Subgroups — #26034530

Order 11392.

1032 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152352	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152350	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152345	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152343	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152315	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152303	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152291	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152291	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152281	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152257	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152254	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152246	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152219	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152216	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152214	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152207	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152190	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152189	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152185	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152185	C₂	1	1	yes	maximal, characteristic, complemented
24	#19152181	C₂	1	1	yes	maximal, characteristic, complemented
25	#19152181	C₂	1	1	yes	maximal, characteristic, complemented
26	#19152175	C₂	1	1	yes	maximal, characteristic, complemented
27	#19152170	C₂	1	1	yes	maximal, characteristic, complemented
28	#19152108	C₂	1	1	yes	maximal, characteristic, complemented
29	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
31	#553×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13083574	C₂²	1	1	yes	characteristic
33	C₂×#13083573	C₂²	1	1	yes	characteristic
34	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
35	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
36	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
38	#15668012	C₂²	1	1	yes	characteristic, complemented
39	#15668011	C₂²	1	1	yes	characteristic, complemented
40	#15668011	C₂²	1	1	yes	characteristic, complemented
41	#15668011	C₂²	1	1	yes	characteristic, complemented
42	#15668011	C₂²	1	1	yes	characteristic, complemented
43	#15668011	C₂²	1	1	yes	characteristic, complemented
44	#15668007	C₂²	1	1	yes	characteristic
45	#15668007	C₂²	1	1	yes	characteristic
46	#15668007	C₂²	1	1	yes	characteristic
47	#15668007	C₂²	1	1	yes	characteristic
48	#15668007	C₂²	1	1	yes	characteristic
49	#15668007	C₂²	1	1	yes	characteristic
50	#15668007	C₂²	1	1	yes	characteristic, complemented
51	#15668007	C₂²	1	1	yes	characteristic, complemented
52	#15668006	C₂²	1	1	yes	characteristic
53	#15668006	C₂²	1	1	yes	characteristic
54	#15668005	C₂²	1	1	yes	characteristic, complemented
55	#15668005	C₂²	1	1	yes	characteristic, complemented
56	#15668004	C₂²	1	1	yes	characteristic, complemented
57	#15668004	C₂²	1	1	yes	characteristic, complemented
58	#15668003	C₂²	1	1	yes	characteristic, complemented
59	#15668003	C₂²	1	1	yes	characteristic, complemented
60	#15668002	C₂²	1	1	yes	characteristic, complemented
61	#15668002	C₂²	1	1	yes	characteristic, complemented
62	#15668002	C₂²	1	1	yes	characteristic, complemented
63	#15668002	C₂²	1	1	yes	characteristic, complemented
64	#15668000	C₂²	1	1	yes	characteristic
65	#15668000	C₂²	1	1	yes	characteristic
66	#15667999	C₂²	1	1	yes	characteristic, complemented
67	#15667998	C₂²	1	1	yes	characteristic
68	#15667998	C₂²	1	1	yes	characteristic
69	#15667998	C₂²	1	1	yes	characteristic
70	#15667998	C₂²	1	1	yes	characteristic
71	#15667998	C₂²	1	1	yes	characteristic
72	#15667998	C₂²	1	1	yes	characteristic
73	#15667998	C₂²	1	1	yes	characteristic, complemented
74	#15667998	C₂²	1	1	yes	characteristic, complemented
75	#15667997	C₂²	1	1	yes	characteristic
76	#15667997	C₂²	1	1	yes	characteristic
77	#15667997	C₂²	1	1	yes	characteristic
78	#15667996	C₂²	1	1	yes	characteristic
