Subgroups — #16776782

Order 3328.

10796 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129649	C₂	1	1	yes	maximal, characteristic, complemented
2	#13129647	C₂	1	1	yes	maximal, characteristic, complemented
3	#13129622	C₂	1	1	yes	maximal, characteristic, complemented
4	#13129621	C₂	1	8	yes	maximal, complemented
5	#13129620	C₂	1	6	yes	maximal, complemented
6	#13129615	C₂	1	1	yes	maximal, characteristic, complemented
7	#13129613	C₂	1	6	yes	maximal, complemented
8	#13129611	C₂	1	8	yes	maximal, complemented
9	#13129608	C₂	1	8	yes	maximal, complemented
10	#13129605	C₂	1	6	yes	maximal, complemented
11	C₂×#11719456	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719475	C₂	1	6	yes	maximal, complemented
13	D₁₃×#577	C₂	1	8	yes	maximal, complemented
14	#13129547	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#585	C₂²	1	1	yes	characteristic, complemented
17	C₁₃×#585	C₂²	1	1	yes	characteristic, complemented
18	#11719652	—	2	2	no	—
19	#11719652	C₂²	1	8	yes	complemented
20	D₁₃×2₋¹⁺⁴	—	2	2	no	—
21	D₁₃×2₋¹⁺⁴	C₂²	1	8	yes	complemented
22	#11719650	—	2	6	no	—
23	#11719650	C₂²	1	8	yes	complemented
24	D₁₃×H(5,𝔽₂)	—	2	6	no	—
25	D₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
26	#11719648	—	2	4	no	—
27	#11719648	—	2	4	no	—
28	#11719648	C₂²	1	1	yes	characteristic
29	#11719648	C₂²	1	6	yes	complemented
30	#11719648	C₂²	1	6	yes	complemented
31	C₂×#88257	—	2	4	no	—
32	C₂×#88257	C₂²	1	6	yes	complemented
33	C₂×#88257	C₂²	1	1	yes	characteristic, complemented
34	C₂×#88256	—	2	4	no	—
35	C₂×#88256	C₂²	1	6	yes	complemented
36	C₂×#88256	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#578	C₂²	1	4	yes	complemented
38	C₁₃×#577	C₂²	1	4	yes	complemented
39	C₁₃×#577	C₂²	1	4	yes	complemented
40	C₁₃×#576	C₂²	1	4	yes	complemented
41	C₁₃×#575	C₂²	1	6	yes	complemented
42	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
43	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
44	#11719543	C₂²	1	8	yes	complemented
45	#11719542	C₂²	1	8	yes	complemented
46	#11719541	C₂²	1	8	yes	complemented
47	#11719540	C₂²	1	8	yes	complemented
48	C₂×#88205	C₂²	1	6	yes	complemented
49	#11719527	C₂²	1	6	yes	complemented
50	#11719527	C₂²	1	6	yes	complemented
51	C₂×#88203	C₂²	1	6	yes	complemented
52	#11719524	C₂²	1	1	yes	characteristic, complemented
53	#11719484	C₂²	1	24	yes	complemented
54	#11719483	C₂²	1	24	yes	complemented
55	#11719482	C₂²	1	24	yes	complemented
56	D₁₃×#137	C₂²	1	24	yes	complemented
57	#11719480	C₂²	1	24	yes	complemented
58	#11719479	C₂²	1	24	yes	complemented
59	#11719478	C₂²	1	24	yes	complemented
60	D₁₃×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
61	#11719476	C₂²	1	12	yes	complemented
62	#11719475	C₂²	1	24	yes	complemented
63	#11719475	C₂²	1	12	yes	complemented
64	#11719475	C₂²	1	24	yes	complemented
65	#11719475	C₂²	1	24	yes	complemented
66	#11719475	C₂²	1	4	yes	complemented
67	#11719474	C₂²	1	12	yes	complemented
68	#11719473	C₂²	1	24	yes	complemented
69	D₁₃×#135	C₂²	1	24	yes	complemented
70	#11719471	C₂²	1	12	yes	complemented
71	C₂×#88172	C₂²	1	12	yes	complemented
72	#11719467	C₂²	1	12	yes	complemented
73	#11719467	C₂²	1	12	yes	complemented
74	C₂×#88170	C₂²	1	12	yes	complemented
75	C₂×SD₁₆×D₁₃	C₂²	1	12	yes	complemented
76	#11719462	C₂²	1	12	yes	complemented
77	C₂×#88165	C₂²	1	12	yes	complemented
78	#11719456	C₂²	1	8	yes	complemented
79	#11719456	C₂²	1	8	yes	complemented
80	#11719455	C₂²	1	8	yes	complemented
81	D₁₃×#131	C₂²	1	8	yes	complemented
82	C₂×#88163	C₂²	1	3	yes	complemented
83	C₂×#88162	C₂²	1	3	yes	complemented
84	#11719450	C₂²	1	6	yes	complemented
85	C₂×#88158	C₂²	1	3	yes	complemented
86	C₂²×#6095	C₂²	1	3	yes	complemented
87	C₂×#88155	C₂²	1	6	yes	complemented
88	C₁₃×2₋¹⁺⁴	—	2	1	no	—
89	C₁₃×2₋¹⁺⁴	—	2	1	no	—
90	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	—
91	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	complemented
92	C₁₃×H(5,𝔽₂)	—	2	3	no	—
93	C₁₃×H(5,𝔽₂)	—	2	3	no	—
94	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	—
95	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	complemented
96	C₂×C₁₃×#41	—	2	4	no	—
97	C₂×C₁₃×#41	—	2	4	no	—
98	C₂×C₁₃×#41	C₂³	1	6	yes	—
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×#41	C₂³	1	6	yes	complemented
101	#88257	—	2	4	no	—
102	#88257	—	2	8	no	—
103	#88257	—	2	24	no	—
104	#88257	—	2	12	no	—
105	#88257	—	2	12	no	—
106	#88257	—	2	6	no	—
107	#88257	—	2	6	no	—
108	#88257	D₄	1	4	yes	—
109	#88257	C₂³	1	4	yes	—
