Subgroups — C₈₉×#35519 #36413367

Order 22784.

2394 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2582	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2581	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2580	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2538	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2450	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2449	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2442	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2441	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2440	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2439	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
16	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic
17	C₂×#389×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
19	#533×C₈₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
27	#520×C₈₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#400×C₈₉	C₂²	1	4	yes	—
43	#399×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	4	yes	—
45	#398×C₈₉	C₂²	1	4	yes	—
46	#396×C₈₉	C₂²	1	4	yes	—
47	#396×C₈₉	C₂²	1	4	yes	—
48	#395×C₈₉	C₂²	1	4	yes	—
49	#393×C₈₉	C₂²	1	4	yes	—
50	#391×C₈₉	C₂²	1	1	yes	characteristic
51	#391×C₈₉	C₂²	1	1	yes	characteristic
52	#391×C₈₉	C₂²	1	2	yes	—
53	#391×C₈₉	C₂²	1	4	yes	—
54	#390×C₈₉	C₂²	1	1	yes	characteristic
55	#390×C₈₉	C₂²	1	1	yes	characteristic
56	#390×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	2	yes	—
60	#389×C₈₉	C₂²	1	2	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#389×C₈₉	C₂²	1	2	yes	—
63	#389×C₈₉	C₂²	1	4	yes	—
64	#389×C₈₉	C₂²	1	2	yes	—
65	#389×C₈₉	C₂²	1	2	yes	—
66	#387×C₈₉	C₂²	1	4	yes	—
67	#387×C₈₉	C₂²	1	4	yes	—
68	#386×C₈₉	C₂²	1	2	yes	—
69	#386×C₈₉	C₂²	1	2	yes	—
70	#386×C₈₉	C₂²	1	4	yes	—
71	#385×C₈₉	C₂²	1	4	yes	—
72	#385×C₈₉	C₂²	1	4	yes	—
73	#385×C₈₉	C₂²	1	4	yes	—
74	#385×C₈₉	C₂²	1	4	yes	—
75	#384×C₈₉	C₂²	1	2	yes	—
76	#384×C₈₉	C₂²	1	2	yes	—
77	#382×C₈₉	C₂²	1	2	yes	—
78	#382×C₈₉	C₂²	1	2	yes	—
79	#380×C₈₉	C₂²	1	2	yes	—
80	#380×C₈₉	C₂²	1	2	yes	—
81	#380×C₈₉	C₂²	1	4	yes	—
82	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₂×#95×C₈₉	C₂²	1	2	yes	—
85	C₂×#41×C₈₉	—	2	4	no	—
86	C₂×#41×C₈₉	—	2	4	no	—
87	C₂×#41×C₈₉	Q₈	1	8	yes	complemented
88	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
96	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
97	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
98	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
99	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₉	—	2	4	no	—
101	C₄⋊Q₈×C₈₉	—	2	4	no	—
102	#125×C₈₉	—	2	4	no	—
103	#125×C₈₉	—	2	4	no	—
104	C₂²⋊Q₈×C₈₉	—	2	8	no	—
105	C₂²⋊Q₈×C₈₉	—	2	8	no	—
106	C₂²⋊Q₈×C₈₉	—	4	8	no	—
107	C₄×Q₈×C₈₉	—	2	8	no	—
108	C₄×Q₈×C₈₉	—	2	8	no	—
109	C₄×Q₈×C₈₉	—	2	8	no	—
110	C₄×D₄×C₈₉	—	2	16	no	—
111	C₄×D₄×C₈₉	—	2	8	no	—
112	#117×C₈₉	—	2	4	no	—
113	#117×C₈₉	—	2	4	no	—
114	#117×C₈₉	—	2	8	no	—
115	#117×C₈₉	D₄	1	8	yes	—
116	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
117	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	4	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	4	yes	—
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	4	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	1	yes	characteristic
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₈₉	—	2	4	no	—
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
158	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
161	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
162	#95×C₈₉	C₂³	1	4	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	2	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	2	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	4	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	4	yes	—
174	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
