Subgroups — #16776779

Order 3328.

10894 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129647	C₂	1	1	yes	maximal, characteristic, complemented
2	#13129646	C₂	1	1	yes	maximal, characteristic, complemented
3	#13129617	C₂	1	1	yes	maximal, characteristic, complemented
4	#13129614	C₂	1	8	yes	maximal, complemented
5	#13129613	C₂	1	6	yes	maximal, complemented
6	#13129612	C₂	1	6	yes	maximal, complemented
7	#13129611	C₂	1	8	yes	maximal, complemented
8	#13129609	C₂	1	6	yes	maximal, complemented
9	#13129608	C₂	1	8	yes	maximal, complemented
10	#13129607	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719479	C₂	1	6	yes	maximal, complemented
12	C₂×#11719540	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#576	C₂	1	8	yes	maximal, complemented
14	#13129549	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#585	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	#11719652	—	2	2	no	—
19	#11719652	C₂²	1	8	yes	complemented
20	#11719650	—	2	4	no	—
21	#11719650	C₂²	1	8	yes	complemented
22	D₁₃×H(5,𝔽₂)	—	2	4	no	—
23	D₁₃×H(5,𝔽₂)	—	2	6	no	—
24	D₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
25	D₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
26	#11719648	—	2	4	no	—
27	#11719648	—	2	2	no	—
28	#11719648	C₂²	1	1	yes	characteristic
29	#11719648	C₂²	1	6	yes	complemented
30	#11719648	C₂²	1	6	yes	complemented
31	#11719648	C₂²	1	1	yes	characteristic, complemented
32	C₂×#88256	—	2	4	no	—
33	C₂×#88256	C₂²	1	6	yes	complemented
34	C₂×#88256	C₂²	1	1	yes	characteristic, complemented
35	C₂×#88251	—	2	6	no	—
36	C₂×#88251	C₂²	1	6	yes	complemented
37	C₁₃×#577	C₂²	1	8	yes	complemented
38	C₁₃×#576	C₂²	1	8	yes	complemented
39	C₁₃×#575	C₂²	1	6	yes	complemented
40	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
41	C₁₃×#568	C₂²	1	1	yes	characteristic, complemented
42	#11719543	C₂²	1	4	yes	complemented
43	#11719542	C₂²	1	4	yes	complemented
44	#11719541	C₂²	1	4	yes	complemented
45	#11719540	C₂²	1	4	yes	complemented
46	#11719540	C₂²	1	8	yes	complemented
47	#11719540	C₂²	1	8	yes	complemented
48	#11719527	C₂²	1	6	yes	complemented
49	C₂×#88204	C₂²	1	3	yes	complemented
50	C₂×#88204	C₂²	1	6	yes	complemented
51	C₂×#88203	C₂²	1	3	yes	complemented
52	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
53	C₂×#88186	C₂²	1	3	yes	complemented
54	C₂²×#6104	C₂²	1	3	yes	complemented
55	#11719484	C₂²	1	12	yes	complemented
56	#11719484	C₂²	1	4	yes	complemented
57	#11719483	C₂²	1	12	yes	complemented
58	#11719483	C₂²	1	12	yes	complemented
59	#11719482	C₂²	1	24	yes	complemented
60	#11719480	C₂²	1	12	yes	complemented
61	#11719480	C₂²	1	12	yes	complemented
62	#11719479	C₂²	1	12	yes	complemented
63	#11719479	C₂²	1	24	yes	complemented
64	#11719479	C₂²	1	12	yes	complemented
65	#11719479	C₂²	1	24	yes	complemented
66	#11719479	C₂²	1	24	yes	complemented
67	#11719478	C₂²	1	24	yes	complemented
68	D₁₃×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
69	D₁₃×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
70	#11719475	C₂²	1	24	yes	complemented
71	#11719474	C₂²	1	24	yes	complemented
72	#11719473	C₂²	1	24	yes	complemented
73	D₁₃×#135	C₂²	1	24	yes	complemented
74	#11719467	C₂²	1	24	yes	complemented
75	C₂×#88170	C₂²	1	12	yes	complemented
76	C₂×#88168	C₂²	1	12	yes	complemented
77	#11719462	C₂²	1	24	yes	complemented
78	C₂×#88165	C₂²	1	12	yes	complemented
79	C₂×D₈×D₁₃	C₂²	1	12	yes	complemented
80	#11719457	C₂²	1	8	yes	complemented
81	#11719456	C₂²	1	8	yes	complemented
82	#11719455	C₂²	1	8	yes	complemented
83	D₁₃×#131	C₂²	1	8	yes	complemented
84	#11719453	C₂²	1	6	yes	complemented
85	C₂×#88162	C₂²	1	6	yes	complemented
86	#11719450	C₂²	1	6	yes	complemented
87	C₂×#88161	C₂²	1	6	yes	complemented
88	C₁₃×2₋¹⁺⁴	—	2	1	no	—
89	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	complemented
90	C₁₃×H(5,𝔽₂)	—	2	4	no	—
91	C₁₃×H(5,𝔽₂)	—	2	3	no	—
92	C₁₃×H(5,𝔽₂)	C₂³	1	8	yes	complemented
93	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	complemented
94	C₂×C₁₃×#41	—	2	4	no	—
95	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×#41	C₂³	1	3	yes	complemented
98	C₂×C₁₃×#41	C₂³	1	6	yes	complemented
99	C₂²×D₄×C₁₃	—	2	3	no	—
100	C₂²×D₄×C₁₃	C₂³	1	3	yes	complemented
101	C₂²×C₂²⋊D₁₃	—	2	12	no	—
102	#88257	—	2	8	no	—
103	#88257	—	2	6	no	—
104	#88257	—	2	6	no	—
105	#88257	D₄	1	4	yes	—
106	#88257	C₂³	1	12	yes	complemented
107	#88257	C₂³	1	4	yes	complemented
108	#88257	C₂³	1	4	yes	complemented