110	#88257	C₂³	1	12	yes	complemented
111	#88257	C₂³	1	24	yes	complemented
112	#88257	C₂³	1	8	yes	complemented
113	#88256	—	2	4	no	—
114	#88256	—	2	8	no	—
115	#88256	—	2	24	no	—
116	#88256	—	2	12	no	—
117	#88256	—	2	12	no	—
118	#88256	—	2	6	no	—
119	#88256	—	2	6	no	—
120	#88256	D₄	1	4	yes	—
121	#88256	C₂³	1	12	yes	—
122	#88256	C₂³	1	24	yes	—
123	#88256	C₂³	1	8	yes	—
124	#88256	C₂³	1	4	yes	complemented
125	#41×D₁₃	—	2	8	no	—
126	#41×D₁₃	—	2	8	no	—
127	#41×D₁₃	—	2	24	no	—
128	#41×D₁₃	—	2	24	no	—
129	#41×D₁₃	—	2	12	no	—
130	#41×D₁₃	—	2	12	no	—
131	#41×D₁₃	C₂³	1	24	yes	—
132	#41×D₁₃	C₂³	1	8	yes	—
133	#41×D₁₃	C₂³	1	24	yes	complemented
134	#88254	—	2	8	no	—
135	#88254	—	2	8	no	—
136	#88254	D₄	1	2	yes	—
137	#88254	C₂³	1	12	yes	—
138	#88254	C₂³	1	12	yes	complemented
139	C₂×#6131	—	2	1	no	—
140	C₂×#6131	—	2	8	no	—
141	C₂×#6131	C₂³	1	12	yes	—
142	C₂×Q₈×D₁₃	—	2	1	no	—
143	C₂×Q₈×D₁₃	—	2	8	no	—
144	C₂×Q₈×D₁₃	C₂³	1	12	yes	complemented
145	#88251	—	2	12	no	—
146	#88251	—	2	12	no	—
147	#88251	—	2	24	no	—
148	#88251	—	2	24	no	—
149	#88251	D₄	1	6	yes	—
150	#88251	C₂³	1	12	yes	—
151	#88251	C₂³	1	12	yes	complemented
152	C₂×#6129	—	2	3	no	—
153	C₂×#6129	—	2	12	no	—
154	C₂×#6129	—	2	24	no	—
155	C₂×#6129	C₂³	1	12	yes	complemented
156	C₂×D₄×D₁₃	—	2	3	no	—
157	C₂×D₄×D₁₃	—	2	12	no	—
158	C₂×D₄×D₁₃	—	2	24	no	—
159	C₂×D₄×D₁₃	C₂³	1	12	yes	—
160	C₂×#6127	—	2	12	no	—
161	C₂×#6127	—	2	12	no	—
162	C₂×#6127	—	2	6	no	—
163	C₂×#6127	—	2	6	no	—
164	C₂×#6127	C₂³	1	6	yes	—
165	C₂×#6127	C₂³	1	3	yes	—
166	C₂×#6127	C₂³	1	3	yes	complemented
167	C₂²×D₅₂	—	2	6	no	—
168	C₂²×D₅₂	C₂³	1	3	yes	—
169	C₂²×Dic₂₆	—	2	6	no	—
170	C₂²×Dic₂₆	C₂³	1	3	yes	complemented
171	C₁₃×#137	C₂³	1	12	yes	complemented
172	C₁₃×#137	C₂³	1	12	yes	complemented
173	C₁₃×AGL(1,ℤ/8)	C₂³	1	12	yes	complemented
174	C₁₃×AGL(1,ℤ/8)	C₂³	1	12	yes	complemented
175	C₁₃×#135	C₂³	1	12	yes	complemented
176	C₁₃×#135	C₂³	1	12	yes	complemented
177	C₁₃×#135	C₂³	1	12	yes	complemented
178	C₁₃×#135	C₂³	1	4	yes	complemented
179	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	complemented
180	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	complemented
181	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	complemented
182	C₂×C₁₃×D₈	C₂³	1	6	yes	complemented
183	C₁₃×#131	C₂³	1	4	yes	complemented
184	C₁₃×#131	C₂³	1	4	yes	complemented
185	C₂×C₁₃×M₁₆	C₂³	1	3	yes	complemented
186	C₂²×C₈×C₁₃	C₂³	1	3	yes	complemented
187	#88205	C₂³	1	12	yes	complemented
188	#88205	C₂³	1	24	yes	complemented
189	#88205	C₂³	1	4	yes	complemented
190	#88204	C₂³	1	24	yes	complemented
191	#88204	C₂³	1	24	yes	complemented
192	#88203	C₂³	1	4	yes	complemented
193	#88203	C₂³	1	12	yes	complemented
194	#88203	C₂³	1	24	yes	complemented
195	#88202	C₂³	1	8	yes	complemented
196	C₂×#6107	C₂³	1	12	yes	complemented
197	#88196	C₂³	1	12	yes	complemented
198	#88196	C₂³	1	12	yes	complemented
199	C₂×#6106	C₂³	1	12	yes	complemented
200	C₂×#6105	C₂³	1	12	yes	complemented
201	#88186	C₂³	1	12	yes	complemented
202	#88186	C₂³	1	12	yes	complemented
203	C₂×#6104	C₂³	1	12	yes	complemented
204	C₂×#6099	C₂³	1	6	yes	complemented
205	#88173	C₂³	1	24	yes	complemented
206	#88172	C₂³	1	24	yes	complemented
207	#88172	C₂³	1	48	yes	complemented
208	#88172	C₂³	1	8	yes	complemented
209	Q₁₆×D₁₃	C₂³	1	24	yes	complemented
210	#88170	C₂³	1	24	yes	complemented
211	#88170	C₂³	1	48	yes	complemented
212	#88170	C₂³	1	8	yes	complemented
213	#88169	C₂³	1	24	yes	complemented
214	#88169	C₂³	1	24	yes	complemented
215	#88168	C₂³	1	24	yes	complemented
216	#88168	C₂³	1	24	yes	complemented
217	SD₁₆×D₁₃	C₂³	1	24	yes	complemented
218	SD₁₆×D₁₃	C₂³	1	48	yes	complemented
219	SD₁₆×D₁₃	C₂³	1	8	yes	complemented
220	#88166	C₂³	1	24	yes	complemented
221	#88165	C₂³	1	24	yes	complemented
222	#88165	C₂³	1	48	yes	complemented
223	#88165	C₂³	1	8	yes	complemented
224	D₈×D₁₃	C₂³	1	24	yes	complemented
225	#88163	C₂³	1	24	yes	complemented
226	#88162	C₂³	1	24	yes	complemented
227	#88161	C₂³	1	24	yes	complemented
228	M₁₆×D₁₃	C₂³	1	24	yes	complemented
229	C₂×Dic₅₂	C₂³	1	3	yes	complemented
230	#88158	C₂³	1	12	yes	complemented
231	#88158	C₂³	1	12	yes	complemented
232	C₂×D₁₀₄	C₂³	1	3	yes	complemented
233	C₂×#6095	C₂³	1	3	yes	complemented
234	C₂×#6095	C₂³	1	6	yes	complemented
235	C₂×#6095	C₂³	1	12	yes	complemented
236	C₂×#6095	C₂³	1	12	yes	complemented
237	C₂×#6095	C₂³	1	1	yes	characteristic, complemented
238	#88155	C₂³	1	4	yes	complemented