175	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
176	#41×C₈₉	—	2	32	no	—
177	C₂×Q₈×C₈₉	—	2	2	no	—
178	C₂×Q₈×C₈₉	—	2	4	no	—
179	C₂×Q₈×C₈₉	—	2	4	no	—
180	C₂×Q₈×C₈₉	—	2	2	no	—
181	C₂×Q₈×C₈₉	—	2	4	no	—
182	C₂×Q₈×C₈₉	—	2	4	no	—
183	C₂×Q₈×C₈₉	—	4	2	no	—
184	C₂×Q₈×C₈₉	—	4	2	no	—
185	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
186	C₂×D₄×C₈₉	—	2	4	no	—
187	C₂×D₄×C₈₉	—	2	4	no	—
188	C₂×D₄×C₈₉	—	2	2	no	—
189	C₂×D₄×C₈₉	—	2	2	no	—
190	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
191	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	2	no	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	2	no	—
200	C₂²×C₄×C₈₉	—	2	8	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	1	no	—
203	C₂²×C₄×C₈₉	—	4	1	no	—
204	C₂²×C₄×C₈₉	—	4	2	no	—
205	C₂²×C₄×C₈₉	—	4	2	no	—
206	C₂²×C₄×C₈₉	—	4	4	no	—
207	C₂²×C₄×C₈₉	—	4	4	no	—
208	C₂²×C₄×C₈₉	—	4	2	no	—
209	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
211	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
212	C₂²×C₄×C₈₉	#41	1	4	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₈₉	—	2	4	no	—
229	C₄⋊C₄×C₈₉	—	2	8	no	—
230	C₄⋊C₄×C₈₉	—	2	4	no	—
231	C₄⋊C₄×C₈₉	—	2	2	no	—
232	C₄⋊C₄×C₈₉	—	2	2	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	4	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	4	no	—
239	C₄⋊C₄×C₈₉	—	2	4	no	—
240	C₄⋊C₄×C₈₉	—	2	4	no	—
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	8	no	—
244	C₄⋊C₄×C₈₉	—	4	4	no	—
245	C₄⋊C₄×C₈₉	—	4	4	no	—
246	C₄⋊C₄×C₈₉	—	4	4	no	—
247	C₄⋊C₄×C₈₉	—	4	4	no	—
248	C₄⋊C₄×C₈₉	—	4	4	no	—
249	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₈₉	—	2	4	no	—
252	C₂²⋊C₄×C₈₉	—	2	4	no	—
253	C₂²⋊C₄×C₈₉	—	2	8	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	4	2	no	—
257	C₂²⋊C₄×C₈₉	—	4	2	no	—
258	C₂²⋊C₄×C₈₉	—	4	4	no	—
259	C₂²⋊C₄×C₈₉	—	4	4	no	—
260	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
261	C₄²×C₈₉	—	2	2	no	—
262	C₄²×C₈₉	—	2	2	no	—
263	C₄²×C₈₉	—	2	2	no	—
264	C₄²×C₈₉	—	2	2	no	—
265	C₄²×C₈₉	—	2	8	no	—
266	C₄²×C₈₉	—	2	4	no	—
267	C₄²×C₈₉	—	2	4	no	—
268	C₄²×C₈₉	C₂×D₄	1	8	yes	—
269	C₂³×C₈₉	—	2	1	no	—
270	C₂³×C₈₉	—	2	1	no	—
271	C₂³×C₈₉	—	2	1	no	—
272	C₂³×C₈₉	—	2	1	no	—
273	C₂³×C₈₉	—	2	2	no	—
274	C₂³×C₈₉	—	2	2	no	—
275	C₂³×C₈₉	—	2	2	no	—
276	C₂³×C₈₉	—	2	2	no	—
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
280	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
281	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
282	C₂³×C₈₉	C₂×#41	1	2	yes	—
283	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
284	Q₈×C₈₉	—	2	8	no	—
285	Q₈×C₈₉	—	4	8	no	—
286	Q₈×C₈₉	—	4	8	no	—
287	D₄×C₈₉	—	2	16	no	—
288	D₄×C₈₉	—	2	8	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	1	no	—
292	C₂×C₄×C₈₉	—	2	2	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	2	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	1	no	—
298	C₂×C₄×C₈₉	—	2	1	no	—
299	C₂×C₄×C₈₉	—	2	16	no	—
300	C₂×C₄×C₈₉	—	2	1	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	4	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	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	4	no	—
311	C₂×C₄×C₈₉	—	2	4	no	—
312	C₂×C₄×C₈₉	—	2	1	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	1	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	1	no	—
317	C₂×C₄×C₈₉	—	2	1	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	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	—	4	4	no	—
325	C₂×C₄×C₈₉	—	4	4	no	—
326	C₂×C₄×C₈₉	—	4	8	no	—
327	C₂×C₄×C₈₉	—	8	8	no	—
328	C₂×C₄×C₈₉	—	8	4	no	—
329	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	complemented
330	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
331	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
332	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
335	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
