Subgroups — #26034422

Order 11392.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152347	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152345	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152344	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152336	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152332	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152297	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152296	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152285	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152283	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152277	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152275	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152271	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152247	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152237	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152222	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152218	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152200	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152198	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152197	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152195	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152185	C₂	1	1	yes	maximal, characteristic, complemented
23	#19152184	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	#19152162	C₂	1	1	yes	maximal, characteristic, complemented
27	#19152159	C₂	1	1	yes	maximal, characteristic, complemented
28	#19152106	C₂	1	1	yes	maximal, characteristic, complemented
29	#19152105	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#15667997	C₂	1	1	yes	maximal, characteristic, complemented
31	#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13083573	C₂²	1	1	yes	characteristic
33	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
34	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
36	#15668010	C₂²	1	1	yes	characteristic, complemented
37	#15668008	C₂²	1	1	yes	characteristic
38	#15668008	C₂²	1	1	yes	characteristic, complemented
39	#15668007	C₂²	1	1	yes	characteristic, complemented
40	#15668007	C₂²	1	1	yes	characteristic, complemented
41	#15668007	C₂²	1	1	yes	characteristic, complemented
42	#15668007	C₂²	1	1	yes	characteristic, complemented
43	#15668007	C₂²	1	1	yes	characteristic, complemented
44	#15668007	C₂²	1	1	yes	characteristic, complemented
45	#15668007	C₂²	1	1	yes	characteristic, complemented
46	#15668007	C₂²	1	1	yes	characteristic, complemented
47	#15668006	C₂²	1	1	yes	characteristic, complemented
48	#15668006	C₂²	1	1	yes	characteristic, complemented
49	#15668005	C₂²	1	1	yes	characteristic, complemented
50	#15668005	C₂²	1	1	yes	characteristic, complemented
51	#15668003	C₂²	1	1	yes	characteristic, complemented
52	#15668003	C₂²	1	1	yes	characteristic, complemented
53	#15668002	C₂²	1	1	yes	characteristic, complemented
54	#15668002	C₂²	1	1	yes	characteristic, complemented
55	#15668002	C₂²	1	1	yes	characteristic, complemented
56	#15668002	C₂²	1	1	yes	characteristic, complemented
57	#15668001	C₂²	1	1	yes	characteristic
58	#15668001	C₂²	1	1	yes	characteristic, complemented
59	#15668001	C₂²	1	1	yes	characteristic, complemented
60	#15668000	C₂²	1	1	yes	characteristic, complemented
61	#15667998	C₂²	1	1	yes	characteristic, complemented
62	#15667998	C₂²	1	1	yes	characteristic, complemented
63	#15667998	C₂²	1	1	yes	characteristic, complemented
64	#15667998	C₂²	1	1	yes	characteristic, complemented
65	#15667998	C₂²	1	1	yes	characteristic, complemented
66	#15667998	C₂²	1	1	yes	characteristic, complemented
67	#15667997	C₂²	1	1	yes	characteristic
68	#15667997	C₂²	1	1	yes	characteristic
69	#15667997	C₂²	1	1	yes	characteristic
70	#15667997	C₂²	1	1	yes	characteristic