239	#88155	C₂³	1	12	yes	complemented
240	#88155	C₂³	1	12	yes	complemented
241	#88155	C₂³	1	12	yes	complemented
242	C₂×#6094	C₂³	1	12	yes	complemented
243	C₂×C₈×D₁₃	C₂³	1	12	yes	complemented
244	#63092	—	13	1	no	maximal, Sylow
245	C₂³×D₁₃	—	2	3	no	—
246	C₂³×D₁₃	—	2	12	no	—
247	C₁₃×#41	—	2	4	no	—
248	C₁₃×#41	—	2	4	no	—
249	C₁₃×#41	—	2	12	no	—
250	C₁₃×#41	—	2	12	no	—
251	C₁₃×#41	—	2	6	no	—
252	C₁₃×#41	—	2	6	no	—
253	C₁₃×#41	—	2	6	no	—
254	C₁₃×#41	—	2	6	no	—
255	C₁₃×#41	C₂×D₄	1	4	yes	—
256	C₁₃×#41	C₂⁴	1	4	yes	—
257	C₁₃×#41	C₂⁴	1	12	yes	—
258	C₁₃×#41	C₂⁴	1	4	yes	—
259	C₁₃×#41	C₂⁴	1	12	yes	—
260	C₁₃×#41	C₂⁴	1	4	yes	—
261	C₂×Q₈×C₁₃	—	2	4	no	—
262	C₂×Q₈×C₁₃	—	2	4	no	—
263	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
265	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
266	C₂×D₄×C₁₃	—	2	6	no	—
267	C₂×D₄×C₁₃	—	2	6	no	—
268	C₂×D₄×C₁₃	—	2	12	no	—
269	C₂×D₄×C₁₃	—	2	12	no	—
270	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
273	C₂²×C₄×C₁₃	—	2	6	no	—
274	C₂²×C₄×C₁₃	—	2	6	no	—
275	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
276	C₂×C₂²⋊D₁₃	—	2	3	no	—
277	C₂×C₂²⋊D₁₃	—	2	3	no	—
278	C₂×C₂²⋊D₁₃	—	2	12	no	—
279	C₂×C₂²⋊D₁₃	—	2	24	no	—
280	C₂×C₂²⋊D₁₃	—	2	24	no	—
281	C₂×C₂²⋊D₁₃	—	2	12	no	—
282	C₂×C₂²⋊D₁₃	C₂×D₄	1	12	yes	—
283	C₂²×Dic₁₃	—	2	3	no	—
284	C₂²×Dic₁₃	—	2	12	no	—
285	#6131	—	2	8	no	—
286	#6131	—	2	12	no	—
287	#6131	—	2	12	no	—
288	#6131	—	2	24	no	—
289	#6131	C₂×D₄	1	8	yes	—
290	#6131	C₂⁴	1	8	yes	—
291	#6131	C₂⁴	1	24	yes	—
292	Q₈×D₁₃	—	2	8	no	—
293	Q₈×D₁₃	—	2	24	no	—
294	Q₈×D₁₃	—	2	12	no	—
295	Q₈×D₁₃	—	2	12	no	—
296	Q₈×D₁₃	C₂×D₄	1	8	yes	—
297	Q₈×D₁₃	C₂⁴	1	24	yes	—
298	Q₈×D₁₃	C₂⁴	1	8	yes	—
299	#6129	—	2	24	no	—
300	#6129	—	2	48	no	—
301	#6129	—	2	24	no	—
302	#6129	—	2	8	no	—
303	#6129	—	2	24	no	—
304	#6129	—	2	24	no	—
305	#6129	—	2	24	no	—
306	#6129	—	2	12	no	—
307	#6129	—	2	12	no	—
308	#6129	C₂×D₄	1	24	yes	—
309	#6129	C₂⁴	1	24	yes	—
310	#6129	C₂⁴	1	8	yes	—
311	D₄×D₁₃	—	2	24	no	—
312	D₄×D₁₃	—	2	24	no	—
313	D₄×D₁₃	—	2	24	no	—
314	D₄×D₁₃	—	2	48	no	—
315	D₄×D₁₃	—	2	24	no	—
316	D₄×D₁₃	—	2	8	no	—
317	D₄×D₁₃	—	2	12	no	—
318	D₄×D₁₃	—	2	12	no	—
319	D₄×D₁₃	—	2	24	no	—
320	D₄×D₁₃	C₂×D₄	1	24	yes	—
321	D₄×D₁₃	C₂⁴	1	8	yes	—
322	D₄×D₁₃	C₂⁴	1	24	yes	—
323	#6127	—	2	6	no	—
324	#6127	—	2	6	no	—
325	#6127	—	2	24	no	—
326	#6127	—	2	24	no	—
327	#6127	—	2	4	no	—
328	#6127	—	2	12	no	—
329	#6127	—	2	24	no	—
330	#6127	—	2	24	no	—
331	#6127	—	2	24	no	—
332	#6127	—	2	12	no	—
333	#6127	—	2	4	no	—
334	#6127	—	2	24	no	—
335	#6127	C₂×D₄	1	12	yes	—
336	#6127	C₂×D₄	1	12	yes	—
337	#6127	C₂⁴	1	4	yes	—
338	#6127	C₂⁴	1	12	yes	—
339	#6127	C₂⁴	1	12	yes	—
340	#6127	C₂⁴	1	12	yes	—
341	C₂×D₅₂	—	2	12	no	—
342	C₂×D₅₂	—	2	6	no	—
343	C₂×D₅₂	—	2	3	no	—
344	C₂×D₅₂	—	2	12	no	—
345	C₂×D₅₂	—	2	24	no	—
346	C₂×D₅₂	—	2	4	no	—
347	C₂×D₅₂	C₂×D₄	1	6	yes	—
348	C₂×D₅₂	C₂⁴	1	3	yes	—
349	C₂×D₅₂	C₂⁴	1	12	yes	—
350	C₂×D₅₂	C₂⁴	1	1	yes	characteristic
351	C₂×C₄×D₁₃	—	2	12	no	—
352	C₂×C₄×D₁₃	—	2	3	no	—
353	C₂×C₄×D₁₃	—	2	3	no	—
354	C₂×C₄×D₁₃	—	2	12	no	—
355	C₂×C₄×D₁₃	—	2	24	no	—
356	C₂×C₄×D₁₃	—	2	24	no	—
357	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
358	C₂×Dic₂₆	—	2	6	no	—
359	C₂×Dic₂₆	—	2	3	no	—
360	C₂×Dic₂₆	—	2	12	no	—
361	C₂×Dic₂₆	—	2	12	no	—
362	C₂×Dic₂₆	—	2	24	no	—
363	C₂×Dic₂₆	—	2	4	no	—
364	C₂×Dic₂₆	C₂×D₄	1	6	yes	—
365	C₂×Dic₂₆	C₂⁴	1	3	yes	—
366	C₂×Dic₂₆	C₂⁴	1	12	yes	—
367	C₂×Dic₂₆	C₂⁴	1	1	yes	characteristic
368	C₁₃×Q₁₆	C₂⁴	1	12	yes	—
369	C₁₃×Q₁₆	C₂⁴	1	4	yes	—
370	C₁₃×SD₁₆	C₂⁴	1	4	yes	—
371	C₁₃×SD₁₆	C₂⁴	1	12	yes	—
372	C₁₃×SD₁₆	C₂⁴	1	4	yes	—
373	C₁₃×SD₁₆	C₂⁴	1	12	yes	—
374	C₁₃×D₈	C₂⁴	1	12	yes	—
375	C₁₃×D₈	C₂⁴	1	4	yes	—
376	C₁₃×M₁₆	C₂⁴	1	12	yes	—
377	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
378	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
381	#6107	C₂⁴	1	8	yes	—
382	#6107	C₂⁴	1	24	yes	—
383	#6106	C₂⁴	1	24	yes	—
384	#6106	C₂⁴	1	8	yes	—
385	#6105	C₂⁴	1	24	yes	—
386	#6105	C₂⁴	1	8	yes	—
387	#6104	C₂⁴	1	8	yes	—
388	#6104	C₂⁴	1	24	yes	—
389	#6099	C₂⁴	1	4	yes	—
390	#6099	C₂⁴	1	12	yes	—
391	C₂×#1055	C₂⁴	1	12	yes	—
392	Dic₅₂	C₂⁴	1	12	yes	—
393	D₁₀₄	C₂⁴	1	12	yes	—
394	#6095	C₂⁴	1	6	yes	—
395	#6095	C₂⁴	1	6	yes	—
396	#6095	C₂⁴	1	24	yes	—
397	#6095	C₂⁴	1	2	yes	—
398	#6095	C₂⁴	1	2	yes	—
399	#6094	C₂⁴	1	8	yes	—
400	#6094	C₂⁴	1	24	yes	—
401	C₈×D₁₃	C₂⁴	1	8	yes	—
402	C₈×D₁₃	C₂⁴	1	24	yes	—
403	2₋¹⁺⁶	—	13	1	no	—
404	H(7,𝔽₂)	—	13	1	no	—
405	#3586	—	13	1	no	—
406	#3586	—	13	8	no	—
407	#3586	—	13	6	no	—
