Subgroups — C₈₉×#62893 #36440741

Order 22784.

6998 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3561	C₂	1	6	yes	maximal, complemented
2	C₈₉×#3552	C₂	1	12	yes	maximal, complemented
3	C₈₉×#3541	C₂	1	12	yes	maximal, complemented
4	C₈₉×#3538	C₂	1	6	yes	maximal, complemented
5	C₈₉×#3523	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3516	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3505	C₂	1	6	yes	maximal, complemented
8	C₈₉×#3501	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3489	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3486	C₂	1	4	yes	maximal, complemented
11	C₂×D₄×Q₈×C₈₉	C₂	1	2	yes	maximal, complemented
12	C₂×#548×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3459	C₂	1	3	yes	maximal, complemented
14	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
16	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₈₉	C₂²	1	2	yes	complemented
18	#563×C₈₉	C₂²	1	24	yes	complemented
19	#563×C₈₉	C₂²	1	12	yes	complemented
20	#562×C₈₉	C₂²	1	12	yes	complemented
21	#557×C₈₉	C₂²	1	2	yes	complemented
22	#557×C₈₉	C₂²	1	6	yes	complemented
23	#556×C₈₉	C₂²	1	12	yes	complemented
24	#556×C₈₉	C₂²	1	6	yes	complemented
25	#554×C₈₉	C₂²	1	12	yes	complemented
26	#554×C₈₉	C₂²	1	24	yes	complemented
27	#553×C₈₉	C₂²	1	12	yes	complemented
28	#553×C₈₉	C₂²	1	24	yes	complemented
29	#552×C₈₉	C₂²	1	12	yes	complemented
30	#552×C₈₉	C₂²	1	12	yes	complemented
31	#551×C₈₉	C₂²	1	24	yes	complemented
32	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
33	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
34	D₄×Q₈×C₈₉	C₂²	1	12	yes	complemented
35	D₄×Q₈×C₈₉	C₂²	1	12	yes	complemented
36	D₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
37	D₄×Q₈×C₈₉	C₂²	1	12	yes	complemented
38	D₄×Q₈×C₈₉	C₂²	1	12	yes	complemented
39	#548×C₈₉	C₂²	1	4	yes	complemented
40	#548×C₈₉	C₂²	1	12	yes	complemented
41	#548×C₈₉	C₂²	1	4	yes	complemented
42	#548×C₈₉	C₂²	1	12	yes	complemented
43	#548×C₈₉	C₂²	1	12	yes	complemented
44	#547×C₈₉	C₂²	1	12	yes	complemented
45	#546×C₈₉	C₂²	1	12	yes	complemented
46	#544×C₈₉	C₂²	1	6	yes	complemented
47	#544×C₈₉	C₂²	1	12	yes	complemented
48	#543×C₈₉	C₂²	1	3	yes	—
49	#543×C₈₉	C₂²	1	6	yes	complemented
50	#542×C₈₉	C₂²	1	12	yes	complemented
51	#542×C₈₉	C₂²	1	24	yes	complemented
52	#541×C₈₉	C₂²	1	12	yes	complemented
53	#541×C₈₉	C₂²	1	12	yes	complemented
54	#539×C₈₉	C₂²	1	6	yes	—
55	#539×C₈₉	C₂²	1	12	yes	complemented
56	#539×C₈₉	C₂²	1	12	yes	complemented
57	#539×C₈₉	C₂²	1	12	yes	complemented
58	#538×C₈₉	C₂²	1	6	yes	—
59	#538×C₈₉	C₂²	1	12	yes	complemented
60	#538×C₈₉	C₂²	1	12	yes	complemented
61	#537×C₈₉	C₂²	1	6	yes	complemented
62	#536×C₈₉	C₂²	1	12	yes	complemented
63	#536×C₈₉	C₂²	1	12	yes	complemented
64	#536×C₈₉	C₂²	1	6	yes	complemented
65	#534×C₈₉	C₂²	1	1	yes	characteristic
66	#534×C₈₉	C₂²	1	6	yes	—
67	#533×C₈₉	C₂²	1	6	yes	complemented
68	C₂×C₄⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
69	#529×C₈₉	C₂²	1	6	yes	—
70	#529×C₈₉	C₂²	1	12	yes	complemented
71	#529×C₈₉	C₂²	1	12	yes	complemented
72	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
73	#525×C₈₉	C₂²	1	6	yes	—
74	#525×C₈₉	C₂²	1	12	yes	complemented
75	#525×C₈₉	C₂²	1	12	yes	complemented
76	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
77	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	complemented
78	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
79	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
80	C₂×#121×C₈₉	C₂²	1	3	yes	—
81	#520×C₈₉	C₂²	1	2	yes	complemented
82	#519×C₈₉	C₂²	1	4	yes	complemented
83	#518×C₈₉	C₂²	1	6	yes	—
84	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
86	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
87	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
88	2₋¹⁺⁴×C₈₉	—	4	8	no	—
89	C₂×#41×C₈₉	—	4	4	no	—
90	C₂×#41×C₈₉	C₂³	1	2	yes	—
91	C₂×#41×C₈₉	C₂³	1	6	yes	—
92	C₂×#41×C₈₉	C₂³	1	12	yes	—
93	C₂×#41×C₈₉	C₂³	1	6	yes	—
94	C₂²×Q₈×C₈₉	—	4	4	no	—
95	C₂²×Q₈×C₈₉	—	4	8	no	—
96	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
97	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
99	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
100	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
101	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
102	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
103	C₂²×Q₈×C₈₉	C₂³	1	12	yes	—
104	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
105	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
106	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
107	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