79	#15667996	C₂²	1	1	yes	characteristic
80	#15667996	C₂²	1	1	yes	characteristic
81	#15667996	C₂²	1	1	yes	characteristic
82	#15667995	C₂²	1	1	yes	characteristic
83	#15667995	C₂²	1	1	yes	characteristic
84	#15667994	C₂²	1	1	yes	characteristic
85	#15667994	C₂²	1	1	yes	characteristic
86	#15667994	C₂²	1	1	yes	characteristic
87	#15667994	C₂²	1	1	yes	characteristic, complemented
88	#15667994	C₂²	1	1	yes	characteristic, complemented
89	#15667993	C₂²	1	1	yes	characteristic, complemented
90	#15667993	C₂²	1	1	yes	characteristic, complemented
91	#15667992	C₂²	1	1	yes	characteristic
92	#15667992	C₂²	1	1	yes	characteristic, complemented
93	#15667992	C₂²	1	1	yes	characteristic, complemented
94	#15667991	C₂²	1	1	yes	characteristic
95	#15667991	C₂²	1	1	yes	characteristic
96	#15667991	C₂²	1	1	yes	characteristic
97	#15667991	C₂²	1	1	yes	characteristic, complemented
98	#15667991	C₂²	1	1	yes	characteristic, complemented
99	#15667991	C₂²	1	1	yes	characteristic, complemented
100	#15667990	C₂²	1	1	yes	characteristic
101	#15667990	C₂²	1	1	yes	characteristic
102	#15667990	C₂²	1	1	yes	characteristic
103	#15667990	C₂²	1	1	yes	characteristic
104	#15667990	C₂²	1	1	yes	characteristic
105	#15667990	C₂²	1	1	yes	characteristic
106	#15667990	C₂²	1	1	yes	characteristic
107	#15667990	C₂²	1	1	yes	characteristic
108	#15667990	C₂²	1	1	yes	characteristic
109	#15667990	C₂²	1	1	yes	characteristic, complemented
110	#15667990	C₂²	1	1	yes	characteristic, complemented
111	#15667989	C₂²	1	1	yes	characteristic
112	#15667989	C₂²	1	1	yes	characteristic
113	#15667989	C₂²	1	1	yes	characteristic
114	#15667989	C₂²	1	1	yes	characteristic, complemented
115	#15667989	C₂²	1	1	yes	characteristic, complemented
116	#15667989	C₂²	1	1	yes	characteristic, complemented
117	#15667989	C₂²	1	1	yes	characteristic, complemented
118	#15667989	C₂²	1	1	yes	characteristic, complemented
119	#15667989	C₂²	1	1	yes	characteristic, complemented
120	#15667989	C₂²	1	1	yes	characteristic, complemented
121	#15667989	C₂²	1	1	yes	characteristic, complemented
122	#15667986	C₂²	1	1	yes	characteristic
123	#15667986	C₂²	1	1	yes	characteristic
124	#15667985	C₂²	1	1	yes	characteristic
125	#15667985	C₂²	1	1	yes	characteristic
126	#15667985	C₂²	1	1	yes	characteristic
127	#15667984	C₂²	1	1	yes	characteristic
128	#15667984	C₂²	1	1	yes	characteristic
129	#15667984	C₂²	1	1	yes	characteristic
130	#15667984	C₂²	1	1	yes	characteristic
131	#15667984	C₂²	1	1	yes	characteristic
132	#15667984	C₂²	1	1	yes	characteristic
133	#15667984	C₂²	1	1	yes	characteristic
134	#15667984	C₂²	1	1	yes	characteristic, complemented
135	#15667984	C₂²	1	1	yes	characteristic, complemented
136	#15667983	C₂²	1	1	yes	characteristic
137	#15667982	C₂²	1	1	yes	characteristic
138	#15667980	C₂²	1	1	yes	characteristic
139	#15667980	C₂²	1	1	yes	characteristic
140	#15667980	C₂²	1	1	yes	characteristic
141	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
142	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
143	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
144	#15667977	C₂²	1	1	yes	characteristic, complemented
145	#15667977	C₂²	1	1	yes	characteristic, complemented
146	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
147	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
148	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
149	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
150	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
151	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
152	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
153	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
154	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
156	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
157	#15667972	C₂²	1	1	yes	characteristic
158	#15667972	C₂²	1	1	yes	characteristic
159	#15667972	C₂²	1	1	yes	characteristic, complemented
160	#15667972	C₂²	1	1	yes	characteristic, complemented
161	#15667970	C₂²	1	1	yes	characteristic