408	#3585	—	13	1	no	—
409	#3585	—	13	8	no	—
410	#3585	—	13	6	no	—
411	#3584	—	13	8	no	—
412	#3584	—	13	6	no	—
413	#3584	D₁₃	1	1	yes	characteristic, complemented
414	C₂×#577	—	13	8	no	—
415	C₂×#577	—	13	6	no	—
416	C₂×#577	—	13	1	no	—
417	#3573	—	13	1	no	—
418	C₂³×C₁₃	—	2	6	no	—
419	C₂³×C₁₃	—	2	6	no	—
420	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
421	C₂²×D₁₃	—	2	1	no	—
422	C₂²×D₁₃	—	2	3	no	—
423	C₂²×D₁₃	—	2	12	no	—
424	C₂²×D₁₃	—	2	8	no	—
425	C₂²×D₁₃	—	2	24	no	—
426	C₂²×D₁₃	—	16	12	no	—
427	C₂²×D₁₃	—	16	3	no	—
428	C₂²×D₁₃	C₂²×D₄	1	12	yes	—
429	Q₈×C₁₃	—	2	6	no	—
430	Q₈×C₁₃	—	2	6	no	—
431	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
432	Q₈×C₁₃	C₂⁵	1	4	yes	—
433	Q₈×C₁₃	C₂⁵	1	4	yes	—
434	D₄×C₁₃	—	2	4	no	—
435	D₄×C₁₃	—	2	12	no	—
436	D₄×C₁₃	—	2	4	no	—
437	D₄×C₁₃	—	2	12	no	—
438	D₄×C₁₃	—	2	6	no	—
439	D₄×C₁₃	—	2	6	no	—
440	D₄×C₁₃	C₂²×D₄	1	12	yes	—
441	D₄×C₁₃	C₂⁵	1	4	yes	—
442	D₄×C₁₃	C₂⁵	1	4	yes	—
443	C₂×C₄×C₁₃	—	2	6	no	—
444	C₂×C₄×C₁₃	—	2	6	no	—
445	C₂×C₄×C₁₃	—	2	4	no	—
446	C₂×C₄×C₁₃	—	2	12	no	—
447	C₂×C₄×C₁₃	—	2	4	no	—
448	C₂×C₄×C₁₃	—	2	12	no	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
450	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
451	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
452	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
453	C₂²⋊D₁₃	—	2	12	no	—
454	C₂²⋊D₁₃	—	2	12	no	—
455	C₂²⋊D₁₃	—	2	8	no	—
456	C₂²⋊D₁₃	—	2	24	no	—
457	C₂²⋊D₁₃	—	2	24	no	—
458	C₂²⋊D₁₃	—	2	8	no	—
459	C₂²⋊D₁₃	C₂²×D₄	1	24	yes	—
460	C₂²⋊D₁₃	C₂²×D₄	1	8	yes	—
461	C₂×Dic₁₃	—	2	3	no	—
462	C₂×Dic₁₃	—	2	12	no	—
463	C₂×Dic₁₃	—	2	1	no	—
464	C₂×Dic₁₃	—	2	24	no	—
465	C₂×Dic₁₃	—	2	8	no	—
466	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
467	D₅₂	—	2	24	no	—
468	D₅₂	—	2	8	no	—
469	D₅₂	—	2	3	no	—
470	D₅₂	—	2	1	no	—
471	D₅₂	—	2	12	no	—
472	D₅₂	C₂²×D₄	1	4	yes	—
473	D₅₂	C₂²×D₄	1	12	yes	—
474	D₅₂	C₂⁵	1	6	yes	—
475	D₅₂	C₂⁵	1	2	yes	—
476	C₄×D₁₃	—	2	8	no	—
477	C₄×D₁₃	—	2	24	no	—
478	C₄×D₁₃	—	2	12	no	—
479	C₄×D₁₃	—	2	12	no	—
480	C₄×D₁₃	—	2	24	no	—
481	C₄×D₁₃	—	2	8	no	—
482	C₄×D₁₃	C₂²×D₄	1	24	yes	—
483	C₄×D₁₃	C₂⁵	1	8	yes	—
484	Dic₂₆	—	2	3	no	—
485	Dic₂₆	—	2	1	no	—
486	Dic₂₆	—	2	12	no	—
487	Dic₂₆	—	2	24	no	—
488	Dic₂₆	—	2	8	no	—
489	Dic₂₆	C₂²×D₄	1	4	yes	—
490	Dic₂₆	C₂²×D₄	1	12	yes	—
491	Dic₂₆	C₂⁵	1	6	yes	—
492	Dic₂₆	C₂⁵	1	2	yes	—
493	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
494	C₈×C₁₃	C₂⁵	1	6	yes	—
495	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
496	#1055	C₂⁵	1	8	yes	—
497	#585	—	13	1	no	—
498	#585	—	13	8	no	—
499	#585	—	13	8	no	—
500	#585	—	13	6	no	—
501	#585	—	13	6	no	—
502	#585	—	26	4	no	—
503	#585	—	26	4	no	—
504	#585	—	26	6	no	—
505	#585	—	26	2	no	—
506	#585	C₂×D₁₃	1	1	yes	characteristic, complemented
507	#585	C₂×D₁₃	1	1	yes	characteristic, complemented
508	C₂×2₋¹⁺⁴	—	13	8	no	—
509	C₂×2₋¹⁺⁴	—	13	1	no	—
510	C₂×2₋¹⁺⁴	—	13	6	no	—
511	C₂×2₋¹⁺⁴	—	26	4	no	—
512	C₂×2₋¹⁺⁴	—	26	2	no	—
513	C₂×H(5,𝔽₂)	—	13	8	no	—
514	C₂×H(5,𝔽₂)	—	13	6	no	—
515	C₂×H(5,𝔽₂)	—	13	1	no	—
516	C₂×H(5,𝔽₂)	—	26	4	no	—
517	C₂×H(5,𝔽₂)	—	26	6	no	—
518	#578	—	13	8	no	—
519	#578	—	13	24	no	—
520	#578	—	13	12	no	—
521	#578	—	13	12	no	—
522	#578	C₂×D₁₃	1	4	yes	complemented
523	#577	—	13	8	no	—
524	#577	—	13	8	no	—
525	#577	—	13	24	no	—
526	#577	—	13	24	no	—
527	#577	—	13	4	no	—
528	#577	—	13	24	no	—
529	#577	—	13	12	no	—
530	#577	—	13	24	no	—
531	#577	—	13	24	no	—
532	#577	—	13	12	no	—
533	#577	—	13	12	no	—
534	#577	—	13	8	no	—
535	#577	—	13	8	no	—
536	#577	C₂×D₁₃	1	4	yes	complemented
537	#577	C₂×D₁₃	1	4	yes	complemented
538	#576	—	13	8	no	—
539	#576	—	13	24	no	—
540	#576	—	13	12	no	—
541	#576	—	13	12	no	—
542	#576	C₂×D₁₃	1	4	yes	complemented
543	#575	—	13	6	no	—
544	#575	—	13	6	no	—
545	#575	—	13	24	no	—
546	#575	—	13	24	no	—
547	#575	—	13	24	no	—
548	#575	C₂×D₁₃	1	6	yes	complemented
549	C₂×#137	—	13	6	no	—
550	C₂×#137	—	13	24	no	—
551	C₂×#137	—	13	12	no	—
552	C₂×#137	—	13	3	no	—
553	C₂×AGL(1,ℤ/8)	—	13	6	no	—
554	C₂×AGL(1,ℤ/8)	—	13	24	no	—
555	C₂×AGL(1,ℤ/8)	—	13	12	no	—
556	C₂×AGL(1,ℤ/8)	—	13	3	no	—
557	C₂×#135	—	13	24	no	—
558	C₂×#135	—	13	12	no	—
559	C₂×#135	—	13	3	no	—
560	C₂×#135	C₂×D₁₃	1	6	yes	complemented
561	C₂²×SD₁₆	—	13	12	no	—
562	C₂²×SD₁₆	—	13	3	no	—
563	#568	—	13	1	no	—
564	#568	—	13	8	no	—
565	#568	—	13	6	no	—
566	C₂×#131	—	13	8	no	—
567	C₂×#131	—	13	6	no	—
568	C₂×#131	C₂×D₁₃	1	1	yes	characteristic, complemented
569	C₂²×C₁₃	—	2	4	no	—
570	C₂²×C₁₃	—	2	4	no	—
