈₉	1	1	yes	characteristic, complemented
444	#3482	C₂×C₈₉	1	1	yes	characteristic, complemented
445	#3393	C₂×C₈₉	1	2	yes	complemented
446	#3364	C₂×C₈₉	1	2	yes	complemented
447	#3330	C₂×C₈₉	1	2	yes	complemented
448	#3327	C₂×C₈₉	1	4	yes	complemented
449	#3277	C₂×C₈₉	1	4	yes	complemented
450	#3276	C₂×C₈₉	1	2	yes	complemented
451	#3254	C₂×C₈₉	1	1	yes	characteristic, complemented
452	#3252	C₂×C₈₉	1	2	yes	complemented
453	#3212	C₂×C₈₉	1	2	yes	complemented
454	#3209	C₂×C₈₉	1	1	yes	characteristic, complemented
455	#3106	C₂×C₈₉	1	1	yes	characteristic, complemented
456	#3104	C₂×C₈₉	1	2	yes	complemented
457	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
458	#3037	C₂×C₈₉	1	2	yes	complemented
459	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
460	C₈₉	#61998	1	1	yes	characteristic, direct product factor, Sylow
461	C₂×#137	C₂²×C₈₉	1	4	yes	—
462	C₂×#137	C₂²×C₈₉	1	2	yes	—
463	#557	C₂²×C₈₉	1	1	yes	characteristic
464	#556	—	2	1	no	—
465	#556	C₂²×C₈₉	1	2	yes	—
466	#556	C₂²×C₈₉	1	1	yes	characteristic
467	#555	—	2	1	no	—
468	#554	—	2	1	no	—
469	#553	—	2	2	no	—
470	#552	—	2	2	no	—
471	#552	C₂²×C₈₉	1	2	yes	—
472	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
473	#548	C₂²×C₈₉	1	2	yes	—
474	#548	C₂²×C₈₉	1	4	yes	—
475	#547	—	2	1	no	—
476	#547	C₂²×C₈₉	1	2	yes	—
477	#547	C₂²×C₈₉	1	1	yes	characteristic
478	#542	—	2	2	no	—
479	#537	—	2	1	no	—
480	#533	—	2	1	no	—
481	#533	C₂²×C₈₉	1	2	yes	—
482	#533	C₂²×C₈₉	1	1	yes	characteristic
483	#532	C₂²×C₈₉	1	2	yes	—
484	#532	C₂²×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
486	#529	—	2	2	no	—
487	#529	C₂²×C₈₉	1	2	yes	—
488	#520	—	2	1	no	—
489	C₄×#41	—	2	1	no	—
490	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
491	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
493	#495	C₂²×C₈₉	1	4	yes	—
494	#494	C₂²×C₈₉	1	2	yes	—
495	#488	C₂²×C₈₉	1	4	yes	—
496	#487	C₂²×C₈₉	1	2	yes	—
497	#484	C₂²×C₈₉	1	4	yes	—
498	#482	C₂²×C₈₉	1	2	yes	—
499	#479	C₂²×C₈₉	1	4	yes	—
500	#477	C₂²×C₈₉	1	1	yes	characteristic
501	#477	C₂²×C₈₉	1	2	yes	—
502	#476	C₂²×C₈₉	1	1	yes	characteristic
503	#474	C₂²×C₈₉	1	2	yes	—
504	#470	C₂²×C₈₉	1	4	yes	—
505	#468	C₂²×C₈₉	1	4	yes	—
506	#468	C₂²×C₈₉	1	4	yes	—
507	#464	C₂²×C₈₉	1	4	yes	—
508	#464	C₂²×C₈₉	1	4	yes	—
509	#464	C₂²×C₈₉	1	4	yes	—
510	#462	C₂²×C₈₉	1	2	yes	—
511	#462	C₂²×C₈₉	1	2	yes	—
512	#462	C₂²×C₈₉	1	2	yes	—
513	#462	C₂²×C₈₉	1	2	yes	—
514	#461	C₂²×C₈₉	1	2	yes	—
515	#461	C₂²×C₈₉	1	2	yes	—
516	#461	C₂²×C₈₉	1	2	yes	—
517	#460	C₂²×C₈₉	1	1	yes	characteristic
518	#460	C₂²×C₈₉	1	2	yes	—
519	#459	C₂²×C₈₉	1	1	yes	characteristic
520	#452	C₂²×C₈₉	1	4	yes	—
521	#451	C₂²×C₈₉	1	4	yes	—
522	#451	C₂²×C₈₉	1	4	yes	—
523	#449	C₂²×C₈₉	1	4	yes	—
524	#449	C₂²×C₈₉	1	2	yes	—
525	C₈×Q₈	C₂²×C₈₉	1	2	yes	—
526	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
527	C₄×Q₁₆	C₂²×C₈₉	1	4	yes	—
528	C₄×SD₁₆	C₂²×C₈₉	1	2	yes	—
529	C₄×D₈	C₂²×C₈₉	1	2	yes	—
530	#436	C₂²×C₈₉	1	2	yes	—
531	#436	C₂²×C₈₉	1	4	yes	—
532	#431	C₂²×C₈₉	1	2	yes	—
533	#431	C₂²×C₈₉	1	1	yes	characteristic
534	#423	C₂²×C₈₉	1	2	yes	—
535	#423	C₂²×C₈₉	1	1	yes	characteristic
536	#419	C₂²×C₈₉	1	2	yes	—
537	#417	C₂²×C₈₉	1	4	yes	—
538	C₂×#41	—	2	1	no	—
539	C₂×#41	—	2	1	no	—
540	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
541	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
542	C₂×#41	C₂³×C₈₉	1	4	yes	—
543	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
544	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
545	#137	—	4	8	no	—
546	#137	—	4	4	no	—
547	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
549	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
552	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
553	C₂×D₈	C₂³×C₈₉	1	2	yes	—
554	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
555	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	—	2	1	no	—
558	C₄⋊Q₈	—	2	1	no	—
559	C₄⋊Q₈	—	2	1	no	—
560	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
562	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
565	#127	C₂³×C₈₉	1	1	yes	characteristic
566	#126	—	2	2	no	—
567	#126	—	2	4	no	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#125	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	—	2	1	no	—
