Subgroups — C₂×C₈₉×#3266 #36438872

Order 22784.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#546×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#3266	C₂	1	16	yes	maximal, direct product factor
6	C₂×#497×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#467×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#451×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#448×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#450×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#440×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#435×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#137×C₈₉	—	2	8	no	—
22	C₂×#137×C₈₉	C₂²	1	8	yes	complemented
23	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂²×SD₁₆×C₈₉	—	2	8	no	—
27	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×SD₁₆×C₈₉	C₂²	1	8	yes	complemented
34	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
36	D₄×Q₈×C₈₉	—	2	4	no	—
37	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
38	#546×C₈₉	—	2	4	no	—
39	#546×C₈₉	C₂²	1	8	yes	—
40	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
41	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#123×C₈₉	—	2	1	no	—
44	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
45	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
46	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×#121×C₈₉	—	2	1	no	—
50	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
51	C₂×#120×C₈₉	—	2	1	no	—
52	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×D₄×C₈₉	—	2	1	no	—
54	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
57	#497×C₈₉	C₂²	1	8	yes	complemented
58	#468×C₈₉	C₂²	1	8	yes	complemented
59	#467×C₈₉	C₂²	1	8	yes	complemented
60	#464×C₈₉	C₂²	1	8	yes	complemented
61	#461×C₈₉	C₂²	1	8	yes	complemented
62	#452×C₈₉	C₂²	1	8	yes	complemented
63	#451×C₈₉	C₂²	1	8	yes	complemented
64	#450×C₈₉	C₂²	1	8	yes	complemented
65	#448×C₈₉	C₂²	1	8	yes	complemented
66	#440×C₈₉	C₂²	1	8	yes	complemented
67	#435×C₈₉	C₂²	1	8	yes	complemented
68	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
70	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
71	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
72	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
73	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	C₂⁵×C₈₉	—	2	1	no	—
80	C₂×#41×C₈₉	—	2	2	no	—
81	C₂×#41×C₈₉	—	2	4	no	—
82	C₂×#41×C₈₉	—	4	2	no	—
83	C₂×#41×C₈₉	C₂³	1	4	yes	—
84	C₂²×Q₈×C₈₉	—	2	1	no	—
85	C₂²×Q₈×C₈₉	—	2	1	no	—
86	C₂²×Q₈×C₈₉	—	2	2	no	—
87	C₂²×Q₈×C₈₉	—	2	2	no	—
88	C₂²×Q₈×C₈₉	—	2	4	no	—
89	C₂²×Q₈×C₈₉	—	2	4	no	—
90	C₂²×Q₈×C₈₉	—	4	2	no	—
91	C₂²×Q₈×C₈₉	—	4	2	no	—
92	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
96	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	C₂³	1	4	yes	complemented
98	C₂²×D₄×C₈₉	—	2	4	no	—
99	C₂²×D₄×C₈₉	—	2	1	no	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	—	2	2	no	—
103	C₂²×D₄×C₈₉	—	4	2	no	—
104	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
105	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
107	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₈₉	—	2	1	no	—
109	C₂³×C₄×C₈₉	—	2	1	no	—
110	C₂³×C₄×C₈₉	—	2	1	no	—
111	C₂³×C₄×C₈₉	—	2	1	no	—
112	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
114	#137×C₈₉	—	2	32	no	—
115	C₂×Q₁₆×C₈₉	—	2	4	no	—
116	C₂×Q₁₆×C₈₉	—	2	4	no	—
117	C₂×Q₁₆×C₈₉	—	4	2	no	—
118	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
119	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
120	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
121	C₂×SD₁₆×C₈₉	—	2	4	no	—
122	C₂×SD₁₆×C₈₉	—	2	4	no	—
123	C₂×SD₁₆×C₈₉	—	2	4	no	—
124	C₂×SD₁₆×C₈₉	—	2	32	no	—
125	C₂×SD₁₆×C₈₉	—	2	4	no	—
126	C₂×SD₁₆×C₈₉	—	4	2	no	—
127	C₂×SD₁₆×C₈₉	D₄	1	8	yes	complemented
128	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
129	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