571	C₂²×C₁₃	—	4	3	no	—
572	C₂²×C₁₃	—	8	6	no	—
573	C₂²×C₁₃	—	8	6	no	—
574	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
575	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
576	C₂×D₁₃	—	2	2	no	—
577	C₂×D₁₃	—	2	6	no	—
578	C₂×D₁₃	—	4	12	no	—
579	C₂×D₁₃	—	8	8	no	—
580	C₂×D₁₃	—	8	24	no	—
581	C₂×D₁₃	—	8	1	no	—
582	C₂×D₁₃	—	8	12	no	—
583	C₂×D₁₃	—	8	3	no	—
584	C₂×D₁₃	C₂³×D₄	1	8	yes	—
585	C₄×C₁₃	—	2	4	no	—
586	C₄×C₁₃	—	2	4	no	—
587	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
588	C₄×C₁₃	C₂³×D₄	1	6	yes	—
589	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
590	Dic₁₃	—	2	6	no	—
591	Dic₁₃	—	2	2	no	—
592	Dic₁₃	C₂³×D₄	1	8	yes	—
593	2₋¹⁺⁴	—	2	1	no	—
594	2₋¹⁺⁴	—	2	1	no	—
595	2₋¹⁺⁴	—	13	4	no	—
596	2₋¹⁺⁴	—	13	2	no	—
597	2₋¹⁺⁴	—	13	24	no	—
598	2₋¹⁺⁴	—	13	12	no	—
599	2₋¹⁺⁴	—	13	8	no	—
600	2₋¹⁺⁴	—	13	4	no	—
601	2₋¹⁺⁴	—	13	12	no	—
602	2₋¹⁺⁴	—	13	12	no	—
603	2₋¹⁺⁴	—	26	8	no	—
604	2₋¹⁺⁴	—	26	8	no	—
605	2₋¹⁺⁴	—	26	8	no	—
606	2₋¹⁺⁴	—	26	6	no	—
607	2₋¹⁺⁴	—	26	6	no	—
608	2₋¹⁺⁴	—	26	24	no	—
609	2₋¹⁺⁴	—	26	12	no	—
610	2₋¹⁺⁴	—	26	12	no	—
611	2₋¹⁺⁴	—	26	4	no	—
612	2₋¹⁺⁴	C₂²×D₁₃	1	4	yes	—
613	2₋¹⁺⁴	C₂²×D₁₃	1	4	yes	complemented
614	H(5,𝔽₂)	—	2	3	no	—
615	H(5,𝔽₂)	—	2	3	no	—
616	H(5,𝔽₂)	—	13	4	no	—
617	H(5,𝔽₂)	—	13	6	no	—
618	H(5,𝔽₂)	—	13	4	no	—
619	H(5,𝔽₂)	—	13	24	no	—
620	H(5,𝔽₂)	—	13	12	no	—
621	H(5,𝔽₂)	—	13	8	no	—
622	H(5,𝔽₂)	—	13	12	no	—
623	H(5,𝔽₂)	—	13	12	no	—
624	H(5,𝔽₂)	—	26	12	no	—
625	H(5,𝔽₂)	—	26	12	no	—
626	H(5,𝔽₂)	—	26	24	no	—
627	H(5,𝔽₂)	—	26	24	no	—
628	H(5,𝔽₂)	—	26	24	no	—
629	H(5,𝔽₂)	—	26	6	no	—
630	H(5,𝔽₂)	—	26	6	no	—
631	H(5,𝔽₂)	—	26	8	no	—
632	H(5,𝔽₂)	—	26	12	no	—
633	H(5,𝔽₂)	—	26	12	no	—
634	H(5,𝔽₂)	—	26	4	no	—
635	H(5,𝔽₂)	C₂²×D₁₃	1	4	yes	—
636	H(5,𝔽₂)	C₂²×D₁₃	1	4	yes	complemented
637	C₂×#41	—	2	4	no	—
638	C₂×#41	—	2	4	no	—
639	C₂×#41	—	13	8	no	—
640	C₂×#41	—	13	6	no	—
641	C₂×#41	—	13	24	no	—
642	C₂×#41	—	13	24	no	—
643	C₂×#41	—	13	12	no	—
644	C₂×#41	—	13	12	no	—
645	C₂×#41	—	13	3	no	—
646	C₂×#41	—	13	3	no	—
647	C₂×#41	—	26	6	no	—
648	C₂×#41	—	26	6	no	—
649	C₂×#41	—	26	12	no	—
650	C₂×#41	—	26	12	no	—
651	C₂×#41	—	26	12	no	—
652	C₂×#41	—	26	24	no	—
653	C₂×#41	—	26	24	no	—
654	C₂×#41	—	26	8	no	—
655	C₂×#41	—	26	8	no	—
656	C₂×#41	—	26	24	no	—
657	C₂×#41	—	26	12	no	—
658	C₂×#41	—	26	8	no	—
659	C₂×#41	—	26	12	no	—
660	C₂×#41	—	26	1	no	—
661	C₂×#41	—	26	3	no	—
662	C₂×#41	C₂²×D₁₃	1	6	yes	—
663	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
664	C₂×#41	C₂²×D₁₃	1	6	yes	complemented
665	C₂²×Q₈	—	13	12	no	—
666	C₂²×Q₈	—	13	3	no	—
667	C₂²×Q₈	—	26	6	no	—
668	C₂²×Q₈	—	26	8	no	—
669	C₂²×Q₈	—	26	1	no	—
670	C₂²×D₄	—	13	12	no	—
671	C₂²×D₄	—	13	3	no	—
672	C₂²×D₄	—	26	6	no	—
673	C₂²×D₄	—	26	12	no	—
674	C₂²×D₄	—	26	24	no	—
675	C₂²×D₄	—	26	3	no	—
676	#137	—	13	24	no	—
677	#137	—	13	12	no	—
678	#137	—	13	4	no	—
679	#137	—	13	12	no	—
680	#137	—	13	12	no	—
681	#137	—	13	48	no	—
682	#137	—	13	24	no	—
683	#137	—	13	8	no	—
684	#137	—	13	24	no	—
685	#137	—	13	24	no	—
686	#137	—	13	24	no	—
687	#137	C₂²×D₁₃	1	12	yes	complemented
688	#137	C₂²×D₁₃	1	12	yes	complemented
689	AGL(1,ℤ/8)	—	13	24	no	—
690	AGL(1,ℤ/8)	—	13	12	no	—
691	AGL(1,ℤ/8)	—	13	4	no	—
692	AGL(1,ℤ/8)	—	13	12	no	—
693	AGL(1,ℤ/8)	—	13	12	no	—
694	AGL(1,ℤ/8)	—	13	24	no	—
695	AGL(1,ℤ/8)	—	13	24	no	—
696	AGL(1,ℤ/8)	—	13	48	no	—
697	AGL(1,ℤ/8)	—	13	24	no	—
698	AGL(1,ℤ/8)	—	13	8	no	—
699	AGL(1,ℤ/8)	—	13	24	no	—
700	AGL(1,ℤ/8)	C₂²×D₁₃	1	12	yes	complemented
701	AGL(1,ℤ/8)	C₂²×D₁₃	1	12	yes	complemented
702	#135	—	13	24	no	—
703	#135	—	13	24	no	—
704	#135	—	13	24	no	—
705	#135	—	13	24	no	—
706	#135	—	13	8	no	—
707	#135	—	13	48	no	—
708	#135	—	13	24	no	—
709	#135	—	13	12	no	—
710	#135	—	13	12	no	—
711	#135	C₂²×D₁₃	1	12	yes	complemented
712	#135	C₂²×D₁₃	1	4	yes	complemented
713	#135	C₂²×D₁₃	1	12	yes	complemented
714	#135	C₂²×D₁₃	1	12	yes	complemented
715	C₂×Q₁₆	—	13	12	no	—
716	C₂×Q₁₆	—	13	24	no	—
717	C₂×Q₁₆	—	13	3	no	—
718	C₂×Q₁₆	C₂²×D₁₃	1	6	yes	complemented
719	C₂×SD₁₆	—	13	12	no	—
720	C₂×SD₁₆	—	13	12	no	—
721	C₂×SD₁₆	—	13	24	no	—
722	C₂×SD₁₆	—	13	48	no	—
723	C₂×SD₁₆	—	13	8	no	—
724	C₂×SD₁₆	—	13	12	no	—
725	C₂×SD₁₆	—	13	3	no	—
726	C₂×SD₁₆	—	13	12	no	—
727	C₂×SD₁₆	—	13	6	no	—
728	C₂×SD₁₆	—	13	1	no	—
729	C₂×SD₁₆	C₂²×D₁₃	1	6	yes	complemented
730	C₂×SD₁₆	C₂²×D₁₃	1	6	yes	complemented
731	C₂×D₈	—	13	12	no	—
732	C₂×D₈	—	13	24	no	—
733	C₂×D₈	—	13	3	no	—
734	C₂×D₈	C₂²×D₁₃	1	6	yes	complemented
735	#131	—	13	8	no	—
736	#131	—	13	24	no	—