71	#15667997	C₂²	1	1	yes	characteristic
72	#15667997	C₂²	1	1	yes	characteristic
73	#15667997	C₂²	1	1	yes	characteristic, complemented
74	#15667997	C₂²	1	1	yes	characteristic, complemented
75	#15667997	C₂²	1	1	yes	characteristic, complemented
76	#15667997	C₂²	1	1	yes	characteristic, complemented
77	#15667997	C₂²	1	1	yes	characteristic, complemented
78	#15667997	C₂²	1	1	yes	characteristic, complemented
79	#15667996	C₂²	1	1	yes	characteristic, complemented
80	#15667996	C₂²	1	1	yes	characteristic, complemented
81	#15667996	C₂²	1	1	yes	characteristic, complemented
82	#15667995	C₂²	1	1	yes	characteristic
83	#15667995	C₂²	1	1	yes	characteristic
84	#15667995	C₂²	1	1	yes	characteristic, complemented
85	#15667995	C₂²	1	1	yes	characteristic, complemented
86	#15667995	C₂²	1	1	yes	characteristic, complemented
87	#15667995	C₂²	1	1	yes	characteristic, complemented
88	#15667994	C₂²	1	1	yes	characteristic, complemented
89	#15667994	C₂²	1	1	yes	characteristic, complemented
90	#15667993	C₂²	1	1	yes	characteristic
91	#15667993	C₂²	1	1	yes	characteristic, complemented
92	#15667993	C₂²	1	1	yes	characteristic, complemented
93	#15667992	C₂²	1	1	yes	characteristic, complemented
94	#15667992	C₂²	1	1	yes	characteristic, complemented
95	#15667991	C₂²	1	1	yes	characteristic, complemented
96	#15667991	C₂²	1	1	yes	characteristic, complemented
97	#15667990	C₂²	1	1	yes	characteristic, complemented
98	#15667990	C₂²	1	1	yes	characteristic, complemented
99	#15667990	C₂²	1	1	yes	characteristic, complemented
100	#15667990	C₂²	1	1	yes	characteristic, complemented
101	#15667989	C₂²	1	1	yes	characteristic, complemented
102	#15667989	C₂²	1	1	yes	characteristic, complemented
103	#15667988	C₂²	1	1	yes	characteristic, complemented
104	#15667988	C₂²	1	1	yes	characteristic, complemented
105	#15667988	C₂²	1	1	yes	characteristic, complemented
106	#15667988	C₂²	1	1	yes	characteristic, complemented
107	#15667987	C₂²	1	1	yes	characteristic
108	#15667987	C₂²	1	1	yes	characteristic
109	#15667986	C₂²	1	1	yes	characteristic
110	#15667986	C₂²	1	1	yes	characteristic
111	#15667986	C₂²	1	1	yes	characteristic, complemented
112	#15667986	C₂²	1	1	yes	characteristic, complemented
113	#15667986	C₂²	1	1	yes	characteristic, complemented
114	#15667986	C₂²	1	1	yes	characteristic, complemented
115	#15667985	C₂²	1	1	yes	characteristic
116	#15667985	C₂²	1	1	yes	characteristic
117	#15667985	C₂²	1	1	yes	characteristic, complemented
118	#15667985	C₂²	1	1	yes	characteristic, complemented
119	#15667985	C₂²	1	1	yes	characteristic, complemented
120	#15667985	C₂²	1	1	yes	characteristic, complemented
121	#15667984	C₂²	1	1	yes	characteristic
122	#15667984	C₂²	1	1	yes	characteristic, complemented
123	#15667984	C₂²	1	1	yes	characteristic, complemented
124	#15667984	C₂²	1	1	yes	characteristic, complemented
125	#15667984	C₂²	1	1	yes	characteristic, complemented
126	#15667984	C₂²	1	1	yes	characteristic, complemented
127	#15667983	C₂²	1	1	yes	characteristic, complemented
128	#15667983	C₂²	1	1	yes	characteristic, complemented
129	#15667982	C₂²	1	1	yes	characteristic
130	#15667982	C₂²	1	1	yes	characteristic
131	#15667982	C₂²	1	1	yes	characteristic
132	#15667980	C₂²	1	1	yes	characteristic
133	#15667980	C₂²	1	1	yes	characteristic
134	#15667980	C₂²	1	1	yes	characteristic
135	#15667980	C₂²	1	1	yes	characteristic, complemented
136	#15667980	C₂²	1	1	yes	characteristic, complemented
137	#15667980	C₂²	1	1	yes	characteristic, complemented
138	#15667980	C₂²	1	1	yes	characteristic, complemented
139	#15667977	C₂²	1	1	yes	characteristic, complemented
140	#15667977	C₂²	1	1	yes	characteristic, complemented
141	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
142	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