109	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
110	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
111	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
112	C₄⋊Q₈×C₈₉	C₂³	1	24	yes	—
113	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
114	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
115	C₄⋊Q₈×C₈₉	C₂³	1	24	yes	—
116	#126×C₈₉	C₂³	1	12	yes	—
117	#126×C₈₉	C₂³	1	12	yes	—
118	#126×C₈₉	C₂³	1	12	yes	—
119	#126×C₈₉	C₂³	1	24	yes	—
120	#126×C₈₉	C₂³	1	24	yes	—
121	#126×C₈₉	C₂³	1	24	yes	—
122	#125×C₈₉	C₂³	1	6	yes	—
123	#125×C₈₉	C₂³	1	12	yes	—
124	#125×C₈₉	C₂³	1	12	yes	—
125	#125×C₈₉	C₂³	1	12	yes	—
126	#125×C₈₉	C₂³	1	24	yes	—
127	#125×C₈₉	C₂³	1	24	yes	—
128	#124×C₈₉	C₂³	1	12	yes	—
129	#124×C₈₉	C₂³	1	12	yes	—
130	#124×C₈₉	C₂³	1	6	yes	—
131	#124×C₈₉	C₂³	1	12	yes	—
132	#124×C₈₉	C₂³	1	12	yes	—
133	#124×C₈₉	C₂³	1	24	yes	—
134	#123×C₈₉	C₂³	1	12	yes	—
135	#123×C₈₉	C₂³	1	12	yes	—
136	#123×C₈₉	C₂³	1	12	yes	—
137	#123×C₈₉	C₂³	1	24	yes	—
138	#123×C₈₉	C₂³	1	12	yes	—
139	#123×C₈₉	C₂³	1	4	yes	—
140	#123×C₈₉	C₂³	1	12	yes	—
141	#123×C₈₉	C₂³	1	24	yes	—
142	#123×C₈₉	C₂³	1	24	yes	—
143	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
144	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
145	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
146	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
147	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
148	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
149	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
150	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
151	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
152	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
156	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
157	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
158	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
159	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
160	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
161	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
162	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
163	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
164	#121×C₈₉	C₂³	1	12	yes	—
165	#121×C₈₉	C₂³	1	12	yes	—
166	#121×C₈₉	C₂³	1	2	yes	—
167	#121×C₈₉	C₂³	1	6	yes	—
168	#121×C₈₉	C₂³	1	12	yes	—
169	#121×C₈₉	C₂³	1	12	yes	—
170	#121×C₈₉	C₂³	1	12	yes	—
171	#121×C₈₉	C₂³	1	2	yes	—
172	#121×C₈₉	C₂³	1	12	yes	—
173	#121×C₈₉	C₂³	1	24	yes	—
174	#120×C₈₉	C₂³	1	12	yes	—
175	#120×C₈₉	C₂³	1	12	yes	—
176	#120×C₈₉	C₂³	1	4	yes	—
177	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
178	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
179	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
180	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
181	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
182	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
183	C₄×Q₈×C₈₉	C₂³	1	6	yes	—
184	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
185	C₄×D₄×C₈₉	C₂³	1	12	yes	—
186	C₄×D₄×C₈₉	C₂³	1	12	yes	—
187	C₄×D₄×C₈₉	C₂³	1	12	yes	—
188	C₄×D₄×C₈₉	C₂³	1	12	yes	—
189	C₄×D₄×C₈₉	C₂³	1	12	yes	—
190	C₄×D₄×C₈₉	C₂³	1	12	yes	—
191	C₄×D₄×C₈₉	C₂³	1	24	yes	—
192	C₄×D₄×C₈₉	C₂³	1	24	yes	—
193	C₄×D₄×C₈₉	C₂³	1	12	yes	—
194	C₄×D₄×C₈₉	C₂³	1	12	yes	—
195	C₄×D₄×C₈₉	C₂³	1	6	yes	—
196	C₄×D₄×C₈₉	C₂³	1	24	yes	—
197	#117×C₈₉	C₂³	1	12	yes	—
198	#117×C₈₉	C₂³	1	12	yes	—
199	#117×C₈₉	C₂³	1	12	yes	—
200	#117×C₈₉	C₂³	1	6	yes	—
201	#117×C₈₉	C₂³	1	24	yes	—
202	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
203	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
204	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
205	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
206	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
207	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
208	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	—
209	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
211	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
212	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
213	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
214	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
215	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
216	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
217	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
218	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
219	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
220	#41×C₈₉	—	2	8	no	—
221	#41×C₈₉	—	4	12	no	—
222	#41×C₈₉	—	4	12	no	—
223	#41×C₈₉	—	4	24	no	—