737	#131	—	13	12	no	—
738	#131	—	13	4	no	—
739	#131	—	13	12	no	—
740	#131	—	13	12	no	—
741	#131	C₂²×D₁₃	1	4	yes	complemented
742	#131	C₂²×D₁₃	1	4	yes	complemented
743	C₂×M₁₆	—	13	6	no	—
744	C₂×M₁₆	—	13	24	no	—
745	C₂×M₁₆	—	13	12	no	—
746	C₂×M₁₆	C₂²×D₁₃	1	3	yes	complemented
747	C₂²×C₈	—	13	12	no	—
748	C₂²×C₈	C₂²×D₁₃	1	3	yes	complemented
749	C₂×C₁₃	—	2	6	no	—
750	C₂×C₁₃	—	2	1	no	—
751	C₂×C₁₃	—	4	4	no	—
752	C₂×C₁₃	—	4	4	no	—
753	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
754	D₁₃	—	2	8	no	—
755	D₁₃	—	4	2	no	—
756	D₁₃	—	4	6	no	—
757	C₂⁴	—	26	12	no	—
758	C₂⁴	—	26	3	no	—
759	#41	—	2	4	no	—
760	#41	—	2	4	no	—
761	#41	—	2	12	no	—
762	#41	—	2	12	no	—
763	#41	—	2	6	no	—
764	#41	—	2	6	no	—
765	#41	—	2	6	no	—
766	#41	—	2	6	no	—
767	#41	—	13	8	no	—
768	#41	—	13	24	no	—
769	#41	—	13	12	no	—
770	#41	—	13	12	no	—
771	#41	—	13	12	no	—
772	#41	—	13	4	no	—
773	#41	—	13	8	no	—
774	#41	—	13	24	no	—
775	#41	—	13	24	no	—
776	#41	—	13	8	no	—
777	#41	—	13	12	no	—
778	#41	—	13	12	no	—
779	#41	—	26	24	no	—
780	#41	—	26	24	no	—
781	#41	—	26	24	no	—
782	#41	—	26	4	no	—
783	#41	—	26	24	no	—
784	#41	—	26	12	no	—
785	#41	—	26	24	no	—
786	#41	—	26	12	no	—
787	#41	—	26	24	no	—
788	#41	—	26	4	no	—
789	#41	—	26	24	no	—
790	#41	—	26	24	no	—
791	#41	—	26	24	no	—
792	#41	—	26	24	no	—
793	#41	—	26	8	no	—
794	#41	—	26	24	no	—
795	#41	—	26	48	no	—
796	#41	—	26	12	no	—
797	#41	—	26	12	no	—
798	#41	—	26	12	no	—
799	#41	—	26	12	no	—
800	#41	—	26	8	no	—
801	#41	—	26	24	no	—
802	#41	—	26	6	no	—
803	#41	—	26	6	no	—
804	#41	D₄×D₁₃	1	4	yes	—
805	#41	C₂³×D₁₃	1	12	yes	—
806	#41	C₂³×D₁₃	1	12	yes	—
807	#41	C₂³×D₁₃	1	4	yes	—
808	#41	C₂³×D₁₃	1	4	yes	—
809	#41	C₂³×D₁₃	1	4	yes	—
810	C₂×Q₈	—	2	4	no	—
811	C₂×Q₈	—	2	4	no	—
812	C₂×Q₈	—	13	8	no	—
813	C₂×Q₈	—	13	6	no	—
814	C₂×Q₈	—	13	24	no	—
815	C₂×Q₈	—	13	8	no	—
816	C₂×Q₈	—	13	12	no	—
817	C₂×Q₈	—	13	3	no	—
818	C₂×Q₈	—	13	1	no	—
819	C₂×Q₈	—	26	12	no	—
820	C₂×Q₈	—	26	12	no	—
821	C₂×Q₈	—	26	24	no	—
822	C₂×Q₈	—	26	4	no	—
823	C₂×Q₈	—	26	24	no	—
824	C₂×Q₈	—	26	12	no	—
825	C₂×Q₈	—	26	12	no	—
826	C₂×Q₈	—	26	8	no	—
827	C₂×Q₈	—	26	6	no	—
828	C₂×Q₈	—	26	3	no	—
829	C₂×Q₈	D₄×D₁₃	1	1	yes	characteristic
830	C₂×Q₈	C₂³×D₁₃	1	6	yes	—
831	C₂×Q₈	C₂³×D₁₃	1	6	yes	—
832	C₂×D₄	—	2	6	no	—
833	C₂×D₄	—	2	6	no	—
834	C₂×D₄	—	2	12	no	—
835	C₂×D₄	—	2	12	no	—
836	C₂×D₄	—	13	12	no	—
837	C₂×D₄	—	13	24	no	—
838	C₂×D₄	—	13	8	no	—
839	C₂×D₄	—	13	24	no	—
840	C₂×D₄	—	13	6	no	—
841	C₂×D₄	—	13	1	no	—
842	C₂×D₄	—	13	12	no	—
843	C₂×D₄	—	13	3	no	—
844	C₂×D₄	—	26	12	no	—
845	C₂×D₄	—	26	24	no	—
846	C₂×D₄	—	26	4	no	—
847	C₂×D₄	—	26	12	no	—
848	C₂×D₄	—	26	24	no	—
849	C₂×D₄	—	26	12	no	—
850	C₂×D₄	—	26	24	no	—
851	C₂×D₄	—	26	48	no	—
852	C₂×D₄	—	26	12	no	—
853	C₂×D₄	—	26	8	no	—
854	C₂×D₄	—	26	12	no	—
855	C₂×D₄	—	26	24	no	—
856	C₂×D₄	—	26	24	no	—
857	C₂×D₄	—	26	24	no	—
858	C₂×D₄	—	26	24	no	—
859	C₂×D₄	—	26	12	no	—
860	C₂×D₄	—	26	3	no	—
861	C₂×D₄	—	26	3	no	—
862	C₂×D₄	—	26	24	no	—
863	C₂×D₄	—	26	6	no	—
864	C₂×D₄	—	26	3	no	—
865	C₂×D₄	D₄×D₁₃	1	3	yes	—
866	C₂×D₄	C₂³×D₁₃	1	6	yes	—
867	C₂×D₄	C₂³×D₁₃	1	6	yes	—
868	C₂²×C₄	—	2	6	no	—
869	C₂²×C₄	—	2	6	no	—
870	C₂²×C₄	—	13	12	no	—
871	C₂²×C₄	—	26	12	no	—
872	C₂²×C₄	—	26	24	no	—
873	C₂²×C₄	—	26	24	no	—
874	C₂²×C₄	—	26	12	no	—
875	C₂²×C₄	—	26	12	no	—
876	C₂²×C₄	—	26	3	no	—
877	C₂²×C₄	—	26	3	no	—
878	C₂²×C₄	—	26	3	no	—
879	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
880	Q₁₆	—	13	24	no	—
881	Q₁₆	—	13	8	no	—
882	Q₁₆	—	13	12	no	—
883	Q₁₆	C₂³×D₁₃	1	12	yes	—
884	Q₁₆	C₂³×D₁₃	1	4	yes	—
885	SD₁₆	—	13	24	no	—
886	SD₁₆	—	13	8	no	—
887	SD₁₆	—	13	24	no	—
888	SD₁₆	—	13	8	no	—
889	SD₁₆	—	13	6	no	—
890	SD₁₆	—	13	2	no	—
891	SD₁₆	—	13	24	no	—
892	SD₁₆	—	13	6	no	—
893	SD₁₆	—	13	2	no	—
894	SD₁₆	C₂³×D₁₃	1	4	yes	—
895	SD₁₆	C₂³×D₁₃	1	12	yes	—
896	SD₁₆	C₂³×D₁₃	1	4	yes	—
897	SD₁₆	C₂³×D₁₃	1	12	yes	—
898	D₈	—	13	8	no	—
899	D₈	—	13	24	no	—
900	D₈	—	13	12	no	—
901	D₈	C₂³×D₁₃	1	12	yes	—
902	D₈	C₂³×D₁₃	1	4	yes	—
903	M₁₆	—	13	12	no	—
904	M₁₆	—	13	4	no	—
905	M₁₆	—	13	24	no	—
906	M₁₆	—	13	8	no	—
907	M₁₆	C₂³×D₁₃	1	12	yes	—
908	C₂×C₈	—	13	12	no	—
909	C₂×C₈	—	13	8	no	—
910	C₂×C₈	—	13	24	no	—
911	C₂×C₈	C₂³×D₁₃	1	6	yes	—
912	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₁₃	1	6	yes	—
914	C₂×C₈	C₂³×D₁₃	1	3	yes	—
915	C₁₃	#63092	1	1	yes	characteristic, complemented, Sylow
916	C₂³	—	2	6	no	—
917	C₂³	—	2	6	no	—
918	C₂³	—	13	12	no	—
919	C₂³	—	26	8	no	—
920	C₂³	—	26	24	no	—
921	C₂³	—	26	1	no	—
922	C₂³	—	26	12	no	—