130	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
131	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
132	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
133	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
134	C₂×M₁₆×C₈₉	—	2	4	no	—
135	C₂×M₁₆×C₈₉	C₂³	1	4	yes	complemented
136	C₂²×C₈×C₈₉	—	2	4	no	—
137	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
141	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₈₉	—	2	8	no	—
143	C₄⋊Q₈×C₈₉	—	2	2	no	—
144	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
145	#124×C₈₉	—	2	2	no	—
146	#124×C₈₉	C₂³	1	4	yes	—
147	#123×C₈₉	—	2	8	no	—
148	C₂²⋊Q₈×C₈₉	—	2	2	no	—
149	C₂²⋊Q₈×C₈₉	—	2	2	no	—
150	C₂²⋊Q₈×C₈₉	—	2	2	no	—
151	C₂²⋊Q₈×C₈₉	—	2	8	no	—
152	C₂²⋊Q₈×C₈₉	—	2	8	no	—
153	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
154	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
155	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
156	#121×C₈₉	—	2	2	no	—
157	#121×C₈₉	—	2	8	no	—
158	#121×C₈₉	C₂³	1	4	yes	—
159	#120×C₈₉	—	2	8	no	—
160	C₄×Q₈×C₈₉	—	2	2	no	—
161	C₄×Q₈×C₈₉	C₂³	1	4	yes	complemented
162	C₄×D₄×C₈₉	—	2	8	no	—
163	C₄×D₄×C₈₉	—	2	2	no	—
164	C₄×D₄×C₈₉	D₄	1	4	yes	—
165	C₄×D₄×C₈₉	C₂³	1	4	yes	—
166	C₄×D₄×C₈₉	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
168	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
169	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
170	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
171	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
172	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
173	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
177	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
178	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
179	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
180	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
181	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
182	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
183	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
184	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₈₉	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₈₉	—	2	1	no	—
187	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
188	#107×C₈₉	C₂³	1	4	yes	complemented
189	C₄⋊C₈×C₈₉	C₂³	1	4	yes	complemented
190	#103×C₈₉	C₂³	1	4	yes	complemented
191	#103×C₈₉	C₂³	1	4	yes	complemented
192	#103×C₈₉	C₂³	1	4	yes	complemented
193	#103×C₈₉	C₂³	1	4	yes	complemented
194	#102×C₈₉	C₂³	1	4	yes	—
195	#102×C₈₉	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
197	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	complemented
198	#97×C₈₉	C₂³	1	4	yes	complemented
199	C₂⁴×C₈₉	—	2	1	no	—
200	C₂⁴×C₈₉	—	2	1	no	—
201	C₂⁴×C₈₉	—	2	4	no	—
202	C₂⁴×C₈₉	—	4	4	no	—
203	C₂⁴×C₈₉	—	4	4	no	—
204	C₂⁴×C₈₉	—	8	2	no	—
205	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
207	#41×C₈₉	—	2	8	no	—
208	#41×C₈₉	—	4	4	no	—
209	#41×C₈₉	—	4	8	no	—
210	C₂×Q₈×C₈₉	—	2	1	no	—
211	C₂×Q₈×C₈₉	—	2	1	no	—
212	C₂×Q₈×C₈₉	—	2	4	no	—
213	C₂×Q₈×C₈₉	—	2	1	no	—
214	C₂×Q₈×C₈₉	—	2	1	no	—
215	C₂×Q₈×C₈₉	—	2	4	no	—
216	C₂×Q₈×C₈₉	—	2	2	no	—
217	C₂×Q₈×C₈₉	—	2	8	no	—
218	C₂×Q₈×C₈₉	—	2	8	no	—
219	C₂×Q₈×C₈₉	—	2	2	no	—
220	C₂×Q₈×C₈₉	—	2	2	no	—
221	C₂×Q₈×C₈₉	—	2	2	no	—
222	C₂×Q₈×C₈₉	—	2	2	no	—
223	C₂×Q₈×C₈₉	—	2	2	no	—
224	C₂×Q₈×C₈₉	—	2	2	no	—
225	C₂×Q₈×C₈₉	—	4	4	no	—
226	C₂×Q₈×C₈₉	—	4	4	no	—
227	C₂×Q₈×C₈₉	—	4	4	no	—
228	C₂×Q₈×C₈₉	—	4	4	no	—
229	C₂×Q₈×C₈₉	—	4	8	no	—
230	C₂×Q₈×C₈₉	—	4	8	no	—
231	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
232	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
233	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
236	C₂×D₄×C₈₉	—	2	4	no	—
237	C₂×D₄×C₈₉	—	2	8	no	—
238	C₂×D₄×C₈₉	—	2	4	no	—
239	C₂×D₄×C₈₉	—	2	4	no	—
240	C₂×D₄×C₈₉	—	2	1	no	—
241	C₂×D₄×C₈₉	—	2	2	no	—
242	C₂×D₄×C₈₉	—	2	4	no	—
243	C₂×D₄×C₈₉	—	2	1	no	—
244	C₂×D₄×C₈₉	—	2	2	no	—