224	C₂×Q₈×C₈₉	—	2	8	no	—
225	C₂×Q₈×C₈₉	—	2	4	no	—
226	C₂×Q₈×C₈₉	—	2	16	no	—
227	C₂×Q₈×C₈₉	—	4	6	no	—
228	C₂×Q₈×C₈₉	—	4	12	no	—
229	C₂×Q₈×C₈₉	—	4	12	no	—
230	C₂×Q₈×C₈₉	—	4	24	no	—
231	C₂×Q₈×C₈₉	—	4	12	no	—
232	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
233	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
234	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
235	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
236	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
237	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
238	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
239	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×D₄×C₈₉	—	2	8	no	—
241	C₂×D₄×C₈₉	—	2	12	no	—
242	C₂×D₄×C₈₉	—	4	6	no	—
243	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
244	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
245	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
246	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
247	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
248	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
250	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
251	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
252	C₂²×C₄×C₈₉	—	4	6	no	—
253	C₂²×C₄×C₈₉	—	4	12	no	—
254	C₂²×C₄×C₈₉	—	4	6	no	—
255	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
257	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
258	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
259	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
260	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
261	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
263	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
264	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
265	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
266	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
268	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
269	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
270	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
271	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
272	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
273	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
274	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
275	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
276	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
277	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
278	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
279	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
280	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
281	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
282	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
283	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
284	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
285	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
286	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
287	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
288	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
289	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
291	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
292	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
293	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
294	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
295	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
296	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
297	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
298	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
299	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
300	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
301	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
302	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
303	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
304	C₄²×C₈₉	C₂⁴	1	12	yes	—
305	C₄²×C₈₉	C₂⁴	1	6	yes	—
306	C₄²×C₈₉	C₂⁴	1	12	yes	—
307	C₄²×C₈₉	C₂⁴	1	6	yes	—
308	C₄²×C₈₉	C₂⁴	1	24	yes	—
309	C₂³×C₈₉	—	2	4	no	—
310	C₂³×C₈₉	—	2	6	no	—
311	C₂³×C₈₉	—	4	1	no	—
312	C₂³×C₈₉	—	4	2	no	—
313	C₂³×C₈₉	—	4	1	no	—
314	C₂³×C₈₉	—	4	2	no	—
315	C₂³×C₈₉	—	4	3	no	—
316	C₂³×C₈₉	—	4	3	no	—
317	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	complemented
318	C₂³×C₈₉	C₂⁵	1	4	yes	—
319	C₂³×C₈₉	C₂⁵	1	6	yes	—
320	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
321	C₂³×C₈₉	C₂⁵	1	2	yes	—
322	Q₈×C₈₉	—	2	12	no	—
323	Q₈×C₈₉	—	2	24	no	—
324	Q₈×C₈₉	—	2	6	no	—