923	C₂³	—	26	3	no	—
924	C₂³	—	208	3	no	—
925	C₂³	—	208	12	no	—
926	C₂³	C₂×D₄×D₁₃	1	3	yes	—
927	Q₈	—	2	6	no	—
928	Q₈	—	2	6	no	—
929	Q₈	—	13	4	no	—
930	Q₈	—	13	12	no	—
931	Q₈	—	13	6	no	—
932	Q₈	—	13	2	no	—
933	Q₈	—	26	24	no	—
934	Q₈	—	26	8	no	—
935	Q₈	—	26	3	no	—
936	Q₈	—	26	12	no	—
937	Q₈	—	26	1	no	—
938	Q₈	C₂×D₄×D₁₃	1	4	yes	—
939	Q₈	C₂⁴×D₁₃	1	4	yes	—
940	Q₈	C₂⁴×D₁₃	1	4	yes	—
941	D₄	—	2	12	no	—
942	D₄	—	2	4	no	—
943	D₄	—	2	12	no	—
944	D₄	—	2	4	no	—
945	D₄	—	2	6	no	—
946	D₄	—	2	6	no	—
947	D₄	—	13	24	no	—
948	D₄	—	13	8	no	—
949	D₄	—	13	4	no	—
950	D₄	—	13	12	no	—
951	D₄	—	13	2	no	—
952	D₄	—	13	6	no	—
953	D₄	—	26	24	no	—
954	D₄	—	26	8	no	—
955	D₄	—	26	24	no	—
956	D₄	—	26	8	no	—
957	D₄	—	26	8	no	—
958	D₄	—	26	24	no	—
959	D₄	—	26	12	no	—
960	D₄	—	26	12	no	—
961	D₄	—	26	3	no	—
962	D₄	—	26	12	no	—
963	D₄	—	26	1	no	—
964	D₄	C₂×D₄×D₁₃	1	12	yes	—
965	D₄	C₂⁴×D₁₃	1	4	yes	—
966	D₄	C₂⁴×D₁₃	1	4	yes	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	6	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	12	no	—
972	C₂×C₄	—	2	12	no	—
973	C₂×C₄	—	13	12	no	—
974	C₂×C₄	—	13	24	no	—
975	C₂×C₄	—	13	8	no	—
976	C₂×C₄	—	26	24	no	—
977	C₂×C₄	—	26	8	no	—
978	C₂×C₄	—	26	8	no	—
979	C₂×C₄	—	26	24	no	—
980	C₂×C₄	—	26	8	no	—
981	C₂×C₄	—	26	24	no	—
982	C₂×C₄	—	26	1	no	—
983	C₂×C₄	—	26	12	no	—
984	C₂×C₄	—	26	3	no	—
985	C₂×C₄	—	26	12	no	—
986	C₂×C₄	—	26	12	no	—
987	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
988	C₂×C₄	C₂×D₄×D₁₃	1	3	yes	—
989	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
990	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
991	C₈	—	13	8	no	—
992	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
993	C₈	C₂⁴×D₁₃	1	6	yes	—
994	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
995	C₂²	—	2	4	no	—
996	C₂²	—	2	4	no	—
997	C₂²	—	4	3	no	—
998	C₂²	—	8	6	no	—
999	C₂²	—	8	6	no	—
1000	C₂²	—	13	8	no	—
1001	C₂²	—	26	2	no	—
1002	C₂²	—	26	6	no	—
1003	C₂²	—	52	12	no	—
1004	C₂²	—	104	1	no	—
1005	C₂²	—	104	3	no	—
1006	C₂²	—	104	12	no	—
1007	C₂²	—	104	8	no	—
1008	C₂²	—	104	24	no	—
1009	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
1010	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1011	C₄	—	2	4	no	—
1012	C₄	—	2	4	no	—
1013	C₄	—	13	8	no	—
1014	C₄	—	26	2	no	—
1015	C₄	—	26	6	no	—
1016	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
1017	C₄	C₂²×D₄×D₁₃	1	6	yes	—
1018	C₄	C₂⁵×D₁₃	1	1	yes	characteristic
1019	C₂	—	2	1	no	—
1020	C₂	—	2	6	no	—
1021	C₂	—	4	4	no	—
1022	C₂	—	4	4	no	—
1023	C₂	—	26	8	no	—
1024	C₂	—	52	6	no	—
1025	C₂	—	52	2	no	—
1026	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁶
Frattini	C₄	C₂⁵×D₁₃
Fitting	C₁₃×#3584	C₂
socle	C₂×C₁₃	C₂⁴×D₄
hypercenter	#3584	D₁₃
hypocenter	C₁₃	#63092
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #13129649	C₂	semidirect
2. #13129647	C₂	semidirect
3. #13129622	C₂	semidirect
4. #13129621	C₂	semidirect
5. #13129620	C₂	semidirect
6. #13129615	C₂	semidirect
7. #13129613	C₂	semidirect
8. #13129611	C₂	semidirect
9. #13129608	C₂	semidirect
10. #13129605	C₂	semidirect
11. C₂×#11719456	C₂	semidirect
12. C₂×#11719475	C₂	semidirect
13. D₁₃×#577	C₂	semidirect
14. #13129547	C₂	semidirect
15. C₁₃×#3584	C₂	semidirect
16. C₁₃×#585	C₂²	semidirect
17. C₁₃×#585	C₂²	semidirect
19. #11719652	C₂²	semidirect
21. D₁₃×2₋¹⁺⁴	C₂²	semidirect
23. #11719650	C₂²	semidirect
25. D₁₃×H(5,𝔽₂)	C₂²	semidirect
29. #11719648	C₂²	semidirect
30. #11719648	C₂²	semidirect
32. C₂×#88257	C₂²	semidirect
33. C₂×#88257	C₂²	semidirect
35. C₂×#88256	C₂²	semidirect
36. C₂×#88256	C₂²	semidirect
37. C₁₃×#578	C₂²	semidirect
38. C₁₃×#577	C₂²	semidirect
39. C₁₃×#577	C₂²	semidirect
40. C₁₃×#576	C₂²	semidirect
41. C₁₃×#575	C₂²	semidirect
42. C₂×C₁₃×#135	C₂²	semidirect
43. C₂×C₁₃×#131	C₂²	semidirect
44. #11719543	C₂²	semidirect
45. #11719542	C₂²	semidirect
46. #11719541	C₂²	semidirect
47. #11719540	C₂²	semidirect
48. C₂×#88205	C₂²	semidirect
49. #11719527	C₂²	semidirect
50. #11719527	C₂²	semidirect
51. C₂×#88203	C₂²	semidirect
52. #11719524	C₂²	semidirect
53. #11719484	C₂²	semidirect
54. #11719483	C₂²	semidirect
55. #11719482	C₂²	semidirect
56. D₁₃×#137	C₂²	semidirect
57. #11719480	C₂²	semidirect
58. #11719479	C₂²	semidirect
59. #11719478	C₂²	semidirect
60. D₁₃×AGL(1,ℤ/8)	C₂²	semidirect
61. #11719476	C₂²	semidirect
62. #11719475	C₂²	semidirect
63. #11719475	C₂²	semidirect
64. #11719475	C₂²	semidirect
65. #11719475	C₂²	semidirect
66. #11719475	C₂²	semidirect
