Subgroups — #16771313

Order 3328.

7856 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	#13128921	C₂	1	2	yes	maximal, complemented
2	#13128868	C₂	1	6	yes	maximal, complemented
3	#13128842	C₂	1	2	yes	maximal, complemented
4	#13128797	C₂	1	6	yes	maximal, complemented
5	#13128747	C₂	1	3	yes	maximal, complemented
6	#13128712	C₂	1	3	yes	maximal, complemented
7	#13128655	C₂	1	1	yes	maximal, characteristic, complemented
8	#13128614	C₂	1	1	yes	maximal, characteristic, complemented
9	#13128571	C₂	1	6	yes	maximal, complemented
10	#13128505	C₂	1	2	yes	maximal, complemented
11	#13128462	C₂	1	2	yes	maximal, complemented
12	#13128446	C₂	1	6	yes	maximal, complemented
13	#13128431	C₂	1	2	yes	maximal, complemented
14	D₄×#6127	C₂	1	6	yes	maximal, complemented
15	#13128252	C₂	1	6	yes	maximal, complemented
16	#13128132	C₂	1	3	yes	maximal, complemented
17	C₂×#11719182	C₂	1	3	yes	maximal, complemented
18	C₄×#88256	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
21	C₂×#88256	C₂²	1	2	yes	—
22	C₂²×#6127	C₂²	1	6	yes	complemented
23	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
26	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
28	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
29	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
30	C₄×C₁₃×#41	C₂²	1	3	yes	complemented
31	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
34	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
35	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
36	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
37	#11719539	C₂²	1	4	yes	complemented
38	#11719538	C₂²	1	6	yes	complemented
39	#11719535	C₂²	1	6	yes	complemented
40	#11719534	C₂²	1	12	yes	complemented
41	#11719532	C₂²	1	2	yes	—
42	#11719522	C₂²	1	4	yes	complemented
43	D₄×C₂²⋊D₁₃	C₂²	1	12	yes	complemented
44	#11719496	C₂²	1	6	yes	complemented
45	#11719496	C₂²	1	6	yes	complemented
46	#11719496	C₂²	1	6	yes	complemented
47	C₂×#88184	C₂²	1	6	yes	complemented
48	C₂×#88184	C₂²	1	6	yes	complemented
49	#11719290	C₂²	1	6	yes	complemented
50	#11719290	C₂²	1	6	yes	complemented
51	#11719289	C₂²	1	6	yes	complemented
52	#11719287	C₂²	1	12	yes	complemented
53	#11719285	C₂²	1	12	yes	complemented
54	#11719284	C₂²	1	6	yes	complemented
55	#11719282	C₂²	1	2	yes	complemented
56	#11719282	C₂²	1	2	yes	complemented
57	#11719279	C₂²	1	4	yes	complemented
58	C₄×#6131	C₂²	1	4	yes	complemented
59	#11719275	C₂²	1	2	yes	complemented
60	Q₈×Dic₂₆	C₂²	1	2	yes	complemented
61	#11719270	C₂²	1	12	yes	complemented
62	#11719268	C₂²	1	6	yes	complemented
63	#11719267	C₂²	1	12	yes	complemented
64	#11719265	C₂²	1	24	yes	complemented
65	#11719258	C₂²	1	6	yes	complemented
66	#11719258	C₂²	1	6	yes	complemented
67	#11719257	C₂²	1	12	yes	complemented
68	#11719256	C₂²	1	6	yes	complemented
69	#11719255	C₂²	1	12	yes	complemented
70	#11719255	C₂²	1	12	yes	complemented
71	D₄×D₅₂	C₂²	1	6	yes	complemented
72	D₄×D₅₂	C₂²	1	6	yes	complemented
73	#11719253	C₂²	1	12	yes	complemented
74	#11719252	C₂²	1	24	yes	complemented
75	#11719250	C₂²	1	12	yes	complemented
76	C₄×D₄×D₁₃	C₂²	1	12	yes	complemented
77	#11719248	C₂²	1	6	yes	complemented
78	D₄×Dic₂₆	C₂²	1	6	yes	complemented
