Subgroups — #26034686

Order 11392.

1004 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152350	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152350	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152347	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152325	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152315	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152302	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152299	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152293	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152258	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152256	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152246	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152227	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152225	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152218	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152212	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152207	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152205	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152196	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152194	C₂	1	1	yes	maximal, characteristic, complemented
24	#19152191	C₂	1	1	yes	maximal, characteristic, complemented
25	#19152189	C₂	1	1	yes	maximal, characteristic, complemented
26	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
27	#19152170	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
29	#19152131	C₂	1	1	yes	maximal, characteristic, complemented
30	#19152131	C₂	1	1	yes	maximal, characteristic, complemented
31	#563×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	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
36	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
37	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
38	#15668012	C₂²	1	1	yes	characteristic
39	#15668011	C₂²	1	1	yes	characteristic
40	#15668011	C₂²	1	1	yes	characteristic
41	#15668011	C₂²	1	1	yes	characteristic
42	#15668011	C₂²	1	1	yes	characteristic
43	#15668011	C₂²	1	1	yes	characteristic
44	#15668011	C₂²	1	1	yes	characteristic
45	#15668011	C₂²	1	1	yes	characteristic
46	#15668011	C₂²	1	1	yes	characteristic
47	#15668011	C₂²	1	1	yes	characteristic
48	#15668010	C₂²	1	1	yes	characteristic
49	#15668010	C₂²	1	1	yes	characteristic
50	#15668010	C₂²	1	1	yes	characteristic
51	#15668010	C₂²	1	1	yes	characteristic
52	#15668007	C₂²	1	1	yes	characteristic
53	#15668007	C₂²	1	1	yes	characteristic
54	#15668007	C₂²	1	1	yes	characteristic
55	#15668007	C₂²	1	1	yes	characteristic
56	#15668007	C₂²	1	1	yes	characteristic
57	#15668006	C₂²	1	1	yes	characteristic
58	#15668006	C₂²	1	1	yes	characteristic
59	#15668006	C₂²	1	1	yes	characteristic