67. #11719474	C₂²	semidirect
68. #11719473	C₂²	semidirect
69. D₁₃×#135	C₂²	semidirect
70. #11719471	C₂²	semidirect
71. C₂×#88172	C₂²	semidirect
72. #11719467	C₂²	semidirect
73. #11719467	C₂²	semidirect
74. C₂×#88170	C₂²	semidirect
75. C₂×SD₁₆×D₁₃	C₂²	semidirect
76. #11719462	C₂²	semidirect
77. C₂×#88165	C₂²	semidirect
78. #11719456	C₂²	semidirect
79. #11719456	C₂²	semidirect
80. #11719455	C₂²	semidirect
81. D₁₃×#131	C₂²	semidirect
82. C₂×#88163	C₂²	semidirect
83. C₂×#88162	C₂²	semidirect
84. #11719450	C₂²	semidirect
85. C₂×#88158	C₂²	semidirect
86. C₂²×#6095	C₂²	semidirect
87. C₂×#88155	C₂²	semidirect
91. C₁₃×2₋¹⁺⁴	C₂³	semidirect
95. C₁₃×H(5,𝔽₂)	C₂³	semidirect
100. C₂×C₁₃×#41	C₂³	semidirect
110. #88257	C₂³	semidirect
111. #88257	C₂³	semidirect
112. #88257	C₂³	semidirect
124. #88256	C₂³	semidirect
133. #41×D₁₃	C₂³	semidirect
138. #88254	C₂³	semidirect
144. C₂×Q₈×D₁₃	C₂³	semidirect
151. #88251	C₂³	semidirect
155. C₂×#6129	C₂³	semidirect
166. C₂×#6127	C₂³	semidirect
170. C₂²×Dic₂₆	C₂³	semidirect
171. C₁₃×#137	C₂³	semidirect
172. C₁₃×#137	C₂³	semidirect
173. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
174. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
175. C₁₃×#135	C₂³	semidirect
176. C₁₃×#135	C₂³	semidirect
177. C₁₃×#135	C₂³	semidirect
178. C₁₃×#135	C₂³	semidirect
179. C₂×C₁₃×Q₁₆	C₂³	semidirect
180. C₂×C₁₃×SD₁₆	C₂³	semidirect
181. C₂×C₁₃×SD₁₆	C₂³	semidirect
182. C₂×C₁₃×D₈	C₂³	semidirect
183. C₁₃×#131	C₂³	semidirect
184. C₁₃×#131	C₂³	semidirect
185. C₂×C₁₃×M₁₆	C₂³	semidirect
186. C₂²×C₈×C₁₃	C₂³	semidirect
187. #88205	C₂³	semidirect
188. #88205	C₂³	semidirect
189. #88205	C₂³	semidirect
190. #88204	C₂³	semidirect
191. #88204	C₂³	semidirect
192. #88203	C₂³	semidirect
193. #88203	C₂³	semidirect
194. #88203	C₂³	semidirect
195. #88202	C₂³	semidirect
196. C₂×#6107	C₂³	semidirect
197. #88196	C₂³	semidirect
198. #88196	C₂³	semidirect
199. C₂×#6106	C₂³	semidirect
200. C₂×#6105	C₂³	semidirect
201. #88186	C₂³	semidirect
202. #88186	C₂³	semidirect
203. C₂×#6104	C₂³	semidirect
204. C₂×#6099	C₂³	semidirect
205. #88173	C₂³	semidirect
206. #88172	C₂³	semidirect
207. #88172	C₂³	semidirect
208. #88172	C₂³	semidirect
209. Q₁₆×D₁₃	C₂³	semidirect
210. #88170	C₂³	semidirect
211. #88170	C₂³	semidirect
212. #88170	C₂³	semidirect
213. #88169	C₂³	semidirect
214. #88169	C₂³	semidirect
215. #88168	C₂³	semidirect
216. #88168	C₂³	semidirect
217. SD₁₆×D₁₃	C₂³	semidirect
218. SD₁₆×D₁₃	C₂³	semidirect
219. SD₁₆×D₁₃	C₂³	semidirect
220. #88166	C₂³	semidirect
221. #88165	C₂³	semidirect
222. #88165	C₂³	semidirect
223. #88165	C₂³	semidirect
224. D₈×D₁₃	C₂³	semidirect
225. #88163	C₂³	semidirect
226. #88162	C₂³	semidirect
227. #88161	C₂³	semidirect
228. M₁₆×D₁₃	C₂³	semidirect
229. C₂×Dic₅₂	C₂³	semidirect
230. #88158	C₂³	semidirect
231. #88158	C₂³	semidirect
232. C₂×D₁₀₄	C₂³	semidirect
233. C₂×#6095	C₂³	semidirect
234. C₂×#6095	C₂³	semidirect
235. C₂×#6095	C₂³	semidirect
236. C₂×#6095	C₂³	semidirect
237. C₂×#6095	C₂³	semidirect
238. #88155	C₂³	semidirect
239. #88155	C₂³	semidirect
240. #88155	C₂³	semidirect
241. #88155	C₂³	semidirect
242. C₂×#6094	C₂³	semidirect
243. C₂×C₈×D₁₃	C₂³	semidirect
413. #3584	D₁₃	semidirect
506. #585	C₂×D₁₃	semidirect
507. #585	C₂×D₁₃	semidirect
522. #578	C₂×D₁₃	semidirect
536. #577	C₂×D₁₃	semidirect
537. #577	C₂×D₁₃	semidirect
542. #576	C₂×D₁₃	semidirect
548. #575	C₂×D₁₃	semidirect
560. C₂×#135	C₂×D₁₃	semidirect
568. C₂×#131	C₂×D₁₃	semidirect
613. 2₋¹⁺⁴	C₂²×D₁₃	semidirect
636. H(5,𝔽₂)	C₂²×D₁₃	semidirect
664. C₂×#41	C₂²×D₁₃	semidirect
687. #137	C₂²×D₁₃	semidirect
688. #137	C₂²×D₁₃	semidirect
700. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
701. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
711. #135	C₂²×D₁₃	semidirect
712. #135	C₂²×D₁₃	semidirect
713. #135	C₂²×D₁₃	semidirect
714. #135	C₂²×D₁₃	semidirect
718. C₂×Q₁₆	C₂²×D₁₃	semidirect
729. C₂×SD₁₆	C₂²×D₁₃	semidirect
730. C₂×SD₁₆	C₂²×D₁₃	semidirect
734. C₂×D₈	C₂²×D₁₃	semidirect
741. #131	C₂²×D₁₃	semidirect
742. #131	C₂²×D₁₃	semidirect
746. C₂×M₁₆	C₂²×D₁₃	semidirect
748. C₂²×C₈	C₂²×D₁₃	semidirect
915. C₁₃	#63092	semidirect

Maximal subgroups

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

subgroup	index
#13129649	2
#13129647	2
#13129622	2
#13129621	2
#13129620	2
#13129615	2
#13129613	2
#13129611	2
#13129608	2
#13129605	2
C₂×#11719456	2
C₂×#11719475	2
D₁₃×#577	2
#13129547	2
C₁₃×#3584	2
#63092	13