245	C₂×D₄×C₈₉	—	2	2	no	—
246	C₂×D₄×C₈₉	—	4	4	no	—
247	C₂×D₄×C₈₉	—	4	8	no	—
248	C₂×D₄×C₈₉	—	4	4	no	—
249	C₂×D₄×C₈₉	—	4	4	no	—
250	C₂×D₄×C₈₉	—	8	2	no	—
251	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
252	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₈₉	—	2	1	no	—
256	C₂²×C₄×C₈₉	—	2	2	no	—
257	C₂²×C₄×C₈₉	—	2	2	no	—
258	C₂²×C₄×C₈₉	—	2	2	no	—
259	C₂²×C₄×C₈₉	—	2	2	no	—
260	C₂²×C₄×C₈₉	—	2	4	no	—
261	C₂²×C₄×C₈₉	—	2	4	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	1	no	—
266	C₂²×C₄×C₈₉	—	2	1	no	—
267	C₂²×C₄×C₈₉	—	2	4	no	—
268	C₂²×C₄×C₈₉	—	2	4	no	—
269	C₂²×C₄×C₈₉	—	4	4	no	—
270	C₂²×C₄×C₈₉	—	4	4	no	—
271	C₂²×C₄×C₈₉	—	4	4	no	—
272	C₂²×C₄×C₈₉	—	8	2	no	—
273	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
282	Q₁₆×C₈₉	—	2	8	no	—
283	Q₁₆×C₈₉	—	2	8	no	—
284	Q₁₆×C₈₉	—	4	4	no	—
285	SD₁₆×C₈₉	—	2	8	no	—
286	SD₁₆×C₈₉	—	2	8	no	—
287	SD₁₆×C₈₉	—	2	8	no	—
288	SD₁₆×C₈₉	—	2	8	no	—
289	SD₁₆×C₈₉	—	4	4	no	—
290	SD₁₆×C₈₉	C₂×D₄	1	16	yes	complemented
291	M₁₆×C₈₉	—	2	8	no	—
292	C₂×C₈×C₈₉	—	2	2	no	—
293	C₂×C₈×C₈₉	—	2	2	no	—
294	C₂×C₈×C₈₉	—	2	2	no	—
295	C₂×C₈×C₈₉	—	2	8	no	—
296	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
297	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
298	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
299	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
300	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
301	C₄⋊C₄×C₈₉	—	2	4	no	—
302	C₄⋊C₄×C₈₉	—	2	4	no	—
303	C₄⋊C₄×C₈₉	—	2	4	no	—
304	C₄⋊C₄×C₈₉	—	2	4	no	—
305	C₄⋊C₄×C₈₉	—	2	4	no	—
306	C₄⋊C₄×C₈₉	—	2	4	no	—
307	C₄⋊C₄×C₈₉	—	2	1	no	—
308	C₄⋊C₄×C₈₉	—	2	1	no	—
309	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
310	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
311	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
312	C₂²⋊C₄×C₈₉	—	2	4	no	—
313	C₂²⋊C₄×C₈₉	—	2	4	no	—
314	C₂²⋊C₄×C₈₉	—	2	4	no	—
315	C₂²⋊C₄×C₈₉	—	2	4	no	—
316	C₂²⋊C₄×C₈₉	—	2	4	no	—
317	C₂²⋊C₄×C₈₉	—	2	4	no	—
318	C₂²⋊C₄×C₈₉	—	2	4	no	—
319	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
320	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
321	C₄²×C₈₉	—	2	4	no	—
322	C₄²×C₈₉	C₂×D₄	1	2	yes	—
323	C₄²×C₈₉	C₂⁴	1	2	yes	—
324	C₂³×C₈₉	—	2	2	no	—
325	C₂³×C₈₉	—	2	2	no	—
326	C₂³×C₈₉	—	2	2	no	—
327	C₂³×C₈₉	—	2	4	no	—
328	C₂³×C₈₉	—	2	2	no	—
329	C₂³×C₈₉	—	2	2	no	—
330	C₂³×C₈₉	—	2	2	no	—
331	C₂³×C₈₉	—	2	2	no	—
332	C₂³×C₈₉	—	4	8	no	—
333	C₂³×C₈₉	—	4	2	no	—
334	C₂³×C₈₉	—	4	2	no	—
335	C₂³×C₈₉	—	4	2	no	—
336	C₂³×C₈₉	—	4	2	no	—
337	C₂³×C₈₉	—	4	8	no	—
338	C₂³×C₈₉	—	4	2	no	—
339	C₂³×C₈₉	—	8	4	no	—
340	C₂³×C₈₉	—	8	16	no	—
341	C₂³×C₈₉	#137	1	4	yes	complemented
342	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
343	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₈₉	—	2	4	no	—
346	Q₈×C₈₉	—	2	2	no	—
347	Q₈×C₈₉	—	2	2	no	—
348	Q₈×C₈₉	—	2	2	no	—
349	Q₈×C₈₉	—	2	2	no	—
350	Q₈×C₈₉	—	2	2	no	—
351	Q₈×C₈₉	—	2	2	no	—
352	Q₈×C₈₉	—	2	2	no	—
353	Q₈×C₈₉	—	4	8	no	—
354	Q₈×C₈₉	—	4	8	no	—
355	Q₈×C₈₉	—	4	2	no	—
356	Q₈×C₈₉	—	4	2	no	—
357	Q₈×C₈₉	—	4	2	no	—
358	Q₈×C₈₉	C₂²×D₄	1	4	yes	—
359	D₄×C₈₉	—	2	8	no	—
360	D₄×C₈₉	—	2	4	no	—
361	D₄×C₈₉	—	2	2	no	—
362	D₄×C₈₉	—	2	2	no	—
363	D₄×C₈₉	—	2	2	no	—
364	D₄×C₈₉	—	4	8	no	—
365	D₄×C₈₉	—	4	8	no	—
366	D₄×C₈₉	—	4	2	no	—
367	D₄×C₈₉	—	8	4	no	—
368	D₄×C₈₉	C₂²×D₄	1	4	yes	—
369	C₂×C₄×C₈₉	—	2	2	no	—
370	C₂×C₄×C₈₉	—	2	2	no	—
371	C₂×C₄×C₈₉	—	2	4	no	—
372	C₂×C₄×C₈₉	—	2	2	no	—
373	C₂×C₄×C₈₉	—	2	2	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	4	no	—
376	C₂×C₄×C₈₉	—	2	4	no	—
377	C₂×C₄×C₈₉	—	2	2	no	—
378	C₂×C₄×C₈₉	—	2	2	no	—
379	C₂×C₄×C₈₉	—	2	2	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	2	no	—
384	C₂×C₄×C₈₉	—	2	2	no	—
385	C₂×C₄×C₈₉	—	2	2	no	—
386	C₂×C₄×C₈₉	—	4	8	no	—
387	C₂×C₄×C₈₉	—	4	8	no	—
388	C₂×C₄×C₈₉	—	4	8	no	—
389	C₂×C₄×C₈₉	—	4	2	no	—
390	C₂×C₄×C₈₉	—	4	2	no	—
391	C₂×C₄×C₈₉	—	4	2	no	—
392	C₂×C₄×C₈₉	—	4	2	no	—
393	C₂×C₄×C₈₉	—	4	2	no	—