162	#15667969	C₂²	1	1	yes	characteristic
163	#15667968	C₂²	1	1	yes	characteristic, complemented
164	#15667968	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13083553	C₂²	1	1	yes	characteristic
166	C₂×#13083553	C₂²	1	1	yes	characteristic
167	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
168	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
169	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
170	C₂×#13083551	C₂²	1	1	yes	characteristic
171	C₂×#13083551	C₂²	1	1	yes	characteristic
172	#126×C₈₉	C₂²	1	1	yes	characteristic, complemented
173	#126×C₈₉	C₂²	1	1	yes	characteristic, complemented
174	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
176	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
177	#121×C₈₉	C₂²	1	1	yes	characteristic
178	#121×C₈₉	C₂²	1	1	yes	characteristic
179	#121×C₈₉	C₂²	1	1	yes	characteristic
180	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
183	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
187	C₂³×D₈₉	C₂³	1	1	yes	characteristic
188	#13083574	—	4	2	no	—
189	#13083573	—	4	2	no	—
190	#13083573	—	4	2	no	—
191	C₂×Dic₁₇₈	—	4	2	no	—
192	C₂×Dic₁₇₈	—	4	2	no	—
193	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
194	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
196	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
197	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
198	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
199	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
200	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
201	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
202	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
203	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
204	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
215	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
216	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
217	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
218	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
219	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
221	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
222	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
223	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₈₉	—	4	2	no	—
225	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
232	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
233	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
234	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
235	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
236	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
237	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
238	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
244	#13083553	C₂³	1	1	yes	characteristic
245	#13083553	C₂³	1	1	yes	characteristic
246	#13083553	C₂³	1	1	yes	characteristic
247	#13083553	C₂³	1	1	yes	characteristic
248	#13083553	C₂³	1	1	yes	characteristic
249	#13083553	C₂³	1	1	yes	characteristic
250	#13083553	C₂³	1	1	yes	characteristic
251	#13083553	C₂³	1	1	yes	characteristic
252	#13083553	C₂³	1	1	yes	characteristic
253	#13083553	C₂³	1	1	yes	characteristic
254	#13083553	C₂³	1	1	yes	characteristic
255	#13083553	C₂³	1	1	yes	characteristic
256	#13083553	C₂³	1	1	yes	characteristic
257	#13083553	C₂³	1	1	yes	characteristic
258	#13083553	C₂³	1	1	yes	characteristic
259	#13083553	C₂³	1	1	yes	characteristic
260	#13083553	C₂³	1	1	yes	characteristic
261	#13083553	C₂³	1	1	yes	characteristic
262	#13083553	C₂³	1	1	yes	characteristic
263	#13083553	C₂³	1	1	yes	characteristic
264	#13083553	C₂³	1	1	yes	characteristic
265	#13083553	C₂³	1	1	yes	characteristic
266	#13083553	C₂³	1	1	yes	characteristic
267	#13083553	C₂³	1	1	yes	characteristic
268	#13083553	C₂³	1	1	yes	characteristic
269	#13083553	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
281	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