143	#15667974	C₂²	1	1	yes	characteristic, complemented
144	#15667974	C₂²	1	1	yes	characteristic, complemented
145	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
147	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
153	#15667972	C₂²	1	1	yes	characteristic, complemented
154	#15667972	C₂²	1	1	yes	characteristic, complemented
155	#15667972	C₂²	1	1	yes	characteristic, complemented
156	#15667972	C₂²	1	1	yes	characteristic, complemented
157	#15667971	C₂²	1	1	yes	characteristic, complemented
158	#15667971	C₂²	1	1	yes	characteristic, complemented
159	#15667970	C₂²	1	1	yes	characteristic, complemented
160	#15667970	C₂²	1	1	yes	characteristic, complemented
161	#15667969	C₂²	1	1	yes	characteristic, complemented
162	#15667968	C₂²	1	1	yes	characteristic, complemented
163	#15667968	C₂²	1	1	yes	characteristic, complemented
164	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
165	C₂×#13083553	C₂²	1	1	yes	characteristic, complemented
166	C₂×#13083551	C₂²	1	1	yes	characteristic
167	C₂×#13083551	C₂²	1	1	yes	characteristic
168	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
169	C₂×#13083551	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
171	C₂²⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
172	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
173	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
174	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
175	#123×C₈₉	C₂²	1	1	yes	characteristic
176	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
177	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
178	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
181	#121×C₈₉	C₂²	1	1	yes	characteristic
182	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₈₉	C₂³	1	1	yes	characteristic
188	C₂³×D₈₉	C₂³	1	1	yes	characteristic
189	C₂³×D₈₉	C₂³	1	1	yes	characteristic
190	#13083573	—	4	2	no	—
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×D₃₅₆	—	4	2	no	—
195	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
196	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
197	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
198	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
199	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
200	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
201	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₈₉	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	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
216	D₄×D₈₉	—	4	2	no	—
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	C₂×C₄×D₈₉	—	4	2	no	—
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	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	#13083553	C₂³	1	1	yes	characteristic
241	#13083553	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	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
270	#13083551	C₂³	1	1	yes	characteristic
271	#13083551	C₂³	1	1	yes	characteristic
272	#13083551	C₂³	1	1	yes	characteristic
273	#13083551	C₂³	1	1	yes	characteristic
274	#13083551	C₂³	1	1	yes	characteristic
275	#13083551	C₂³	1	1	yes	characteristic
276	#13083551	C₂³	1	1	yes	characteristic
277	#13083551	C₂³	1	1	yes	characteristic
278	#13083551	C₂³	1	1	yes	characteristic
279	#13083551	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	#13083551	C₂³	1	1	yes	characteristic
301	#13083551	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	#41×C₈₉	—	4	2	no	—
312	#41×C₈₉	—	4	2	no	—
313	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
314	C₂×Q₈×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	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
320	C₂×D₄×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	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
326	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