336	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
337	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
340	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
341	C₂²×C₈₉	—	2	2	no	—
342	C₂²×C₈₉	—	2	2	no	—
343	C₂²×C₈₉	—	2	2	no	—
344	C₂²×C₈₉	—	2	2	no	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	2	2	no	—
347	C₂²×C₈₉	—	2	4	no	—
348	C₂²×C₈₉	—	2	4	no	—
349	C₂²×C₈₉	—	2	4	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
355	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
357	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂²×C₈₉	#585	1	1	yes	characteristic
361	C₂²×C₈₉	#585	1	1	yes	characteristic
362	C₄×C₈₉	—	2	4	no	—
363	C₄×C₈₉	—	2	2	no	—
364	C₄×C₈₉	—	2	4	no	—
365	C₄×C₈₉	—	2	2	no	—
366	C₄×C₈₉	—	2	4	no	—
367	C₄×C₈₉	—	4	1	no	—
368	C₄×C₈₉	—	4	4	no	—
369	C₄×C₈₉	—	4	2	no	—
370	C₄×C₈₉	—	4	1	no	—
371	C₄×C₈₉	—	4	2	no	—
372	C₄×C₈₉	—	4	2	no	—
373	C₄×C₈₉	—	4	4	no	—
374	C₄×C₈₉	—	4	2	no	—
375	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
376	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
377	#35519	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
378	C₂×C₈₉	—	2	4	no	—
379	C₂×C₈₉	—	4	4	no	—
380	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂×C₈₉	#3488	1	1	yes	characteristic
382	C₂×C₈₉	#3489	1	1	yes	characteristic
383	C₂×C₈₉	#3503	1	1	yes	characteristic
384	C₂×C₈₉	#3504	1	1	yes	characteristic
385	C₂×C₈₉	#3506	1	1	yes	characteristic
386	C₂×C₈₉	#3507	1	1	yes	characteristic
387	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₂×#520	C₂×C₈₉	1	1	yes	characteristic
389	#2582	C₂×C₈₉	1	2	yes	complemented
390	#2581	C₂×C₈₉	1	2	yes	complemented
391	#2580	C₂×C₈₉	1	2	yes	complemented
392	#2538	C₂×C₈₉	1	2	yes	complemented
393	#2450	C₂×C₈₉	1	4	yes	complemented
394	#2449	C₂×C₈₉	1	4	yes	complemented
395	#2442	C₂×C₈₉	1	2	yes	complemented
396	#2441	C₂×C₈₉	1	2	yes	complemented
397	#2440	C₂×C₈₉	1	2	yes	complemented
398	#2439	C₂×C₈₉	1	2	yes	complemented
399	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
400	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
401	#2311	C₂×C₈₉	1	1	yes	characteristic
402	#2297	C₂×C₈₉	1	1	yes	characteristic
403	C₂×#389	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₈₉	#35519	1	1	yes	characteristic, direct product factor, Sylow
405	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
406	#533	—	2	8	no	—
407	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
409	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
411	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
413	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
414	#520	—	2	8	no	—
415	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
416	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
417	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
419	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
420	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#117	C₂²×C₈₉	1	2	yes	—
423	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
425	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
426	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
427	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
428	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
429	#400	C₂²×C₈₉	1	4	yes	—
430	#399	C₂²×C₈₉	1	4	yes	—
431	#398	C₂²×C₈₉	1	4	yes	—
432	#398	C₂²×C₈₉	1	4	yes	—
433	#396	C₂²×C₈₉	1	4	yes	—
434	#396	C₂²×C₈₉	1	4	yes	—
435	#395	C₂²×C₈₉	1	4	yes	—
436	#393	C₂²×C₈₉	1	4	yes	—
437	#391	C₂²×C₈₉	1	2	yes	—
438	#391	C₂²×C₈₉	1	1	yes	characteristic
439	#391	C₂²×C₈₉	1	1	yes	characteristic
440	#391	C₂²×C₈₉	1	4	yes	—
441	#390	C₂²×C₈₉	1	2	yes	—
442	#390	C₂²×C₈₉	1	1	yes	characteristic
443	#390	C₂²×C₈₉	1	1	yes	characteristic
444	#389	C₂²×C₈₉	1	2	yes	—
445	#389	C₂²×C₈₉	1	2	yes	—
446	#389	C₂²×C₈₉	1	2	yes	—