282	#13083551	C₂³	1	1	yes	characteristic
283	#13083551	C₂³	1	1	yes	characteristic
284	#13083551	C₂³	1	1	yes	characteristic
285	#13083551	C₂³	1	1	yes	characteristic
286	#13083551	C₂³	1	1	yes	characteristic
287	#13083551	C₂³	1	1	yes	characteristic
288	#13083551	C₂³	1	1	yes	characteristic
289	#13083551	C₂³	1	1	yes	characteristic
290	#13083551	C₂³	1	1	yes	characteristic
291	#13083551	C₂³	1	1	yes	characteristic
292	#13083551	C₂³	1	1	yes	characteristic
293	#13083551	C₂³	1	1	yes	characteristic
294	#13083551	C₂³	1	1	yes	characteristic
295	#13083551	C₂³	1	1	yes	characteristic
296	#13083551	C₂³	1	1	yes	characteristic
297	#13083551	C₂³	1	1	yes	characteristic
298	#13083551	C₂³	1	1	yes	characteristic
299	#13083551	C₂³	1	1	yes	characteristic
300	#13083551	C₂³	1	1	yes	characteristic
301	#13083551	C₂³	1	1	yes	characteristic
302	#13083551	C₂³	1	1	yes	characteristic
303	#13083551	C₂³	1	1	yes	characteristic
304	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
305	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
306	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
307	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
308	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
309	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
310	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
311	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
312	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
313	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
314	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
319	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
345	C₄²×C₈₉	C₂³	1	1	yes	characteristic
346	C₄²×C₈₉	C₂³	1	1	yes	characteristic
347	C₄²×C₈₉	C₂³	1	1	yes	characteristic
348	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
350	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
351	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
352	C₂²×D₈₉	—	2	2	no	—
353	C₂²×D₈₉	—	4	1	no	—
354	C₂²×D₈₉	—	4	1	no	—
355	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
356	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
357	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
358	D₄×C₈₉	—	2	2	no	—
359	D₄×C₈₉	—	2	2	no	—
360	D₄×C₈₉	—	2	2	no	—
361	D₄×C₈₉	—	4	1	no	—
362	D₄×C₈₉	—	4	1	no	—
363	D₄×C₈₉	—	4	1	no	—
364	C₂×C₄×C₈₉	—	4	1	no	—
365	C₂×C₄×C₈₉	—	4	1	no	—
366	C₂×C₄×C₈₉	—	4	1	no	—
367	C₂×C₄×C₈₉	—	4	1	no	—
368	C₂×C₄×C₈₉	—	4	1	no	—
369	C₂×C₄×C₈₉	—	4	1	no	—
370	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
378	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
381	C₂²⋊D₈₉	—	2	2	no	—
382	C₂²⋊D₈₉	—	2	2	no	—
383	C₂²⋊D₈₉	—	4	1	no	—
384	C₂²⋊D₈₉	—	4	1	no	—
385	C₂²⋊D₈₉	—	4	1	no	—
386	C₂²⋊D₈₉	—	4	1	no	—
387	C₂²⋊D₈₉	—	4	1	no	—
388	C₂²⋊D₈₉	—	4	1	no	—
389	C₂²⋊D₈₉	—	4	1	no	—
390	C₂²⋊D₈₉	—	4	1	no	—
391	C₂×Dic₈₉	—	2	2	no	—
392	C₂×Dic₈₉	—	2	2	no	—
393	C₂×Dic₈₉	—	2	2	no	—
394	C₂×Dic₈₉	—	4	1	no	—
395	C₂×Dic₈₉	—	4	1	no	—
396	C₂×Dic₈₉	—	4	1	no	—
397	C₂×Dic₈₉	—	4	1	no	—
398	C₂×Dic₈₉	—	4	1	no	—
399	C₂×Dic₈₉	—	4	1	no	—
400	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
406	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
407	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
413	D₃₅₆	—	4	1	no	—
414	D₃₅₆	—	4	1	no	—
415	C₄×D₈₉	—	2	2	no	—
416	C₄×D₈₉	—	2	2	no	—
417	C₄×D₈₉	—	4	1	no	—
418	C₄×D₈₉	—	4	1	no	—
419	C₄×D₈₉	—	4	1	no	—
420	C₄×D₈₉	—	4	1	no	—
421	C₄×D₈₉	—	4	1	no	—
422	Dic₁₇₈	—	2	2	no	—
423	Dic₁₇₈	—	2	2	no	—
424	Dic₁₇₈	—	2	2	no	—
425	Dic₁₇₈	—	4	1	no	—
426	Dic₁₇₈	—	4	1	no	—
427	Dic₁₇₈	—	4	1	no	—
428	Dic₁₇₈	—	4	1	no	—
429	Dic₁₇₈	—	4	1	no	—
430	Dic₁₇₈	—	4	1	no	—
431	Dic₁₇₈	—	4	1	no	—
432	C₂²×C₈₉	—	2	1	no	—
433	C₂²×C₈₉	—	2	1	no	—
434	C₂²×C₈₉	—	2	1	no	—
435	C₂²×C₈₉	—	2	1	no	—
436	C₂²×C₈₉	—	2	1	no	—
437	C₂²×C₈₉	—	2	1	no	—
438	C₂²×C₈₉	—	2	1	no	—
439	C₂²×C₈₉	—	2	1	no	—
440	C₂²×C₈₉	—	2	1	no	—
441	C₂²×C₈₉	—	2	1	no	—
442	C₂²×C₈₉	—	2	1	no	—
443	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
444	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
