Subgroups — C₈₉×#36546 #36414394

Order 22784.

2910 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2848	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2583	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2579	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2502	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2473	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2449	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2440	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2417	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2360	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2345	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#120×C₈₉	C₂	1	2	yes	maximal
17	C₄×#120×C₈₉	C₂	1	1	yes	maximal, characteristic
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
20	#554×C₈₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
29	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
35	C₂²×C₄⋊C₄×C₈₉	—	2	8	no	—
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#400×C₈₉	C₂²	1	2	yes	complemented
44	#399×C₈₉	C₂²	1	2	yes	complemented
45	#398×C₈₉	C₂²	1	4	yes	complemented
46	#398×C₈₉	C₂²	1	4	yes	complemented
47	#398×C₈₉	C₂²	1	4	yes	complemented
48	#396×C₈₉	C₂²	1	4	yes	complemented
49	#395×C₈₉	C₂²	1	4	yes	complemented
50	#391×C₈₉	C₂²	1	2	yes	complemented
51	#389×C₈₉	C₂²	1	4	yes	complemented
52	#389×C₈₉	C₂²	1	4	yes	complemented
53	#389×C₈₉	C₂²	1	2	yes	complemented
54	#389×C₈₉	C₂²	1	2	yes	complemented
55	#387×C₈₉	C₂²	1	4	yes	complemented
56	#387×C₈₉	C₂²	1	4	yes	complemented
57	#386×C₈₉	C₂²	1	1	yes	characteristic
58	#386×C₈₉	C₂²	1	2	yes	—
59	#386×C₈₉	C₂²	1	4	yes	—
60	#386×C₈₉	C₂²	1	2	yes	—
61	#385×C₈₉	C₂²	1	1	yes	characteristic
62	#385×C₈₉	C₂²	1	2	yes	—
63	#385×C₈₉	C₂²	1	4	yes	—
64	#385×C₈₉	C₂²	1	2	yes	—
65	#385×C₈₉	C₂²	1	2	yes	—
66	#385×C₈₉	C₂²	1	2	yes	—
67	#385×C₈₉	C₂²	1	2	yes	—
68	#385×C₈₉	C₂²	1	4	yes	—
69	#385×C₈₉	C₂²	1	4	yes	—
70	#385×C₈₉	C₂²	1	4	yes	—
71	#385×C₈₉	C₂²	1	4	yes	complemented
72	#384×C₈₉	C₂²	1	2	yes	complemented
73	#380×C₈₉	C₂²	1	2	yes	—
74	#380×C₈₉	C₂²	1	1	yes	characteristic
75	#380×C₈₉	C₂²	1	2	yes	—
76	#380×C₈₉	C₂²	1	4	yes	—
77	#380×C₈₉	C₂²	1	2	yes	complemented
78	#379×C₈₉	C₂²	1	2	yes	—
79	#379×C₈₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
85	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₈₉	—	2	4	no	—
91	C₂³×C₄×C₈₉	—	2	8	no	—
92	C₂³×C₄×C₈₉	—	2	8	no	—
93	C₂³×C₄×C₈₉	—	4	8	no	—
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
98	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
101	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
102	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
103	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₈₉	—	2	4	no	—
105	#125×C₈₉	—	2	8	no	—
106	C₂²⋊Q₈×C₈₉	—	2	8	no	—
107	C₂²⋊Q₈×C₈₉	—	2	4	no	—
108	C₂²⋊Q₈×C₈₉	—	2	8	no	—
109	C₂²⋊Q₈×C₈₉	—	2	8	no	—
110	C₂²⋊Q₈×C₈₉	—	2	4	no	—
111	C₂²⋊Q₈×C₈₉	—	4	8	no	—
112	#120×C₈₉	Q₈	1	8	yes	complemented
113	C₄×Q₈×C₈₉	—	2	4	no	—
114	C₄×D₄×C₈₉	—	2	8	no	—
115	C₄×D₄×C₈₉	—	2	4	no	—
116	C₄×D₄×C₈₉	—	2	8	no	—
117	C₄×D₄×C₈₉	—	4	8	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
120	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
121	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
122	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
123	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	4	yes	—
168	#95×C₈₉	C₂³	1	2	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	#95×C₈₉	C₂³	1	2	yes	—
174	#95×C₈₉	C₂³	1	4	yes	—
175	C₂⁴×C₈₉	—	2	2	no	—
176	C₂⁴×C₈₉	—	2	4	no	—
177	C₂⁴×C₈₉	—	2	4	no	—
178	C₂⁴×C₈₉	—	2	2	no	—