447	#389	C₂²×C₈₉	1	2	yes	—
448	#389	C₂²×C₈₉	1	2	yes	—
449	#389	C₂²×C₈₉	1	2	yes	—
450	#389	C₂²×C₈₉	1	4	yes	—
451	#389	C₂²×C₈₉	1	2	yes	—
452	#389	C₂²×C₈₉	1	2	yes	—
453	#387	C₂²×C₈₉	1	4	yes	—
454	#387	C₂²×C₈₉	1	4	yes	—
455	#386	C₂²×C₈₉	1	4	yes	—
456	#386	C₂²×C₈₉	1	2	yes	—
457	#386	C₂²×C₈₉	1	2	yes	—
458	#385	C₂²×C₈₉	1	4	yes	—
459	#385	C₂²×C₈₉	1	4	yes	—
460	#385	C₂²×C₈₉	1	4	yes	—
461	#385	C₂²×C₈₉	1	4	yes	—
462	#384	C₂²×C₈₉	1	2	yes	—
463	#384	C₂²×C₈₉	1	2	yes	—
464	#382	C₂²×C₈₉	1	2	yes	—
465	#382	C₂²×C₈₉	1	2	yes	—
466	#380	C₂²×C₈₉	1	2	yes	—
467	#380	C₂²×C₈₉	1	2	yes	—
468	#380	C₂²×C₈₉	1	4	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
471	C₂×#95	C₂²×C₈₉	1	2	yes	—
472	C₂×#41	—	2	4	no	—
473	C₂×#41	—	2	4	no	—
474	C₂×#41	Q₈×C₈₉	1	8	yes	complemented
475	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
476	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
477	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
479	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
483	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
484	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
485	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
486	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
487	C₄⋊Q₈	—	2	4	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	#125	—	2	4	no	—
490	#125	—	2	4	no	—
491	C₂²⋊Q₈	—	2	8	no	—
492	C₂²⋊Q₈	—	2	8	no	—
493	C₂²⋊Q₈	—	4	8	no	—
494	C₄×Q₈	—	2	8	no	—
495	C₄×Q₈	—	2	8	no	—
496	C₄×Q₈	—	2	8	no	—
497	C₄×D₄	—	2	16	no	—
498	C₄×D₄	—	2	8	no	—
499	#117	—	2	4	no	—
500	#117	—	2	4	no	—
501	#117	—	2	8	no	—
502	#117	D₄×C₈₉	1	8	yes	—
503	C₂×C₄⋊C₄	—	2	4	no	—
504	C₂×C₄⋊C₄	—	2	4	no	—
505	C₂×C₄⋊C₄	—	2	8	no	—
506	C₂×C₄⋊C₄	—	4	4	no	—
507	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
510	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	4	yes	—
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
526	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
529	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
530	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
531	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
532	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
540	C₂×C₄²	—	2	4	no	—
541	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
542	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
543	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
544	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
549	#95	C₂³×C₈₉	1	4	yes	—
550	#95	C₂³×C₈₉	1	4	yes	—
551	#95	C₂³×C₈₉	1	2	yes	—
552	#95	C₂³×C₈₉	1	2	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	4	yes	—
558	#95	C₂³×C₈₉	1	4	yes	—
559	#95	C₂³×C₈₉	1	4	yes	—
560	#95	C₂³×C₈₉	1	4	yes	—
561	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
562	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
563	#41	—	2	32	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
578	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
579	C₂²×C₄	—	2	4	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	8	no	—
588	C₂²×C₄	—	4	2	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	2	no	—
593	C₂²×C₄	—	4	4	no	—
594	C₂²×C₄	—	4	4	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
597	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
598	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
599	C₂²×C₄	#41×C₈₉	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
604	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	8	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	8	no	—
631	C₄⋊C₄	—	4	4	no	—
632	C₄⋊C₄	—	4	4	no	—
633	C₄⋊C₄	—	4	4	no	—
634	C₄⋊C₄	—	4	4	no	—
635	C₄⋊C₄	—	4	4	no	—
636	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
637	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	8	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	2	no	—
