Subgroups — C₂×C₈₉×#3401 #36439246

Order 22784.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3401	C₂	1	16	yes	maximal, direct product factor
4	C₂×#497×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#496×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#495×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#464×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#460×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#461×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#446×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
26	#559×C₈₉	—	2	4	no	—
27	#559×C₈₉	C₂²	1	8	yes	complemented
28	#556×C₈₉	—	2	4	no	—
29	#556×C₈₉	C₂²	1	8	yes	complemented
30	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#126×C₈₉	—	2	1	no	—
33	C₂×#126×C₈₉	—	2	1	no	—
34	C₂×#124×C₈₉	—	2	1	no	—
35	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#123×C₈₉	—	2	1	no	—
40	C₂×#123×C₈₉	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
42	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₈₉	—	2	1	no	—
47	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#117×C₈₉	—	2	1	no	—
51	#497×C₈₉	C₂²	1	8	yes	complemented
52	#496×C₈₉	C₂²	1	8	yes	—
53	#495×C₈₉	C₂²	1	8	yes	complemented
54	#464×C₈₉	C₂²	1	8	yes	complemented
55	#464×C₈₉	C₂²	1	8	yes	complemented
56	#463×C₈₉	C₂²	1	8	yes	complemented
57	#463×C₈₉	C₂²	1	8	yes	complemented
58	#461×C₈₉	C₂²	1	8	yes	complemented
59	#460×C₈₉	C₂²	1	8	yes	complemented
60	#446×C₈₉	C₂²	1	8	yes	complemented
61	#442×C₈₉	C₂²	1	8	yes	complemented
62	#441×C₈₉	C₂²	1	8	yes	complemented
63	C₄×SD₁₆×C₈₉	C₂²	1	8	yes	complemented
64	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
68	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
69	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
70	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
71	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
73	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
74	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
75	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
78	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	—	2	1	no	—
82	C₂²×D₄×C₈₉	—	2	1	no	—
83	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₈₉	—	2	1	no	—
87	C₂³×C₄×C₈₉	—	2	1	no	—
88	C₂³×C₄×C₈₉	—	2	1	no	—
89	C₂×Q₁₆×C₈₉	—	2	4	no	—
90	C₂×Q₁₆×C₈₉	—	4	2	no	—
91	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
92	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₈₉	—	2	4	no	—
94	C₂×SD₁₆×C₈₉	—	4	2	no	—
95	C₂×SD₁₆×C₈₉	—	4	2	no	—
96	C₂×SD₁₆×C₈₉	—	4	2	no	—
97	C₂×SD₁₆×C₈₉	—	4	2	no	—
98	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
99	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
103	C₂×D₈×C₈₉	—	2	4	no	—
104	C₂×D₈×C₈₉	—	4	2	no	—
105	C₂×D₈×C₈₉	C₂³	1	4	yes	—
106	C₂×D₈×C₈₉	C₂³	1	4	yes	—
107	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₈₉	—	2	2	no	—
112	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
113	#127×C₈₉	—	2	2	no	—
114	#127×C₈₉	C₂³	1	4	yes	—
115	#126×C₈₉	—	2	8	no	—
116	#126×C₈₉	—	2	8	no	—
117	#124×C₈₉	—	2	8	no	—
118	#124×C₈₉	—	2	2	no	—
119	#124×C₈₉	—	2	2	no	—
120	#124×C₈₉	—	2	2	no	—
121	#124×C₈₉	—	2	2	no	—
122	#124×C₈₉	C₂³	1	4	yes	—
123	#124×C₈₉	C₂³	1	4	yes	—
124	#124×C₈₉	C₂³	1	4	yes	—
125	#124×C₈₉	C₂³	1	4	yes	—
126	#123×C₈₉	—	2	8	no	—
127	#123×C₈₉	—	2	8	no	—
128	C₂²⋊Q₈×C₈₉	—	2	8	no	—
129	C₄×Q₈×C₈₉	—	2	2	no	—
130	C₄×Q₈×C₈₉	—	2	2	no	—
131	C₄×Q₈×C₈₉	—	2	2	no	—
132	C₄×Q₈×C₈₉	D₄	1	4	yes	—
133	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
134	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
135	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