325	Q₈×C₈₉	—	4	6	no	—
326	Q₈×C₈₉	—	4	12	no	—
327	Q₈×C₈₉	—	4	6	no	—
328	Q₈×C₈₉	—	4	6	no	—
329	Q₈×C₈₉	H(5,𝔽₂)	1	4	yes	—
330	D₄×C₈₉	—	2	8	no	—
331	D₄×C₈₉	—	2	8	no	—
332	D₄×C₈₉	—	2	24	no	—
333	D₄×C₈₉	—	2	12	no	—
334	D₄×C₈₉	—	4	6	no	—
335	D₄×C₈₉	—	4	12	no	—
336	D₄×C₈₉	—	4	2	no	—
337	D₄×C₈₉	—	4	2	no	—
338	D₄×C₈₉	—	4	12	no	—
339	C₂×C₄×C₈₉	—	2	6	no	—
340	C₂×C₄×C₈₉	—	2	4	no	—
341	C₂×C₄×C₈₉	—	2	6	no	—
342	C₂×C₄×C₈₉	—	2	12	no	—
343	C₂×C₄×C₈₉	—	2	24	no	—
344	C₂×C₄×C₈₉	—	2	12	no	—
345	C₂×C₄×C₈₉	—	4	1	no	—
346	C₂×C₄×C₈₉	—	4	6	no	—
347	C₂×C₄×C₈₉	—	4	6	no	—
348	C₂×C₄×C₈₉	—	4	12	no	—
349	C₂×C₄×C₈₉	—	4	3	no	—
350	C₂×C₄×C₈₉	—	4	6	no	—
351	C₂×C₄×C₈₉	—	4	6	no	—
352	C₂×C₄×C₈₉	—	4	12	no	—
353	C₂×C₄×C₈₉	—	4	1	no	—
354	C₂×C₄×C₈₉	—	4	12	no	—
355	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
356	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
357	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
358	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
359	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
360	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
361	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
362	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
363	C₂×C₄×C₈₉	C₂⁵	1	3	yes	—
364	C₂²×C₈₉	—	2	2	no	—
365	C₂²×C₈₉	—	2	1	no	—
366	C₂²×C₈₉	—	2	2	no	—
367	C₂²×C₈₉	—	2	1	no	—
368	C₂²×C₈₉	—	2	4	no	—
369	C₂²×C₈₉	—	2	6	no	—
370	C₂²×C₈₉	—	2	4	no	—
371	C₂²×C₈₉	—	2	6	no	—
372	C₂²×C₈₉	—	2	6	no	—
373	C₂²×C₈₉	—	2	4	no	—
374	C₂²×C₈₉	—	4	4	no	—
375	C₂²×C₈₉	—	4	8	no	—
376	C₂²×C₈₉	—	8	6	no	—
377	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
378	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	4	yes	—
379	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
380	C₄×C₈₉	—	2	2	no	—
381	C₄×C₈₉	—	2	3	no	—
382	C₄×C₈₉	—	2	12	no	—
383	C₄×C₈₉	—	2	6	no	—
384	C₄×C₈₉	—	2	6	no	—
385	C₄×C₈₉	—	2	4	no	—
386	C₄×C₈₉	—	2	12	no	—
387	C₄×C₈₉	—	2	2	no	—
388	C₄×C₈₉	C₂×H(5,𝔽₂)	1	6	yes	—
389	#62893	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
390	C₂×C₈₉	—	2	4	no	—
391	C₂×C₈₉	—	2	2	no	—
392	C₂×C₈₉	—	4	4	no	—
393	C₂×C₈₉	—	4	6	no	—
394	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
396	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
397	#3561	C₂×C₈₉	1	6	yes	complemented
398	#3552	C₂×C₈₉	1	12	yes	complemented
399	#3541	C₂×C₈₉	1	12	yes	complemented
400	#3538	C₂×C₈₉	1	6	yes	complemented
401	#3523	C₂×C₈₉	1	2	yes	complemented
402	#3516	C₂×C₈₉	1	4	yes	complemented
403	#3505	C₂×C₈₉	1	6	yes	complemented
404	#3501	C₂×C₈₉	1	3	yes	complemented
405	#3489	C₂×C₈₉	1	2	yes	complemented
406	#3486	C₂×C₈₉	1	4	yes	complemented
407	C₂×D₄×Q₈	C₂×C₈₉	1	2	yes	complemented
408	C₂×#548	C₂×C₈₉	1	1	yes	characteristic, complemented
409	#3459	C₂×C₈₉	1	3	yes	complemented
410	C₈₉	#62893	1	1	yes	characteristic, direct product factor, Sylow
411	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
412	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
413	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
414	C₂³×Q₈	C₂²×C₈₉	1	2	yes	complemented
415	#563	C₂²×C₈₉	1	24	yes	complemented
416	#563	C₂²×C₈₉	1	12	yes	complemented
417	#562	C₂²×C₈₉	1	12	yes	complemented
418	#557	C₂²×C₈₉	1	2	yes	complemented
419	#557	C₂²×C₈₉	1	6	yes	complemented
420	#556	C₂²×C₈₉	1	12	yes	complemented
421	#556	C₂²×C₈₉	1	6	yes	complemented
422	#554	C₂²×C₈₉	1	12	yes	complemented
423	#554	C₂²×C₈₉	1	24	yes	complemented
424	#553	C₂²×C₈₉	1	12	yes	complemented
425	#553	C₂²×C₈₉	1	24	yes	complemented
426	#552	C₂²×C₈₉	1	12	yes	complemented
427	#552	C₂²×C₈₉	1	12	yes	complemented
428	#551	C₂²×C₈₉	1	24	yes	complemented
429	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
430	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
431	D₄×Q₈	C₂²×C₈₉	1	12	yes	complemented
432	D₄×Q₈	C₂²×C₈₉	1	12	yes	complemented
433	D₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
434	D₄×Q₈	C₂²×C₈₉	1	12	yes	complemented
435	D₄×Q₈	C₂²×C₈₉	1	12	yes	complemented
436	#548	C₂²×C₈₉	1	4	yes	complemented
437	#548	C₂²×C₈₉	1	12	yes	complemented
438	#548	C₂²×C₈₉	1	4	yes	complemented
439	#548	C₂²×C₈₉	1	12	yes	complemented
440	#548	C₂²×C₈₉	1	12	yes	complemented
441	#547	C₂²×C₈₉	1	12	yes	complemented
442	#546	C₂²×C₈₉	1	12	yes	complemented
443	#544	C₂²×C₈₉	1	6	yes	complemented
444	#544	C₂²×C₈₉	1	12	yes	complemented
445	#543	C₂²×C₈₉	1	3	yes	—
446	#543	C₂²×C₈₉	1	6	yes	complemented
447	#542	C₂²×C₈₉	1	12	yes	complemented
448	#542	C₂²×C₈₉	1	24	yes	complemented
449	#541	C₂²×C₈₉	1	12	yes	complemented
450	#541	C₂²×C₈₉	1	12	yes	complemented
451	#539	C₂²×C₈₉	1	6	yes	—
452	#539	C₂²×C₈₉	1	12	yes	complemented