327	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
328	C₂²×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	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
338	C₄⋊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	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×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	—	2	2	no	—
354	C₂²×D₈₉	—	4	1	no	—
355	C₂²×D₈₉	—	4	1	no	—
356	C₂²×D₈₉	—	4	1	no	—
357	C₂²×D₈₉	—	4	1	no	—
358	C₂²×D₈₉	—	4	1	no	—
359	C₂²×D₈₉	—	4	1	no	—
360	C₂²×D₈₉	—	4	1	no	—
361	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
362	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
363	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
364	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
365	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
366	Q₈×C₈₉	—	4	1	no	—
367	Q₈×C₈₉	—	4	1	no	—
368	D₄×C₈₉	—	2	2	no	—
369	D₄×C₈₉	—	2	2	no	—
370	D₄×C₈₉	—	2	2	no	—
371	D₄×C₈₉	—	4	1	no	—
372	D₄×C₈₉	—	4	1	no	—
373	D₄×C₈₉	—	4	1	no	—
374	C₂×C₄×C₈₉	—	2	2	no	—
375	C₂×C₄×C₈₉	—	2	2	no	—
376	C₂×C₄×C₈₉	—	4	1	no	—
377	C₂×C₄×C₈₉	—	4	1	no	—
378	C₂×C₄×C₈₉	—	4	1	no	—
379	C₂×C₄×C₈₉	—	4	1	no	—
380	C₂×C₄×C₈₉	—	4	1	no	—
381	C₂×C₄×C₈₉	—	4	1	no	—
382	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
393	C₂²⋊D₈₉	—	2	2	no	—
394	C₂²⋊D₈₉	—	4	1	no	—
395	C₂²⋊D₈₉	—	4	1	no	—
396	C₂²⋊D₈₉	—	4	1	no	—
397	C₂²⋊D₈₉	—	4	1	no	—
398	C₂²⋊D₈₉	—	4	1	no	—
399	C₂²⋊D₈₉	—	4	1	no	—
400	C₂²⋊D₈₉	—	4	1	no	—
401	C₂²⋊D₈₉	—	4	1	no	—
402	C₂²⋊D₈₉	—	4	1	no	—
403	C₂²⋊D₈₉	—	4	1	no	—
404	C₂²⋊D₈₉	—	4	1	no	—
405	C₂²⋊D₈₉	—	4	1	no	—
406	C₂²⋊D₈₉	—	4	1	no	—
407	C₂×Dic₈₉	—	2	2	no	—
408	C₂×Dic₈₉	—	4	1	no	—
409	C₂×Dic₈₉	—	4	1	no	—
410	C₂×Dic₈₉	—	4	1	no	—
411	C₂×Dic₈₉	—	4	1	no	—
412	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
421	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
423	D₃₅₆	—	4	1	no	—
424	D₃₅₆	—	4	1	no	—
425	D₃₅₆	—	4	1	no	—
426	D₃₅₆	—	4	1	no	—
427	D₃₅₆	—	4	1	no	—
428	D₃₅₆	—	4	1	no	—
429	D₃₅₆	—	4	1	no	—
430	C₄×D₈₉	—	4	1	no	—
431	C₄×D₈₉	—	4	1	no	—
432	C₄×D₈₉	—	4	1	no	—
433	C₄×D₈₉	—	4	1	no	—
434	C₄×D₈₉	—	4	1	no	—
435	C₄×D₈₉	—	4	1	no	—
436	C₄×D₈₉	—	4	1	no	—
437	C₄×D₈₉	—	4	1	no	—
438	C₄×D₈₉	—	4	1	no	—
439	Dic₁₇₈	—	4	1	no	—
440	Dic₁₇₈	—	4	1	no	—
441	Dic₁₇₈	—	4	1	no	—
442	C₂²×C₈₉	—	2	1	no	—
443	C₂²×C₈₉	—	2	1	no	—
444	C₂²×C₈₉	—	2	1	no	—
445	C₂²×C₈₉	—	2	1	no	—
446	C₂²×C₈₉	—	2	1	no	—
447	C₂²×C₈₉	—	2	1	no	—
448	C₂²×C₈₉	—	2	1	no	—
449	C₂²×C₈₉	—	2	1	no	—
450	C₂²×C₈₉	—	2	1	no	—
451	C₂²×C₈₉	—	2	1	no	—
452	C₂²×C₈₉	—	2	1	no	—
453	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
454	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
455	C₂×D₈₉	—	2	1	no	—
456	C₂×D₈₉	—	2	1	no	—
457	C₂×D₈₉	—	2	1	no	—
458	C₂×D₈₉	—	2	1	no	—
459	C₂×D₈₉	—	2	1	no	—
460	C₂×D₈₉	—	2	1	no	—
461	C₂×D₈₉	—	2	1	no	—
462	C₂×D₈₉	—	2	1	no	—
463	C₂×D₈₉	—	2	1	no	—
464	C₂×D₈₉	—	2	1	no	—
465	C₂×D₈₉	—	2	1	no	—
466	C₂×D₈₉	—	2	1	no	—
467	C₂×D₈₉	—	2	1	no	—
468	C₂×D₈₉	—	2	1	no	—
469	C₂×D₈₉	—	2	1	no	—
470	C₂×D₈₉	—	4	4	no	—
471	C₂×D₈₉	—	8	2	no	—
472	C₂×D₈₉	—	8	2	no	—
473	C₄×C₈₉	—	2	1	no	—
474	C₄×C₈₉	—	2	1	no	—
475	C₄×C₈₉	—	2	1	no	—
476	C₄×C₈₉	—	2	1	no	—
477	C₄×C₈₉	—	2	1	no	—
478	C₄×C₈₉	—	2	1	no	—
479	C₄×C₈₉	—	2	1	no	—
480	C₄×C₈₉	—	2	1	no	—
481	C₄×C₈₉	—	2	1	no	—
482	C₄×C₈₉	—	2	1	no	—
483	C₄×C₈₉	—	2	1	no	—
484	Dic₈₉	—	2	1	no	—
485	Dic₈₉	—	2	1	no	—
486	Dic₈₉	—	2	1	no	—
487	Dic₈₉	—	2	1	no	—
488	Dic₈₉	—	2	1	no	—
489	Dic₈₉	—	2	1	no	—
490	Dic₈₉	—	2	1	no	—
491	Dic₈₉	—	2	1	no	—
492	Dic₈₉	—	2	1	no	—
493	Dic₈₉	—	2	1	no	—
494	Dic₈₉	—	2	1	no	—
495	C₂×C₈₉	—	2	2	no	—
496	C₂×C₈₉	—	4	1	no	—
497	C₂×C₈₉	—	4	1	no	—
498	C₂×C₈₉	—	4	1	no	—
499	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×C₈₉	#585	1	1	yes	characteristic
501	C₂×C₈₉	#585	1	1	yes	characteristic
502	D₈₉	—	4	1	no	—
503	D₈₉	—	4	1	no	—
504	D₈₉	—	4	1	no	—