109	#88256	—	2	4	no	—
110	#88256	—	2	8	no	—
111	#88256	—	2	8	no	—
112	#88256	—	2	24	no	—
113	#88256	—	2	12	no	—
114	#88256	—	2	12	no	—
115	#88256	—	2	6	no	—
116	#88256	—	2	6	no	—
117	#88256	D₄	1	4	yes	—
118	#88256	C₂³	1	12	yes	complemented
119	#88256	C₂³	1	24	yes	complemented
120	#88256	C₂³	1	12	yes	complemented
121	#88256	C₂³	1	8	yes	complemented
122	#88256	C₂³	1	4	yes	complemented
123	#41×D₁₃	—	2	4	no	—
124	#41×D₁₃	—	2	8	no	—
125	#41×D₁₃	—	2	8	no	—
126	#41×D₁₃	—	2	8	no	—
127	#41×D₁₃	—	2	24	no	—
128	#41×D₁₃	—	2	12	no	—
129	#41×D₁₃	—	2	12	no	—
130	#41×D₁₃	C₂³	1	8	yes	—
131	#41×D₁₃	C₂³	1	24	yes	complemented
132	#41×D₁₃	C₂³	1	24	yes	complemented
133	#88254	—	2	1	no	—
134	#88254	—	2	8	no	—
135	#88254	D₄	1	2	yes	—
136	#88254	C₂³	1	12	yes	complemented
137	#88254	C₂³	1	4	yes	complemented
138	C₂×#6131	—	2	1	no	—
139	C₂×#6131	—	2	8	no	—
140	C₂×#6131	C₂³	1	12	yes	complemented
141	#88251	—	2	3	no	—
142	#88251	—	2	12	no	—
143	#88251	—	2	12	no	—
144	#88251	—	2	24	no	—
145	#88251	—	2	24	no	—
146	#88251	—	2	24	no	—
147	#88251	—	2	12	no	—
148	#88251	—	2	12	no	—
149	#88251	D₄	1	6	yes	—
150	#88251	C₂³	1	12	yes	complemented
151	#88251	C₂³	1	24	yes	complemented
152	#88251	C₂³	1	12	yes	complemented
153	C₂×#6129	—	2	24	no	—
154	C₂×#6129	—	2	6	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	—	2	24	no	—
160	C₂×D₄×D₁₃	—	2	6	no	—
161	C₂×D₄×D₁₃	C₂³	1	12	yes	complemented
162	C₂×D₄×D₁₃	C₂³	1	12	yes	complemented
163	C₂×#6127	—	2	12	no	—
164	C₂×#6127	—	2	12	no	—
165	C₂×#6127	—	2	6	no	—
166	C₂×#6127	C₂³	1	6	yes	—
167	C₂×#6127	C₂³	1	6	yes	complemented
168	C₂×#6127	C₂³	1	3	yes	complemented
169	C₂²×D₅₂	—	2	6	no	—
170	C₂²×D₅₂	C₂³	1	3	yes	complemented
171	C₁₃×#137	C₂³	1	12	yes	complemented
172	C₁₃×#137	C₂³	1	4	yes	complemented
173	C₁₃×AGL(1,ℤ/8)	C₂³	1	12	yes	complemented
174	C₁₃×AGL(1,ℤ/8)	C₂³	1	24	yes	complemented
175	C₁₃×AGL(1,ℤ/8)	C₂³	1	12	yes	complemented
176	C₁₃×#135	C₂³	1	24	yes	complemented
177	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	complemented
178	C₂×C₁₃×D₈	C₂³	1	12	yes	complemented
179	C₁₃×#131	C₂³	1	8	yes	complemented
180	C₂×C₁₃×M₁₆	C₂³	1	6	yes	complemented
181	#88205	C₂³	1	12	yes	complemented
182	#88204	C₂³	1	12	yes	complemented
183	#88204	C₂³	1	12	yes	complemented
184	#88204	C₂³	1	12	yes	complemented
185	#88204	C₂³	1	12	yes	complemented
186	#88204	C₂³	1	4	yes	complemented
187	#88204	C₂³	1	12	yes	complemented
188	#88203	C₂³	1	12	yes	complemented
189	#88203	C₂³	1	24	yes	complemented
190	#88202	C₂³	1	4	yes	complemented
191	#88202	C₂³	1	4	yes	complemented
192	C₂×#6107	C₂³	1	6	yes	complemented
193	C₂×#6107	C₂³	1	1	yes	characteristic, complemented
194	#88196	C₂³	1	12	yes	complemented
195	C₂×#6106	C₂³	1	6	yes	complemented
196	C₂×#6106	C₂³	1	3	yes	complemented
197	C₂×#6105	C₂³	1	6	yes	complemented
198	C₂×#6105	C₂³	1	3	yes	complemented
199	#88186	C₂³	1	12	yes	complemented
200	#88186	C₂³	1	24	yes	complemented
201	C₂×#6104	C₂³	1	6	yes	complemented
202	C₂×#6104	C₂³	1	12	yes	complemented
203	C₂×#6104	C₂³	1	12	yes	complemented
204	C₂×#6104	C₂³	1	3	yes	complemented
205	C₂×#6104	C₂³	1	6	yes	complemented
206	C₂×#6099	C₂³	1	3	yes	complemented
207	C₂²×#1055	C₂³	1	3	yes	complemented
208	#88173	C₂³	1	24	yes	complemented
209	#88172	C₂³	1	8	yes	complemented
210	#88172	C₂³	1	24	yes	complemented
211	Q₁₆×D₁₃	C₂³	1	8	yes	complemented
212	#88170	C₂³	1	24	yes	complemented
213	#88170	C₂³	1	48	yes	complemented
214	#88170	C₂³	1	8	yes	complemented
215	#88169	C₂³	1	24	yes	complemented
216	#88169	C₂³	1	8	yes	complemented
217	#88168	C₂³	1	24	yes	complemented
218	#88168	C₂³	1	48	yes	complemented
219	#88168	C₂³	1	24	yes	complemented
220	SD₁₆×D₁₃	C₂³	1	24	yes	complemented
221	SD₁₆×D₁₃	C₂³	1	24	yes	complemented
222	#88166	C₂³	1	24	yes	complemented
223	#88165	C₂³	1	24	yes	complemented
224	#88165	C₂³	1	48	yes	complemented
225	#88165	C₂³	1	24	yes	complemented
226	D₈×D₁₃	C₂³	1	24	yes	complemented
227	D₈×D₁₃	C₂³	1	48	yes	complemented
228	#88163	C₂³	1	4	yes	complemented
229	#88163	C₂³	1	12	yes	complemented
230	#88162	C₂³	1	12	yes	complemented
231	#88162	C₂³	1	24	yes	complemented
232	#88162	C₂³	1	12	yes	complemented
233	#88161	C₂³	1	4	yes	complemented
234	#88161	C₂³	1	12	yes	complemented
235	#88161	C₂³	1	12	yes	complemented
236	#88161	C₂³	1	12	yes	complemented
237	M₁₆×D₁₃	C₂³	1	24	yes	complemented
238	#88158	C₂³	1	24	yes	complemented
239	C₂×D₁₀₄	C₂³	1	12	yes	complemented
240	C₂×#6095	C₂³	1	12	yes	complemented