60	#15668005	C₂²	1	1	yes	characteristic
61	#15668005	C₂²	1	1	yes	characteristic
62	#15668005	C₂²	1	1	yes	characteristic
63	#15668005	C₂²	1	1	yes	characteristic
64	#15668004	C₂²	1	1	yes	characteristic
65	#15668003	C₂²	1	1	yes	characteristic
66	#15668003	C₂²	1	1	yes	characteristic
67	#15668003	C₂²	1	1	yes	characteristic
68	#15668002	C₂²	1	1	yes	characteristic
69	#15668002	C₂²	1	1	yes	characteristic
70	#15668002	C₂²	1	1	yes	characteristic
71	#15668002	C₂²	1	1	yes	characteristic
72	#15668002	C₂²	1	1	yes	characteristic
73	#15668002	C₂²	1	1	yes	characteristic
74	#15668002	C₂²	1	1	yes	characteristic
75	#15668002	C₂²	1	1	yes	characteristic
76	#15668002	C₂²	1	1	yes	characteristic
77	#15668002	C₂²	1	1	yes	characteristic
78	#15668001	C₂²	1	1	yes	characteristic
79	#15667998	C₂²	1	1	yes	characteristic
80	#15667998	C₂²	1	1	yes	characteristic
81	#15667998	C₂²	1	1	yes	characteristic
82	#15667998	C₂²	1	1	yes	characteristic
83	#15667998	C₂²	1	1	yes	characteristic
84	#15667998	C₂²	1	1	yes	characteristic
85	#15667997	C₂²	1	1	yes	characteristic
86	#15667997	C₂²	1	1	yes	characteristic
87	#15667997	C₂²	1	1	yes	characteristic
88	#15667997	C₂²	1	1	yes	characteristic
89	#15667997	C₂²	1	1	yes	characteristic
90	#15667996	C₂²	1	1	yes	characteristic
91	#15667996	C₂²	1	1	yes	characteristic
92	#15667995	C₂²	1	1	yes	characteristic
93	#15667994	C₂²	1	1	yes	characteristic
94	#15667994	C₂²	1	1	yes	characteristic
95	#15667994	C₂²	1	1	yes	characteristic
96	#15667994	C₂²	1	1	yes	characteristic
97	#15667994	C₂²	1	1	yes	characteristic
98	#15667993	C₂²	1	1	yes	characteristic
99	#15667992	C₂²	1	1	yes	characteristic
100	#15667992	C₂²	1	1	yes	characteristic
101	#15667992	C₂²	1	1	yes	characteristic
102	#15667991	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
110	#15667990	C₂²	1	1	yes	characteristic
111	#15667990	C₂²	1	1	yes	characteristic
112	#15667990	C₂²	1	1	yes	characteristic
113	#15667990	C₂²	1	1	yes	characteristic
114	#15667990	C₂²	1	1	yes	characteristic
115	#15667989	C₂²	1	1	yes	characteristic
116	#15667989	C₂²	1	1	yes	characteristic
117	#15667989	C₂²	1	1	yes	characteristic
118	#15667989	C₂²	1	1	yes	characteristic
119	#15667989	C₂²	1	1	yes	characteristic
120	#15667989	C₂²	1	1	yes	characteristic
121	#15667989	C₂²	1	1	yes	characteristic
122	#15667989	C₂²	1	1	yes	characteristic
123	#15667988	C₂²	1	1	yes	characteristic
124	#15667988	C₂²	1	1	yes	characteristic
125	#15667988	C₂²	1	1	yes	characteristic
126	#15667988	C₂²	1	1	yes	characteristic
127	#15667987	C₂²	1	1	yes	characteristic
128	#15667985	C₂²	1	1	yes	characteristic
129	#15667985	C₂²	1	1	yes	characteristic
130	#15667985	C₂²	1	1	yes	characteristic
131	#15667985	C₂²	1	1	yes	characteristic
132	#15667985	C₂²	1	1	yes	characteristic