445	C₂×D₈₉	—	2	1	no	—
446	C₂×D₈₉	—	2	1	no	—
447	C₂×D₈₉	—	2	1	no	—
448	C₂×D₈₉	—	2	1	no	—
449	C₂×D₈₉	—	2	1	no	—
450	C₂×D₈₉	—	2	1	no	—
451	C₂×D₈₉	—	2	1	no	—
452	C₂×D₈₉	—	2	1	no	—
453	C₂×D₈₉	—	2	1	no	—
454	C₂×D₈₉	—	4	4	no	—
455	C₄×C₈₉	—	2	1	no	—
456	C₄×C₈₉	—	2	1	no	—
457	C₄×C₈₉	—	2	1	no	—
458	C₄×C₈₉	—	2	1	no	—
459	C₄×C₈₉	—	2	1	no	—
460	C₄×C₈₉	—	2	1	no	—
461	C₄×C₈₉	—	2	1	no	—
462	C₄×C₈₉	—	2	1	no	—
463	C₄×C₈₉	—	2	1	no	—
464	C₄×C₈₉	—	2	1	no	—
465	C₄×C₈₉	—	2	1	no	—
466	Dic₈₉	—	2	1	no	—
467	Dic₈₉	—	2	1	no	—
468	Dic₈₉	—	2	1	no	—
469	Dic₈₉	—	2	1	no	—
470	Dic₈₉	—	2	1	no	—
471	Dic₈₉	—	2	1	no	—
472	Dic₈₉	—	2	1	no	—
473	Dic₈₉	—	2	1	no	—
474	Dic₈₉	—	2	1	no	—
475	Dic₈₉	—	2	1	no	—
476	Dic₈₉	—	2	1	no	—
477	Dic₈₉	—	2	1	no	—
478	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
479	C₂×C₈₉	—	2	2	no	—
480	C₂×C₈₉	—	4	1	no	—
481	C₂×C₈₉	—	4	1	no	—
482	C₂×C₈₉	—	4	1	no	—
483	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
484	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
485	C₂×C₈₉	#585	1	1	yes	characteristic
486	D₈₉	—	4	1	no	—
487	D₈₉	—	4	1	no	—
488	D₈₉	—	4	1	no	—
489	#3541	—	89	1	no	maximal, Sylow
490	C₈₉	#3541	1	1	yes	characteristic, complemented, Sylow
491	#563	—	89	1	no	—
492	#563	—	89	1	no	—
493	#562	—	89	1	no	—
494	#562	—	89	1	no	—
495	#556	—	89	1	no	—
496	#554	—	89	1	no	—
497	#554	—	89	1	no	—
498	#554	—	89	1	no	—
499	#553	—	89	1	no	—
500	#553	—	89	1	no	—
501	#553	D₈₉	1	1	yes	characteristic, complemented
502	#552	—	89	1	no	—
503	D₄×Q₈	—	89	1	no	—
504	#548	—	89	1	no	—
505	#548	—	89	1	no	—
506	#547	—	89	1	no	—
507	#542	—	89	1	no	—
508	#542	—	89	1	no	—
509	#542	—	89	1	no	—
510	#541	—	89	1	no	—
511	#539	—	89	1	no	—
512	#539	—	89	1	no	—
513	#538	—	89	1	no	—
514	#538	—	89	1	no	—
515	#538	—	89	1	no	—
516	#538	—	89	1	no	—
517	#537	—	89	1	no	—
518	#536	—	89	1	no	—
519	#525	—	89	1	no	—
520	#525	—	89	1	no	—
521	C₂×C₂²⋊Q₈	—	89	1	no	—
522	C₂×#41	—	89	1	no	—
523	C₂×#41	—	89	1	no	—
524	C₂×#41	—	89	1	no	—
525	C₂²×Q₈	—	89	1	no	—
526	C₂²×Q₈	—	89	1	no	—
527	C₂³×C₄	—	89	1	no	—
528	C₄⋊Q₈	—	89	1	no	—
529	C₄⋊Q₈	—	89	1	no	—
530	C₄⋊Q₈	—	89	1	no	—
531	C₄⋊Q₈	—	89	1	no	—
532	C₄⋊Q₈	—	89	1	no	—
533	C₄⋊Q₈	—	89	1	no	—
534	#126	—	89	1	no	—
535	#126	—	89	1	no	—
536	#126	—	89	1	no	—
537	#126	—	89	1	no	—
538	#126	—	89	1	no	—
539	#126	—	89	1	no	—
540	#126	—	89	1	no	—
541	#126	—	89	1	no	—
542	#126	—	89	1	no	—
543	#126	—	89	1	no	—
544	#126	—	89	1	no	—
545	#126	—	89	1	no	—
546	#126	C₂×D₈₉	1	1	yes	characteristic, complemented
547	#126	C₂×D₈₉	1	1	yes	characteristic, complemented
548	#125	—	89	1	no	—
549	#125	—	89	1	no	—
550	#125	—	89	1	no	—
551	#125	—	89	1	no	—
552	#125	—	89	1	no	—
553	#125	—	89	1	no	—
554	#125	—	89	1	no	—
555	#125	—	89	1	no	—
556	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
557	#124	—	89	1	no	—
558	#124	—	89	1	no	—
559	#124	—	89	1	no	—
560	#124	—	89	1	no	—
561	#124	—	89	1	no	—
562	#124	—	89	1	no	—
563	#124	—	89	1	no	—
564	#124	—	89	1	no	—
565	#124	—	89	1	no	—
566	#124	—	89	1	no	—
567	#124	—	89	1	no	—
568	#123	—	89	1	no	—
569	#123	—	89	1	no	—
570	#123	—	89	1	no	—
571	#123	—	89	1	no	—
572	#123	—	89	1	no	—
573	#123	—	89	1	no	—
574	#123	—	89	1	no	—
575	#123	—	89	1	no	—
576	#123	—	89	1	no	—
577	#123	—	89	1	no	—
578	#123	—	89	1	no	—
579	#123	—	89	1	no	—
580	#123	—	89	1	no	—
581	#123	—	89	1	no	—
582	#123	—	89	1	no	—
583	#123	—	89	1	no	—
584	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
585	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
586	C₂²⋊Q₈	—	89	1	no	—
587	C₂²⋊Q₈	—	89	1	no	—
588	C₂²⋊Q₈	—	89	1	no	—
589	C₂²⋊Q₈	—	89	1	no	—
590	C₂²⋊Q₈	—	89	1	no	—
591	C₂²⋊Q₈	—	89	1	no	—
592	C₂²⋊Q₈	—	89	1	no	—
593	C₂²⋊Q₈	—	89	1	no	—
594	C₂²⋊Q₈	—	89	1	no	—
595	C₂²⋊Q₈	—	89	1	no	—
596	C₂²⋊Q₈	—	89	1	no	—
597	C₂²⋊Q₈	—	89	1	no	—
598	C₂²⋊Q₈	—	89	1	no	—
599	C₂²⋊Q₈	—	89	1	no	—
600	C₂²⋊Q₈	—	89	1	no	—
601	C₂²⋊Q₈	—	89	1	no	—
602	C₂²⋊Q₈	—	89	1	no	—
603	C₂²⋊Q₈	—	89	1	no	—
604	C₂²⋊Q₈	—	89	1	no	—
605	C₂²⋊Q₈	—	89	1	no	—
606	C₂²⋊Q₈	—	89	1	no	—