241	#88155	C₂³	1	24	yes	complemented
242	C₂×#6094	C₂³	1	12	yes	complemented
243	C₂×C₈×D₁₃	C₂³	1	12	yes	complemented
244	#63091	—	13	1	no	maximal, Sylow
245	C₂⁴×C₁₃	—	2	3	no	—
246	C₂³×D₁₃	—	2	3	no	—
247	C₂³×D₁₃	—	2	12	no	—
248	C₂³×D₁₃	—	2	12	no	—
249	C₁₃×#41	—	2	4	no	—
250	C₁₃×#41	—	2	8	no	—
251	C₁₃×#41	—	2	12	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	12	yes	—
257	C₁₃×#41	C₂⁴	1	12	yes	—
258	C₁₃×#41	C₂⁴	1	4	yes	—
259	C₁₃×#41	C₂⁴	1	4	yes	—
260	C₂×Q₈×C₁₃	—	2	4	no	—
261	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
262	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
264	C₂×D₄×C₁₃	—	2	6	no	—
265	C₂×D₄×C₁₃	—	2	3	no	—
266	C₂×D₄×C₁₃	—	2	12	no	—
267	C₂×D₄×C₁₃	—	2	24	no	—
268	C₂×D₄×C₁₃	—	2	6	no	—
269	C₂×D₄×C₁₃	—	2	3	no	—
270	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
271	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
272	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
273	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
274	C₂²×C₄×C₁₃	—	2	6	no	—
275	C₂²×C₄×C₁₃	—	2	3	no	—
276	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
277	C₂×C₂²⋊D₁₃	—	2	3	no	—
278	C₂×C₂²⋊D₁₃	—	2	6	no	—
279	C₂×C₂²⋊D₁₃	—	2	12	no	—
280	C₂×C₂²⋊D₁₃	—	2	24	no	—
281	C₂×C₂²⋊D₁₃	—	2	24	no	—
282	C₂×C₂²⋊D₁₃	—	2	48	no	—
283	C₂×C₂²⋊D₁₃	—	2	12	no	—
284	C₂×C₂²⋊D₁₃	—	2	12	no	—
285	C₂×C₂²⋊D₁₃	C₂×D₄	1	12	yes	—
286	C₂²×Dic₁₃	—	2	12	no	—
287	#6131	—	2	8	no	—
288	#6131	—	2	4	no	—
289	#6131	—	2	12	no	—
290	#6131	—	2	4	no	—
291	#6131	—	2	24	no	—
292	#6131	C₂×D₄	1	8	yes	—
293	#6131	C₂⁴	1	24	yes	—
294	#6131	C₂⁴	1	8	yes	—
295	Q₈×D₁₃	—	2	4	no	—
296	Q₈×D₁₃	—	2	12	no	—
297	Q₈×D₁₃	—	2	4	no	—
298	Q₈×D₁₃	C₂×D₄	1	8	yes	—
299	Q₈×D₁₃	C₂⁴	1	8	yes	—
300	Q₈×D₁₃	C₂⁴	1	8	yes	—
301	#6129	—	2	12	no	—
302	#6129	—	2	24	no	—
303	#6129	—	2	8	no	—
304	#6129	—	2	24	no	—
305	#6129	—	2	24	no	—
306	#6129	—	2	24	no	—
307	#6129	—	2	12	no	—
308	#6129	—	2	24	no	—
309	#6129	—	2	12	no	—
310	#6129	C₂×D₄	1	24	yes	—
311	#6129	C₂⁴	1	8	yes	—
312	#6129	C₂⁴	1	24	yes	—
313	D₄×D₁₃	—	2	24	no	—
314	D₄×D₁₃	—	2	24	no	—
315	D₄×D₁₃	—	2	12	no	—
316	D₄×D₁₃	—	2	24	no	—
317	D₄×D₁₃	—	2	24	no	—
318	D₄×D₁₃	—	2	24	no	—
319	D₄×D₁₃	—	2	48	no	—
320	D₄×D₁₃	—	2	12	no	—
321	D₄×D₁₃	—	2	24	no	—
322	D₄×D₁₃	—	2	12	no	—
323	D₄×D₁₃	—	2	24	no	—
324	D₄×D₁₃	—	2	24	no	—
325	D₄×D₁₃	C₂×D₄	1	24	yes	—
326	D₄×D₁₃	C₂⁴	1	24	yes	—
327	D₄×D₁₃	C₂⁴	1	24	yes	—
328	#6127	—	2	6	no	—
329	#6127	—	2	6	no	—
330	#6127	—	2	6	no	—
331	#6127	—	2	8	no	—
332	#6127	—	2	24	no	—
333	#6127	—	2	4	no	—
334	#6127	—	2	12	no	—
335	#6127	—	2	24	no	—
336	#6127	—	2	24	no	—
337	#6127	—	2	12	no	—
338	#6127	—	2	12	no	—
339	#6127	—	2	24	no	—
340	#6127	C₂×D₄	1	12	yes	—
341	#6127	C₂×D₄	1	12	yes	—
342	#6127	C₂⁴	1	12	yes	—
343	#6127	C₂⁴	1	4	yes	—
344	#6127	C₂⁴	1	12	yes	—
345	#6127	C₂⁴	1	12	yes	—
346	#6127	C₂⁴	1	4	yes	—
347	C₂×D₅₂	—	2	12	no	—
348	C₂×D₅₂	—	2	6	no	—
349	C₂×D₅₂	—	2	3	no	—
350	C₂×D₅₂	—	2	12	no	—
351	C₂×D₅₂	—	2	24	no	—
352	C₂×D₅₂	—	2	12	no	—
353	C₂×D₅₂	C₂×D₄	1	6	yes	—
354	C₂×D₅₂	C₂⁴	1	12	yes	—
355	C₂×D₅₂	C₂⁴	1	6	yes	—
356	C₂×D₅₂	C₂⁴	1	3	yes	—
357	C₂×C₄×D₁₃	—	2	6	no	—
358	C₂×C₄×D₁₃	—	2	3	no	—
359	C₂×C₄×D₁₃	—	2	12	no	—
360	C₂×C₄×D₁₃	—	2	24	no	—
361	C₂×C₄×D₁₃	—	2	24	no	—
362	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
363	C₂×Dic₂₆	—	2	4	no	—
364	C₂×Dic₂₆	—	2	12	no	—
365	C₂×Dic₂₆	C₂×D₄	1	6	yes	—
366	C₂×Dic₂₆	C₂⁴	1	6	yes	—
367	C₂×Dic₂₆	C₂⁴	1	1	yes	characteristic
368	C₁₃×Q₁₆	C₂⁴	1	8	yes	—
369	C₁₃×SD₁₆	C₂⁴	1	8	yes	—
370	C₁₃×SD₁₆	C₂⁴	1	24	yes	—
371	C₁₃×D₈	C₂⁴	1	24	yes	—
372	C₁₃×M₁₆	C₂⁴	1	12	yes	—
373	C₁₃×M₁₆	C₂⁴	1	4	yes	—
374	C₂×C₈×C₁₃	C₂⁴	1	12	yes	—
375	#6107	C₂⁴	1	2	yes	—
376	#6107	C₂⁴	1	12	yes	—
377	#6107	C₂⁴	1	4	yes	—
378	#6107	C₂⁴	1	2	yes	—
379	#6106	C₂⁴	1	12	yes	—
380	#6106	C₂⁴	1	12	yes	—
381	#6106	C₂⁴	1	4	yes	—
382	#6105	C₂⁴	1	4	yes	—
383	#6105	C₂⁴	1	12	yes	—
384	#6105	C₂⁴	1	12	yes	—
385	#6104	C₂⁴	1	4	yes	—
386	#6104	C₂⁴	1	12	yes	—
387	#6104	C₂⁴	1	6	yes	—
388	#6104	C₂⁴	1	24	yes	—
389	#6104	C₂⁴	1	6	yes	—
390	#6099	C₂⁴	1	12	yes	—
391	C₂×#1055	C₂⁴	1	6	yes	—
392	C₂×#1055	C₂⁴	1	6	yes	—
393	C₂×#1055	C₂⁴	1	1	yes	characteristic
394	C₂×#1055	C₂⁴	1	3	yes	—
395	Dic₅₂	C₂⁴	1	8	yes	—
396	D₁₀₄	C₂⁴	1	24	yes	—
397	#6095	C₂⁴	1	24	yes	—
398	#6095	C₂⁴	1	8	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	H(7,𝔽₂)	—	13	1	no	—
404	H(7,𝔽₂)	—	13	1	no	—
405	#3585	—	13	8	no	—
406	#3585	—	13	8	no	—
407	#3585	—	13	6	no	—
408	#3585	—	13	6	no	—