133	#15667984	C₂²	1	1	yes	characteristic
134	#15667983	C₂²	1	1	yes	characteristic
135	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
136	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
137	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
138	#15667977	C₂²	1	1	yes	characteristic
139	#15667977	C₂²	1	1	yes	characteristic
140	#15667977	C₂²	1	1	yes	characteristic
141	#15667977	C₂²	1	1	yes	characteristic
142	#15667977	C₂²	1	1	yes	characteristic
143	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
144	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
145	#15667974	C₂²	1	1	yes	characteristic
146	#15667974	C₂²	1	1	yes	characteristic
147	#15667974	C₂²	1	1	yes	characteristic
148	#15667974	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
152	#15667972	C₂²	1	1	yes	characteristic
153	#15667972	C₂²	1	1	yes	characteristic
154	#15667972	C₂²	1	1	yes	characteristic
155	#15667972	C₂²	1	1	yes	characteristic
156	#15667972	C₂²	1	1	yes	characteristic
157	#15667972	C₂²	1	1	yes	characteristic
158	#15667972	C₂²	1	1	yes	characteristic
159	#15667970	C₂²	1	1	yes	characteristic
160	#15667970	C₂²	1	1	yes	characteristic
161	#15667969	C₂²	1	1	yes	characteristic
162	#15667968	C₂²	1	1	yes	characteristic
163	#15667968	C₂²	1	1	yes	characteristic
164	#15667968	C₂²	1	1	yes	characteristic
165	C₂×#13083553	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
169	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
170	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
171	C₄²×D₈₉	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
173	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
174	#126×C₈₉	C₂²	1	1	yes	characteristic
175	#126×C₈₉	C₂²	1	1	yes	characteristic
176	#126×C₈₉	C₂²	1	1	yes	characteristic
177	#126×C₈₉	C₂²	1	1	yes	characteristic
178	#125×C₈₉	C₂²	1	1	yes	characteristic
179	#125×C₈₉	C₂²	1	1	yes	characteristic
180	#124×C₈₉	C₂²	1	1	yes	characteristic
181	#123×C₈₉	C₂²	1	1	yes	characteristic
182	#123×C₈₉	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
184	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
185	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
186	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
187	#13083574	—	4	2	no	—
188	#13083573	—	4	2	no	—
189	C₂×Dic₁₇₈	—	4	2	no	—
190	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
191	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
192	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
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	Q₈×D₈₉	—	4	2	no	—
202	Q₈×D₈₉	—	4	2	no	—
203	Q₈×D₈₉	—	4	2	no	—
204	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
205	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