79	#11719240	C₂²	1	12	yes	complemented
80	#11719239	C₂²	1	12	yes	complemented
81	#11719237	C₂²	1	12	yes	complemented
82	#11719235	C₂²	1	12	yes	complemented
83	#11719232	C₂²	1	24	yes	complemented
84	#11719230	C₂²	1	6	yes	complemented
85	#11719228	C₂²	1	6	yes	complemented
86	#11719226	C₂²	1	6	yes	complemented
87	#11719224	C₂²	1	6	yes	complemented
88	#11719219	C₂²	1	12	yes	complemented
89	#11719212	C₂²	1	12	yes	complemented
90	#11719195	C₂²	1	24	yes	complemented
91	#11719184	C₂²	1	6	yes	complemented
92	#11719184	C₂²	1	6	yes	complemented
93	#11719184	C₂²	1	6	yes	complemented
94	#11719184	C₂²	1	6	yes	complemented
95	#11719184	C₂²	1	6	yes	complemented
96	#11719184	C₂²	1	6	yes	complemented
97	#11719182	C₂²	1	3	yes	complemented
98	#11719182	C₂²	1	6	yes	complemented
99	#11719182	C₂²	1	6	yes	complemented
100	#11719182	C₂²	1	3	yes	complemented
101	#11719182	C₂²	1	6	yes	complemented
102	#11719182	C₂²	1	6	yes	complemented
103	#11719182	C₂²	1	6	yes	complemented
104	#11719182	C₂²	1	6	yes	complemented
105	#11719182	C₂²	1	6	yes	complemented
106	#11719182	C₂²	1	3	yes	complemented
107	C₂×#88129	C₂²	1	6	yes	complemented
108	C₂×#88128	C₂²	1	3	yes	complemented
109	C₄×#6127	C₂²	1	6	yes	complemented
110	C₄×#6127	C₂²	1	6	yes	complemented
111	C₄×#6127	C₂²	1	6	yes	complemented
112	C₂×C₄×D₅₂	C₂²	1	6	yes	complemented
113	C₂×C₄×D₅₂	C₂²	1	6	yes	complemented
114	#11719175	C₂²	1	3	yes	complemented
115	#11719175	C₂²	1	3	yes	complemented
116	#11719175	C₂²	1	1	yes	characteristic, complemented
117	C₂×#88123	C₂²	1	3	yes	complemented
118	C₂×C₁₃×#41	—	2	8	no	—
119	C₂×C₁₃×#41	C₂³	1	3	yes	—
120	C₂×C₁₃×#41	C₂³	1	3	yes	—
121	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
125	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
126	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
127	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
128	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
129	#88256	—	2	16	no	—
130	C₂×#6131	C₂³	1	4	yes	—
131	C₂×D₄×D₁₃	C₂³	1	12	yes	—
132	C₂×#6127	—	4	24	no	—
133	C₂×#6127	C₂³	1	6	yes	—
134	C₂×#6127	C₂³	1	6	yes	—
135	C₂×#6127	C₂³	1	6	yes	—
136	C₂×#6127	C₂³	1	12	yes	—
137	C₂×#6127	C₂³	1	12	yes	—
138	C₂×#6127	C₂³	1	12	yes	—
139	C₂²×D₅₂	C₂³	1	6	yes	—
140	C₂²×D₅₂	C₂³	1	6	yes	—
141	C₂²×D₅₂	C₂³	1	6	yes	—
142	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
143	C₂²×Dic₂₆	C₂³	1	6	yes	—
144	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
145	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
151	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
152	C₄×D₄×C₁₃	C₂³	1	3	yes	—
153	C₄×D₄×C₁₃	C₂³	1	3	yes	—
154	C₄×D₄×C₁₃	C₂³	1	3	yes	—
155	C₄×D₄×C₁₃	C₂³	1	3	yes	—
156	C₄×D₄×C₁₃	C₂³	1	6	yes	—
157	C₄×D₄×C₁₃	C₂³	1	3	yes	—
158	C₄×D₄×C₁₃	C₂³	1	6	yes	—
159	C₄×D₄×C₁₃	C₂³	1	6	yes	—
160	C₄×D₄×C₁₃	C₂³	1	3	yes	—
161	C₄×D₄×C₁₃	C₂³	1	3	yes	—
162	C₄×D₄×C₁₃	C₂³	1	6	yes	—
163	C₄×D₄×C₁₃	C₂³	1	3	yes	—
164	C₁₃×#117	C₂³	1	3	yes	—
165	C₁₃×#117	C₂³	1	3	yes	—
166	C₁₃×#117	C₂³	1	6	yes	—
167	C₁₃×#117	C₂³	1	3	yes	—
168	C₁₃×#117	C₂³	1	3	yes	—
169	C₁₃×#117	C₂³	1	6	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
172	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