409	#3585	—	13	1	no	—
410	#3585	D₁₃	1	1	yes	characteristic, complemented
411	#3584	—	13	1	no	—
412	#3584	—	13	8	no	—
413	#3584	—	13	6	no	—
414	C₂×#576	—	13	1	no	—
415	C₂×#576	—	13	8	no	—
416	C₂×#576	—	13	6	no	—
417	#3573	—	13	1	no	—
418	C₂³×C₁₃	—	2	12	no	—
419	C₂³×C₁₃	—	2	3	no	—
420	C₂³×C₁₃	—	2	6	no	—
421	C₂³×C₁₃	—	16	3	no	—
422	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
423	C₂²×D₁₃	—	2	12	no	—
424	C₂²×D₁₃	—	2	3	no	—
425	C₂²×D₁₃	—	2	6	no	—
426	C₂²×D₁₃	—	2	24	no	—
427	C₂²×D₁₃	—	2	24	no	—
428	C₂²×D₁₃	—	16	12	no	—
429	C₂²×D₁₃	—	16	12	no	—
430	C₂²×D₁₃	—	16	3	no	—
431	C₂²×D₁₃	C₂²×D₄	1	12	yes	—
432	Q₈×C₁₃	—	2	1	no	—
433	Q₈×C₁₃	—	2	6	no	—
434	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
435	Q₈×C₁₃	C₂⁵	1	2	yes	—
436	Q₈×C₁₃	C₂⁵	1	4	yes	—
437	D₄×C₁₃	—	2	12	no	—
438	D₄×C₁₃	—	2	4	no	—
439	D₄×C₁₃	—	2	12	no	—
440	D₄×C₁₃	—	2	6	no	—
441	D₄×C₁₃	—	2	3	no	—
442	D₄×C₁₃	—	2	12	no	—
443	D₄×C₁₃	C₂²×D₄	1	12	yes	—
444	D₄×C₁₃	C₂⁵	1	6	yes	—
445	D₄×C₁₃	C₂⁵	1	4	yes	—
446	C₂×C₄×C₁₃	—	2	6	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	12	no	—
449	C₂×C₄×C₁₃	—	2	4	no	—
450	C₂×C₄×C₁₃	—	2	12	no	—
451	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
453	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
455	C₂²⋊D₁₃	—	2	4	no	—
456	C₂²⋊D₁₃	—	2	12	no	—
457	C₂²⋊D₁₃	—	2	12	no	—
458	C₂²⋊D₁₃	—	2	8	no	—
459	C₂²⋊D₁₃	—	2	24	no	—
460	C₂²⋊D₁₃	—	2	24	no	—
461	C₂²⋊D₁₃	—	2	24	no	—
462	C₂²⋊D₁₃	C₂²×D₄	1	8	yes	—
463	C₂²⋊D₁₃	C₂²×D₄	1	24	yes	—
464	C₂×Dic₁₃	—	2	1	no	—
465	C₂×Dic₁₃	—	2	6	no	—
466	C₂×Dic₁₃	—	2	8	no	—
467	C₂×Dic₁₃	—	2	24	no	—
468	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
469	D₅₂	—	2	24	no	—
470	D₅₂	—	2	8	no	—
471	D₅₂	—	2	3	no	—
472	D₅₂	—	2	12	no	—
473	D₅₂	—	2	6	no	—
474	D₅₂	C₂²×D₄	1	4	yes	—
475	D₅₂	C₂²×D₄	1	12	yes	—
476	D₅₂	C₂⁵	1	6	yes	—
477	D₅₂	C₂⁵	1	4	yes	—
478	C₄×D₁₃	—	2	8	no	—
479	C₄×D₁₃	—	2	8	no	—
480	C₄×D₁₃	—	2	4	no	—
481	C₄×D₁₃	—	2	12	no	—
482	C₄×D₁₃	—	2	12	no	—
483	C₄×D₁₃	—	2	8	no	—
484	C₄×D₁₃	—	2	24	no	—
485	C₄×D₁₃	C₂²×D₄	1	24	yes	—
486	C₄×D₁₃	C₂⁵	1	8	yes	—
487	Dic₂₆	—	2	1	no	—
488	Dic₂₆	—	2	6	no	—
489	Dic₂₆	—	2	8	no	—
490	Dic₂₆	—	2	8	no	—
491	Dic₂₆	C₂²×D₄	1	4	yes	—
492	Dic₂₆	C₂²×D₄	1	12	yes	—
493	Dic₂₆	C₂⁵	1	4	yes	—
494	Dic₂₆	C₂⁵	1	2	yes	—
495	C₈×C₁₃	C₂⁵	1	8	yes	—
496	#1055	C₂⁵	1	1	yes	characteristic
497	#1055	C₂⁵	1	6	yes	—
498	#1055	C₂⁵	1	1	yes	characteristic
499	#585	—	13	1	no	—
500	#585	—	13	8	no	—
501	#585	—	13	8	no	—
502	#585	—	13	1	no	—
503	#585	—	13	6	no	—
504	#585	—	13	6	no	—
505	#585	—	26	4	no	—
506	#585	—	26	2	no	—
507	#585	—	26	4	no	—
508	#585	—	26	2	no	—
509	#585	C₂×D₁₃	1	1	yes	characteristic, complemented
510	C₂×H(5,𝔽₂)	—	13	8	no	—
511	C₂×H(5,𝔽₂)	—	13	8	no	—
512	C₂×H(5,𝔽₂)	—	13	1	no	—
513	C₂×H(5,𝔽₂)	—	13	6	no	—
514	C₂×H(5,𝔽₂)	—	13	6	no	—
515	C₂×H(5,𝔽₂)	—	26	6	no	—
516	C₂×H(5,𝔽₂)	—	26	4	no	—
517	C₂×H(5,𝔽₂)	—	26	4	no	—
518	C₂×H(5,𝔽₂)	—	26	6	no	—
519	C₂×H(5,𝔽₂)	C₂×D₁₃	1	1	yes	characteristic, complemented
520	#578	—	13	4	no	—
521	#578	—	13	12	no	—
522	#578	—	13	4	no	—
523	#577	—	13	4	no	—
524	#577	—	13	4	no	—
525	#577	—	13	12	no	—
526	#577	—	13	12	no	—
527	#577	—	13	12	no	—
528	#577	—	13	12	no	—
529	#577	—	13	24	no	—
530	#577	—	13	24	no	—
531	#577	—	13	8	no	—
532	#577	C₂×D₁₃	1	8	yes	complemented
533	#576	—	13	8	no	—
534	#576	—	13	4	no	—
535	#576	—	13	8	no	—
536	#576	—	13	12	no	—
537	#576	—	13	24	no	—
538	#576	—	13	12	no	—
539	#576	—	13	24	no	—
540	#576	—	13	24	no	—
541	#576	—	13	24	no	—
542	#576	—	13	24	no	—
543	#576	—	13	8	no	—
544	#576	C₂×D₁₃	1	8	yes	complemented
545	#575	—	13	6	no	—
546	#575	—	13	24	no	—
547	#575	—	13	24	no	—
548	#575	—	13	24	no	—
549	#575	—	13	6	no	—
550	#575	C₂×D₁₃	1	6	yes	complemented
551	C₂×AGL(1,ℤ/8)	—	13	3	no	—
552	C₂×AGL(1,ℤ/8)	—	13	3	no	—
553	C₂×AGL(1,ℤ/8)	—	13	24	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	12	no	—
557	C₂×AGL(1,ℤ/8)	—	13	6	no	—
558	C₂×AGL(1,ℤ/8)	C₂×D₁₃	1	6	yes	complemented
559	C₂×#135	—	13	3	no	—
560	C₂×#135	—	13	6	no	—
561	C₂×#135	—	13	24	no	—
562	C₂×#135	—	13	12	no	—
563	C₂²×D₈	—	13	3	no	—
564	C₂²×D₈	—	13	12	no	—
565	#568	—	13	8	no	—
566	#568	—	13	6	no	—
567	#568	C₂×D₁₃	1	1	yes	characteristic, complemented
568	C₂×#131	—	13	1	no	—
569	C₂×#131	—	13	8	no	—
570	C₂×#131	—	13	6	no	—
571	C₂²×C₁₃	—	2	6	no	—
572	C₂²×C₁₃	—	2	4	no	—
573	C₂²×C₁₃	—	4	3	no	—
574	C₂²×C₁₃	—	8	6	no	—
575	C₂²×C₁₃	—	8	12	no	—
576	C₂²×C₁₃	—	8	3	no	—
577	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