206	C₂×D₃₅₆	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	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
214	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
215	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
216	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
231	C₄⋊Dic₈₉	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	#13083553	C₂³	1	1	yes	characteristic
243	#13083553	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	#13083553	C₂³	1	1	yes	characteristic
271	#13083553	C₂³	1	1	yes	characteristic
272	#13083553	C₂³	1	1	yes	characteristic
273	#13083553	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	#13083551	C₂³	1	1	yes	characteristic
281	#13083551	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	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
301	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
302	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
303	C₄×Dic₈₉	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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
315	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
317	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
319	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
321	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
322	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
323	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
324	C₄⋊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	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
351	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
352	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
353	Q₈×C₈₉	—	4	1	no	—
354	Q₈×C₈₉	—	4	1	no	—
355	Q₈×C₈₉	—	4	1	no	—
356	D₄×C₈₉	—	4	1	no	—
357	C₂×C₄×C₈₉	—	4	1	no	—
358	C₂×C₄×C₈₉	—	4	1	no	—
359	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
364	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
372	C₂²⋊D₈₉	—	2	2	no	—
373	C₂²⋊D₈₉	—	2	2	no	—
374	C₂²⋊D₈₉	—	2	2	no	—
375	C₂²⋊D₈₉	—	2	2	no	—
376	C₂²⋊D₈₉	—	4	1	no	—
377	C₂²⋊D₈₉	—	4	1	no	—
378	C₂×Dic₈₉	—	2	2	no	—
379	C₂×Dic₈₉	—	2	2	no	—
380	C₂×Dic₈₉	—	4	1	no	—
381	C₂×Dic₈₉	—	4	1	no	—
382	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
395	D₃₅₆	—	2	2	no	—
396	D₃₅₆	—	2	2	no	—
397	D₃₅₆	—	4	1	no	—
398	C₄×D₈₉	—	2	2	no	—
399	C₄×D₈₉	—	2	2	no	—
400	C₄×D₈₉	—	2	2	no	—
401	C₄×D₈₉	—	2	2	no	—
402	C₄×D₈₉	—	2	2	no	—
403	C₄×D₈₉	—	4	1	no	—
404	C₄×D₈₉	—	4	1	no	—
405	C₄×D₈₉	—	4	1	no	—
406	C₄×D₈₉	—	4	1	no	—
407	C₄×D₈₉	—	4	1	no	—
408	C₄×D₈₉	—	4	1	no	—
409	C₄×D₈₉	—	4	1	no	—
410	C₄×D₈₉	—	4	1	no	—
411	Dic₁₇₈	—	2	2	no	—
412	Dic₁₇₈	—	2	2	no	—
413	Dic₁₇₈	—	2	2	no	—
414	Dic₁₇₈	—	2	2	no	—
415	Dic₁₇₈	—	2	2	no	—
416	Dic₁₇₈	—	2	2	no	—
417	Dic₁₇₈	—	4	1	no	—
418	Dic₁₇₈	—	4	1	no	—
419	Dic₁₇₈	—	4	1	no	—
420	Dic₁₇₈	—	4	1	no	—