179	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
180	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
183	C₂×Q₈×C₈₉	—	2	2	no	—
184	C₂×Q₈×C₈₉	—	2	4	no	—
185	C₂×Q₈×C₈₉	—	2	4	no	—
186	C₂×Q₈×C₈₉	—	4	4	no	—
187	C₂×D₄×C₈₉	—	2	2	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	2	no	—
191	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
192	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
193	C₂²×C₄×C₈₉	—	2	32	no	—
194	C₂²×C₄×C₈₉	—	2	2	no	—
195	C₂²×C₄×C₈₉	—	2	4	no	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	4	no	—
200	C₂²×C₄×C₈₉	—	2	4	no	—
201	C₂²×C₄×C₈₉	—	2	4	no	—
202	C₂²×C₄×C₈₉	—	2	4	no	—
203	C₂²×C₄×C₈₉	—	2	8	no	—
204	C₂²×C₄×C₈₉	—	2	8	no	—
205	C₂²×C₄×C₈₉	—	2	8	no	—
206	C₂²×C₄×C₈₉	—	2	8	no	—
207	C₂²×C₄×C₈₉	—	2	2	no	—
208	C₂²×C₄×C₈₉	—	2	4	no	—
209	C₂²×C₄×C₈₉	—	2	4	no	—
210	C₂²×C₄×C₈₉	—	4	4	no	—
211	C₂²×C₄×C₈₉	—	4	4	no	—
212	C₂²×C₄×C₈₉	—	4	4	no	—
213	C₂²×C₄×C₈₉	—	4	4	no	—
214	C₂²×C₄×C₈₉	—	4	4	no	—
215	C₂²×C₄×C₈₉	—	4	32	no	—
216	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
218	C₂²×C₄×C₈₉	#41	1	8	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₄⋊C₄×C₈₉	—	2	8	no	—
234	C₄⋊C₄×C₈₉	—	2	8	no	—
235	C₄⋊C₄×C₈₉	—	2	4	no	—
236	C₄⋊C₄×C₈₉	—	2	4	no	—
237	C₄⋊C₄×C₈₉	—	2	4	no	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	4	no	—
242	C₄⋊C₄×C₈₉	—	2	4	no	—
243	C₄⋊C₄×C₈₉	—	2	4	no	—
244	C₄⋊C₄×C₈₉	—	2	4	no	—
245	C₄⋊C₄×C₈₉	—	2	4	no	—
246	C₄⋊C₄×C₈₉	—	2	8	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₄⋊C₄×C₈₉	—	4	4	no	—
250	C₄⋊C₄×C₈₉	—	4	4	no	—
251	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
253	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	2	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	8	no	—
258	C₂²⋊C₄×C₈₉	—	2	8	no	—
259	C₂²⋊C₄×C₈₉	—	2	4	no	—
260	C₂²⋊C₄×C₈₉	—	2	4	no	—
261	C₂²⋊C₄×C₈₉	—	2	2	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	2	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	4	4	no	—
266	C₂²⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
267	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
268	C₄²×C₈₉	—	2	4	no	—
269	C₄²×C₈₉	—	2	2	no	—
270	C₄²×C₈₉	—	2	4	no	—
271	C₄²×C₈₉	—	4	4	no	—
272	C₂³×C₈₉	—	2	8	no	—
273	C₂³×C₈₉	—	2	8	no	—
274	C₂³×C₈₉	—	2	16	no	—
275	C₂³×C₈₉	—	2	8	no	—
276	C₂³×C₈₉	—	2	16	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	—	2	2	no	—
280	C₂³×C₈₉	—	2	2	no	—
281	C₂³×C₈₉	—	2	2	no	—
282	C₂³×C₈₉	—	2	2	no	—
283	C₂³×C₈₉	—	2	1	no	—
284	C₂³×C₈₉	—	2	2	no	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	1	no	—
287	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
288	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
289	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
290	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
291	C₂³×C₈₉	C₂×#41	1	4	yes	—
292	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
293	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
294	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
295	Q₈×C₈₉	—	4	4	no	—
296	Q₈×C₈₉	—	8	4	no	—
297	D₄×C₈₉	—	2	8	no	—
298	D₄×C₈₉	—	2	16	no	—
299	C₂×C₄×C₈₉	—	2	16	no	—
300	C₂×C₄×C₈₉	—	2	8	no	—
301	C₂×C₄×C₈₉	—	2	1	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	4	no	—
308	C₂×C₄×C₈₉	—	2	4	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	8	no	—
311	C₂×C₄×C₈₉	—	2	16	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	1	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	2	no	—
318	C₂×C₄×C₈₉	—	2	4	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	4	no	—
321	C₂×C₄×C₈₉	—	2	4	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	4	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	4	no	—