573	#125	—	2	2	no	—
574	#125	C₂³×C₈₉	1	2	yes	—
575	#124	—	2	2	no	—
576	#124	—	2	4	no	—
577	#124	—	2	1	no	—
578	#124	C₂³×C₈₉	1	2	yes	—
579	#124	C₂³×C₈₉	1	4	yes	—
580	#123	—	2	2	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	4	no	—
584	C₂²⋊Q₈	—	2	1	no	—
585	C₂²⋊Q₈	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	1	no	—
588	C₂²⋊Q₈	—	2	1	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	—	2	4	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
593	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
594	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
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	2	no	—
601	#121	C₂³×C₈₉	1	2	yes	—
602	#121	C₂³×C₈₉	1	2	yes	—
603	C₄×Q₈	—	2	1	no	—
604	C₄×Q₈	—	2	2	no	—
605	C₄×Q₈	—	2	2	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
610	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
611	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
612	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
613	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
614	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
615	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	1	no	—
625	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
626	C₄×D₄	D₄×C₈₉	1	2	yes	—
627	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
629	C₄×D₄	C₂³×C₈₉	1	2	yes	—
630	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₈₉	1	2	yes	—
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	—	2	1	no	—
635	#117	—	2	2	no	—
636	#117	—	2	2	no	—
637	#117	—	2	1	no	—
638	#117	—	2	2	no	—
639	#117	D₄×C₈₉	1	1	yes	characteristic
640	#117	D₄×C₈₉	1	2	yes	—
641	#117	C₂³×C₈₉	1	1	yes	characteristic
642	C₂×C₄⋊C₄	—	2	2	no	—
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
647	C₂×C₄²	—	2	2	no	—
648	C₂×C₄²	—	2	1	no	—
649	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
650	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
651	#107	C₂³×C₈₉	1	2	yes	—
652	#107	C₂³×C₈₉	1	4	yes	—
653	#106	C₂³×C₈₉	1	2	yes	—
654	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
655	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
656	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
657	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
658	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
659	#103	C₂³×C₈₉	1	4	yes	—
660	#103	C₂³×C₈₉	1	4	yes	—
661	#103	C₂³×C₈₉	1	4	yes	—
662	#103	C₂³×C₈₉	1	2	yes	—
663	#103	C₂³×C₈₉	1	4	yes	—
664	#103	C₂³×C₈₉	1	4	yes	—
665	#102	C₂³×C₈₉	1	2	yes	—
666	#102	C₂³×C₈₉	1	4	yes	—
667	#102	C₂³×C₈₉	1	2	yes	—
668	#102	C₂³×C₈₉	1	2	yes	—
669	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
671	C₄×C₈	C₂³×C₈₉	1	2	yes	—
672	C₄×C₈	C₂³×C₈₉	1	4	yes	—
673	#41	—	2	2	no	—
674	#41	—	4	2	no	—
675	#41	—	4	1	no	—
676	#41	—	4	4	no	—
677	#41	—	4	4	no	—
678	#41	—	4	4	no	—
679	#41	—	4	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	1	no	—
682	C₂×Q₈	—	2	1	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	—	4	2	no	—
686	C₂×Q₈	—	4	2	no	—
687	C₂×Q₈	—	4	2	no	—
688	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
689	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
690	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	1	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
699	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
700	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
701	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	4	no	—
710	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
713	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
716	Q₁₆	—	2	8	no	—
717	Q₁₆	—	4	4	no	—
718	Q₁₆	—	4	4	no	—
719	SD₁₆	—	2	4	no	—
720	SD₁₆	—	4	4	no	—
721	SD₁₆	—	4	4	no	—
722	D₈	—	4	2	no	—
723	M₁₆	—	4	4	no	—
724	M₁₆	—	4	2	no	—
725	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
726	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
727	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	2	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	1	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	1	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