421	Dic₁₇₈	—	4	1	no	—
422	C₂²×C₈₉	—	2	1	no	—
423	C₂²×C₈₉	—	2	1	no	—
424	C₂²×C₈₉	—	2	1	no	—
425	C₂²×C₈₉	—	2	1	no	—
426	C₂²×C₈₉	—	2	1	no	—
427	C₂²×C₈₉	—	2	1	no	—
428	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
429	C₂×D₈₉	—	2	1	no	—
430	C₂×D₈₉	—	2	1	no	—
431	C₂×D₈₉	—	2	1	no	—
432	C₂×D₈₉	—	2	1	no	—
433	C₂×D₈₉	—	2	1	no	—
434	C₂×D₈₉	—	2	1	no	—
435	C₂×D₈₉	—	2	1	no	—
436	C₂×D₈₉	—	2	1	no	—
437	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	—
438	C₄×C₈₉	—	2	1	no	—
439	C₄×C₈₉	—	2	1	no	—
440	C₄×C₈₉	—	2	1	no	—
441	C₄×C₈₉	—	2	1	no	—
442	C₄×C₈₉	—	2	1	no	—
443	C₄×C₈₉	—	2	1	no	—
444	C₄×C₈₉	—	2	1	no	—
445	C₄×C₈₉	—	2	1	no	—
446	C₄×C₈₉	—	2	1	no	—
447	C₄×C₈₉	—	2	1	no	—
448	C₄×C₈₉	—	2	1	no	—
449	C₄×C₈₉	—	2	1	no	—
450	C₄×C₈₉	—	2	1	no	—
451	Dic₈₉	—	2	1	no	—
452	Dic₈₉	—	2	1	no	—
453	Dic₈₉	—	2	1	no	—
454	Dic₈₉	—	2	1	no	—
455	Dic₈₉	—	2	1	no	—
456	Dic₈₉	—	2	1	no	—
457	Dic₈₉	—	2	1	no	—
458	Dic₈₉	—	2	1	no	—
459	Dic₈₉	—	2	1	no	—
460	Dic₈₉	—	2	1	no	—
461	Dic₈₉	—	2	1	no	—
462	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
463	Dic₈₉	2₋¹⁺⁴	1	2	yes	—
464	C₂×C₈₉	—	4	1	no	—
465	C₂×C₈₉	—	4	1	no	—
466	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
469	D₈₉	—	2	2	no	—
470	D₈₉	—	4	1	no	—
471	D₈₉	—	4	1	no	—
472	#3552	—	89	1	no	maximal, Sylow
473	C₈₉	#3552	1	1	yes	characteristic, complemented, Sylow
474	#563	—	89	1	no	—
475	#563	—	89	1	no	—
476	#563	—	89	1	no	—
477	#563	D₈₉	1	1	yes	characteristic, complemented
478	#557	—	89	1	no	—
479	#556	—	89	1	no	—
480	#554	—	89	1	no	—
481	#554	—	89	1	no	—
482	#553	—	89	1	no	—
483	#553	—	89	1	no	—
484	D₄×Q₈	—	89	1	no	—
485	D₄×Q₈	—	89	1	no	—
486	D₄×Q₈	—	89	1	no	—
487	#548	—	89	1	no	—
488	#548	—	89	1	no	—
489	#547	—	89	1	no	—
490	#544	—	89	1	no	—
491	#544	—	89	1	no	—
492	#542	—	89	1	no	—
493	#542	—	89	1	no	—
494	#541	—	89	1	no	—
495	#541	—	89	1	no	—
496	#539	—	89	1	no	—
497	#539	—	89	1	no	—
498	#539	—	89	1	no	—
499	#539	—	89	1	no	—
500	#536	—	89	1	no	—
501	#536	—	89	1	no	—
502	C₂×C₄⋊Q₈	—	89	1	no	—
503	#529	—	89	1	no	—
504	#529	—	89	1	no	—
505	C₂×#41	—	89	1	no	—
506	C₂×#41	—	89	1	no	—
507	C₂²×Q₈	—	89	1	no	—
508	C₂²×Q₈	—	89	1	no	—
509	C₂²×Q₈	—	89	1	no	—
510	C₂²×Q₈	—	89	1	no	—
511	C₄⋊Q₈	—	89	1	no	—
512	C₄⋊Q₈	—	89	1	no	—
513	C₄⋊Q₈	—	89	1	no	—
514	C₄⋊Q₈	—	89	1	no	—
515	C₄⋊Q₈	—	89	1	no	—
516	C₄⋊Q₈	—	89	1	no	—
517	C₄⋊Q₈	—	89	1	no	—
518	C₄⋊Q₈	—	89	1	no	—
519	C₄⋊Q₈	—	89	1	no	—
520	C₄⋊Q₈	—	89	1	no	—
521	C₄⋊Q₈	—	89	1	no	—
522	C₄⋊Q₈	—	89	1	no	—
523	C₄⋊Q₈	—	89	1	no	—
524	C₄⋊Q₈	—	89	1	no	—
525	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
526	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
527	#126	—	89	1	no	—
528	#126	—	89	1	no	—
529	#126	—	89	1	no	—
530	#126	—	89	1	no	—
531	#126	—	89	1	no	—
532	#126	—	89	1	no	—