326	C₂×C₄×C₈₉	—	2	4	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	4	no	—
329	C₂×C₄×C₈₉	—	4	8	no	—
330	C₂×C₄×C₈₉	—	4	16	no	—
331	C₂×C₄×C₈₉	—	4	16	no	—
332	C₂×C₄×C₈₉	—	4	8	no	—
333	C₂×C₄×C₈₉	—	4	4	no	—
334	C₂×C₄×C₈₉	—	8	4	no	—
335	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
337	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
338	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
340	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
341	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
342	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
343	C₂²×C₈₉	—	2	32	no	—
344	C₂²×C₈₉	—	2	2	no	—
345	C₂²×C₈₉	—	2	4	no	—
346	C₂²×C₈₉	—	2	4	no	—
347	C₂²×C₈₉	—	2	4	no	—
348	C₂²×C₈₉	—	2	4	no	—
349	C₂²×C₈₉	—	2	2	no	—
350	C₂²×C₈₉	—	2	4	no	—
351	C₂²×C₈₉	—	2	4	no	—
352	C₂²×C₈₉	—	2	4	no	—
353	C₂²×C₈₉	—	2	4	no	—
354	C₂²×C₈₉	—	2	2	no	—
355	C₂²×C₈₉	—	2	4	no	—
356	C₂²×C₈₉	—	4	1	no	—
357	C₂²×C₈₉	—	4	1	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	D₄×Q₈	1	4	yes	—
360	C₂²×C₈₉	#554	1	8	yes	complemented
361	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
362	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
363	C₂²×C₈₉	C₂²×#41	1	2	yes	—
364	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
365	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
366	C₄×C₈₉	—	2	2	no	—
367	C₄×C₈₉	—	2	4	no	—
368	C₄×C₈₉	—	2	2	no	—
369	C₄×C₈₉	—	2	4	no	—
370	C₄×C₈₉	—	2	4	no	—
371	C₄×C₈₉	—	2	4	no	—
372	C₄×C₈₉	—	4	1	no	—
373	C₄×C₈₉	—	4	2	no	—
374	C₄×C₈₉	—	4	4	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	1	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	—	4	4	no	—
379	C₄×C₈₉	#525	1	4	yes	—
380	#36546	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂×C₈₉	—	2	4	no	—
382	C₂×C₈₉	—	2	8	no	—
383	C₂×C₈₉	—	4	2	no	—
384	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
385	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
386	C₂×C₈₉	C₂×#554	1	2	yes	—
387	C₂×C₈₉	#3484	1	1	yes	characteristic
388	C₂×C₈₉	#3492	1	2	yes	—
389	C₂×#554	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₂³×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#2848	C₂×C₈₉	1	2	yes	complemented
392	#2848	C₂×C₈₉	1	1	yes	characteristic, complemented
393	#2583	C₂×C₈₉	1	2	yes	complemented
394	#2579	C₂×C₈₉	1	2	yes	complemented
395	#2502	C₂×C₈₉	1	1	yes	characteristic, complemented
396	#2487	C₂×C₈₉	1	1	yes	characteristic, complemented
397	#2473	C₂×C₈₉	1	4	yes	complemented
398	#2449	C₂×C₈₉	1	4	yes	complemented
399	#2440	C₂×C₈₉	1	2	yes	complemented
400	#2417	C₂×C₈₉	1	2	yes	complemented
401	#2360	C₂×C₈₉	1	2	yes	complemented
402	D₄×C₄⋊C₄	C₂×C₈₉	1	2	yes	complemented
403	#2345	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₄×#120	C₂×C₈₉	1	2	yes	—
405	C₄×#120	C₂×C₈₉	1	1	yes	characteristic
406	C₈₉	#36546	1	1	yes	characteristic, direct product factor, Sylow
407	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
408	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
409	#554	—	2	8	no	—
410	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
411	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
412	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
414	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
417	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
418	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
419	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
420	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
421	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
422	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
424	C₂²×C₄⋊C₄	—	2	8	no	—