136	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
137	C₄×D₄×C₈₉	—	2	8	no	—
138	C₄×D₄×C₈₉	—	2	2	no	—
139	C₄×D₄×C₈₉	—	2	2	no	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	C₂³	1	4	yes	—
142	C₄×D₄×C₈₉	C₂³	1	4	yes	—
143	C₄×D₄×C₈₉	C₂³	1	4	yes	—
144	#117×C₈₉	—	2	8	no	—
145	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
165	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
166	C₂×C₄²×C₈₉	—	2	1	no	—
167	C₂×C₄²×C₈₉	—	2	1	no	—
168	C₂×C₄²×C₈₉	—	2	1	no	—
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
172	#106×C₈₉	C₂³	1	4	yes	—
173	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
174	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
175	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
176	#103×C₈₉	C₂³	1	4	yes	—
177	#103×C₈₉	C₂³	1	4	yes	—
178	#103×C₈₉	C₂³	1	4	yes	—
179	#102×C₈₉	C₂³	1	4	yes	—
180	#102×C₈₉	C₂³	1	4	yes	—
181	#102×C₈₉	C₂³	1	4	yes	—
182	#97×C₈₉	C₂³	1	4	yes	—
183	#97×C₈₉	C₂³	1	4	yes	—
184	C₄×C₈×C₈₉	C₂³	1	4	yes	—
185	C₂⁴×C₈₉	—	2	1	no	—
186	C₂⁴×C₈₉	—	2	1	no	—
187	C₂⁴×C₈₉	—	2	1	no	—
188	C₂×Q₈×C₈₉	—	2	1	no	—
189	C₂×Q₈×C₈₉	—	2	1	no	—
190	C₂×Q₈×C₈₉	—	2	1	no	—
191	C₂×Q₈×C₈₉	—	2	2	no	—
192	C₂×Q₈×C₈₉	—	2	2	no	—
193	C₂×Q₈×C₈₉	—	2	2	no	—
194	C₂×Q₈×C₈₉	—	2	2	no	—
195	C₂×Q₈×C₈₉	—	2	2	no	—
196	C₂×Q₈×C₈₉	—	2	2	no	—
197	C₂×Q₈×C₈₉	—	4	2	no	—
198	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
199	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
200	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
201	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
202	C₂×D₄×C₈₉	—	2	1	no	—
203	C₂×D₄×C₈₉	—	2	1	no	—
204	C₂×D₄×C₈₉	—	2	1	no	—
205	C₂×D₄×C₈₉	—	2	4	no	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	2	2	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	2	2	no	—
210	C₂×D₄×C₈₉	—	2	2	no	—
211	C₂×D₄×C₈₉	—	2	2	no	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	4	4	no	—
214	C₂×D₄×C₈₉	—	8	2	no	—
215	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	—	2	1	no	—
219	C₂²×C₄×C₈₉	—	2	1	no	—
220	C₂²×C₄×C₈₉	—	2	1	no	—
221	C₂²×C₄×C₈₉	—	2	1	no	—
222	C₂²×C₄×C₈₉	—	2	1	no	—
223	C₂²×C₄×C₈₉	—	2	4	no	—
224	C₂²×C₄×C₈₉	—	2	4	no	—
225	C₂²×C₄×C₈₉	—	2	4	no	—
226	C₂²×C₄×C₈₉	—	4	4	no	—
227	C₂²×C₄×C₈₉	—	8	2	no	—
228	C₂²×C₄×C₈₉	—	8	2	no	—
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₈₉	—	2	8	no	—
237	Q₁₆×C₈₉	—	4	4	no	—
238	SD₁₆×C₈₉	—	2	8	no	—
239	SD₁₆×C₈₉	—	4	4	no	—
240	SD₁₆×C₈₉	—	4	4	no	—
241	SD₁₆×C₈₉	—	4	4	no	—
242	SD₁₆×C₈₉	—	4	4	no	—
243	D₈×C₈₉	—	2	8	no	—
244	D₈×C₈₉	—	4	4	no	—
245	C₂×C₈×C₈₉	—	2	2	no	—
246	C₂×C₈×C₈₉	—	2	2	no	—
247	C₂×C₈×C₈₉	—	2	2	no	—
248	C₂×C₈×C₈₉	#41	1	4	yes	—
249	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
250	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
251	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
252	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	2	4	no	—
255	C₄⋊C₄×C₈₉	—	2	4	no	—
256	C₄⋊C₄×C₈₉	—	2	4	no	—
257	C₄⋊C₄×C₈₉	—	2	4	no	—
258	C₄⋊C₄×C₈₉	—	2	1	no	—
259	C₄⋊C₄×C₈₉	—	2	1	no	—
260	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
261	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
262	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
263	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₂²⋊C₄×C₈₉	—	2	4	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	4	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	4	no	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	2	4	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	C₂×D₄	1	2	yes	—
280	C₄²×C₈₉	C₂×D₄	1	2	yes	—
281	C₄²×C₈₉	C₂×D₄	1	2	yes	—
282	C₄²×C₈₉	C₂⁴	1	2	yes	—
283	C₄²×C₈₉	C₂⁴	1	2	yes	—
284	C₄²×C₈₉	C₂⁴	1	2	yes	—