394	C₂×C₄×C₈₉	—	8	4	no	—
395	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
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	2	yes	—
399	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
402	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
403	C₈×C₈₉	—	2	2	no	—
404	C₈×C₈₉	—	2	2	no	—
405	C₈×C₈₉	—	2	2	no	—
406	C₈×C₈₉	C₂²×D₄	1	4	yes	—
407	C₂²×C₈₉	—	2	2	no	—
408	C₂²×C₈₉	—	2	8	no	—
409	C₂²×C₈₉	—	2	2	no	—
410	C₂²×C₈₉	—	2	2	no	—
411	C₂²×C₈₉	—	2	4	no	—
412	C₂²×C₈₉	—	2	2	no	—
413	C₂²×C₈₉	—	2	2	no	—
414	C₂²×C₈₉	—	4	4	no	—
415	C₂²×C₈₉	—	4	8	no	—
416	C₂²×C₈₉	—	4	2	no	—
417	C₂²×C₈₉	—	4	2	no	—
418	C₂²×C₈₉	—	4	2	no	—
419	C₂²×C₈₉	—	4	2	no	—
420	C₂²×C₈₉	—	4	2	no	—
421	C₂²×C₈₉	—	8	16	no	—
422	C₂²×C₈₉	—	8	4	no	—
423	C₂²×C₈₉	D₄²	1	2	yes	—
424	C₂²×C₈₉	C₂×#137	1	2	yes	—
425	C₂²×C₈₉	C₂×#137	1	4	yes	complemented
426	C₂²×C₈₉	#577	1	2	yes	—
427	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
428	C₄×C₈₉	—	2	2	no	—
429	C₄×C₈₉	—	2	2	no	—
430	C₄×C₈₉	—	2	4	no	—
431	C₄×C₈₉	—	2	2	no	—
432	C₄×C₈₉	—	2	2	no	—
433	C₄×C₈₉	—	4	2	no	—
434	C₄×C₈₉	—	4	2	no	—
435	C₄×C₈₉	—	4	2	no	—
436	C₄×C₈₉	—	4	2	no	—
437	C₄×C₈₉	—	4	2	no	—
438	C₄×C₈₉	D₄²	1	2	yes	—
439	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂×#3266	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
442	C₂×C₈₉	—	2	4	no	—
443	C₂×C₈₉	—	4	2	no	—
444	C₂×C₈₉	—	4	4	no	—
445	C₂×C₈₉	—	8	2	no	—
446	C₂×C₈₉	#3266	1	4	yes	direct product factor
447	C₂×C₈₉	C₂×D₄²	1	1	yes	characteristic
448	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
449	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
450	C₂²×#137	C₂×C₈₉	1	1	yes	characteristic, complemented
451	C₂³×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
452	C₂×D₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
453	C₂×#546	C₂×C₈₉	1	1	yes	characteristic
454	#3266	C₂×C₈₉	1	16	yes	direct product factor
455	C₂×#497	C₂×C₈₉	1	1	yes	characteristic, complemented
456	C₂×#468	C₂×C₈₉	1	1	yes	characteristic, complemented
457	C₂×#467	C₂×C₈₉	1	1	yes	characteristic, complemented
458	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
459	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
460	C₂×#452	C₂×C₈₉	1	1	yes	characteristic, complemented
461	C₂×#451	C₂×C₈₉	1	1	yes	characteristic, complemented
462	C₂×#448	C₂×C₈₉	1	1	yes	characteristic, complemented
463	C₂×#450	C₂×C₈₉	1	1	yes	characteristic, complemented
464	C₂×#440	C₂×C₈₉	1	1	yes	characteristic, complemented
465	C₂×#435	C₂×C₈₉	1	1	yes	characteristic, complemented
466	C₈₉	C₂×#3266	1	1	yes	characteristic, direct product factor, Sylow
467	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
468	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
469	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
470	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
471	C₂×#137	—	2	8	no	—
472	C₂×#137	C₂²×C₈₉	1	8	yes	complemented
473	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
474	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
475	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
476	C₂²×SD₁₆	—	2	8	no	—
477	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
478	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
479	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
480	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
481	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
482	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
483	C₂²×SD₁₆	C₂²×C₈₉	1	8	yes	complemented
484	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
485	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
486	D₄×Q₈	—	2	4	no	—
487	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
488	#546	—	2	4	no	—
489	#546	C₂²×C₈₉	1	8	yes	—
490	C₂×C₄⋊Q₈	—	2	1	no	—
491	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
492	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