425	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
426	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
428	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
429	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
431	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
432	#400	C₂²×C₈₉	1	2	yes	complemented
433	#399	C₂²×C₈₉	1	2	yes	complemented
434	#398	C₂²×C₈₉	1	4	yes	complemented
435	#398	C₂²×C₈₉	1	4	yes	complemented
436	#398	C₂²×C₈₉	1	4	yes	complemented
437	#396	C₂²×C₈₉	1	4	yes	complemented
438	#395	C₂²×C₈₉	1	4	yes	complemented
439	#391	C₂²×C₈₉	1	2	yes	complemented
440	#389	C₂²×C₈₉	1	4	yes	complemented
441	#389	C₂²×C₈₉	1	4	yes	complemented
442	#389	C₂²×C₈₉	1	2	yes	complemented
443	#389	C₂²×C₈₉	1	2	yes	complemented
444	#387	C₂²×C₈₉	1	4	yes	complemented
445	#387	C₂²×C₈₉	1	4	yes	complemented
446	#386	C₂²×C₈₉	1	1	yes	characteristic
447	#386	C₂²×C₈₉	1	2	yes	—
448	#386	C₂²×C₈₉	1	4	yes	—
449	#386	C₂²×C₈₉	1	2	yes	—
450	#385	C₂²×C₈₉	1	2	yes	—
451	#385	C₂²×C₈₉	1	2	yes	—
452	#385	C₂²×C₈₉	1	1	yes	characteristic
453	#385	C₂²×C₈₉	1	2	yes	—
454	#385	C₂²×C₈₉	1	2	yes	—
455	#385	C₂²×C₈₉	1	4	yes	—
456	#385	C₂²×C₈₉	1	4	yes	—
457	#385	C₂²×C₈₉	1	4	yes	—
458	#385	C₂²×C₈₉	1	4	yes	—
459	#385	C₂²×C₈₉	1	2	yes	—
460	#385	C₂²×C₈₉	1	4	yes	complemented
461	#384	C₂²×C₈₉	1	2	yes	complemented
462	#380	C₂²×C₈₉	1	2	yes	—
463	#380	C₂²×C₈₉	1	1	yes	characteristic
464	#380	C₂²×C₈₉	1	2	yes	—
465	#380	C₂²×C₈₉	1	4	yes	—
466	#380	C₂²×C₈₉	1	2	yes	complemented
467	#379	C₂²×C₈₉	1	2	yes	—
468	#379	C₂²×C₈₉	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
470	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
472	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
473	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
474	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
475	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
477	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
479	C₂³×C₄	—	2	4	no	—
480	C₂³×C₄	—	2	8	no	—
481	C₂³×C₄	—	2	8	no	—
482	C₂³×C₄	—	4	8	no	—
483	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
484	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
485	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
487	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
488	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
490	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
491	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
492	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
493	C₄⋊Q₈	—	2	4	no	—
494	#125	—	2	8	no	—
495	C₂²⋊Q₈	—	2	8	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	8	no	—
498	C₂²⋊Q₈	—	2	8	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	4	8	no	—
501	#120	Q₈×C₈₉	1	8	yes	complemented
502	C₄×Q₈	—	2	4	no	—
503	C₄×D₄	—	2	8	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	8	no	—
506	C₄×D₄	—	4	8	no	—
507	C₂×C₄⋊C₄	—	2	8	no	—
508	C₂×C₄⋊C₄	—	2	4	no	—
509	C₂×C₄⋊C₄	—	2	8	no	—
510	C₂×C₄⋊C₄	—	2	16	no	—
511	C₂×C₄⋊C₄	—	2	8	no	—
512	C₂×C₄⋊C₄	—	2	4	no	—
513	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
517	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
531	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
549	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
550	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
551	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
552	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
553	#95	C₂³×C₈₉	1	2	yes	—
554	#95	C₂³×C₈₉	1	2	yes	—
555	#95	C₂³×C₈₉	1	4	yes	—
556	#95	C₂³×C₈₉	1	4	yes	—
557	#95	C₂³×C₈₉	1	2	yes	—
558	#95	C₂³×C₈₉	1	4	yes	—
559	#95	C₂³×C₈₉	1	4	yes	—
560	#95	C₂³×C₈₉	1	4	yes	—