607	C₂²⋊Q₈	—	89	1	no	—
608	C₂²⋊Q₈	—	89	1	no	—
609	C₂²⋊Q₈	—	89	1	no	—
610	C₂²⋊Q₈	—	89	1	no	—
611	C₂²⋊Q₈	—	89	1	no	—
612	C₂²⋊Q₈	—	89	1	no	—
613	C₂²⋊Q₈	—	89	1	no	—
614	C₂²⋊Q₈	—	89	1	no	—
615	C₂²⋊Q₈	—	89	1	no	—
616	C₂²⋊Q₈	—	89	1	no	—
617	#121	—	89	1	no	—
618	#121	—	89	1	no	—
619	#121	—	89	1	no	—
620	#121	—	89	1	no	—
621	#121	—	89	1	no	—
622	#121	—	89	1	no	—
623	#121	—	89	1	no	—
624	#121	—	89	1	no	—
625	#121	—	89	1	no	—
626	#121	—	89	1	no	—
627	#121	—	89	1	no	—
628	#121	—	89	1	no	—
629	#121	—	89	1	no	—
630	#121	—	89	1	no	—
631	#121	—	89	1	no	—
632	#121	C₂×D₈₉	1	1	yes	characteristic
633	#121	C₂×D₈₉	1	1	yes	characteristic
634	#121	C₂×D₈₉	1	1	yes	characteristic
635	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
636	#120	—	89	1	no	—
637	#120	—	89	1	no	—
638	#120	—	89	1	no	—
639	#120	—	89	1	no	—
640	C₄×Q₈	—	89	1	no	—
641	C₄×Q₈	—	89	1	no	—
642	C₄×Q₈	—	89	1	no	—
643	C₄×Q₈	—	89	1	no	—
644	C₄×Q₈	—	89	1	no	—
645	C₄×D₄	—	89	1	no	—
646	C₄×D₄	—	89	1	no	—
647	C₄×D₄	—	89	1	no	—
648	C₄×D₄	—	89	1	no	—
649	C₄×D₄	—	89	1	no	—
650	C₄×D₄	—	89	1	no	—
651	C₄×D₄	—	89	1	no	—
652	C₄×D₄	—	89	1	no	—
653	C₄×D₄	—	89	1	no	—
654	C₄×D₄	—	89	1	no	—
655	C₄×D₄	—	89	1	no	—
656	C₄×D₄	—	89	1	no	—
657	C₄×D₄	—	89	1	no	—
658	C₄×D₄	—	89	1	no	—
659	C₄×D₄	—	89	1	no	—
660	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
661	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
662	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
663	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
664	#117	—	89	1	no	—
665	#117	—	89	1	no	—
666	#117	—	89	1	no	—
667	#117	—	89	1	no	—
668	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
669	C₂×C₄⋊C₄	—	89	1	no	—
670	C₂×C₄⋊C₄	—	89	1	no	—
671	C₂×C₄⋊C₄	—	89	1	no	—
672	C₂×C₄⋊C₄	—	89	1	no	—
673	C₂×C₄⋊C₄	—	89	1	no	—
674	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	—	89	1	no	—
676	C₂×C₂²⋊C₄	—	89	1	no	—
677	C₂⁴	—	89	1	no	—
678	#41	—	356	2	no	—
679	#41	—	356	2	no	—
680	#41	—	356	2	no	—
681	C₂×Q₈	—	89	1	no	—
682	C₂×Q₈	—	89	1	no	—
683	C₂×Q₈	—	89	1	no	—
684	C₂×Q₈	—	89	1	no	—
685	C₂×Q₈	—	89	1	no	—
686	C₂×Q₈	—	89	1	no	—
687	C₂×Q₈	—	89	1	no	—
688	C₂×Q₈	—	89	1	no	—
689	C₂×Q₈	—	89	1	no	—
690	C₂×Q₈	—	89	1	no	—
691	C₂×Q₈	—	356	2	no	—
692	C₂×Q₈	—	356	2	no	—
693	C₂×D₄	—	89	1	no	—
694	C₂×D₄	—	89	1	no	—
695	C₂×D₄	—	89	1	no	—
696	C₂×D₄	—	89	1	no	—
697	C₂×D₄	—	89	1	no	—
698	C₂×D₄	—	89	1	no	—
699	C₂×D₄	—	89	1	no	—
700	C₂×D₄	—	89	1	no	—
701	C₂×D₄	—	89	1	no	—
702	C₂×D₄	—	89	1	no	—
703	C₂×D₄	—	89	1	no	—
704	C₂×D₄	—	89	1	no	—
705	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
706	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
707	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
708	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
709	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
710	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
711	C₂²×C₄	—	89	1	no	—
712	C₂²×C₄	—	89	1	no	—
713	C₂²×C₄	—	89	1	no	—
714	C₂²×C₄	—	89	1	no	—
715	C₂²×C₄	—	89	1	no	—
716	C₂²×C₄	—	89	1	no	—
717	C₂²×C₄	—	89	1	no	—
718	C₂²×C₄	—	89	1	no	—
719	C₂²×C₄	—	89	1	no	—
720	C₂²×C₄	—	89	1	no	—
721	C₂²×C₄	—	89	1	no	—
722	C₂²×C₄	—	89	1	no	—
723	C₂²×C₄	—	89	1	no	—
724	C₂²×C₄	—	89	1	no	—
725	C₂²×C₄	—	89	1	no	—
726	C₂²×C₄	—	89	1	no	—
727	C₂²×C₄	—	356	2	no	—
728	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
733	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
734	C₄⋊C₄	—	89	1	no	—
735	C₄⋊C₄	—	89	1	no	—
736	C₄⋊C₄	—	89	1	no	—
737	C₄⋊C₄	—	89	1	no	—
738	C₄⋊C₄	—	89	1	no	—
739	C₄⋊C₄	—	89	1	no	—
740	C₄⋊C₄	—	89	1	no	—
741	C₄⋊C₄	—	89	1	no	—
742	C₄⋊C₄	—	89	1	no	—
743	C₄⋊C₄	—	89	1	no	—
744	C₄⋊C₄	—	89	1	no	—
745	C₄⋊C₄	—	89	1	no	—
746	C₄⋊C₄	—	89	1	no	—
747	C₄⋊C₄	—	89	1	no	—
748	C₄⋊C₄	—	89	1	no	—
749	C₄⋊C₄	—	89	1	no	—
750	C₄⋊C₄	—	89	1	no	—
751	C₄⋊C₄	—	89	1	no	—
752	C₄⋊C₄	—	89	1	no	—
753	C₄⋊C₄	—	89	1	no	—
754	C₄⋊C₄	—	89	1	no	—
755	C₄⋊C₄	—	89	1	no	—
756	C₄⋊C₄	—	89	1	no	—
757	C₄⋊C₄	—	89	1	no	—
758	C₄⋊C₄	—	89	1	no	—
759	C₄⋊C₄	—	89	1	no	—
760	C₄⋊C₄	—	89	1	no	—