505	D₈₉	—	4	1	no	—
506	D₈₉	—	4	1	no	—
507	#3533	—	89	1	no	maximal, Sylow
508	C₈₉	#3533	1	1	yes	characteristic, complemented, Sylow
509	#563	—	89	1	no	—
510	#562	—	89	1	no	—
511	#562	—	89	1	no	—
512	#560	—	89	1	no	—
513	#559	—	89	1	no	—
514	#553	—	89	1	no	—
515	#553	—	89	1	no	—
516	#552	—	89	1	no	—
517	#552	—	89	1	no	—
518	#551	—	89	1	no	—
519	#551	—	89	1	no	—
520	#551	—	89	1	no	—
521	#547	—	89	1	no	—
522	#547	D₈₉	1	1	yes	characteristic, complemented
523	#546	—	89	1	no	—
524	#546	—	89	1	no	—
525	#542	—	89	1	no	—
526	#542	—	89	1	no	—
527	#540	—	89	1	no	—
528	#540	—	89	1	no	—
529	#539	—	89	1	no	—
530	#539	—	89	1	no	—
531	#538	—	89	1	no	—
532	#538	—	89	1	no	—
533	#538	—	89	1	no	—
534	#538	—	89	1	no	—
535	#535	—	89	1	no	—
536	#534	—	89	1	no	—
537	#525	—	89	1	no	—
538	#525	—	89	1	no	—
539	C₂×#123	—	89	1	no	—
540	C₂×#41	—	89	1	no	—
541	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
542	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
543	C₂²×D₄	—	89	1	no	—
544	C₂²×D₄	—	89	1	no	—
545	C₂³×C₄	—	89	1	no	—
546	C₄⋊Q₈	—	89	1	no	—
547	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
548	#127	—	89	1	no	—
549	#127	—	89	1	no	—
550	#126	—	89	1	no	—
551	#126	—	89	1	no	—
552	#126	—	89	1	no	—
553	#126	—	89	1	no	—
554	#126	—	89	1	no	—
555	#126	—	89	1	no	—
556	#126	—	89	1	no	—
557	#126	—	89	1	no	—
558	#126	—	89	1	no	—
559	#126	—	89	1	no	—
560	#126	—	89	1	no	—
561	#126	—	89	1	no	—
562	#125	—	89	1	no	—
563	#125	—	89	1	no	—
564	#125	—	89	1	no	—
565	#125	—	89	1	no	—
566	#125	—	89	1	no	—
567	#125	—	89	1	no	—
568	#124	—	89	1	no	—
569	#124	—	89	1	no	—
570	#124	—	89	1	no	—
571	#124	—	89	1	no	—
572	#124	—	89	1	no	—
573	#124	—	89	1	no	—
574	#124	—	89	1	no	—
575	#124	—	89	1	no	—
576	#124	—	89	1	no	—
577	#124	—	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	—	89	1	no	—
585	#123	—	89	1	no	—
586	#123	—	89	1	no	—
587	#123	—	89	1	no	—
588	#123	—	89	1	no	—
589	#123	—	89	1	no	—
590	#123	—	89	1	no	—
591	#123	—	89	1	no	—
592	#123	—	89	1	no	—
593	#123	—	89	1	no	—
594	#123	—	89	1	no	—
595	#123	—	89	1	no	—
596	#123	—	89	1	no	—
597	#123	—	89	1	no	—
598	#123	—	89	1	no	—
599	#123	—	89	1	no	—
600	#123	—	89	1	no	—
601	#123	—	89	1	no	—
602	#123	—	89	1	no	—
603	#123	—	89	1	no	—
604	#123	C₂×D₈₉	1	1	yes	characteristic
605	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
606	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
607	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
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	C₂²⋊Q₈	—	89	1	no	—
618	C₂²⋊Q₈	—	89	1	no	—
619	C₂²⋊Q₈	—	89	1	no	—
620	C₂²⋊Q₈	—	89	1	no	—
621	C₂²⋊Q₈	—	89	1	no	—
622	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
623	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
633	#121	—	89	1	no	—
634	#121	—	89	1	no	—
635	#121	—	89	1	no	—
636	#121	—	89	1	no	—
637	#121	—	89	1	no	—
638	#121	—	89	1	no	—
639	#121	—	89	1	no	—
640	#121	—	89	1	no	—
641	#121	—	89	1	no	—
642	#121	—	89	1	no	—
643	#121	—	89	1	no	—
644	#121	—	89	1	no	—
645	#121	—	89	1	no	—
646	#121	C₂×D₈₉	1	1	yes	characteristic
647	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
648	#120	—	89	1	no	—
649	#120	—	89	1	no	—
650	#120	—	89	1	no	—
651	#120	—	89	1	no	—
652	#120	—	89	1	no	—
653	#120	—	89	1	no	—
654	#120	—	89	1	no	—
655	#120	—	89	1	no	—
656	#120	—	89	1	no	—
657	#120	—	89	1	no	—
658	C₄×Q₈	—	89	1	no	—
659	C₄×Q₈	—	89	1	no	—
660	C₄×D₄	—	89	1	no	—
661	C₄×D₄	—	89	1	no	—
662	C₄×D₄	—	89	1	no	—
663	C₄×D₄	—	89	1	no	—
664	C₄×D₄	—	89	1	no	—
665	C₄×D₄	—	89	1	no	—
666	C₄×D₄	—	89	1	no	—
667	C₄×D₄	—	89	1	no	—
668	C₄×D₄	—	89	1	no	—
669	C₄×D₄	—	89	1	no	—
670	C₄×D₄	—	89	1	no	—
671	C₄×D₄	—	89	1	no	—
672	C₄×D₄	—	89	1	no	—
673	C₄×D₄	—	89	1	no	—
674	C₄×D₄	—	89	1	no	—
675	C₄×D₄	—	89	1	no	—
676	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