578	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
579	C₂×D₁₃	—	2	6	no	—
580	C₂×D₁₃	—	2	4	no	—
581	C₂×D₁₃	—	4	12	no	—
582	C₂×D₁₃	—	8	24	no	—
583	C₂×D₁₃	—	8	24	no	—
584	C₂×D₁₃	—	8	12	no	—
585	C₂×D₁₃	—	8	6	no	—
586	C₂×D₁₃	—	8	3	no	—
587	C₂×D₁₃	C₂³×D₄	1	8	yes	—
588	C₄×C₁₃	—	2	2	no	—
589	C₄×C₁₃	—	2	4	no	—
590	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
591	C₄×C₁₃	C₂³×D₄	1	6	yes	—
592	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
593	Dic₁₃	—	2	2	no	—
594	Dic₁₃	—	2	4	no	—
595	Dic₁₃	C₂³×D₄	1	8	yes	—
596	2₋¹⁺⁴	—	2	1	no	—
597	2₋¹⁺⁴	—	13	4	no	—
598	2₋¹⁺⁴	—	13	2	no	—
599	2₋¹⁺⁴	—	13	4	no	—
600	2₋¹⁺⁴	—	13	12	no	—
601	2₋¹⁺⁴	—	13	4	no	—
602	2₋¹⁺⁴	—	13	4	no	—
603	2₋¹⁺⁴	—	13	12	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	1	no	—
609	2₋¹⁺⁴	C₂²×D₁₃	1	4	yes	complemented
610	H(5,𝔽₂)	—	2	4	no	—
611	H(5,𝔽₂)	—	2	3	no	—
612	H(5,𝔽₂)	—	13	4	no	—
613	H(5,𝔽₂)	—	13	6	no	—
614	H(5,𝔽₂)	—	13	12	no	—
615	H(5,𝔽₂)	—	13	12	no	—
616	H(5,𝔽₂)	—	13	24	no	—
617	H(5,𝔽₂)	—	13	8	no	—
618	H(5,𝔽₂)	—	13	4	no	—
619	H(5,𝔽₂)	—	13	12	no	—
620	H(5,𝔽₂)	—	13	24	no	—
621	H(5,𝔽₂)	—	13	12	no	—
622	H(5,𝔽₂)	—	26	12	no	—
623	H(5,𝔽₂)	—	26	12	no	—
624	H(5,𝔽₂)	—	26	24	no	—
625	H(5,𝔽₂)	—	26	24	no	—
626	H(5,𝔽₂)	—	26	24	no	—
627	H(5,𝔽₂)	—	26	12	no	—
628	H(5,𝔽₂)	—	26	12	no	—
629	H(5,𝔽₂)	—	26	24	no	—
630	H(5,𝔽₂)	—	26	6	no	—
631	H(5,𝔽₂)	—	26	6	no	—
632	H(5,𝔽₂)	—	26	8	no	—
633	H(5,𝔽₂)	—	26	8	no	—
634	H(5,𝔽₂)	—	26	12	no	—
635	H(5,𝔽₂)	—	26	12	no	—
636	H(5,𝔽₂)	—	26	4	no	—
637	H(5,𝔽₂)	—	26	3	no	—
638	H(5,𝔽₂)	C₂²×D₁₃	1	8	yes	complemented
639	H(5,𝔽₂)	C₂²×D₁₃	1	4	yes	complemented
640	C₂×#41	—	2	4	no	—
641	C₂×#41	—	2	1	no	—
642	C₂×#41	—	13	8	no	—
643	C₂×#41	—	13	6	no	—
644	C₂×#41	—	13	24	no	—
645	C₂×#41	—	13	24	no	—
646	C₂×#41	—	13	12	no	—
647	C₂×#41	—	13	12	no	—
648	C₂×#41	—	13	3	no	—
649	C₂×#41	—	13	6	no	—
650	C₂×#41	—	26	6	no	—
651	C₂×#41	—	26	12	no	—
652	C₂×#41	—	26	12	no	—
653	C₂×#41	—	26	6	no	—
654	C₂×#41	—	26	24	no	—
655	C₂×#41	—	26	8	no	—
656	C₂×#41	—	26	8	no	—
657	C₂×#41	—	26	8	no	—
658	C₂×#41	—	26	8	no	—
659	C₂×#41	—	26	24	no	—
660	C₂×#41	—	26	12	no	—
661	C₂×#41	—	26	12	no	—
662	C₂×#41	—	26	4	no	—
663	C₂×#41	—	26	1	no	—
664	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
665	C₂×#41	C₂²×D₁₃	1	3	yes	complemented
666	C₂×#41	C₂²×D₁₃	1	6	yes	complemented
667	C₂²×D₄	—	2	3	no	—
668	C₂²×D₄	—	13	12	no	—
669	C₂²×D₄	—	13	12	no	—
670	C₂²×D₄	—	13	3	no	—
671	C₂²×D₄	—	26	6	no	—
672	C₂²×D₄	—	26	12	no	—
673	C₂²×D₄	—	26	24	no	—
674	C₂²×D₄	—	26	24	no	—
675	C₂²×D₄	—	26	6	no	—
676	C₂²×D₄	—	26	12	no	—
677	C₂²×D₄	—	26	3	no	—
678	C₂²×D₄	C₂²×D₁₃	1	3	yes	complemented
679	#137	—	13	12	no	—
680	#137	—	13	12	no	—
681	#137	—	13	24	no	—
682	#137	—	13	8	no	—
683	#137	—	13	8	no	—
684	#137	—	13	24	no	—
685	#137	—	13	12	no	—
686	#137	—	13	4	no	—
687	#137	C₂²×D₁₃	1	12	yes	complemented
688	#137	C₂²×D₁₃	1	4	yes	complemented
689	AGL(1,ℤ/8)	—	13	24	no	—
690	AGL(1,ℤ/8)	—	13	12	no	—
691	AGL(1,ℤ/8)	—	13	24	no	—
692	AGL(1,ℤ/8)	—	13	12	no	—
693	AGL(1,ℤ/8)	—	13	24	no	—
694	AGL(1,ℤ/8)	—	13	48	no	—
695	AGL(1,ℤ/8)	—	13	24	no	—
696	AGL(1,ℤ/8)	—	13	24	no	—
697	AGL(1,ℤ/8)	—	13	48	no	—
698	AGL(1,ℤ/8)	—	13	24	no	—
699	AGL(1,ℤ/8)	—	13	12	no	—
700	AGL(1,ℤ/8)	—	13	24	no	—
701	AGL(1,ℤ/8)	—	13	12	no	—
702	AGL(1,ℤ/8)	C₂²×D₁₃	1	12	yes	complemented
703	AGL(1,ℤ/8)	C₂²×D₁₃	1	24	yes	complemented
704	AGL(1,ℤ/8)	C₂²×D₁₃	1	12	yes	complemented
705	#135	—	13	4	no	—
706	#135	—	13	12	no	—
707	#135	—	13	12	no	—
708	#135	—	13	12	no	—
709	#135	—	13	12	no	—
710	#135	—	13	12	no	—
711	#135	—	13	24	no	—
712	#135	—	13	8	no	—
713	#135	—	13	24	no	—
714	#135	—	13	48	no	—
715	#135	—	13	24	no	—
716	#135	—	13	24	no	—
717	#135	C₂²×D₁₃	1	24	yes	complemented
718	C₂×Q₁₆	—	13	1	no	—
719	C₂×Q₁₆	—	13	6	no	—
720	C₂×Q₁₆	—	13	8	no	—
721	C₂×SD₁₆	—	13	3	no	—
722	C₂×SD₁₆	—	13	6	no	—
723	C₂×SD₁₆	—	13	3	no	—
724	C₂×SD₁₆	—	13	6	no	—
725	C₂×SD₁₆	—	13	24	no	—
726	C₂×SD₁₆	—	13	24	no	—
727	C₂×SD₁₆	—	13	12	no	—
728	C₂×SD₁₆	C₂²×D₁₃	1	12	yes	complemented
729	C₂×D₈	—	13	3	no	—
730	C₂×D₈	—	13	12	no	—
731	C₂×D₈	—	13	6	no	—
732	C₂×D₈	—	13	6	no	—
733	C₂×D₈	—	13	12	no	—
734	C₂×D₈	—	13	24	no	—
735	C₂×D₈	—	13	48	no	—
736	C₂×D₈	—	13	12	no	—
737	C₂×D₈	C₂²×D₁₃	1	12	yes	complemented
738	#131	—	13	4	no	—
739	#131	—	13	4	no	—
740	#131	—	13	12	no	—
741	#131	—	13	4	no	—
742	#131	—	13	12	no	—
743	#131	—	13	12	no	—
744	#131	—	13	24	no	—
745	#131	C₂²×D₁₃	1	8	yes	complemented
746	C₂×M₁₆	—	13	3	no	—