761	C₄⋊C₄	—	89	1	no	—
762	C₄⋊C₄	—	89	1	no	—
763	C₄⋊C₄	—	89	1	no	—
764	C₄⋊C₄	—	89	1	no	—
765	C₄⋊C₄	—	89	1	no	—
766	C₄⋊C₄	—	89	1	no	—
767	C₄⋊C₄	—	89	1	no	—
768	C₄⋊C₄	—	89	1	no	—
769	C₄⋊C₄	—	89	1	no	—
770	C₄⋊C₄	—	89	1	no	—
771	C₄⋊C₄	—	89	1	no	—
772	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
782	C₂²⋊C₄	—	89	1	no	—
783	C₂²⋊C₄	—	89	1	no	—
784	C₂²⋊C₄	—	89	1	no	—
785	C₂²⋊C₄	—	89	1	no	—
786	C₂²⋊C₄	—	89	1	no	—
787	C₂²⋊C₄	—	89	1	no	—
788	C₂²⋊C₄	—	89	1	no	—
789	C₂²⋊C₄	—	89	1	no	—
790	C₂²⋊C₄	—	89	1	no	—
791	C₂²⋊C₄	—	89	1	no	—
792	C₂²⋊C₄	—	89	1	no	—
793	C₂²⋊C₄	—	89	1	no	—
794	C₂²⋊C₄	—	89	1	no	—
795	C₂²⋊C₄	—	89	1	no	—
796	C₂²⋊C₄	—	89	1	no	—
797	C₂²⋊C₄	—	89	1	no	—
798	C₂²⋊C₄	—	89	1	no	—
799	C₂²⋊C₄	—	89	1	no	—
800	C₂²⋊C₄	—	89	1	no	—
801	C₂²⋊C₄	—	89	1	no	—
802	C₂²⋊C₄	—	89	1	no	—
803	C₂²⋊C₄	—	89	1	no	—
804	C₂²⋊C₄	—	89	1	no	—
805	C₂²⋊C₄	—	89	1	no	—
806	C₂²⋊C₄	—	89	1	no	—
807	C₂²⋊C₄	—	89	1	no	—
808	C₂²⋊C₄	—	89	1	no	—
809	C₂²⋊C₄	—	89	1	no	—
810	C₂²⋊C₄	—	89	1	no	—
811	C₂²⋊C₄	—	89	1	no	—
812	C₂²⋊C₄	—	89	1	no	—
813	C₂²⋊C₄	—	89	1	no	—
814	C₂²⋊C₄	—	89	1	no	—
815	C₂²⋊C₄	—	89	1	no	—
816	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
817	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
818	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
819	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
820	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
821	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
822	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
823	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
826	C₄²	—	89	1	no	—
827	C₄²	—	89	1	no	—
828	C₄²	—	89	1	no	—
829	C₄²	—	89	1	no	—
830	C₄²	—	89	1	no	—
831	C₄²	—	89	1	no	—
832	C₄²	—	89	1	no	—
833	C₄²	—	89	1	no	—
834	C₄²	—	89	1	no	—
835	C₄²	C₂²×D₈₉	1	1	yes	characteristic
836	C₄²	C₂²×D₈₉	1	1	yes	characteristic
837	C₄²	C₂²×D₈₉	1	1	yes	characteristic
838	C₂³	—	89	1	no	—
839	C₂³	—	89	1	no	—
840	C₂³	—	89	1	no	—
841	C₂³	—	356	1	no	—
842	C₂³	—	356	1	no	—
843	C₂³	—	178	2	no	—
844	C₂³	C₂³×D₈₉	1	1	yes	characteristic
845	C₂³	C₂³×D₈₉	1	1	yes	characteristic
846	C₂³	C₂³×D₈₉	1	1	yes	characteristic
847	C₂³	C₂³×D₈₉	1	1	yes	characteristic
848	Q₈	—	356	1	no	—
849	Q₈	—	356	1	no	—
850	Q₈	—	356	1	no	—
851	Q₈	—	356	1	no	—
852	Q₈	—	356	1	no	—
853	Q₈	—	356	1	no	—
854	Q₈	—	356	1	no	—
855	Q₈	—	178	2	no	—
856	Q₈	—	178	2	no	—
857	Q₈	—	178	2	no	—
858	D₄	—	2	2	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	4	1	no	—
862	D₄	—	4	1	no	—
863	D₄	—	4	1	no	—
864	D₄	—	356	1	no	—
865	D₄	—	356	1	no	—
866	D₄	—	356	1	no	—
867	D₄	—	356	1	no	—
868	D₄	—	356	1	no	—
869	D₄	—	356	1	no	—
870	D₄	—	356	1	no	—
871	D₄	—	356	1	no	—
872	D₄	—	356	1	no	—
873	D₄	—	356	1	no	—
874	D₄	—	178	2	no	—
875	D₄	—	178	2	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	89	1	no	—
883	C₂×C₄	—	89	1	no	—
884	C₂×C₄	—	89	1	no	—
885	C₂×C₄	—	89	1	no	—
886	C₂×C₄	—	89	1	no	—
887	C₂×C₄	—	89	1	no	—
888	C₂×C₄	—	89	1	no	—
889	C₂×C₄	—	89	1	no	—
890	C₂×C₄	—	89	1	no	—
891	C₂×C₄	—	89	1	no	—
892	C₂×C₄	—	89	1	no	—
893	C₂×C₄	—	89	1	no	—
894	C₂×C₄	—	89	1	no	—
895	C₂×C₄	—	356	1	no	—
896	C₂×C₄	—	356	1	no	—
897	C₂×C₄	—	356	1	no	—
898	C₂×C₄	—	356	1	no	—
899	C₂×C₄	—	356	1	no	—
900	C₂×C₄	—	356	1	no	—
901	C₂×C₄	—	356	1	no	—
902	C₂×C₄	—	356	1	no	—
903	C₂×C₄	—	356	1	no	—
904	C₂×C₄	—	356	1	no	—
905	C₂×C₄	—	356	1	no	—
906	C₂×C₄	—	178	2	no	—
907	C₂×C₄	—	178	2	no	—
908	C₂×C₄	—	178	2	no	—
909	C₂×C₄	—	178	2	no	—
910	C₂×C₄	—	178	2	no	—
911	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	1	no	—
931	C₂²	—	2	1	no	—
932	C₂²	—	2	1	no	—
933	C₂²	—	356	4	no	—
934	C₂²	—	178	1	no	—
935	C₂²	—	178	1	no	—
936	C₂²	—	178	1	no	—
937	C₂²	—	178	1	no	—
938	C₂²	—	178	1	no	—
939	C₂²	—	178	1	no	—
940	C₂²	—	178	1	no	—
941	C₂²	—	178	1	no	—
942	C₂²	—	178	1	no	—
943	C₂²	#15668059	1	2	yes	—
944	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	89	2	no	—
957	C₄	—	178	1	no	—
958	C₄	—	178	1	no	—
959	C₄	—	178	1	no	—
960	C₄	—	178	1	no	—
961	C₄	—	178	1	no	—
962	C₄	—	178	1	no	—
963	C₄	—	178	1	no	—