453	#539	C₂²×C₈₉	1	12	yes	complemented
454	#539	C₂²×C₈₉	1	12	yes	complemented
455	#538	C₂²×C₈₉	1	6	yes	—
456	#538	C₂²×C₈₉	1	12	yes	complemented
457	#538	C₂²×C₈₉	1	12	yes	complemented
458	#537	C₂²×C₈₉	1	6	yes	complemented
459	#536	C₂²×C₈₉	1	12	yes	complemented
460	#536	C₂²×C₈₉	1	12	yes	complemented
461	#536	C₂²×C₈₉	1	6	yes	complemented
462	#534	C₂²×C₈₉	1	1	yes	characteristic
463	#534	C₂²×C₈₉	1	6	yes	—
464	#533	C₂²×C₈₉	1	6	yes	complemented
465	C₂×C₄⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
466	#529	C₂²×C₈₉	1	6	yes	—
467	#529	C₂²×C₈₉	1	12	yes	complemented
468	#529	C₂²×C₈₉	1	12	yes	complemented
469	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
470	#525	C₂²×C₈₉	1	6	yes	—
471	#525	C₂²×C₈₉	1	12	yes	complemented
472	#525	C₂²×C₈₉	1	12	yes	complemented
473	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
474	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	complemented
475	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
476	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
477	C₂×#121	C₂²×C₈₉	1	3	yes	—
478	#520	C₂²×C₈₉	1	2	yes	complemented
479	#519	C₂²×C₈₉	1	4	yes	complemented
480	#518	C₂²×C₈₉	1	6	yes	—
481	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
482	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
483	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
484	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
485	2₋¹⁺⁴	—	4	8	no	—
486	C₂×#41	—	4	4	no	—
487	C₂×#41	C₂³×C₈₉	1	2	yes	—
488	C₂×#41	C₂³×C₈₉	1	6	yes	—
489	C₂×#41	C₂³×C₈₉	1	12	yes	—
490	C₂×#41	C₂³×C₈₉	1	6	yes	—
491	C₂²×Q₈	—	4	4	no	—
492	C₂²×Q₈	—	4	8	no	—
493	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
494	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
496	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
497	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
498	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
499	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
500	C₂²×Q₈	C₂³×C₈₉	1	12	yes	—
501	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
502	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
503	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
504	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
505	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
506	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
507	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
508	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
509	C₄⋊Q₈	C₂³×C₈₉	1	24	yes	—
510	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
511	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
512	C₄⋊Q₈	C₂³×C₈₉	1	24	yes	—
513	#126	C₂³×C₈₉	1	12	yes	—
514	#126	C₂³×C₈₉	1	12	yes	—
515	#126	C₂³×C₈₉	1	12	yes	—
516	#126	C₂³×C₈₉	1	24	yes	—
517	#126	C₂³×C₈₉	1	24	yes	—
518	#126	C₂³×C₈₉	1	24	yes	—
519	#125	C₂³×C₈₉	1	6	yes	—
520	#125	C₂³×C₈₉	1	12	yes	—
521	#125	C₂³×C₈₉	1	12	yes	—
522	#125	C₂³×C₈₉	1	12	yes	—
523	#125	C₂³×C₈₉	1	24	yes	—
524	#125	C₂³×C₈₉	1	24	yes	—
525	#124	C₂³×C₈₉	1	12	yes	—
526	#124	C₂³×C₈₉	1	12	yes	—
527	#124	C₂³×C₈₉	1	6	yes	—
528	#124	C₂³×C₈₉	1	12	yes	—
529	#124	C₂³×C₈₉	1	12	yes	—
530	#124	C₂³×C₈₉	1	24	yes	—
531	#123	C₂³×C₈₉	1	12	yes	—
532	#123	C₂³×C₈₉	1	12	yes	—
533	#123	C₂³×C₈₉	1	12	yes	—
534	#123	C₂³×C₈₉	1	24	yes	—
535	#123	C₂³×C₈₉	1	12	yes	—
536	#123	C₂³×C₈₉	1	4	yes	—
537	#123	C₂³×C₈₉	1	12	yes	—
538	#123	C₂³×C₈₉	1	24	yes	—
539	#123	C₂³×C₈₉	1	24	yes	—
540	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
541	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
542	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
543	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
544	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
545	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
546	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
547	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
548	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
549	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
550	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
551	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
552	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
553	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
554	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
555	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
556	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
557	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
558	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
559	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