747	C₂×M₁₆	—	13	24	no	—
748	C₂×M₁₆	—	13	12	no	—
749	C₂×M₁₆	C₂²×D₁₃	1	6	yes	complemented
750	C₂²×C₈	—	13	3	no	—
751	C₂²×C₈	—	13	12	no	—
752	C₂×C₁₃	—	2	6	no	—
753	C₂×C₁₃	—	2	1	no	—
754	C₂×C₁₃	—	4	4	no	—
755	C₂×C₁₃	—	4	6	no	—
756	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
757	D₁₃	—	2	8	no	—
758	D₁₃	—	4	6	no	—
759	D₁₃	—	4	4	no	—
760	C₂⁴	—	2	3	no	—
761	C₂⁴	—	26	12	no	—
762	C₂⁴	—	26	12	no	—
763	C₂⁴	—	26	3	no	—
764	#41	—	2	8	no	—
765	#41	—	2	4	no	—
766	#41	—	2	12	no	—
767	#41	—	2	6	no	—
768	#41	—	2	6	no	—
769	#41	—	2	6	no	—
770	#41	—	13	8	no	—
771	#41	—	13	24	no	—
772	#41	—	13	12	no	—
773	#41	—	13	12	no	—
774	#41	—	13	4	no	—
775	#41	—	13	12	no	—
776	#41	—	13	8	no	—
777	#41	—	13	24	no	—
778	#41	—	13	24	no	—
779	#41	—	13	8	no	—
780	#41	—	13	4	no	—
781	#41	—	13	12	no	—
782	#41	—	13	12	no	—
783	#41	—	26	24	no	—
784	#41	—	26	24	no	—
785	#41	—	26	8	no	—
786	#41	—	26	24	no	—
787	#41	—	26	4	no	—
788	#41	—	26	12	no	—
789	#41	—	26	12	no	—
790	#41	—	26	12	no	—
791	#41	—	26	24	no	—
792	#41	—	26	24	no	—
793	#41	—	26	24	no	—
794	#41	—	26	24	no	—
795	#41	—	26	24	no	—
796	#41	—	26	24	no	—
797	#41	—	26	8	no	—
798	#41	—	26	12	no	—
799	#41	—	26	24	no	—
800	#41	—	26	12	no	—
801	#41	—	26	12	no	—
802	#41	—	26	4	no	—
803	#41	—	26	8	no	—
804	#41	—	26	4	no	—
805	#41	—	26	12	no	—
806	#41	—	26	6	no	—
807	#41	—	26	6	no	—
808	#41	—	26	6	no	—
809	#41	D₄×D₁₃	1	4	yes	—
810	#41	C₂³×D₁₃	1	4	yes	—
811	#41	C₂³×D₁₃	1	12	yes	—
812	#41	C₂³×D₁₃	1	12	yes	—
813	#41	C₂³×D₁₃	1	4	yes	—
814	C₂×Q₈	—	2	4	no	—
815	C₂×Q₈	—	13	8	no	—
816	C₂×Q₈	—	13	6	no	—
817	C₂×Q₈	—	13	8	no	—
818	C₂×Q₈	—	13	8	no	—
819	C₂×Q₈	—	13	1	no	—
820	C₂×Q₈	—	13	6	no	—
821	C₂×Q₈	—	26	4	no	—
822	C₂×Q₈	—	26	12	no	—
823	C₂×Q₈	—	26	12	no	—
824	C₂×Q₈	—	26	4	no	—
825	C₂×Q₈	—	26	4	no	—
826	C₂×Q₈	D₄×D₁₃	1	1	yes	characteristic
827	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
828	C₂×Q₈	C₂³×D₁₃	1	6	yes	—
829	C₂×D₄	—	2	3	no	—
830	C₂×D₄	—	2	6	no	—
831	C₂×D₄	—	2	24	no	—
832	C₂×D₄	—	2	12	no	—
833	C₂×D₄	—	2	3	no	—
834	C₂×D₄	—	2	6	no	—
835	C₂×D₄	—	13	12	no	—
836	C₂×D₄	—	13	24	no	—
837	C₂×D₄	—	13	24	no	—
838	C₂×D₄	—	13	24	no	—
839	C₂×D₄	—	13	6	no	—
840	C₂×D₄	—	13	3	no	—
841	C₂×D₄	—	13	12	no	—
842	C₂×D₄	—	13	6	no	—
843	C₂×D₄	—	26	12	no	—
844	C₂×D₄	—	26	12	no	—
845	C₂×D₄	—	26	24	no	—
846	C₂×D₄	—	26	12	no	—
847	C₂×D₄	—	26	24	no	—
848	C₂×D₄	—	26	24	no	—
849	C₂×D₄	—	26	12	no	—
850	C₂×D₄	—	26	12	no	—
851	C₂×D₄	—	26	24	no	—
852	C₂×D₄	—	26	24	no	—
853	C₂×D₄	—	26	48	no	—
854	C₂×D₄	—	26	24	no	—
855	C₂×D₄	—	26	12	no	—
856	C₂×D₄	—	26	12	no	—
857	C₂×D₄	—	26	24	no	—
858	C₂×D₄	—	26	24	no	—
859	C₂×D₄	—	26	24	no	—
860	C₂×D₄	—	26	24	no	—
861	C₂×D₄	—	26	48	no	—
862	C₂×D₄	—	26	12	no	—
863	C₂×D₄	—	26	6	no	—
864	C₂×D₄	—	26	3	no	—
865	C₂×D₄	—	26	12	no	—
866	C₂×D₄	—	26	24	no	—
867	C₂×D₄	—	26	6	no	—
868	C₂×D₄	—	26	3	no	—
869	C₂×D₄	D₄×D₁₃	1	3	yes	—
870	C₂×D₄	C₂³×D₁₃	1	3	yes	—
871	C₂×D₄	C₂³×D₁₃	1	12	yes	—
872	C₂×D₄	C₂³×D₁₃	1	6	yes	—
873	C₂²×C₄	—	2	3	no	—
874	C₂²×C₄	—	2	6	no	—
875	C₂²×C₄	—	13	12	no	—
876	C₂²×C₄	—	26	12	no	—
877	C₂²×C₄	—	26	24	no	—
878	C₂²×C₄	—	26	24	no	—
879	C₂²×C₄	—	26	12	no	—
880	C₂²×C₄	—	26	6	no	—
881	C₂²×C₄	—	26	3	no	—
882	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
883	Q₁₆	—	13	2	no	—
884	Q₁₆	—	13	4	no	—
885	Q₁₆	—	13	2	no	—
886	Q₁₆	—	13	12	no	—
887	Q₁₆	—	13	8	no	—
888	Q₁₆	C₂³×D₁₃	1	8	yes	—
889	SD₁₆	—	13	12	no	—
890	SD₁₆	—	13	4	no	—
891	SD₁₆	—	13	12	no	—
892	SD₁₆	—	13	12	no	—
893	SD₁₆	—	13	4	no	—
894	SD₁₆	—	13	12	no	—
895	SD₁₆	—	13	8	no	—
896	SD₁₆	—	13	24	no	—
897	SD₁₆	C₂³×D₁₃	1	8	yes	—
898	SD₁₆	C₂³×D₁₃	1	24	yes	—
899	D₈	—	13	6	no	—
900	D₈	—	13	4	no	—
901	D₈	—	13	6	no	—
902	D₈	—	13	24	no	—
903	D₈	—	13	12	no	—
904	D₈	—	13	24	no	—
905	D₈	C₂³×D₁₃	1	24	yes	—
906	M₁₆	—	13	12	no	—
907	M₁₆	—	13	24	no	—
908	M₁₆	—	13	8	no	—
909	M₁₆	C₂³×D₁₃	1	12	yes	—
910	M₁₆	C₂³×D₁₃	1	4	yes	—
911	C₂×C₈	—	13	1	no	—
912	C₂×C₈	—	13	6	no	—
913	C₂×C₈	—	13	3	no	—
914	C₂×C₈	—	13	6	no	—
915	C₂×C₈	—	13	8	no	—
916	C₂×C₈	—	13	24	no	—
917	C₂×C₈	C₂³×D₁₃	1	12	yes	—
918	C₁₃	#63091	1	1	yes	characteristic, complemented, Sylow
919	C₂³	—	2	6	no	—
920	C₂³	—	2	3	no	—
921	C₂³	—	2	12	no	—
922	C₂³	—	13	12	no	—
923	C₂³	—	16	3	no	—
924	C₂³	—	26	24	no	—
925	C₂³	—	26	24	no	—
926	C₂³	—	26	12	no	—
927	C₂³	—	26	6	no	—
928	C₂³	—	26	3	no	—
929	C₂³	—	208	3	no	—
930	C₂³	—	208	12	no	—
931	C₂³	—	208	12	no	—
932	C₂³	C₂×D₄×D₁₃	1	3	yes	—
933	Q₈	—	2	6	no	—
934	Q₈	—	2	1	no	—