677	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
678	#117	—	89	1	no	—
679	#117	—	89	1	no	—
680	#117	—	89	1	no	—
681	#117	—	89	1	no	—
682	#117	—	89	1	no	—
683	#117	—	89	1	no	—
684	#117	—	89	1	no	—
685	C₂×C₄⋊C₄	—	89	1	no	—
686	C₂×C₄⋊C₄	—	89	1	no	—
687	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
688	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
689	C₂×C₂²⋊C₄	—	89	1	no	—
690	C₂×C₂²⋊C₄	—	89	1	no	—
691	C₂×C₂²⋊C₄	—	89	1	no	—
692	C₂×C₂²⋊C₄	—	89	1	no	—
693	C₂×C₂²⋊C₄	—	89	1	no	—
694	C₂×C₂²⋊C₄	—	89	1	no	—
695	C₂⁴	—	89	1	no	—
696	C₂⁴	—	89	1	no	—
697	C₂⁴	—	89	1	no	—
698	#41	—	4	2	no	—
699	#41	—	4	2	no	—
700	#41	—	356	2	no	—
701	C₂×Q₈	—	89	1	no	—
702	C₂×Q₈	—	89	1	no	—
703	C₂×Q₈	—	89	1	no	—
704	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
705	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
706	C₂×D₄	—	89	1	no	—
707	C₂×D₄	—	89	1	no	—
708	C₂×D₄	—	89	1	no	—
709	C₂×D₄	—	89	1	no	—
710	C₂×D₄	—	89	1	no	—
711	C₂×D₄	—	89	1	no	—
712	C₂×D₄	—	89	1	no	—
713	C₂×D₄	—	89	1	no	—
714	C₂×D₄	—	89	1	no	—
715	C₂×D₄	—	89	1	no	—
716	C₂×D₄	—	89	1	no	—
717	C₂×D₄	—	89	1	no	—
718	C₂×D₄	—	89	1	no	—
719	C₂×D₄	—	89	1	no	—
720	C₂×D₄	—	89	1	no	—
721	C₂×D₄	—	89	1	no	—
722	C₂×D₄	—	89	1	no	—
723	C₂×D₄	—	89	1	no	—
724	C₂×D₄	—	89	1	no	—
725	C₂×D₄	—	89	1	no	—
726	C₂×D₄	—	89	1	no	—
727	C₂×D₄	—	356	2	no	—
728	C₂×D₄	—	356	2	no	—
729	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
730	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
735	C₂²×C₄	—	89	1	no	—
736	C₂²×C₄	—	89	1	no	—
737	C₂²×C₄	—	89	1	no	—
738	C₂²×C₄	—	89	1	no	—
739	C₂²×C₄	—	89	1	no	—
740	C₂²×C₄	—	89	1	no	—
741	C₂²×C₄	—	89	1	no	—
742	C₂²×C₄	—	89	1	no	—
743	C₂²×C₄	—	89	1	no	—
744	C₂²×C₄	—	89	1	no	—
745	C₂²×C₄	—	89	1	no	—
746	C₂²×C₄	—	89	1	no	—
747	C₂²×C₄	—	89	1	no	—
748	C₂²×C₄	—	89	1	no	—
749	C₂²×C₄	—	356	2	no	—
750	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
751	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
752	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
773	C₄⋊C₄	—	89	1	no	—
774	C₄⋊C₄	—	89	1	no	—
775	C₄⋊C₄	—	89	1	no	—
776	C₄⋊C₄	—	89	1	no	—
777	C₄⋊C₄	—	89	1	no	—
778	C₄⋊C₄	—	89	1	no	—
779	C₄⋊C₄	—	89	1	no	—
780	C₄⋊C₄	—	89	1	no	—
781	C₄⋊C₄	—	89	1	no	—
782	C₄⋊C₄	—	89	1	no	—
783	C₄⋊C₄	—	89	1	no	—
784	C₄⋊C₄	—	89	1	no	—
785	C₄⋊C₄	—	89	1	no	—
786	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	1	no	—
817	C₂²⋊C₄	—	89	1	no	—
818	C₂²⋊C₄	—	89	1	no	—
819	C₂²⋊C₄	—	89	1	no	—
820	C₂²⋊C₄	—	89	1	no	—
821	C₂²⋊C₄	—	89	1	no	—
822	C₂²⋊C₄	—	89	1	no	—
823	C₂²⋊C₄	—	89	1	no	—
824	C₂²⋊C₄	—	89	1	no	—
825	C₂²⋊C₄	—	89	1	no	—
826	C₂²⋊C₄	—	89	1	no	—
827	C₂²⋊C₄	—	89	1	no	—
828	C₂²⋊C₄	—	89	1	no	—
829	C₂²⋊C₄	—	89	1	no	—
830	C₂²⋊C₄	—	89	1	no	—
831	C₂²⋊C₄	—	89	1	no	—
832	C₂²⋊C₄	—	89	1	no	—
833	C₂²⋊C₄	—	89	1	no	—
834	C₂²⋊C₄	—	89	1	no	—
835	C₂²⋊C₄	—	89	1	no	—
836	C₂²⋊C₄	—	89	1	no	—
837	C₂²⋊C₄	—	89	1	no	—
838	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
846	C₄²	—	89	1	no	—
847	C₄²	—	89	1	no	—
848	C₄²	—	89	1	no	—
849	C₄²	—	89	1	no	—
850	C₄²	—	89	1	no	—
851	C₄²	—	89	1	no	—
852	C₄²	—	89	1	no	—
853	C₄²	—	89	1	no	—
854	C₄²	—	89	1	no	—
855	C₄²	C₂²×D₈₉	1	1	yes	characteristic
856	C₂³	—	89	1	no	—
857	C₂³	—	89	1	no	—
858	C₂³	—	89	1	no	—
859	C₂³	—	89	1	no	—
860	C₂³	—	89	1	no	—
861	C₂³	—	356	1	no	—
862	C₂³	—	356	1	no	—
863	C₂³	—	356	1	no	—
864	C₂³	—	356	1	no	—
865	C₂³	—	356	1	no	—
866	C₂³	—	356	1	no	—
867	C₂³	—	356	1	no	—
868	C₂³	—	178	2	no	—
869	C₂³	—	178	2	no	—
870	C₂³	C₂³×D₈₉	1	1	yes	characteristic
871	C₂³	C₂³×D₈₉	1	1	yes	characteristic
872	C₂³	C₂³×D₈₉	1	1	yes	characteristic
873	C₂³	C₂³×D₈₉	1	1	yes	characteristic
874	Q₈	—	4	1	no	—
875	Q₈	—	4	1	no	—
876	Q₈	—	356	1	no	—
877	Q₈	—	356	1	no	—
878	Q₈	—	356	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	2	2	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	356	1	no	—