533	#126	—	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	C₂×D₈₉	1	1	yes	characteristic
540	#126	C₂×D₈₉	1	1	yes	characteristic
541	#126	C₂×D₈₉	1	1	yes	characteristic
542	#126	C₂×D₈₉	1	1	yes	characteristic
543	#125	—	89	1	no	—
544	#125	—	89	1	no	—
545	#125	—	89	1	no	—
546	#125	—	89	1	no	—
547	#125	—	89	1	no	—
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	—	89	1	no	—
557	#125	C₂×D₈₉	1	1	yes	characteristic
558	#125	C₂×D₈₉	1	1	yes	characteristic
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	C₂×D₈₉	1	1	yes	characteristic
567	#123	—	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	C₂×D₈₉	1	1	yes	characteristic
582	#123	C₂×D₈₉	1	1	yes	characteristic
583	C₂²⋊Q₈	—	89	1	no	—
584	C₂²⋊Q₈	—	89	1	no	—
585	C₂²⋊Q₈	—	89	1	no	—
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	C₂×D₈₉	1	1	yes	characteristic
612	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
615	#121	—	89	1	no	—
616	#121	—	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	C₄×Q₈	—	89	1	no	—
624	C₄×Q₈	—	89	1	no	—
625	C₄×Q₈	—	89	1	no	—
626	C₄×Q₈	—	89	1	no	—
627	C₄×Q₈	—	89	1	no	—
628	C₄×Q₈	—	89	1	no	—
629	C₄×Q₈	—	89	1	no	—
630	C₄×Q₈	—	89	1	no	—
631	C₄×D₄	—	89	1	no	—
632	C₄×D₄	—	89	1	no	—
633	C₄×D₄	—	89	1	no	—
634	C₄×D₄	—	89	1	no	—
635	C₄×D₄	—	89	1	no	—
636	C₄×D₄	—	89	1	no	—
637	C₄×D₄	—	89	1	no	—
638	C₄×D₄	—	89	1	no	—
639	C₄×D₄	—	89	1	no	—
640	C₄×D₄	—	89	1	no	—
641	C₄×D₄	—	89	1	no	—
642	C₄×D₄	—	89	1	no	—
643	C₄×D₄	—	89	1	no	—
644	C₄×D₄	—	89	1	no	—
645	C₄×D₄	—	89	1	no	—
646	C₄×D₄	—	89	1	no	—
647	#117	—	89	1	no	—
648	#117	—	89	1	no	—
649	#117	—	89	1	no	—
650	#117	—	89	1	no	—
651	#117	—	89	1	no	—
652	#117	—	89	1	no	—
653	C₂×C₄⋊C₄	—	89	1	no	—
654	C₂×C₄⋊C₄	—	89	1	no	—
655	C₂×C₄⋊C₄	—	89	1	no	—
656	C₂×C₄⋊C₄	—	89	1	no	—
657	C₂×C₄⋊C₄	—	89	1	no	—
658	C₂×C₄⋊C₄	—	89	1	no	—
659	C₂×C₄²	—	89	1	no	—
660	#41	—	356	2	no	—
661	#41	—	356	2	no	—
662	C₂×Q₈	—	89	1	no	—
663	C₂×Q₈	—	89	1	no	—
664	C₂×Q₈	—	89	1	no	—
665	C₂×Q₈	—	89	1	no	—
666	C₂×Q₈	—	89	1	no	—
667	C₂×Q₈	—	89	1	no	—
668	C₂×Q₈	—	89	1	no	—
669	C₂×Q₈	—	89	1	no	—
670	C₂×Q₈	—	89	1	no	—
671	C₂×Q₈	—	89	1	no	—
672	C₂×Q₈	—	89	1	no	—
673	C₂×Q₈	—	356	2	no	—
674	C₂×Q₈	—	356	2	no	—
675	C₂×Q₈	—	356	2	no	—
676	C₂×Q₈	—	356	2	no	—
677	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
678	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
679	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
680	C₂×D₄	—	89	1	no	—
681	C₂×D₄	—	89	1	no	—
682	C₂×D₄	—	89	1	no	—
683	C₂×D₄	—	89	1	no	—
684	C₂×D₄	—	89	1	no	—
685	C₂×D₄	—	89	1	no	—
686	C₂×D₄	—	89	1	no	—
687	C₂×D₄	—	89	1	no	—
688	C₂×D₄	—	89	1	no	—
689	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
690	C₂²×C₄	—	89	1	no	—
691	C₂²×C₄	—	89	1	no	—
692	C₂²×C₄	—	89	1	no	—
693	C₂²×C₄	—	89	1	no	—