560	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
561	#121	C₂³×C₈₉	1	12	yes	—
562	#121	C₂³×C₈₉	1	12	yes	—
563	#121	C₂³×C₈₉	1	2	yes	—
564	#121	C₂³×C₈₉	1	6	yes	—
565	#121	C₂³×C₈₉	1	12	yes	—
566	#121	C₂³×C₈₉	1	12	yes	—
567	#121	C₂³×C₈₉	1	12	yes	—
568	#121	C₂³×C₈₉	1	2	yes	—
569	#121	C₂³×C₈₉	1	12	yes	—
570	#121	C₂³×C₈₉	1	24	yes	—
571	#120	C₂³×C₈₉	1	12	yes	—
572	#120	C₂³×C₈₉	1	12	yes	—
573	#120	C₂³×C₈₉	1	4	yes	—
574	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
575	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
576	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
577	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
578	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
579	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
580	C₄×Q₈	C₂³×C₈₉	1	6	yes	—
581	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
582	C₄×D₄	C₂³×C₈₉	1	12	yes	—
583	C₄×D₄	C₂³×C₈₉	1	12	yes	—
584	C₄×D₄	C₂³×C₈₉	1	12	yes	—
585	C₄×D₄	C₂³×C₈₉	1	12	yes	—
586	C₄×D₄	C₂³×C₈₉	1	12	yes	—
587	C₄×D₄	C₂³×C₈₉	1	12	yes	—
588	C₄×D₄	C₂³×C₈₉	1	24	yes	—
589	C₄×D₄	C₂³×C₈₉	1	24	yes	—
590	C₄×D₄	C₂³×C₈₉	1	12	yes	—
591	C₄×D₄	C₂³×C₈₉	1	12	yes	—
592	C₄×D₄	C₂³×C₈₉	1	6	yes	—
593	C₄×D₄	C₂³×C₈₉	1	24	yes	—
594	#117	C₂³×C₈₉	1	12	yes	—
595	#117	C₂³×C₈₉	1	12	yes	—
596	#117	C₂³×C₈₉	1	12	yes	—
597	#117	C₂³×C₈₉	1	6	yes	—
598	#117	C₂³×C₈₉	1	24	yes	—
599	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
600	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
601	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
602	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
603	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
604	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
605	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
612	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
613	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
614	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
615	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
616	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
617	#41	—	2	8	no	—
618	#41	—	4	12	no	—
619	#41	—	4	12	no	—
620	#41	—	4	24	no	—
621	C₂×Q₈	—	2	8	no	—
622	C₂×Q₈	—	2	4	no	—
623	C₂×Q₈	—	2	16	no	—
624	C₂×Q₈	—	4	6	no	—
625	C₂×Q₈	—	4	12	no	—
626	C₂×Q₈	—	4	12	no	—
627	C₂×Q₈	—	4	24	no	—
628	C₂×Q₈	—	4	12	no	—
629	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
630	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
631	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
632	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
633	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
634	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
635	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
636	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
637	C₂×D₄	—	2	8	no	—
638	C₂×D₄	—	2	12	no	—
639	C₂×D₄	—	4	6	no	—
640	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
641	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
642	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
643	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
644	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
645	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
646	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
647	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
648	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
649	C₂²×C₄	—	4	6	no	—
650	C₂²×C₄	—	4	12	no	—
651	C₂²×C₄	—	4	6	no	—
652	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
654	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
655	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
656	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
657	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
658	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
660	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
661	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
662	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
663	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
665	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
666	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
667	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
668	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
669	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
670	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
672	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
673	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
674	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