886	D₄	—	356	1	no	—
887	D₄	—	356	1	no	—
888	D₄	—	356	1	no	—
889	D₄	—	356	1	no	—
890	D₄	—	356	1	no	—
891	D₄	—	356	1	no	—
892	D₄	—	356	1	no	—
893	D₄	—	356	1	no	—
894	D₄	—	356	1	no	—
895	D₄	—	356	1	no	—
896	D₄	—	356	1	no	—
897	D₄	—	356	1	no	—
898	D₄	—	356	1	no	—
899	D₄	—	356	1	no	—
900	D₄	—	356	1	no	—
901	D₄	—	356	1	no	—
902	D₄	—	356	1	no	—
903	D₄	—	356	1	no	—
904	D₄	—	356	1	no	—
905	D₄	—	178	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	89	1	no	—
915	C₂×C₄	—	89	1	no	—
916	C₂×C₄	—	89	1	no	—
917	C₂×C₄	—	89	1	no	—
918	C₂×C₄	—	89	1	no	—
919	C₂×C₄	—	89	1	no	—
920	C₂×C₄	—	89	1	no	—
921	C₂×C₄	—	89	1	no	—
922	C₂×C₄	—	89	1	no	—
923	C₂×C₄	—	89	1	no	—
924	C₂×C₄	—	89	1	no	—
925	C₂×C₄	—	356	1	no	—
926	C₂×C₄	—	356	1	no	—
927	C₂×C₄	—	356	1	no	—
928	C₂×C₄	—	356	1	no	—
929	C₂×C₄	—	356	1	no	—
930	C₂×C₄	—	356	1	no	—
931	C₂×C₄	—	356	1	no	—
932	C₂×C₄	—	356	1	no	—
933	C₂×C₄	—	356	1	no	—
934	C₂×C₄	—	356	1	no	—
935	C₂×C₄	—	356	1	no	—
936	C₂×C₄	—	356	1	no	—
937	C₂×C₄	—	356	1	no	—
938	C₂×C₄	—	178	2	no	—
939	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	356	4	no	—
962	C₂²	—	178	1	no	—
963	C₂²	—	178	1	no	—
964	C₂²	—	178	1	no	—
965	C₂²	—	178	1	no	—
966	C₂²	—	178	1	no	—
967	C₂²	—	178	1	no	—
968	C₂²	—	178	1	no	—
969	C₂²	—	178	1	no	—
970	C₂²	—	178	1	no	—
971	C₂²	—	178	1	no	—
972	C₂²	—	178	1	no	—
973	C₂²	—	178	1	no	—
974	C₂²	—	178	1	no	—
975	C₂²	—	178	1	no	—
976	C₂²	—	178	1	no	—
977	C₂²	—	712	2	no	—
978	C₂²	—	712	2	no	—
979	C₂²	#15668057	1	2	yes	—
980	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	178	1	no	—
993	C₄	—	178	1	no	—
994	C₄	—	178	1	no	—
995	C₄	—	178	1	no	—
996	C₄	—	178	1	no	—
997	C₄	—	178	1	no	—
998	C₄	—	178	1	no	—
999	C₄	—	178	1	no	—
1000	C₄	—	178	1	no	—
1001	C₄	—	178	1	no	—
1002	C₄	—	178	1	no	—
1003	C₂	—	2	2	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	356	1	no	—
1008	C₂	—	356	1	no	—
1009	C₂	—	356	1	no	—
1010	C₂	—	356	1	no	—
1011	C₂	—	356	1	no	—
1012	C₂	C₂×#15668057	1	1	yes	characteristic
1013	C₂	#19152434	1	1	yes	characteristic
1014	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#547×C₈₉	C₂
hypercenter	#547	D₈₉
hypocenter	C₈₉	#3533
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #19152347	C₂	semidirect
2. #19152345	C₂	semidirect
3. #19152344	C₂	semidirect
4. #19152336	C₂	semidirect
5. #19152332	C₂	semidirect
6. #19152297	C₂	semidirect
7. #19152296	C₂	semidirect
8. #19152285	C₂	semidirect
9. #19152283	C₂	semidirect
10. #19152277	C₂	semidirect
11. #19152275	C₂	semidirect
12. #19152271	C₂	semidirect
13. #19152247	C₂	semidirect
14. #19152237	C₂	semidirect
15. #19152236	C₂	semidirect
16. #19152222	C₂	semidirect
17. #19152218	C₂	semidirect
18. #19152200	C₂	semidirect
19. #19152198	C₂	semidirect
20. #19152197	C₂	semidirect
21. #19152195	C₂	semidirect
22. #19152185	C₂	semidirect
23. #19152184	C₂	semidirect
24. #19152181	C₂	semidirect
25. #19152181	C₂	semidirect
26. #19152162	C₂	semidirect
27. #19152159	C₂	semidirect
28. #19152106	C₂	semidirect
29. #19152105	C₂	semidirect
30. C₂×#15667997	C₂	semidirect
31. #547×C₈₉	C₂	semidirect
35. C₂²×C₄×D₈₉	C₂²	semidirect
36. #15668010	C₂²	semidirect
38. #15668008	C₂²	semidirect
39. #15668007	C₂²	semidirect
40. #15668007	C₂²	semidirect
41. #15668007	C₂²	semidirect
42. #15668007	C₂²	semidirect
43. #15668007	C₂²	semidirect
44. #15668007	C₂²	semidirect
45. #15668007	C₂²	semidirect
46. #15668007	C₂²	semidirect
47. #15668006	C₂²	semidirect
48. #15668006	C₂²	semidirect
49. #15668005	C₂²	semidirect
50. #15668005	C₂²	semidirect
51. #15668003	C₂²	semidirect
52. #15668003	C₂²	semidirect
53. #15668002	C₂²	semidirect
54. #15668002	C₂²	semidirect
55. #15668002	C₂²	semidirect
56. #15668002	C₂²	semidirect
58. #15668001	C₂²	semidirect
59. #15668001	C₂²	semidirect
60. #15668000	C₂²	semidirect