694	C₂²×C₄	—	89	1	no	—
695	C₂²×C₄	—	89	1	no	—
696	C₂²×C₄	—	89	1	no	—
697	C₂²×C₄	—	89	1	no	—
698	C₂²×C₄	—	89	1	no	—
699	C₂²×C₄	—	89	1	no	—
700	C₂²×C₄	—	89	1	no	—
701	C₂²×C₄	—	89	1	no	—
702	C₂²×C₄	—	89	1	no	—
703	C₂²×C₄	—	89	1	no	—
704	C₂²×C₄	—	89	1	no	—
705	C₂²×C₄	—	89	1	no	—
706	C₂²×C₄	—	89	1	no	—
707	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
708	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
709	C₄⋊C₄	—	89	1	no	—
710	C₄⋊C₄	—	89	1	no	—
711	C₄⋊C₄	—	89	1	no	—
712	C₄⋊C₄	—	89	1	no	—
713	C₄⋊C₄	—	89	1	no	—
714	C₄⋊C₄	—	89	1	no	—
715	C₄⋊C₄	—	89	1	no	—
716	C₄⋊C₄	—	89	1	no	—
717	C₄⋊C₄	—	89	1	no	—
718	C₄⋊C₄	—	89	1	no	—
719	C₄⋊C₄	—	89	1	no	—
720	C₄⋊C₄	—	89	1	no	—
721	C₄⋊C₄	—	89	1	no	—
722	C₄⋊C₄	—	89	1	no	—
723	C₄⋊C₄	—	89	1	no	—
724	C₄⋊C₄	—	89	1	no	—
725	C₄⋊C₄	—	89	1	no	—
726	C₄⋊C₄	—	89	1	no	—
727	C₄⋊C₄	—	89	1	no	—
728	C₄⋊C₄	—	89	1	no	—
729	C₄⋊C₄	—	89	1	no	—
730	C₄⋊C₄	—	89	1	no	—
731	C₄⋊C₄	—	89	1	no	—
732	C₄⋊C₄	—	89	1	no	—
733	C₄⋊C₄	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
765	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
769	C₂²⋊C₄	—	89	1	no	—
770	C₂²⋊C₄	—	89	1	no	—
771	C₂²⋊C₄	—	89	1	no	—
772	C₂²⋊C₄	—	89	1	no	—
773	C₂²⋊C₄	—	89	1	no	—
774	C₂²⋊C₄	—	89	1	no	—
775	C₂²⋊C₄	—	89	1	no	—
776	C₂²⋊C₄	—	89	1	no	—
777	C₂²⋊C₄	—	89	1	no	—
778	C₂²⋊C₄	—	89	1	no	—
779	C₂²⋊C₄	—	89	1	no	—
780	C₂²⋊C₄	—	89	1	no	—
781	C₂²⋊C₄	—	89	1	no	—
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	C₂²×D₈₉	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
805	C₄²	—	89	1	no	—
806	C₄²	—	89	1	no	—
807	C₄²	—	89	1	no	—
808	C₄²	—	89	1	no	—
809	C₄²	—	89	1	no	—
810	C₄²	—	89	1	no	—
811	C₄²	—	89	1	no	—
812	C₄²	—	89	1	no	—
813	C₄²	—	89	1	no	—
814	C₄²	—	89	1	no	—
815	C₄²	—	89	1	no	—
816	C₄²	—	89	1	no	—
817	C₄²	—	89	1	no	—
818	C₄²	C₂²×D₈₉	1	1	yes	characteristic
819	C₄²	C₂²×D₈₉	1	1	yes	characteristic
820	C₄²	C₂²×D₈₉	1	1	yes	characteristic
821	C₂³	—	89	1	no	—
822	C₂³	—	89	1	no	—
823	C₂³	—	89	1	no	—
824	C₂³	C₂³×D₈₉	1	1	yes	characteristic
825	C₂³	C₂³×D₈₉	1	1	yes	characteristic
826	Q₈	—	4	1	no	—
827	Q₈	—	4	1	no	—
828	Q₈	—	4	1	no	—
829	Q₈	—	356	1	no	—
830	Q₈	—	356	1	no	—
831	Q₈	—	356	1	no	—
832	Q₈	—	356	1	no	—
833	Q₈	—	356	1	no	—
834	Q₈	—	178	2	no	—
835	Q₈	—	178	2	no	—
836	Q₈	—	178	2	no	—
837	Q₈	—	178	2	no	—
838	Q₈	—	178	2	no	—
839	Q₈	—	178	2	no	—
840	D₄	—	4	1	no	—
841	D₄	—	356	1	no	—
842	D₄	—	356	1	no	—
843	D₄	—	356	1	no	—
844	D₄	—	178	2	no	—
845	D₄	—	178	2	no	—
846	D₄	—	178	2	no	—
847	D₄	—	178	2	no	—
848	D₄	—	178	2	no	—
849	D₄	—	178	2	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	89	1	no	—
853	C₂×C₄	—	89	1	no	—
854	C₂×C₄	—	89	1	no	—
855	C₂×C₄	—	89	1	no	—
856	C₂×C₄	—	89	1	no	—
857	C₂×C₄	—	89	1	no	—
858	C₂×C₄	—	89	1	no	—
859	C₂×C₄	—	89	1	no	—
860	C₂×C₄	—	89	1	no	—