493	C₂×#123	—	2	1	no	—
494	C₂×C₂²⋊Q₈	—	2	1	no	—
495	C₂×C₂²⋊Q₈	—	2	1	no	—
496	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
497	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
498	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
499	C₂×#121	—	2	1	no	—
500	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
501	C₂×#120	—	2	1	no	—
502	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
503	C₂×C₄×D₄	—	2	1	no	—
504	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
506	C₂²×C₂²⋊C₄	—	2	1	no	—
507	#497	C₂²×C₈₉	1	8	yes	complemented
508	#468	C₂²×C₈₉	1	8	yes	complemented
509	#467	C₂²×C₈₉	1	8	yes	complemented
510	#464	C₂²×C₈₉	1	8	yes	complemented
511	#461	C₂²×C₈₉	1	8	yes	complemented
512	#452	C₂²×C₈₉	1	8	yes	complemented
513	#451	C₂²×C₈₉	1	8	yes	complemented
514	#450	C₂²×C₈₉	1	8	yes	complemented
515	#448	C₂²×C₈₉	1	8	yes	complemented
516	#440	C₂²×C₈₉	1	8	yes	complemented
517	#435	C₂²×C₈₉	1	8	yes	complemented
518	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
519	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
520	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
521	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
522	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
523	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic, complemented
524	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
525	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
527	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
528	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic, complemented
529	C₂⁵	—	2	1	no	—
530	C₂×#41	—	2	2	no	—
531	C₂×#41	—	2	4	no	—
532	C₂×#41	—	4	2	no	—
533	C₂×#41	C₂³×C₈₉	1	4	yes	—
534	C₂²×Q₈	—	2	1	no	—
535	C₂²×Q₈	—	2	1	no	—
536	C₂²×Q₈	—	2	2	no	—
537	C₂²×Q₈	—	2	2	no	—
538	C₂²×Q₈	—	2	4	no	—
539	C₂²×Q₈	—	2	4	no	—
540	C₂²×Q₈	—	4	2	no	—
541	C₂²×Q₈	—	4	2	no	—
542	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
543	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
546	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
547	C₂²×Q₈	C₂³×C₈₉	1	4	yes	complemented
548	C₂²×D₄	—	2	4	no	—
549	C₂²×D₄	—	2	1	no	—
550	C₂²×D₄	—	2	1	no	—
551	C₂²×D₄	—	2	1	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	4	2	no	—
554	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
557	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	—	2	1	no	—
562	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
564	#137	—	2	32	no	—
565	C₂×Q₁₆	—	2	4	no	—
566	C₂×Q₁₆	—	2	4	no	—
567	C₂×Q₁₆	—	4	2	no	—
568	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
569	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
570	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
571	C₂×SD₁₆	—	2	4	no	—
572	C₂×SD₁₆	—	2	4	no	—
573	C₂×SD₁₆	—	2	4	no	—
574	C₂×SD₁₆	—	2	32	no	—
575	C₂×SD₁₆	—	2	4	no	—
576	C₂×SD₁₆	—	4	2	no	—
577	C₂×SD₁₆	D₄×C₈₉	1	8	yes	complemented
578	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
579	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
583	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
584	C₂×M₁₆	—	2	4	no	—
585	C₂×M₁₆	C₂³×C₈₉	1	4	yes	complemented
586	C₂²×C₈	—	2	4	no	—
587	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
588	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
589	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
590	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
591	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
592	C₄⋊Q₈	—	2	8	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
595	#124	—	2	2	no	—
596	#124	C₂³×C₈₉	1	4	yes	—
597	#123	—	2	8	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	2	no	—
601	C₂²⋊Q₈	—	2	8	no	—
602	C₂²⋊Q₈	—	2	8	no	—
603	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
604	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
605	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
606	#121	—	2	2	no	—