61. #15667998	C₂²	semidirect
62. #15667998	C₂²	semidirect
63. #15667998	C₂²	semidirect
64. #15667998	C₂²	semidirect
65. #15667998	C₂²	semidirect
66. #15667998	C₂²	semidirect
73. #15667997	C₂²	semidirect
74. #15667997	C₂²	semidirect
75. #15667997	C₂²	semidirect
76. #15667997	C₂²	semidirect
77. #15667997	C₂²	semidirect
78. #15667997	C₂²	semidirect
79. #15667996	C₂²	semidirect
80. #15667996	C₂²	semidirect
81. #15667996	C₂²	semidirect
84. #15667995	C₂²	semidirect
85. #15667995	C₂²	semidirect
86. #15667995	C₂²	semidirect
87. #15667995	C₂²	semidirect
88. #15667994	C₂²	semidirect
89. #15667994	C₂²	semidirect
91. #15667993	C₂²	semidirect
92. #15667993	C₂²	semidirect
93. #15667992	C₂²	semidirect
94. #15667992	C₂²	semidirect
95. #15667991	C₂²	semidirect
96. #15667991	C₂²	semidirect
97. #15667990	C₂²	semidirect
98. #15667990	C₂²	semidirect
99. #15667990	C₂²	semidirect
100. #15667990	C₂²	semidirect
101. #15667989	C₂²	semidirect
102. #15667989	C₂²	semidirect
103. #15667988	C₂²	semidirect
104. #15667988	C₂²	semidirect
105. #15667988	C₂²	semidirect
106. #15667988	C₂²	semidirect
111. #15667986	C₂²	semidirect
112. #15667986	C₂²	semidirect
113. #15667986	C₂²	semidirect
114. #15667986	C₂²	semidirect
117. #15667985	C₂²	semidirect
118. #15667985	C₂²	semidirect
119. #15667985	C₂²	semidirect
120. #15667985	C₂²	semidirect
122. #15667984	C₂²	semidirect
123. #15667984	C₂²	semidirect
124. #15667984	C₂²	semidirect
125. #15667984	C₂²	semidirect
126. #15667984	C₂²	semidirect
127. #15667983	C₂²	semidirect
128. #15667983	C₂²	semidirect
135. #15667980	C₂²	semidirect
136. #15667980	C₂²	semidirect
137. #15667980	C₂²	semidirect
138. #15667980	C₂²	semidirect
139. #15667977	C₂²	semidirect
140. #15667977	C₂²	semidirect
142. D₄×Dic₈₉	C₂²	semidirect
143. #15667974	C₂²	semidirect
144. #15667974	C₂²	semidirect
146. C₄×C₂²⋊D₈₉	C₂²	semidirect
147. C₄×C₂²⋊D₈₉	C₂²	semidirect
148. C₄×C₂²⋊D₈₉	C₂²	semidirect
149. C₄×C₂²⋊D₈₉	C₂²	semidirect
150. C₄×C₂²⋊D₈₉	C₂²	semidirect
151. C₄×C₂²⋊D₈₉	C₂²	semidirect
152. C₄×C₂²⋊D₈₉	C₂²	semidirect
153. #15667972	C₂²	semidirect
154. #15667972	C₂²	semidirect
155. #15667972	C₂²	semidirect
156. #15667972	C₂²	semidirect
157. #15667971	C₂²	semidirect
158. #15667971	C₂²	semidirect
159. #15667970	C₂²	semidirect
160. #15667970	C₂²	semidirect
161. #15667969	C₂²	semidirect
162. #15667968	C₂²	semidirect
163. #15667968	C₂²	semidirect
164. C₂×#13083553	C₂²	semidirect
165. C₂×#13083553	C₂²	semidirect
168. C₂×#13083551	C₂²	semidirect
169. C₂×#13083551	C₂²	semidirect
171. C₂²⋊C₄×D₈₉	C₂²	semidirect
173. C₂×#41×C₈₉	C₂²	semidirect
174. C₄⋊Q₈×C₈₉	C₂²	semidirect
176. #123×C₈₉	C₂²	semidirect
177. #123×C₈₉	C₂²	semidirect
178. #123×C₈₉	C₂²	semidirect
179. C₂²⋊Q₈×C₈₉	C₂²	semidirect
180. C₂²⋊Q₈×C₈₉	C₂²	semidirect
182. #121×C₈₉	C₂²	semidirect
183. C₄×D₄×C₈₉	C₂²	semidirect
184. C₄×D₄×C₈₉	C₂²	semidirect
185. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
186. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
508. C₈₉	#3533	semidirect
522. #547	D₈₉	semidirect
542. C₂×#41	C₂×D₈₉	semidirect
547. C₄⋊Q₈	C₂×D₈₉	semidirect
605. #123	C₂×D₈₉	semidirect
606. #123	C₂×D₈₉	semidirect
607. #123	C₂×D₈₉	semidirect
622. C₂²⋊Q₈	C₂×D₈₉	semidirect
623. C₂²⋊Q₈	C₂×D₈₉	semidirect
647. #121	C₂×D₈₉	semidirect
676. C₄×D₄	C₂×D₈₉	semidirect
677. C₄×D₄	C₂×D₈₉	semidirect
687. C₂×C₄⋊C₄	C₂×D₈₉	semidirect
688. C₂×C₄⋊C₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152347	2
#19152345	2
#19152344	2
#19152336	2
#19152332	2
#19152297	2
#19152296	2
#19152285	2
#19152283	2
#19152277	2
#19152275	2
#19152271	2
#19152247	2
#19152237	2
#19152236	2
#19152222	2
#19152218	2
#19152200	2
#19152198	2
#19152197	2
#19152195	2
#19152185	2
#19152184	2
#19152181	2
#19152162	2
#19152159	2
#19152106	2
#19152105	2
C₂×#15667997	2
#547×C₈₉	2
#3533	89