935	Q₈	—	13	12	no	—
936	Q₈	—	13	4	no	—
937	Q₈	—	13	4	no	—
938	Q₈	—	13	2	no	—
939	Q₈	—	26	8	no	—
940	Q₈	—	26	8	no	—
941	Q₈	—	26	6	no	—
942	Q₈	—	26	1	no	—
943	Q₈	C₂×D₄×D₁₃	1	4	yes	—
944	Q₈	C₂⁴×D₁₃	1	2	yes	—
945	Q₈	C₂⁴×D₁₃	1	4	yes	—
946	D₄	—	2	12	no	—
947	D₄	—	2	12	no	—
948	D₄	—	2	4	no	—
949	D₄	—	2	12	no	—
950	D₄	—	2	3	no	—
951	D₄	—	2	6	no	—
952	D₄	—	13	24	no	—
953	D₄	—	13	8	no	—
954	D₄	—	13	12	no	—
955	D₄	—	13	4	no	—
956	D₄	—	13	6	no	—
957	D₄	—	13	4	no	—
958	D₄	—	26	8	no	—
959	D₄	—	26	24	no	—
960	D₄	—	26	24	no	—
961	D₄	—	26	24	no	—
962	D₄	—	26	8	no	—
963	D₄	—	26	24	no	—
964	D₄	—	26	12	no	—
965	D₄	—	26	12	no	—
966	D₄	—	26	4	no	—
967	D₄	—	26	12	no	—
968	D₄	—	26	6	no	—
969	D₄	—	26	3	no	—
970	D₄	C₂×D₄×D₁₃	1	12	yes	—
971	D₄	C₂⁴×D₁₃	1	6	yes	—
972	D₄	C₂⁴×D₁₃	1	4	yes	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	6	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	12	no	—
977	C₂×C₄	—	2	12	no	—
978	C₂×C₄	—	13	12	no	—
979	C₂×C₄	—	13	24	no	—
980	C₂×C₄	—	13	8	no	—
981	C₂×C₄	—	26	8	no	—
982	C₂×C₄	—	26	24	no	—
983	C₂×C₄	—	26	8	no	—
984	C₂×C₄	—	26	8	no	—
985	C₂×C₄	—	26	8	no	—
986	C₂×C₄	—	26	24	no	—
987	C₂×C₄	—	26	6	no	—
988	C₂×C₄	—	26	1	no	—
989	C₂×C₄	—	26	12	no	—
990	C₂×C₄	—	26	12	no	—
991	C₂×C₄	—	26	4	no	—
992	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
993	C₂×C₄	C₂×D₄×D₁₃	1	3	yes	—
994	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
996	C₈	—	13	1	no	—
997	C₈	—	13	6	no	—
998	C₈	—	13	1	no	—
999	C₈	C₂⁴×D₁₃	1	8	yes	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	6	no	—
1002	C₂²	—	4	3	no	—
1003	C₂²	—	8	3	no	—
1004	C₂²	—	8	12	no	—
1005	C₂²	—	8	6	no	—
1006	C₂²	—	13	8	no	—
1007	C₂²	—	26	6	no	—
1008	C₂²	—	26	4	no	—
1009	C₂²	—	52	12	no	—
1010	C₂²	—	104	3	no	—
1011	C₂²	—	104	12	no	—
1012	C₂²	—	104	6	no	—
1013	C₂²	—	104	24	no	—
1014	C₂²	—	104	24	no	—
1015	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
1016	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	13	8	no	—
1020	C₄	—	26	2	no	—
1021	C₄	—	26	4	no	—
1022	C₄	C₂²×D₄×D₁₃	1	6	yes	—
1023	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
1024	C₄	C₂⁵×D₁₃	1	1	yes	characteristic
1025	C₂	—	2	1	no	—
1026	C₂	—	2	6	no	—
1027	C₂	—	4	6	no	—
1028	C₂	—	4	4	no	—
1029	C₂	—	26	8	no	—
1030	C₂	—	52	6	no	—
1031	C₂	—	52	4	no	—
1032	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×#3585	C₂
socle	C₂×C₁₃	C₂⁴×D₄
hypercenter	#3585	D₁₃
hypocenter	C₁₃	#63091
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3585

Complements

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

N	H ≅ G/N	type
1. #13129647	C₂	semidirect
2. #13129646	C₂	semidirect
3. #13129617	C₂	semidirect
4. #13129614	C₂	semidirect
5. #13129613	C₂	semidirect
6. #13129612	C₂	semidirect
7. #13129611	C₂	semidirect
8. #13129609	C₂	semidirect
9. #13129608	C₂	semidirect
10. #13129607	C₂	semidirect
11. C₂×#11719479	C₂	semidirect
12. C₂×#11719540	C₂	semidirect
13. D₁₃×#576	C₂	semidirect
14. #13129549	C₂	semidirect
15. C₁₃×#3585	C₂	semidirect
16. C₁₃×#585	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. #11719652	C₂²	semidirect
21. #11719650	C₂²	semidirect
24. D₁₃×H(5,𝔽₂)	C₂²	semidirect
25. D₁₃×H(5,𝔽₂)	C₂²	semidirect
29. #11719648	C₂²	semidirect
30. #11719648	C₂²	semidirect
31. #11719648	C₂²	semidirect
33. C₂×#88256	C₂²	semidirect
34. C₂×#88256	C₂²	semidirect
36. C₂×#88251	C₂²	semidirect
37. C₁₃×#577	C₂²	semidirect
38. C₁₃×#576	C₂²	semidirect
39. C₁₃×#575	C₂²	semidirect
40. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
41. C₁₃×#568	C₂²	semidirect
42. #11719543	C₂²	semidirect
43. #11719542	C₂²	semidirect
44. #11719541	C₂²	semidirect
45. #11719540	C₂²	semidirect
46. #11719540	C₂²	semidirect
47. #11719540	C₂²	semidirect
48. #11719527	C₂²	semidirect
49. C₂×#88204	C₂²	semidirect
50. C₂×#88204	C₂²	semidirect
51. C₂×#88203	C₂²	semidirect
52. C₂×#88202	C₂²	semidirect
53. C₂×#88186	C₂²	semidirect
54. C₂²×#6104	C₂²	semidirect
55. #11719484	C₂²	semidirect
56. #11719484	C₂²	semidirect
57. #11719483	C₂²	semidirect
58. #11719483	C₂²	semidirect
59. #11719482	C₂²	semidirect
60. #11719480	C₂²	semidirect
61. #11719480	C₂²	semidirect
62. #11719479	C₂²	semidirect
63. #11719479	C₂²	semidirect
64. #11719479	C₂²	semidirect
65. #11719479	C₂²	semidirect
66. #11719479	C₂²	semidirect
67. #11719478	C₂²	semidirect
68. D₁₃×AGL(1,ℤ/8)	C₂²	semidirect
69. D₁₃×AGL(1,ℤ/8)	C₂²	semidirect
70. #11719475	C₂²	semidirect
71. #11719474	C₂²	semidirect