607	#121	—	2	8	no	—
608	#121	C₂³×C₈₉	1	4	yes	—
609	#120	—	2	8	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	C₂³×C₈₉	1	4	yes	complemented
612	C₄×D₄	—	2	8	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	D₄×C₈₉	1	4	yes	—
615	C₄×D₄	C₂³×C₈₉	1	4	yes	—
616	C₄×D₄	C₂³×C₈₉	1	4	yes	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	1	no	—
619	C₂×C₄⋊C₄	—	2	1	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	—	2	1	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	1	no	—
629	C₂×C₂²⋊C₄	—	2	1	no	—
630	C₂×C₂²⋊C₄	—	2	1	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	1	no	—
633	C₂×C₂²⋊C₄	—	2	8	no	—
634	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	D₄×C₈₉	1	1	yes	characteristic
636	C₂×C₄²	—	2	1	no	—
637	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
638	#107	C₂³×C₈₉	1	4	yes	complemented
639	C₄⋊C₈	C₂³×C₈₉	1	4	yes	complemented
640	#103	C₂³×C₈₉	1	4	yes	complemented
641	#103	C₂³×C₈₉	1	4	yes	complemented
642	#103	C₂³×C₈₉	1	4	yes	complemented
643	#103	C₂³×C₈₉	1	4	yes	complemented
644	#102	C₂³×C₈₉	1	4	yes	—
645	#102	C₂³×C₈₉	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
647	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	complemented
648	#97	C₂³×C₈₉	1	4	yes	complemented
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	2	1	no	—
651	C₂⁴	—	2	4	no	—
652	C₂⁴	—	4	4	no	—
653	C₂⁴	—	4	4	no	—
654	C₂⁴	—	8	2	no	—
655	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
656	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
657	#41	—	2	8	no	—
658	#41	—	4	4	no	—
659	#41	—	4	8	no	—
660	C₂×Q₈	—	2	1	no	—
661	C₂×Q₈	—	2	1	no	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	4	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	8	no	—
668	C₂×Q₈	—	2	8	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	2	no	—
674	C₂×Q₈	—	2	2	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	—	4	4	no	—
677	C₂×Q₈	—	4	4	no	—
678	C₂×Q₈	—	4	4	no	—
679	C₂×Q₈	—	4	8	no	—
680	C₂×Q₈	—	4	8	no	—
681	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
682	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
683	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
684	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
685	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
686	C₂×D₄	—	2	4	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	1	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	4	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	8	no	—
698	C₂×D₄	—	4	4	no	—
699	C₂×D₄	—	4	4	no	—
700	C₂×D₄	—	8	2	no	—
701	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
702	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
703	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
704	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	4	4	no	—
720	C₂²×C₄	—	4	4	no	—
721	C₂²×C₄	—	4	4	no	—
722	C₂²×C₄	—	8	2	no	—
723	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
724	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
725	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
726	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
728	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
732	Q₁₆	—	2	8	no	—
733	Q₁₆	—	2	8	no	—
734	Q₁₆	—	4	4	no	—
735	SD₁₆	—	2	8	no	—
736	SD₁₆	—	2	8	no	—
737	SD₁₆	—	2	8	no	—
738	SD₁₆	—	2	8	no	—
739	SD₁₆	—	4	4	no	—
740	SD₁₆	C₂×D₄×C₈₉	1	16	yes	complemented
741	M₁₆	—	2	8	no	—
742	C₂×C₈	—	2	2	no	—
743	C₂×C₈	—	2	2	no	—
744	C₂×C₈	—	2	2	no	—
745	C₂×C₈	—	2	8	no	—
746	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
747	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
748	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
749	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
750	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
760	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
761	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