561	#95	C₂³×C₈₉	1	4	yes	—
562	#95	C₂³×C₈₉	1	2	yes	—
563	#95	C₂³×C₈₉	1	4	yes	—
564	C₂⁴	—	2	2	no	—
565	C₂⁴	—	2	4	no	—
566	C₂⁴	—	2	4	no	—
567	C₂⁴	—	2	2	no	—
568	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
569	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
570	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
571	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	4	4	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	—	2	4	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
581	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
582	C₂²×C₄	—	2	32	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	2	4	no	—
592	C₂²×C₄	—	2	8	no	—
593	C₂²×C₄	—	2	8	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	2	8	no	—
596	C₂²×C₄	—	2	2	no	—
597	C₂²×C₄	—	2	4	no	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	32	no	—
605	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
606	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
607	C₂²×C₄	#41×C₈₉	1	8	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
618	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	2	8	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	4	no	—
634	C₄⋊C₄	—	2	4	no	—
635	C₄⋊C₄	—	2	8	no	—
636	C₄⋊C₄	—	4	4	no	—
637	C₄⋊C₄	—	4	4	no	—
638	C₄⋊C₄	—	4	4	no	—
639	C₄⋊C₄	—	4	4	no	—
640	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
641	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
642	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	8	no	—
647	C₂²⋊C₄	—	2	8	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	4	4	no	—
655	C₂²⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
656	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	4	no	—
660	C₄²	—	4	4	no	—
661	C₂³	—	2	8	no	—
662	C₂³	—	2	8	no	—
663	C₂³	—	2	16	no	—
664	C₂³	—	2	8	no	—
665	C₂³	—	2	16	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
677	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
678	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
679	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
680	C₂³	C₂×#41×C₈₉	1	4	yes	—
681	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
682	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
683	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
684	Q₈	—	4	4	no	—
685	Q₈	—	8	4	no	—
686	D₄	—	2	8	no	—
687	D₄	—	2	16	no	—
688	C₂×C₄	—	2	16	no	—
689	C₂×C₄	—	2	8	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	8	no	—
700	C₂×C₄	—	2	16	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	4	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	16	no	—
720	C₂×C₄	—	4	16	no	—
721	C₂×C₄	—	4	8	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	8	4	no	—
724	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
726	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
727	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
728	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
729	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
730	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
731	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
732	C₂²	—	2	32	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	—	4	2	no	—
748	C₂²	D₄×Q₈×C₈₉	1	4	yes	—
749	C₂²	#554×C₈₉	1	8	yes	complemented
750	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
751	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
752	C₂²	C₂²×#41×C₈₉	1	2	yes	—
753	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
754	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
755	C₄	—	2	2	no	—
756	C₄	—	2	4	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	4	no	—