72. #11719473	C₂²	semidirect
73. D₁₃×#135	C₂²	semidirect
74. #11719467	C₂²	semidirect
75. C₂×#88170	C₂²	semidirect
76. C₂×#88168	C₂²	semidirect
77. #11719462	C₂²	semidirect
78. C₂×#88165	C₂²	semidirect
79. C₂×D₈×D₁₃	C₂²	semidirect
80. #11719457	C₂²	semidirect
81. #11719456	C₂²	semidirect
82. #11719455	C₂²	semidirect
83. D₁₃×#131	C₂²	semidirect
84. #11719453	C₂²	semidirect
85. C₂×#88162	C₂²	semidirect
86. #11719450	C₂²	semidirect
87. C₂×#88161	C₂²	semidirect
89. C₁₃×2₋¹⁺⁴	C₂³	semidirect
92. C₁₃×H(5,𝔽₂)	C₂³	semidirect
93. C₁₃×H(5,𝔽₂)	C₂³	semidirect
97. C₂×C₁₃×#41	C₂³	semidirect
98. C₂×C₁₃×#41	C₂³	semidirect
100. C₂²×D₄×C₁₃	C₂³	semidirect
106. #88257	C₂³	semidirect
107. #88257	C₂³	semidirect
108. #88257	C₂³	semidirect
118. #88256	C₂³	semidirect
119. #88256	C₂³	semidirect
120. #88256	C₂³	semidirect
121. #88256	C₂³	semidirect
122. #88256	C₂³	semidirect
131. #41×D₁₃	C₂³	semidirect
132. #41×D₁₃	C₂³	semidirect
136. #88254	C₂³	semidirect
137. #88254	C₂³	semidirect
140. C₂×#6131	C₂³	semidirect
150. #88251	C₂³	semidirect
151. #88251	C₂³	semidirect
152. #88251	C₂³	semidirect
155. C₂×#6129	C₂³	semidirect
161. C₂×D₄×D₁₃	C₂³	semidirect
162. C₂×D₄×D₁₃	C₂³	semidirect
167. C₂×#6127	C₂³	semidirect
168. C₂×#6127	C₂³	semidirect
170. C₂²×D₅₂	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×AGL(1,ℤ/8)	C₂³	semidirect
176. C₁₃×#135	C₂³	semidirect
177. C₂×C₁₃×SD₁₆	C₂³	semidirect
178. C₂×C₁₃×D₈	C₂³	semidirect
179. C₁₃×#131	C₂³	semidirect
180. C₂×C₁₃×M₁₆	C₂³	semidirect
181. #88205	C₂³	semidirect
182. #88204	C₂³	semidirect
183. #88204	C₂³	semidirect
184. #88204	C₂³	semidirect
185. #88204	C₂³	semidirect
186. #88204	C₂³	semidirect
187. #88204	C₂³	semidirect
188. #88203	C₂³	semidirect
189. #88203	C₂³	semidirect
190. #88202	C₂³	semidirect
191. #88202	C₂³	semidirect
192. C₂×#6107	C₂³	semidirect
193. C₂×#6107	C₂³	semidirect
194. #88196	C₂³	semidirect
195. C₂×#6106	C₂³	semidirect
196. C₂×#6106	C₂³	semidirect
197. C₂×#6105	C₂³	semidirect
198. C₂×#6105	C₂³	semidirect
199. #88186	C₂³	semidirect
200. #88186	C₂³	semidirect
201. C₂×#6104	C₂³	semidirect
202. C₂×#6104	C₂³	semidirect
203. C₂×#6104	C₂³	semidirect
204. C₂×#6104	C₂³	semidirect
205. C₂×#6104	C₂³	semidirect
206. C₂×#6099	C₂³	semidirect
207. C₂²×#1055	C₂³	semidirect
208. #88173	C₂³	semidirect
209. #88172	C₂³	semidirect
210. #88172	C₂³	semidirect
211. Q₁₆×D₁₃	C₂³	semidirect
212. #88170	C₂³	semidirect
213. #88170	C₂³	semidirect
214. #88170	C₂³	semidirect
215. #88169	C₂³	semidirect
216. #88169	C₂³	semidirect
217. #88168	C₂³	semidirect
218. #88168	C₂³	semidirect
219. #88168	C₂³	semidirect
220. SD₁₆×D₁₃	C₂³	semidirect
221. SD₁₆×D₁₃	C₂³	semidirect
222. #88166	C₂³	semidirect
223. #88165	C₂³	semidirect
224. #88165	C₂³	semidirect
225. #88165	C₂³	semidirect
226. D₈×D₁₃	C₂³	semidirect
227. D₈×D₁₃	C₂³	semidirect
228. #88163	C₂³	semidirect
229. #88163	C₂³	semidirect
230. #88162	C₂³	semidirect
231. #88162	C₂³	semidirect
232. #88162	C₂³	semidirect
233. #88161	C₂³	semidirect
234. #88161	C₂³	semidirect
235. #88161	C₂³	semidirect
236. #88161	C₂³	semidirect
237. M₁₆×D₁₃	C₂³	semidirect
238. #88158	C₂³	semidirect
239. C₂×D₁₀₄	C₂³	semidirect
240. C₂×#6095	C₂³	semidirect
241. #88155	C₂³	semidirect
242. C₂×#6094	C₂³	semidirect
243. C₂×C₈×D₁₃	C₂³	semidirect
410. #3585	D₁₃	semidirect
509. #585	C₂×D₁₃	semidirect
519. C₂×H(5,𝔽₂)	C₂×D₁₃	semidirect
532. #577	C₂×D₁₃	semidirect
544. #576	C₂×D₁₃	semidirect
550. #575	C₂×D₁₃	semidirect
558. C₂×AGL(1,ℤ/8)	C₂×D₁₃	semidirect
567. #568	C₂×D₁₃	semidirect
609. 2₋¹⁺⁴	C₂²×D₁₃	semidirect
638. H(5,𝔽₂)	C₂²×D₁₃	semidirect
639. H(5,𝔽₂)	C₂²×D₁₃	semidirect
665. C₂×#41	C₂²×D₁₃	semidirect
666. C₂×#41	C₂²×D₁₃	semidirect
678. C₂²×D₄	C₂²×D₁₃	semidirect
687. #137	C₂²×D₁₃	semidirect
688. #137	C₂²×D₁₃	semidirect
702. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
703. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
704. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
717. #135	C₂²×D₁₃	semidirect
728. C₂×SD₁₆	C₂²×D₁₃	semidirect
737. C₂×D₈	C₂²×D₁₃	semidirect
745. #131	C₂²×D₁₃	semidirect
749. C₂×M₁₆	C₂²×D₁₃	semidirect
918. C₁₃	#63091	semidirect

Maximal subgroups

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

subgroup	index
#13129647	2
#13129646	2
#13129617	2
#13129614	2
#13129613	2
#13129612	2
#13129611	2
#13129609	2
#13129608	2
#13129607	2
C₂×#11719479	2
C₂×#11719540	2
D₁₃×#576	2
#13129549	2
C₁₃×#3585	2
#63091	13