770	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
771	C₄²	—	2	4	no	—
772	C₄²	C₂×D₄×C₈₉	1	2	yes	—
773	C₄²	C₂⁴×C₈₉	1	2	yes	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	4	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	4	8	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	2	no	—
786	C₂³	—	4	2	no	—
787	C₂³	—	4	8	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	8	4	no	—
790	C₂³	—	8	16	no	—
791	C₂³	#137×C₈₉	1	4	yes	complemented
792	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
793	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
794	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
795	Q₈	—	2	4	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	2	no	—
800	Q₈	—	2	2	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	2	2	no	—
803	Q₈	—	4	8	no	—
804	Q₈	—	4	8	no	—
805	Q₈	—	4	2	no	—
806	Q₈	—	4	2	no	—
807	Q₈	—	4	2	no	—
808	Q₈	C₂²×D₄×C₈₉	1	4	yes	—
809	D₄	—	2	8	no	—
810	D₄	—	2	4	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	4	8	no	—
815	D₄	—	4	8	no	—
816	D₄	—	4	2	no	—
817	D₄	—	8	4	no	—
818	D₄	C₂²×D₄×C₈₉	1	4	yes	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	4	no	—
826	C₂×C₄	—	2	4	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	4	8	no	—
837	C₂×C₄	—	4	8	no	—
838	C₂×C₄	—	4	8	no	—
839	C₂×C₄	—	4	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	8	4	no	—
845	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
846	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
847	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
848	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
849	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
850	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
851	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
852	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
853	C₈	—	2	2	no	—
854	C₈	—	2	2	no	—
855	C₈	—	2	2	no	—
856	C₈	C₂²×D₄×C₈₉	1	4	yes	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	4	no	—
867	C₂²	—	4	8	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	8	16	no	—
872	C₂²	—	8	4	no	—
873	C₂²	D₄²×C₈₉	1	2	yes	—
874	C₂²	C₂×#137×C₈₉	1	2	yes	—
875	C₂²	C₂×#137×C₈₉	1	4	yes	complemented
876	C₂²	#577×C₈₉	1	2	yes	—
877	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	2	2	no	—
882	C₄	—	2	4	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	2	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	2	no	—
887	C₄	—	4	2	no	—
888	C₄	D₄²×C₈₉	1	2	yes	—
889	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
890	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
891	C₂	—	2	4	no	—
892	C₂	—	4	2	no	—
893	C₂	—	4	4	no	—
894	C₂	—	8	2	no	—
895	C₂	C₈₉×#3266	1	4	yes	direct product factor
896	C₂	C₂×D₄²×C₈₉	1	1	yes	characteristic
897	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
898	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#546×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×D₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₈₉	C₂	semidirect
2. C₂³×SD₁₆×C₈₉	C₂	semidirect
3. C₂×D₄×Q₈×C₈₉	C₂	semidirect
5. C₈₉×#3266	C₂	direct (N × H)
6. C₂×#497×C₈₉	C₂	semidirect
7. C₂×#468×C₈₉	C₂	semidirect
8. C₂×#467×C₈₉	C₂	semidirect
9. C₂×#464×C₈₉	C₂	semidirect
10. C₂×#461×C₈₉	C₂	semidirect
11. C₂×#452×C₈₉	C₂	semidirect
12. C₂×#451×C₈₉	C₂	semidirect
13. C₂×#448×C₈₉	C₂	semidirect
14. C₂×#450×C₈₉	C₂	semidirect
15. C₂×#440×C₈₉	C₂	semidirect
16. C₂×#435×C₈₉	C₂	semidirect
19. C₂³×Q₈×C₈₉	C₂²	semidirect
22. C₂×#137×C₈₉	C₂²	semidirect
23. C₂²×Q₁₆×C₈₉	C₂²	semidirect
24. C₂²×Q₁₆×C₈₉	C₂²	semidirect
25. C₂²×Q₁₆×C₈₉	C₂²	semidirect
33. C₂²×SD₁₆×C₈₉	C₂²	semidirect
34. C₂²×M₁₆×C₈₉	C₂²	semidirect
37. D₄×Q₈×C₈₉	C₂²	semidirect
41. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
48. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
52. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
57. #497×C₈₉	C₂²	semidirect
58. #468×C₈₉	C₂²	semidirect