285	C₂³×C₈₉	—	2	2	no	—
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	4	2	no	—
289	C₂³×C₈₉	—	4	2	no	—
290	C₂³×C₈₉	—	4	2	no	—
291	C₂³×C₈₉	—	4	2	no	—
292	C₂³×C₈₉	—	4	2	no	—
293	C₂³×C₈₉	—	4	2	no	—
294	C₂³×C₈₉	—	4	2	no	—
295	C₂³×C₈₉	—	4	2	no	—
296	C₂³×C₈₉	—	4	2	no	—
297	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₈₉	—	2	2	no	—
299	Q₈×C₈₉	—	2	2	no	—
300	Q₈×C₈₉	—	2	2	no	—
301	Q₈×C₈₉	—	2	2	no	—
302	Q₈×C₈₉	—	2	2	no	—
303	Q₈×C₈₉	—	2	2	no	—
304	Q₈×C₈₉	—	4	4	no	—
305	Q₈×C₈₉	—	4	2	no	—
306	Q₈×C₈₉	—	4	2	no	—
307	Q₈×C₈₉	—	4	2	no	—
308	D₄×C₈₉	—	2	2	no	—
309	D₄×C₈₉	—	2	2	no	—
310	D₄×C₈₉	—	2	2	no	—
311	D₄×C₈₉	—	2	2	no	—
312	D₄×C₈₉	—	2	2	no	—
313	D₄×C₈₉	—	2	2	no	—
314	D₄×C₈₉	—	4	8	no	—
315	D₄×C₈₉	—	4	2	no	—
316	D₄×C₈₉	—	4	2	no	—
317	D₄×C₈₉	—	4	2	no	—
318	D₄×C₈₉	—	8	4	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	2	2	no	—
326	C₂×C₄×C₈₉	—	2	2	no	—
327	C₂×C₄×C₈₉	—	2	2	no	—
328	C₂×C₄×C₈₉	—	2	2	no	—
329	C₂×C₄×C₈₉	—	2	2	no	—
330	C₂×C₄×C₈₉	—	4	8	no	—
331	C₂×C₄×C₈₉	—	4	2	no	—
332	C₂×C₄×C₈₉	—	4	2	no	—
333	C₂×C₄×C₈₉	—	4	2	no	—
334	C₂×C₄×C₈₉	—	4	2	no	—
335	C₂×C₄×C₈₉	—	4	2	no	—
336	C₂×C₄×C₈₉	—	8	4	no	—
337	C₂×C₄×C₈₉	—	8	4	no	—
338	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
346	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
347	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
348	C₈×C₈₉	—	2	2	no	—
349	C₈×C₈₉	—	2	2	no	—
350	C₈×C₈₉	—	2	2	no	—
351	C₈×C₈₉	C₂×#41	1	4	yes	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	—	4	2	no	—
355	C₂²×C₈₉	—	4	2	no	—
356	C₂²×C₈₉	—	4	2	no	—
357	C₂²×C₈₉	—	4	2	no	—
358	C₂²×C₈₉	—	4	2	no	—
359	C₂²×C₈₉	—	4	2	no	—
360	C₂²×C₈₉	—	4	2	no	—
361	C₂²×C₈₉	—	8	4	no	—
362	C₂²×C₈₉	—	8	4	no	—
363	C₂²×C₈₉	—	8	4	no	—
364	C₂²×C₈₉	#550	1	2	yes	—
365	C₂²×C₈₉	#575	1	2	yes	—
366	C₂²×C₈₉	#577	1	2	yes	—
367	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
368	C₄×C₈₉	—	2	2	no	—
369	C₄×C₈₉	—	2	2	no	—
370	C₄×C₈₉	—	2	2	no	—
371	C₄×C₈₉	—	2	2	no	—
372	C₄×C₈₉	—	2	2	no	—
373	C₄×C₈₉	—	2	2	no	—
374	C₄×C₈₉	—	4	2	no	—
375	C₄×C₈₉	—	4	2	no	—
376	C₄×C₈₉	—	4	2	no	—
377	C₄×C₈₉	—	4	2	no	—
378	C₄×C₈₉	—	4	2	no	—
379	C₄×C₈₉	#550	1	2	yes	—
380	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
381	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×#3401	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₈₉	—	8	2	no	—
384	C₂×C₈₉	—	8	2	no	—
385	C₂×C₈₉	—	8	2	no	—
386	C₂×C₈₉	#3401	1	4	yes	direct product factor
387	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
388	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
389	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
390	C₂×#559	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₂×#556	C₂×C₈₉	1	1	yes	characteristic, complemented
392	#3401	C₂×C₈₉	1	16	yes	direct product factor
393	C₂×#497	C₂×C₈₉	1	1	yes	characteristic, complemented
394	C₂×#496	C₂×C₈₉	1	1	yes	characteristic
395	C₂×#495	C₂×C₈₉	1	1	yes	characteristic, complemented
396	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
397	C₂×#464	C₂×C₈₉	1	1	yes	characteristic, complemented
398	C₂×#460	C₂×C₈₉	1	1	yes	characteristic, complemented
399	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
400	C₂×#463	C₂×C₈₉	1	1	yes	characteristic, complemented
401	C₂×#461	C₂×C₈₉	1	1	yes	characteristic, complemented
402	C₂×#446	C₂×C₈₉	1	1	yes	characteristic, complemented
403	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
404	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
405	C₂×C₄×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
406	C₈₉	C₂×#3401	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
409	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