759	C₄	—	2	4	no	—
760	C₄	—	2	4	no	—
761	C₄	—	4	1	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	4	no	—
768	C₄	#525×C₈₉	1	4	yes	—
769	C₂	—	2	4	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	2	no	—
772	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
773	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
774	C₂	C₂×#554×C₈₉	1	2	yes	—
775	C₂	C₈₉×#3484	1	1	yes	characteristic
776	C₂	C₈₉×#3492	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#120×C₈₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₈₉	C₂	semidirect
2. C₂³×C₄⋊C₄×C₈₉	C₂	semidirect
3. C₈₉×#2848	C₂	semidirect
4. C₈₉×#2848	C₂	semidirect
5. C₈₉×#2583	C₂	semidirect
6. C₈₉×#2579	C₂	semidirect
7. C₈₉×#2502	C₂	semidirect
8. C₈₉×#2487	C₂	semidirect
9. C₈₉×#2473	C₂	semidirect
10. C₈₉×#2449	C₂	semidirect
11. C₈₉×#2440	C₂	semidirect
12. C₈₉×#2417	C₂	semidirect
13. C₈₉×#2360	C₂	semidirect
14. D₄×C₄⋊C₄×C₈₉	C₂	semidirect
15. C₈₉×#2345	C₂	semidirect
21. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
30. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
42. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
43. #400×C₈₉	C₂²	semidirect
44. #399×C₈₉	C₂²	semidirect
45. #398×C₈₉	C₂²	semidirect
46. #398×C₈₉	C₂²	semidirect
47. #398×C₈₉	C₂²	semidirect
48. #396×C₈₉	C₂²	semidirect
49. #395×C₈₉	C₂²	semidirect
50. #391×C₈₉	C₂²	semidirect
51. #389×C₈₉	C₂²	semidirect
52. #389×C₈₉	C₂²	semidirect
53. #389×C₈₉	C₂²	semidirect
54. #389×C₈₉	C₂²	semidirect
55. #387×C₈₉	C₂²	semidirect
56. #387×C₈₉	C₂²	semidirect
71. #385×C₈₉	C₂²	semidirect
72. #384×C₈₉	C₂²	semidirect
77. #380×C₈₉	C₂²	semidirect
80. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
112. #120×C₈₉	Q₈	semidirect
124. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
360. C₂²×C₈₉	#554	semidirect
380. #36546	C₈₉	direct (N × H)
389. C₂×#554	C₂×C₈₉	semidirect
390. C₂³×C₄⋊C₄	C₂×C₈₉	semidirect
391. #2848	C₂×C₈₉	semidirect
392. #2848	C₂×C₈₉	semidirect
393. #2583	C₂×C₈₉	semidirect
394. #2579	C₂×C₈₉	semidirect
395. #2502	C₂×C₈₉	semidirect
396. #2487	C₂×C₈₉	semidirect
397. #2473	C₂×C₈₉	semidirect
398. #2449	C₂×C₈₉	semidirect
399. #2440	C₂×C₈₉	semidirect
400. #2417	C₂×C₈₉	semidirect
401. #2360	C₂×C₈₉	semidirect
402. D₄×C₄⋊C₄	C₂×C₈₉	semidirect
403. #2345	C₂×C₈₉	semidirect
406. C₈₉	#36546	direct (N × H)
410. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
411. C₂×#125	C₂²×C₈₉	semidirect
416. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
417. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
419. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
431. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
432. #400	C₂²×C₈₉	semidirect
433. #399	C₂²×C₈₉	semidirect
434. #398	C₂²×C₈₉	semidirect
435. #398	C₂²×C₈₉	semidirect
436. #398	C₂²×C₈₉	semidirect
437. #396	C₂²×C₈₉	semidirect
438. #395	C₂²×C₈₉	semidirect
439. #391	C₂²×C₈₉	semidirect
440. #389	C₂²×C₈₉	semidirect
441. #389	C₂²×C₈₉	semidirect
442. #389	C₂²×C₈₉	semidirect
443. #389	C₂²×C₈₉	semidirect
444. #387	C₂²×C₈₉	semidirect
445. #387	C₂²×C₈₉	semidirect
460. #385	C₂²×C₈₉	semidirect
461. #384	C₂²×C₈₉	semidirect
466. #380	C₂²×C₈₉	semidirect
469. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
501. #120	Q₈×C₈₉	semidirect
513. C₂×C₄⋊C₄	D₄×C₈₉	semidirect
749. C₂²	#554×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₈₉	2
C₂³×C₄⋊C₄×C₈₉	2
C₈₉×#2848	2
C₈₉×#2583	2
C₈₉×#2579	2
C₈₉×#2502	2
C₈₉×#2487	2
C₈₉×#2473	2
C₈₉×#2449	2
C₈₉×#2440	2
C₈₉×#2417	2
C₈₉×#2360	2
D₄×C₄⋊C₄×C₈₉	2
C₈₉×#2345	2
C₄×#120×C₈₉	2
#36546	89

Subgroups — C89×#36546 #36414394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36546 #36414394