964	C₄	—	178	1	no	—
965	C₄	—	178	1	no	—
966	C₄	—	178	1	no	—
967	C₄	—	178	1	no	—
968	C₄	—	178	1	no	—
969	C₂	—	2	2	no	—
970	C₂	—	4	1	no	—
971	C₂	—	4	1	no	—
972	C₂	—	4	1	no	—
973	C₂	—	356	1	no	—
974	C₂	—	356	1	no	—
975	C₂	—	356	1	no	—
976	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
977	C₂	C₂×#15668059	1	1	yes	characteristic
978	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#553×C₈₉	C₂
hypercenter	#553	D₈₉
hypocenter	C₈₉	#3541
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #19152352	C₂	semidirect
2. #19152350	C₂	semidirect
3. #19152345	C₂	semidirect
4. #19152343	C₂	semidirect
5. #19152315	C₂	semidirect
6. #19152307	C₂	semidirect
7. #19152307	C₂	semidirect
8. #19152303	C₂	semidirect
9. #19152291	C₂	semidirect
10. #19152291	C₂	semidirect
11. #19152281	C₂	semidirect
12. D₄×Dic₁₇₈	C₂	semidirect
13. #19152257	C₂	semidirect
14. #19152254	C₂	semidirect
15. #19152246	C₂	semidirect
16. #19152219	C₂	semidirect
17. #19152216	C₂	semidirect
18. #19152214	C₂	semidirect
19. #19152207	C₂	semidirect
20. #19152190	C₂	semidirect
21. #19152189	C₂	semidirect
22. #19152185	C₂	semidirect
23. #19152185	C₂	semidirect
24. #19152181	C₂	semidirect
25. #19152181	C₂	semidirect
26. #19152175	C₂	semidirect
27. #19152170	C₂	semidirect
28. #19152108	C₂	semidirect
29. #19152107	C₂	semidirect
30. C₂×#15667990	C₂	semidirect
31. #553×C₈₉	C₂	semidirect
34. C₂×#13083573	C₂²	semidirect
36. C₂²×Dic₁₇₈	C₂²	semidirect
38. #15668012	C₂²	semidirect
39. #15668011	C₂²	semidirect
40. #15668011	C₂²	semidirect
41. #15668011	C₂²	semidirect
42. #15668011	C₂²	semidirect
43. #15668011	C₂²	semidirect
50. #15668007	C₂²	semidirect
51. #15668007	C₂²	semidirect
54. #15668005	C₂²	semidirect
55. #15668005	C₂²	semidirect
56. #15668004	C₂²	semidirect
57. #15668004	C₂²	semidirect
58. #15668003	C₂²	semidirect
59. #15668003	C₂²	semidirect
60. #15668002	C₂²	semidirect
61. #15668002	C₂²	semidirect
62. #15668002	C₂²	semidirect
63. #15668002	C₂²	semidirect
66. #15667999	C₂²	semidirect
73. #15667998	C₂²	semidirect
74. #15667998	C₂²	semidirect
87. #15667994	C₂²	semidirect
88. #15667994	C₂²	semidirect
89. #15667993	C₂²	semidirect
90. #15667993	C₂²	semidirect
92. #15667992	C₂²	semidirect
93. #15667992	C₂²	semidirect
97. #15667991	C₂²	semidirect
98. #15667991	C₂²	semidirect
99. #15667991	C₂²	semidirect
109. #15667990	C₂²	semidirect
110. #15667990	C₂²	semidirect
114. #15667989	C₂²	semidirect
115. #15667989	C₂²	semidirect
116. #15667989	C₂²	semidirect
117. #15667989	C₂²	semidirect
118. #15667989	C₂²	semidirect
119. #15667989	C₂²	semidirect
120. #15667989	C₂²	semidirect
121. #15667989	C₂²	semidirect
134. #15667984	C₂²	semidirect
135. #15667984	C₂²	semidirect
141. C₄×Dic₁₇₈	C₂²	semidirect
142. C₄×Dic₁₇₈	C₂²	semidirect
143. C₄×Dic₁₇₈	C₂²	semidirect
144. #15667977	C₂²	semidirect
145. #15667977	C₂²	semidirect
159. #15667972	C₂²	semidirect
160. #15667972	C₂²	semidirect
163. #15667968	C₂²	semidirect
164. #15667968	C₂²	semidirect
167. C₂×#13083553	C₂²	semidirect
168. C₂×#13083553	C₂²	semidirect
169. C₄⋊C₄×D₈₉	C₂²	semidirect
172. #126×C₈₉	C₂²	semidirect
173. #126×C₈₉	C₂²	semidirect
174. #125×C₈₉	C₂²	semidirect
175. #123×C₈₉	C₂²	semidirect
176. #123×C₈₉	C₂²	semidirect
180. #121×C₈₉	C₂²	semidirect
184. C₄×D₄×C₈₉	C₂²	semidirect
185. #117×C₈₉	C₂²	semidirect
490. C₈₉	#3541	semidirect
501. #553	D₈₉	semidirect
546. #126	C₂×D₈₉	semidirect
547. #126	C₂×D₈₉	semidirect
556. #125	C₂×D₈₉	semidirect
584. #123	C₂×D₈₉	semidirect
585. #123	C₂×D₈₉	semidirect
635. #121	C₂×D₈₉	semidirect
663. C₄×D₄	C₂×D₈₉	semidirect
668. #117	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152352	2
#19152350	2
#19152345	2
#19152343	2
#19152315	2
#19152307	2
#19152303	2
#19152291	2
#19152281	2
D₄×Dic₁₇₈	2
#19152257	2
#19152254	2
#19152246	2
#19152219	2
#19152216	2
#19152214	2
#19152207	2
#19152190	2
#19152189	2
#19152185	2
#19152181	2
#19152175	2
#19152170	2
#19152108	2
#19152107	2
C₂×#15667990	2
#553×C₈₉	2
#3541	89