411	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
412	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
413	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
414	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
415	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
416	#559	—	2	4	no	—
417	#559	C₂²×C₈₉	1	8	yes	complemented
418	#556	—	2	4	no	—
419	#556	C₂²×C₈₉	1	8	yes	complemented
420	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
421	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
422	C₂×#126	—	2	1	no	—
423	C₂×#126	—	2	1	no	—
424	C₂×#124	—	2	1	no	—
425	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
426	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
427	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
428	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
429	C₂×#123	—	2	1	no	—
430	C₂×#123	—	2	1	no	—
431	C₂×C₂²⋊Q₈	—	2	1	no	—
432	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
433	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
435	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
436	C₂×C₄×D₄	—	2	1	no	—
437	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
439	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
440	C₂×#117	—	2	1	no	—
441	#497	C₂²×C₈₉	1	8	yes	complemented
442	#496	C₂²×C₈₉	1	8	yes	—
443	#495	C₂²×C₈₉	1	8	yes	complemented
444	#464	C₂²×C₈₉	1	8	yes	complemented
445	#464	C₂²×C₈₉	1	8	yes	complemented
446	#463	C₂²×C₈₉	1	8	yes	complemented
447	#463	C₂²×C₈₉	1	8	yes	complemented
448	#461	C₂²×C₈₉	1	8	yes	complemented
449	#460	C₂²×C₈₉	1	8	yes	complemented
450	#446	C₂²×C₈₉	1	8	yes	complemented
451	#442	C₂²×C₈₉	1	8	yes	complemented
452	#441	C₂²×C₈₉	1	8	yes	complemented
453	C₄×SD₁₆	C₂²×C₈₉	1	8	yes	complemented
454	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
455	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
456	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
457	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
458	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
459	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
460	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
461	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
462	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
463	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
465	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
466	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
467	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
468	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
469	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
474	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
476	C₂³×C₄	—	2	1	no	—
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂×Q₁₆	—	2	4	no	—
480	C₂×Q₁₆	—	4	2	no	—
481	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
482	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
483	C₂×SD₁₆	—	2	4	no	—
484	C₂×SD₁₆	—	4	2	no	—
485	C₂×SD₁₆	—	4	2	no	—
486	C₂×SD₁₆	—	4	2	no	—
487	C₂×SD₁₆	—	4	2	no	—
488	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
489	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
490	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
491	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
493	C₂×D₈	—	2	4	no	—
494	C₂×D₈	—	4	2	no	—
495	C₂×D₈	C₂³×C₈₉	1	4	yes	—
496	C₂×D₈	C₂³×C₈₉	1	4	yes	—
497	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
498	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
499	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
501	C₄⋊Q₈	—	2	2	no	—