749	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
751	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
753	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
754	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
755	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	1	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
770	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
772	C₄²	—	2	1	no	—
773	C₄²	—	2	1	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	4	no	—
779	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
780	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₈₉	1	2	yes	—
782	C₄²	C₂×D₄×C₈₉	1	2	yes	—
783	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
784	C₄²	C₂⁴×C₈₉	1	2	yes	—
785	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	—	2	2	no	—
788	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
789	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
790	Q₈	—	2	2	no	—
791	Q₈	—	2	1	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	4	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	4	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	2	no	—
799	Q₈	—	8	2	no	—
800	Q₈	H(5,𝔽₂)×C₈₉	1	2	yes	—
801	D₄	—	2	2	no	—
802	D₄	—	2	2	no	—
803	D₄	—	2	1	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	2	no	—
806	D₄	—	4	2	no	—
807	D₄	—	4	2	no	—
808	D₄	—	4	2	no	—
809	D₄	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	2	no	—
812	D₄	—	8	4	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	4	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	4	2	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	4	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	2	no	—
834	C₂×C₄	—	8	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
837	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
839	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
844	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
845	C₈	—	2	2	no	—
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₂²	—	2	1	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	2	no	—
860	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
861	C₄	—	2	1	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	1	no	—
866	C₄	—	2	2	no	—
867	C₄	—	2	2	no	—
868	C₄	—	4	1	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	2	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	4	no	—
874	C₄	#575×C₈₉	1	2	yes	—
875	C₄	#578×C₈₉	1	2	yes	—
876	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
877	C₄	#585×C₈₉	1	1	yes	characteristic
878	C₂	—	4	1	no	—
879	C₂	—	4	2	no	—
880	C₂	—	8	1	no	—
881	C₂	—	8	2	no	—
882	C₂	C₈₉×#3488	1	1	yes	characteristic
883	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
884	C₂	C₂×#578×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×#3511	C₂	semidirect
2. C₈₉×#3482	C₂	semidirect
3. C₈₉×#3393	C₂	semidirect
4. C₈₉×#3364	C₂	semidirect
5. C₈₉×#3330	C₂	semidirect
6. C₈₉×#3327	C₂	semidirect
7. C₈₉×#3277	C₂	semidirect
8. C₈₉×#3276	C₂	semidirect
9. C₈₉×#3254	C₂	semidirect
10. C₈₉×#3252	C₂	semidirect
11. C₈₉×#3212	C₂	semidirect
12. C₈₉×#3209	C₂	semidirect
13. C₈₉×#3106	C₂	semidirect
14. C₈₉×#3104	C₂	semidirect
15. C₈₉×#3039	C₂	semidirect
16. C₈₉×#3037	C₂	semidirect
17. C₈₉×#2991	C₂	semidirect
435. #61998	C₈₉	direct (N × H)
443. #3511	C₂×C₈₉	semidirect
444. #3482	C₂×C₈₉	semidirect
445. #3393	C₂×C₈₉	semidirect
446. #3364	C₂×C₈₉	semidirect
447. #3330	C₂×C₈₉	semidirect
448. #3327	C₂×C₈₉	semidirect
449. #3277	C₂×C₈₉	semidirect
450. #3276	C₂×C₈₉	semidirect
451. #3254	C₂×C₈₉	semidirect
452. #3252	C₂×C₈₉	semidirect
453. #3212	C₂×C₈₉	semidirect
454. #3209	C₂×C₈₉	semidirect
455. #3106	C₂×C₈₉	semidirect
456. #3104	C₂×C₈₉	semidirect
457. #3039	C₂×C₈₉	semidirect
458. #3037	C₂×C₈₉	semidirect
459. #2991	C₂×C₈₉	semidirect
460. C₈₉	#61998	direct (N × H)

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×#3482	2
C₈₉×#3393	2
C₈₉×#3364	2
C₈₉×#3330	2
C₈₉×#3327	2
C₈₉×#3277	2
C₈₉×#3276	2
C₈₉×#3254	2
C₈₉×#3252	2
C₈₉×#3212	2
C₈₉×#3209	2
C₈₉×#3106	2
C₈₉×#3104	2
C₈₉×#3039	2
C₈₉×#3037	2
C₈₉×#2991	2
#61998	89

Subgroups — C89×#61998 #36439846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61998 #36439846