676	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
677	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
678	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
679	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
680	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
681	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
682	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
683	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
684	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
685	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
686	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
687	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
688	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
689	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
690	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
692	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
693	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
694	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
695	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
696	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
697	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
698	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
699	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
700	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
701	C₄²	C₂⁴×C₈₉	1	12	yes	—
702	C₄²	C₂⁴×C₈₉	1	6	yes	—
703	C₄²	C₂⁴×C₈₉	1	12	yes	—
704	C₄²	C₂⁴×C₈₉	1	6	yes	—
705	C₄²	C₂⁴×C₈₉	1	24	yes	—
706	C₂³	—	2	4	no	—
707	C₂³	—	2	6	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	2	no	—
712	C₂³	—	4	3	no	—
713	C₂³	—	4	3	no	—
714	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	complemented
715	C₂³	C₂⁵×C₈₉	1	4	yes	—
716	C₂³	C₂⁵×C₈₉	1	6	yes	—
717	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
718	C₂³	C₂⁵×C₈₉	1	2	yes	—
719	Q₈	—	2	12	no	—
720	Q₈	—	2	24	no	—
721	Q₈	—	2	6	no	—
722	Q₈	—	4	6	no	—
723	Q₈	—	4	12	no	—
724	Q₈	—	4	6	no	—
725	Q₈	—	4	6	no	—
726	Q₈	H(5,𝔽₂)×C₈₉	1	4	yes	—
727	D₄	—	2	8	no	—
728	D₄	—	2	8	no	—
729	D₄	—	2	24	no	—
730	D₄	—	2	12	no	—
731	D₄	—	4	6	no	—
732	D₄	—	4	12	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	12	no	—
736	C₂×C₄	—	2	6	no	—
737	C₂×C₄	—	2	4	no	—
738	C₂×C₄	—	2	6	no	—
739	C₂×C₄	—	2	12	no	—
740	C₂×C₄	—	2	24	no	—
741	C₂×C₄	—	2	12	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	6	no	—
745	C₂×C₄	—	4	12	no	—
746	C₂×C₄	—	4	3	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	6	no	—
749	C₂×C₄	—	4	12	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	12	no	—
752	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
753	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
754	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
755	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
756	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
757	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
758	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
759	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
760	C₂×C₄	C₂⁵×C₈₉	1	3	yes	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	6	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	6	no	—
769	C₂²	—	2	6	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	8	no	—
773	C₂²	—	8	6	no	—
774	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
775	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	4	yes	—
776	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
777	C₄	—	2	2	no	—
778	C₄	—	2	3	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	6	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	12	no	—
784	C₄	—	2	2	no	—
785	C₄	C₂×H(5,𝔽₂)×C₈₉	1	6	yes	—
786	C₂	—	2	4	no	—
787	C₂	—	2	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	4	6	no	—
790	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
791	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
792	C₂	C₈₉×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3561	C₂	semidirect
2. C₈₉×#3552	C₂	semidirect
3. C₈₉×#3541	C₂	semidirect
4. C₈₉×#3538	C₂	semidirect
5. C₈₉×#3523	C₂	semidirect
6. C₈₉×#3516	C₂	semidirect
7. C₈₉×#3505	C₂	semidirect
8. C₈₉×#3501	C₂	semidirect
9. C₈₉×#3489	C₂	semidirect
10. C₈₉×#3486	C₂	semidirect
11. C₂×D₄×Q₈×C₈₉	C₂	semidirect
12. C₂×#548×C₈₉	C₂	semidirect
13. C₈₉×#3459	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
15. C₂²×#41×C₈₉	C₂²	semidirect
17. C₂³×Q₈×C₈₉	C₂²	semidirect
18. #563×C₈₉	C₂²	semidirect
19. #563×C₈₉	C₂²	semidirect
20. #562×C₈₉	C₂²	semidirect
21. #557×C₈₉	C₂²	semidirect