502	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
503	#127	—	2	2	no	—
504	#127	C₂³×C₈₉	1	4	yes	—
505	#126	—	2	8	no	—
506	#126	—	2	8	no	—
507	#124	—	2	8	no	—
508	#124	—	2	2	no	—
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	C₂³×C₈₉	1	4	yes	—
513	#124	C₂³×C₈₉	1	4	yes	—
514	#124	C₂³×C₈₉	1	4	yes	—
515	#124	C₂³×C₈₉	1	4	yes	—
516	#123	—	2	8	no	—
517	#123	—	2	8	no	—
518	C₂²⋊Q₈	—	2	8	no	—
519	C₄×Q₈	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	D₄×C₈₉	1	4	yes	—
523	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
524	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
525	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
526	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	C₂³×C₈₉	1	4	yes	—
532	C₄×D₄	C₂³×C₈₉	1	4	yes	—
533	C₄×D₄	C₂³×C₈₉	1	4	yes	—
534	#117	—	2	8	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	1	no	—
537	C₂×C₄⋊C₄	—	2	1	no	—
538	C₂×C₄⋊C₄	—	2	1	no	—
539	C₂×C₄⋊C₄	—	2	1	no	—
540	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
541	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
542	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
543	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	—	2	1	no	—
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	C₂×C₂²⋊C₄	—	2	1	no	—
555	C₂×C₂²⋊C₄	—	2	1	no	—
556	C₂×C₄²	—	2	1	no	—
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
560	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
561	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
562	#106	C₂³×C₈₉	1	4	yes	—
563	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
564	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
565	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
566	#103	C₂³×C₈₉	1	4	yes	—
567	#103	C₂³×C₈₉	1	4	yes	—
568	#103	C₂³×C₈₉	1	4	yes	—
569	#102	C₂³×C₈₉	1	4	yes	—
570	#102	C₂³×C₈₉	1	4	yes	—
571	#102	C₂³×C₈₉	1	4	yes	—
572	#97	C₂³×C₈₉	1	4	yes	—
573	#97	C₂³×C₈₉	1	4	yes	—
574	C₄×C₈	C₂³×C₈₉	1	4	yes	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	4	2	no	—
588	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
589	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	2	2	no	—
599	C₂×D₄	—	2	2	no	—
600	C₂×D₄	—	2	2	no	—
601	C₂×D₄	—	2	2	no	—
602	C₂×D₄	—	2	2	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
606	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
607	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	4	4	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
624	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
625	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
626	Q₁₆	—	2	8	no	—
627	Q₁₆	—	4	4	no	—
628	SD₁₆	—	2	8	no	—
629	SD₁₆	—	4	4	no	—
630	SD₁₆	—	4	4	no	—
631	SD₁₆	—	4	4	no	—
632	SD₁₆	—	4	4	no	—
633	D₈	—	2	8	no	—
634	D₈	—	4	4	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	#41×C₈₉	1	4	yes	—
639	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
640	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
641	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
642	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	4	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
651	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
652	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
653	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂×D₄×C₈₉	1	2	yes	—
670	C₄²	C₂×D₄×C₈₉	1	2	yes	—
671	C₄²	C₂×D₄×C₈₉	1	2	yes	—
672	C₄²	C₂⁴×C₈₉	1	2	yes	—
673	C₄²	C₂⁴×C₈₉	1	2	yes	—
674	C₄²	C₂⁴×C₈₉	1	2	yes	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	2	no	—
687	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	4	4	no	—