59. #467×C₈₉	C₂²	semidirect
60. #464×C₈₉	C₂²	semidirect
61. #461×C₈₉	C₂²	semidirect
62. #452×C₈₉	C₂²	semidirect
63. #451×C₈₉	C₂²	semidirect
64. #450×C₈₉	C₂²	semidirect
65. #448×C₈₉	C₂²	semidirect
66. #440×C₈₉	C₂²	semidirect
67. #435×C₈₉	C₂²	semidirect
68. C₂×#107×C₈₉	C₂²	semidirect
69. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
70. C₂×#103×C₈₉	C₂²	semidirect
71. C₂×#103×C₈₉	C₂²	semidirect
72. C₂×#103×C₈₉	C₂²	semidirect
73. C₂×#103×C₈₉	C₂²	semidirect
77. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
78. C₂×#97×C₈₉	C₂²	semidirect
97. C₂²×Q₈×C₈₉	C₂³	semidirect
118. C₂×Q₁₆×C₈₉	C₂³	semidirect
119. C₂×Q₁₆×C₈₉	C₂³	semidirect
120. C₂×Q₁₆×C₈₉	C₂³	semidirect
127. C₂×SD₁₆×C₈₉	D₄	semidirect
135. C₂×M₁₆×C₈₉	C₂³	semidirect
144. C₄⋊Q₈×C₈₉	C₂³	semidirect
155. C₂²⋊Q₈×C₈₉	C₂³	semidirect
161. C₄×Q₈×C₈₉	C₂³	semidirect
188. #107×C₈₉	C₂³	semidirect
189. C₄⋊C₈×C₈₉	C₂³	semidirect
190. #103×C₈₉	C₂³	semidirect
191. #103×C₈₉	C₂³	semidirect
192. #103×C₈₉	C₂³	semidirect
193. #103×C₈₉	C₂³	semidirect
197. C₂²⋊C₈×C₈₉	C₂³	semidirect
198. #97×C₈₉	C₂³	semidirect
290. SD₁₆×C₈₉	C₂×D₄	semidirect
341. C₂³×C₈₉	#137	semidirect
425. C₂²×C₈₉	C₂×#137	semidirect
441. C₂×#3266	C₈₉	direct (N × H)
446. C₂×C₈₉	#3266	direct (N × H)
450. C₂²×#137	C₂×C₈₉	semidirect
451. C₂³×SD₁₆	C₂×C₈₉	semidirect
452. C₂×D₄×Q₈	C₂×C₈₉	semidirect
454. #3266	C₂×C₈₉	direct (N × H)
455. C₂×#497	C₂×C₈₉	semidirect
456. C₂×#468	C₂×C₈₉	semidirect
457. C₂×#467	C₂×C₈₉	semidirect
458. C₂×#464	C₂×C₈₉	semidirect
459. C₂×#461	C₂×C₈₉	semidirect
460. C₂×#452	C₂×C₈₉	semidirect
461. C₂×#451	C₂×C₈₉	semidirect
462. C₂×#448	C₂×C₈₉	semidirect
463. C₂×#450	C₂×C₈₉	semidirect
464. C₂×#440	C₂×C₈₉	semidirect
465. C₂×#435	C₂×C₈₉	semidirect
466. C₈₉	C₂×#3266	direct (N × H)
469. C₂³×Q₈	C₂²×C₈₉	semidirect
472. C₂×#137	C₂²×C₈₉	semidirect
473. C₂²×Q₁₆	C₂²×C₈₉	semidirect
474. C₂²×Q₁₆	C₂²×C₈₉	semidirect
475. C₂²×Q₁₆	C₂²×C₈₉	semidirect
483. C₂²×SD₁₆	C₂²×C₈₉	semidirect
484. C₂²×M₁₆	C₂²×C₈₉	semidirect
487. D₄×Q₈	C₂²×C₈₉	semidirect
491. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
498. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
502. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
507. #497	C₂²×C₈₉	semidirect
508. #468	C₂²×C₈₉	semidirect
509. #467	C₂²×C₈₉	semidirect
510. #464	C₂²×C₈₉	semidirect
511. #461	C₂²×C₈₉	semidirect
512. #452	C₂²×C₈₉	semidirect
513. #451	C₂²×C₈₉	semidirect
514. #450	C₂²×C₈₉	semidirect
515. #448	C₂²×C₈₉	semidirect
516. #440	C₂²×C₈₉	semidirect
517. #435	C₂²×C₈₉	semidirect
518. C₂×#107	C₂²×C₈₉	semidirect
519. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
520. C₂×#103	C₂²×C₈₉	semidirect
521. C₂×#103	C₂²×C₈₉	semidirect
522. C₂×#103	C₂²×C₈₉	semidirect
523. C₂×#103	C₂²×C₈₉	semidirect
527. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
528. C₂×#97	C₂²×C₈₉	semidirect
547. C₂²×Q₈	C₂³×C₈₉	semidirect
568. C₂×Q₁₆	C₂³×C₈₉	semidirect
569. C₂×Q₁₆	C₂³×C₈₉	semidirect
570. C₂×Q₁₆	C₂³×C₈₉	semidirect
577. C₂×SD₁₆	D₄×C₈₉	semidirect
585. C₂×M₁₆	C₂³×C₈₉	semidirect
594. C₄⋊Q₈	C₂³×C₈₉	semidirect
605. C₂²⋊Q₈	C₂³×C₈₉	semidirect
611. C₄×Q₈	C₂³×C₈₉	semidirect
638. #107	C₂³×C₈₉	semidirect
639. C₄⋊C₈	C₂³×C₈₉	semidirect
640. #103	C₂³×C₈₉	semidirect
641. #103	C₂³×C₈₉	semidirect
642. #103	C₂³×C₈₉	semidirect
643. #103	C₂³×C₈₉	semidirect
647. C₂²⋊C₈	C₂³×C₈₉	semidirect
648. #97	C₂³×C₈₉	semidirect
740. SD₁₆	C₂×D₄×C₈₉	semidirect
791. C₂³	#137×C₈₉	semidirect
875. C₂²	C₂×#137×C₈₉	semidirect
895. C₂	C₈₉×#3266	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₈₉	2
C₂³×SD₁₆×C₈₉	2
C₂×D₄×Q₈×C₈₉	2
C₂×#546×C₈₉	2
C₈₉×#3266	2
C₂×#497×C₈₉	2
C₂×#468×C₈₉	2
C₂×#467×C₈₉	2
C₂×#464×C₈₉	2
C₂×#461×C₈₉	2
C₂×#452×C₈₉	2
C₂×#451×C₈₉	2
C₂×#448×C₈₉	2
C₂×#450×C₈₉	2
C₂×#440×C₈₉	2
C₂×#435×C₈₉	2
C₂×#3266	89

Subgroups — C2×C89×#3266 #36438872

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3266 #36438872