22. #557×C₈₉	C₂²	semidirect
23. #556×C₈₉	C₂²	semidirect
24. #556×C₈₉	C₂²	semidirect
25. #554×C₈₉	C₂²	semidirect
26. #554×C₈₉	C₂²	semidirect
27. #553×C₈₉	C₂²	semidirect
28. #553×C₈₉	C₂²	semidirect
29. #552×C₈₉	C₂²	semidirect
30. #552×C₈₉	C₂²	semidirect
31. #551×C₈₉	C₂²	semidirect
32. D₄×Q₈×C₈₉	C₂²	semidirect
33. D₄×Q₈×C₈₉	C₂²	semidirect
34. D₄×Q₈×C₈₉	C₂²	semidirect
35. D₄×Q₈×C₈₉	C₂²	semidirect
36. D₄×Q₈×C₈₉	C₂²	semidirect
37. D₄×Q₈×C₈₉	C₂²	semidirect
38. D₄×Q₈×C₈₉	C₂²	semidirect
39. #548×C₈₉	C₂²	semidirect
40. #548×C₈₉	C₂²	semidirect
41. #548×C₈₉	C₂²	semidirect
42. #548×C₈₉	C₂²	semidirect
43. #548×C₈₉	C₂²	semidirect
44. #547×C₈₉	C₂²	semidirect
45. #546×C₈₉	C₂²	semidirect
46. #544×C₈₉	C₂²	semidirect
47. #544×C₈₉	C₂²	semidirect
49. #543×C₈₉	C₂²	semidirect
50. #542×C₈₉	C₂²	semidirect
51. #542×C₈₉	C₂²	semidirect
52. #541×C₈₉	C₂²	semidirect
53. #541×C₈₉	C₂²	semidirect
55. #539×C₈₉	C₂²	semidirect
56. #539×C₈₉	C₂²	semidirect
57. #539×C₈₉	C₂²	semidirect
59. #538×C₈₉	C₂²	semidirect
60. #538×C₈₉	C₂²	semidirect
61. #537×C₈₉	C₂²	semidirect
62. #536×C₈₉	C₂²	semidirect
63. #536×C₈₉	C₂²	semidirect
64. #536×C₈₉	C₂²	semidirect
67. #533×C₈₉	C₂²	semidirect
68. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
70. #529×C₈₉	C₂²	semidirect
71. #529×C₈₉	C₂²	semidirect
72. C₂×#124×C₈₉	C₂²	semidirect
74. #525×C₈₉	C₂²	semidirect
75. #525×C₈₉	C₂²	semidirect
77. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
78. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
79. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
81. #520×C₈₉	C₂²	semidirect
82. #519×C₈₉	C₂²	semidirect
84. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
85. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
317. C₂³×C₈₉	2₋¹⁺⁴	semidirect
389. #62893	C₈₉	direct (N × H)
397. #3561	C₂×C₈₉	semidirect
398. #3552	C₂×C₈₉	semidirect
399. #3541	C₂×C₈₉	semidirect
400. #3538	C₂×C₈₉	semidirect
401. #3523	C₂×C₈₉	semidirect
402. #3516	C₂×C₈₉	semidirect
403. #3505	C₂×C₈₉	semidirect
404. #3501	C₂×C₈₉	semidirect
405. #3489	C₂×C₈₉	semidirect
406. #3486	C₂×C₈₉	semidirect
407. C₂×D₄×Q₈	C₂×C₈₉	semidirect
408. C₂×#548	C₂×C₈₉	semidirect
409. #3459	C₂×C₈₉	semidirect
410. C₈₉	#62893	direct (N × H)
411. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
412. C₂²×#41	C₂²×C₈₉	semidirect
414. C₂³×Q₈	C₂²×C₈₉	semidirect
415. #563	C₂²×C₈₉	semidirect
416. #563	C₂²×C₈₉	semidirect
417. #562	C₂²×C₈₉	semidirect
418. #557	C₂²×C₈₉	semidirect
419. #557	C₂²×C₈₉	semidirect
420. #556	C₂²×C₈₉	semidirect
421. #556	C₂²×C₈₉	semidirect
422. #554	C₂²×C₈₉	semidirect
423. #554	C₂²×C₈₉	semidirect
424. #553	C₂²×C₈₉	semidirect
425. #553	C₂²×C₈₉	semidirect
426. #552	C₂²×C₈₉	semidirect
427. #552	C₂²×C₈₉	semidirect
428. #551	C₂²×C₈₉	semidirect
429. D₄×Q₈	C₂²×C₈₉	semidirect
430. D₄×Q₈	C₂²×C₈₉	semidirect
431. D₄×Q₈	C₂²×C₈₉	semidirect
432. D₄×Q₈	C₂²×C₈₉	semidirect
433. D₄×Q₈	C₂²×C₈₉	semidirect
434. D₄×Q₈	C₂²×C₈₉	semidirect
435. D₄×Q₈	C₂²×C₈₉	semidirect
436. #548	C₂²×C₈₉	semidirect
437. #548	C₂²×C₈₉	semidirect
438. #548	C₂²×C₈₉	semidirect
439. #548	C₂²×C₈₉	semidirect
440. #548	C₂²×C₈₉	semidirect
441. #547	C₂²×C₈₉	semidirect
442. #546	C₂²×C₈₉	semidirect
443. #544	C₂²×C₈₉	semidirect
444. #544	C₂²×C₈₉	semidirect
446. #543	C₂²×C₈₉	semidirect
447. #542	C₂²×C₈₉	semidirect
448. #542	C₂²×C₈₉	semidirect
449. #541	C₂²×C₈₉	semidirect
450. #541	C₂²×C₈₉	semidirect
452. #539	C₂²×C₈₉	semidirect
453. #539	C₂²×C₈₉	semidirect
454. #539	C₂²×C₈₉	semidirect
456. #538	C₂²×C₈₉	semidirect
457. #538	C₂²×C₈₉	semidirect
458. #537	C₂²×C₈₉	semidirect
459. #536	C₂²×C₈₉	semidirect
460. #536	C₂²×C₈₉	semidirect
461. #536	C₂²×C₈₉	semidirect
464. #533	C₂²×C₈₉	semidirect
465. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
467. #529	C₂²×C₈₉	semidirect
468. #529	C₂²×C₈₉	semidirect
469. C₂×#124	C₂²×C₈₉	semidirect
471. #525	C₂²×C₈₉	semidirect
472. #525	C₂²×C₈₉	semidirect
474. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
475. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
476. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
478. #520	C₂²×C₈₉	semidirect
479. #519	C₂²×C₈₉	semidirect
481. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
482. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
714. C₂³	2₋¹⁺⁴×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3561	2
C₈₉×#3552	2
C₈₉×#3541	2
C₈₉×#3538	2
C₈₉×#3523	2
C₈₉×#3516	2
C₈₉×#3505	2
C₈₉×#3501	2
C₈₉×#3489	2
C₈₉×#3486	2
C₂×D₄×Q₈×C₈₉	2
C₂×#548×C₈₉	2
C₈₉×#3459	2
#62893	89

Subgroups — C89×#62893 #36440741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62893 #36440741