695	Q₈	—	4	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	2	2	no	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	8	no	—
705	D₄	—	4	2	no	—
706	D₄	—	4	2	no	—
707	D₄	—	4	2	no	—
708	D₄	—	8	4	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	—	8	4	no	—
728	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
734	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
735	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
736	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
737	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	C₂×#41×C₈₉	1	4	yes	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	8	4	no	—
752	C₂²	—	8	4	no	—
753	C₂²	—	8	4	no	—
754	C₂²	#550×C₈₉	1	2	yes	—
755	C₂²	#575×C₈₉	1	2	yes	—
756	C₂²	#577×C₈₉	1	2	yes	—
757	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
758	C₄	—	2	2	no	—
759	C₄	—	2	2	no	—
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	#550×C₈₉	1	2	yes	—
770	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
771	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
772	C₂	—	8	2	no	—
773	C₂	—	8	2	no	—
774	C₂	—	8	2	no	—
775	C₂	C₈₉×#3401	1	4	yes	direct product factor
776	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
777	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
778	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×#496×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₈₉	C₂	semidirect
2. C₂×#556×C₈₉	C₂	semidirect
3. C₈₉×#3401	C₂	direct (N × H)
4. C₂×#497×C₈₉	C₂	semidirect
6. C₂×#495×C₈₉	C₂	semidirect
7. C₂×#464×C₈₉	C₂	semidirect
8. C₂×#464×C₈₉	C₂	semidirect
9. C₂×#460×C₈₉	C₂	semidirect
10. C₂×#463×C₈₉	C₂	semidirect
11. C₂×#463×C₈₉	C₂	semidirect
12. C₂×#461×C₈₉	C₂	semidirect
13. C₂×#446×C₈₉	C₂	semidirect
14. C₂×#442×C₈₉	C₂	semidirect
15. C₂×#441×C₈₉	C₂	semidirect
16. C₂×C₄×SD₁₆×C₈₉	C₂	semidirect
27. #559×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
51. #497×C₈₉	C₂²	semidirect
53. #495×C₈₉	C₂²	semidirect
54. #464×C₈₉	C₂²	semidirect
55. #464×C₈₉	C₂²	semidirect
56. #463×C₈₉	C₂²	semidirect
57. #463×C₈₉	C₂²	semidirect
58. #461×C₈₉	C₂²	semidirect
59. #460×C₈₉	C₂²	semidirect
60. #446×C₈₉	C₂²	semidirect
61. #442×C₈₉	C₂²	semidirect
62. #441×C₈₉	C₂²	semidirect
63. C₄×SD₁₆×C₈₉	C₂²	semidirect
382. C₂×#3401	C₈₉	direct (N × H)
386. C₂×C₈₉	#3401	direct (N × H)
390. C₂×#559	C₂×C₈₉	semidirect
391. C₂×#556	C₂×C₈₉	semidirect
392. #3401	C₂×C₈₉	direct (N × H)
393. C₂×#497	C₂×C₈₉	semidirect
395. C₂×#495	C₂×C₈₉	semidirect
396. C₂×#464	C₂×C₈₉	semidirect
397. C₂×#464	C₂×C₈₉	semidirect
398. C₂×#460	C₂×C₈₉	semidirect
399. C₂×#463	C₂×C₈₉	semidirect
400. C₂×#463	C₂×C₈₉	semidirect
401. C₂×#461	C₂×C₈₉	semidirect
402. C₂×#446	C₂×C₈₉	semidirect
403. C₂×#442	C₂×C₈₉	semidirect
404. C₂×#441	C₂×C₈₉	semidirect
405. C₂×C₄×SD₁₆	C₂×C₈₉	semidirect
406. C₈₉	C₂×#3401	direct (N × H)
417. #559	C₂²×C₈₉	semidirect
419. #556	C₂²×C₈₉	semidirect
441. #497	C₂²×C₈₉	semidirect
443. #495	C₂²×C₈₉	semidirect
444. #464	C₂²×C₈₉	semidirect
445. #464	C₂²×C₈₉	semidirect
446. #463	C₂²×C₈₉	semidirect
447. #463	C₂²×C₈₉	semidirect
448. #461	C₂²×C₈₉	semidirect
449. #460	C₂²×C₈₉	semidirect
450. #446	C₂²×C₈₉	semidirect
451. #442	C₂²×C₈₉	semidirect
452. #441	C₂²×C₈₉	semidirect
453. C₄×SD₁₆	C₂²×C₈₉	semidirect
775. C₂	C₈₉×#3401	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#559×C₈₉	2
C₂×#556×C₈₉	2
C₈₉×#3401	2
C₂×#497×C₈₉	2
C₂×#496×C₈₉	2
C₂×#495×C₈₉	2
C₂×#464×C₈₉	2
C₂×#460×C₈₉	2
C₂×#463×C₈₉	2
C₂×#461×C₈₉	2
C₂×#446×C₈₉	2
C₂×#442×C₈₉	2
C₂×#441×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₂×#3401	89

Subgroups — C2×C89×#3401 #36439246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3401 #36439246