645	C₂²⋊C₄	—	4	2	no	—
646	C₂²⋊C₄	—	4	4	no	—
647	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	2	no	—
652	C₄²	—	2	8	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	C₂×D₄×C₈₉	1	8	yes	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
667	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
668	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
669	C₂³	C₂×#41×C₈₉	1	2	yes	—
670	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
671	Q₈	—	2	8	no	—
672	Q₈	—	4	8	no	—
673	Q₈	—	4	8	no	—
674	D₄	—	2	16	no	—
675	D₄	—	2	8	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	16	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	4	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	8	8	no	—
715	C₂×C₄	—	8	4	no	—
716	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	complemented
717	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
718	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
719	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
721	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
722	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
723	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
724	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
725	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
726	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
727	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
742	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
743	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
744	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
745	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
746	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
747	C₂²	#585×C₈₉	1	1	yes	characteristic
748	C₂²	#585×C₈₉	1	1	yes	characteristic
749	C₄	—	2	4	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	4	no	—
754	C₄	—	4	1	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	4	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
763	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
764	C₂	—	2	4	no	—
765	C₂	—	4	4	no	—
766	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
767	C₂	C₈₉×#3488	1	1	yes	characteristic
768	C₂	C₈₉×#3489	1	1	yes	characteristic
769	C₂	C₈₉×#3503	1	1	yes	characteristic
770	C₂	C₈₉×#3504	1	1	yes	characteristic
771	C₂	C₈₉×#3506	1	1	yes	characteristic
772	C₂	C₈₉×#3507	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#41×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×#533×C₈₉	C₂	semidirect
3. C₈₉×#2582	C₂	semidirect
4. C₈₉×#2581	C₂	semidirect
5. C₈₉×#2580	C₂	semidirect
6. C₈₉×#2538	C₂	semidirect
7. C₈₉×#2450	C₂	semidirect
8. C₈₉×#2449	C₂	semidirect
9. C₈₉×#2442	C₂	semidirect
10. C₈₉×#2441	C₂	semidirect
11. C₈₉×#2440	C₂	semidirect
12. C₈₉×#2439	C₂	semidirect
13. C₈₉×#2317	C₂	semidirect
14. C₈₉×#2317	C₂	semidirect
17. C₂×#389×C₈₉	C₂	semidirect
87. C₂×#41×C₈₉	Q₈	semidirect
329. C₂×C₄×C₈₉	C₂²⋊Q₈	semidirect
377. #35519	C₈₉	direct (N × H)
387. C₂×#533	C₂×C₈₉	semidirect
389. #2582	C₂×C₈₉	semidirect
390. #2581	C₂×C₈₉	semidirect
391. #2580	C₂×C₈₉	semidirect
392. #2538	C₂×C₈₉	semidirect
393. #2450	C₂×C₈₉	semidirect
394. #2449	C₂×C₈₉	semidirect
395. #2442	C₂×C₈₉	semidirect
396. #2441	C₂×C₈₉	semidirect
397. #2440	C₂×C₈₉	semidirect
398. #2439	C₂×C₈₉	semidirect
399. #2317	C₂×C₈₉	semidirect
400. #2317	C₂×C₈₉	semidirect
403. C₂×#389	C₂×C₈₉	semidirect
404. C₈₉	#35519	direct (N × H)
474. C₂×#41	Q₈×C₈₉	semidirect
716. C₂×C₄	C₂²⋊Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2582	2
C₈₉×#2581	2
C₈₉×#2580	2
C₈₉×#2538	2
C₈₉×#2450	2
C₈₉×#2449	2
C₈₉×#2442	2
C₈₉×#2441	2
C₈₉×#2440	2
C₈₉×#2439	2
C₈₉×#2317	2
C₈₉×#2311	2
C₈₉×#2297	2
C₂×#389×C₈₉	2
#35519	89

Subgroups — C89×#35519 #36413367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35519 #36413367