861	C₂×C₄	—	89	1	no	—
862	C₂×C₄	—	89	1	no	—
863	C₂×C₄	—	89	1	no	—
864	C₂×C₄	—	89	1	no	—
865	C₂×C₄	—	356	1	no	—
866	C₂×C₄	—	356	1	no	—
867	C₂×C₄	—	356	1	no	—
868	C₂×C₄	—	356	1	no	—
869	C₂×C₄	—	356	1	no	—
870	C₂×C₄	—	356	1	no	—
871	C₂×C₄	—	356	1	no	—
872	C₂×C₄	—	356	1	no	—
873	C₂×C₄	—	356	1	no	—
874	C₂×C₄	—	356	1	no	—
875	C₂×C₄	—	178	2	no	—
876	C₂×C₄	—	178	2	no	—
877	C₂×C₄	—	178	2	no	—
878	C₂×C₄	—	178	2	no	—
879	C₂×C₄	—	178	2	no	—
880	C₂×C₄	—	178	2	no	—
881	C₂×C₄	—	178	2	no	—
882	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	89	2	no	—
902	C₂²	—	178	1	no	—
903	C₂²	—	178	1	no	—
904	C₂²	—	178	1	no	—
905	C₂²	—	178	1	no	—
906	C₂²	—	178	1	no	—
907	C₂²	—	178	1	no	—
908	C₂²	—	178	1	no	—
909	C₂²	—	178	1	no	—
910	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	89	2	no	—
925	C₄	—	89	2	no	—
926	C₄	—	178	1	no	—
927	C₄	—	178	1	no	—
928	C₄	—	178	1	no	—
929	C₄	—	178	1	no	—
930	C₄	—	178	1	no	—
931	C₄	—	178	1	no	—
932	C₄	—	178	1	no	—
933	C₄	—	178	1	no	—
934	C₄	—	178	1	no	—
935	C₄	—	178	1	no	—
936	C₄	—	178	1	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	1	no	—
939	C₂	—	356	1	no	—
940	C₂	—	356	1	no	—
941	C₂	—	178	2	no	—
942	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
943	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
944	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#563×C₈₉	C₂
hypercenter	#563	D₈₉
hypocenter	C₈₉	#3552
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #19152350	C₂	semidirect
2. #19152350	C₂	semidirect
3. #19152347	C₂	semidirect
4. #19152325	C₂	semidirect
5. #19152315	C₂	semidirect
6. #19152304	C₂	semidirect
7. #19152302	C₂	semidirect
8. #19152299	C₂	semidirect
9. #19152293	C₂	semidirect
10. #19152263	C₂	semidirect
11. #19152261	C₂	semidirect
12. #19152261	C₂	semidirect
13. #19152258	C₂	semidirect
14. #19152256	C₂	semidirect
15. #19152246	C₂	semidirect
16. #19152227	C₂	semidirect
17. #19152225	C₂	semidirect
18. #19152218	C₂	semidirect
19. #19152212	C₂	semidirect
20. #19152207	C₂	semidirect
21. #19152205	C₂	semidirect
22. #19152196	C₂	semidirect
23. #19152194	C₂	semidirect
24. #19152191	C₂	semidirect
25. #19152189	C₂	semidirect
26. #19152171	C₂	semidirect
27. #19152170	C₂	semidirect
28. C₄⋊Q₈×D₈₉	C₂	semidirect
29. #19152131	C₂	semidirect
30. #19152131	C₂	semidirect
31. #563×C₈₉	C₂	semidirect
473. C₈₉	#3552	semidirect
477. #563	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152350	2
#19152347	2
#19152325	2
#19152315	2
#19152304	2
#19152302	2
#19152299	2
#19152293	2
#19152263	2
#19152261	2
#19152258	2
#19152256	2
#19152246	2
#19152227	2
#19152225	2
#19152218	2
#19152212	2
#19152207	2
#19152205	2
#19152196	2
#19152194	2
#19152191	2
#19152189	2
#19152171	2
#19152170	2
C₄⋊Q₈×D₈₉	2
#19152131	2
#563×C₈₉	2
#3552	89