173	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
174	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
176	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
177	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
178	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
179	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
180	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
181	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
182	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
183	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
184	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
185	#88207	C₂³	1	12	yes	—
186	#88201	C₂³	1	12	yes	—
187	#88200	C₂³	1	12	yes	—
188	Q₈×Dic₁₃	C₂³	1	4	yes	—
189	#88194	C₂³	1	12	yes	—
190	#88193	C₂³	1	24	yes	—
191	#88192	C₂³	1	12	yes	—
192	#88191	C₂³	1	24	yes	—
193	D₄×Dic₁₃	C₂³	1	12	yes	—
194	#88184	C₂³	1	6	yes	—
195	#88184	C₂³	1	6	yes	—
196	#88184	C₂³	1	12	yes	—
197	#88184	C₂³	1	12	yes	—
198	#88184	C₂³	1	12	yes	—
199	#88184	C₂³	1	12	yes	—
200	#88184	C₂³	1	12	yes	—
201	#88184	C₂³	1	12	yes	—
202	#88184	C₂³	1	6	yes	—
203	#88184	C₂³	1	6	yes	—
204	#88184	C₂³	1	6	yes	—
205	#88184	C₂³	1	6	yes	—
206	#88183	C₂³	1	12	yes	—
207	#88183	C₂³	1	12	yes	—
208	#88183	C₂³	1	12	yes	—
209	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
210	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
211	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
212	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
213	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
214	C₄×C₂²⋊D₁₃	C₂³	1	12	yes	—
215	C₂×#6103	C₂³	1	12	yes	—
216	C₂×#6103	C₂³	1	12	yes	—
217	#88180	C₂³	1	2	yes	—
218	#88180	C₂³	1	6	yes	—
219	#88180	C₂³	1	6	yes	—
220	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
221	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
222	#88178	C₂³	1	2	yes	—
223	#88178	C₂³	1	2	yes	—
224	#88178	C₂³	1	6	yes	—
225	#88178	C₂³	1	6	yes	—
226	#88178	C₂³	1	6	yes	—
227	#88178	C₂³	1	6	yes	—
228	#88152	C₂³	1	24	yes	—
229	#88150	C₂³	1	24	yes	—
230	#88149	C₂³	1	12	yes	—
231	#88149	C₂³	1	12	yes	—
232	#88148	C₂³	1	24	yes	—
233	#88148	C₂³	1	24	yes	—
234	#88147	C₂³	1	12	yes	—
235	#88147	C₂³	1	12	yes	—
236	#88146	C₂³	1	12	yes	—
237	C₄⋊C₄×D₁₃	C₂³	1	12	yes	—
238	#88144	C₂³	1	12	yes	—
239	#88142	C₂³	1	12	yes	—
240	#88139	C₂³	1	24	yes	—
241	#88138	C₂³	1	24	yes	—
242	#88138	C₂³	1	24	yes	—
243	#88137	C₂³	1	24	yes	—
244	#88136	C₂³	1	24	yes	—
245	#88135	C₂³	1	24	yes	—
246	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	—
247	#88132	C₂³	1	24	yes	—
248	#88130	C₂³	1	12	yes	—
249	#88130	C₂³	1	12	yes	—
250	#88129	C₂³	1	6	yes	—
251	#88129	C₂³	1	12	yes	—
252	#88129	C₂³	1	12	yes	—
253	#88129	C₂³	1	12	yes	—
254	#88129	C₂³	1	6	yes	—
255	#88129	C₂³	1	6	yes	—
256	#88128	C₂³	1	3	yes	—
257	#88128	C₂³	1	6	yes	—
258	#88128	C₂³	1	6	yes	—
259	#88128	C₂³	1	6	yes	—
260	C₄×D₅₂	C₂³	1	6	yes	—
261	C₄×D₅₂	C₂³	1	6	yes	—
262	C₄×D₅₂	C₂³	1	12	yes	—
263	C₄×D₅₂	C₂³	1	12	yes	—
264	C₄×D₅₂	C₂³	1	12	yes	—
265	C₄×D₅₂	C₂³	1	12	yes	—
266	C₄×D₅₂	C₂³	1	12	yes	—
267	C₄×D₅₂	C₂³	1	12	yes	—
268	C₄×D₅₂	C₂³	1	6	yes	—
269	C₄×D₅₂	C₂³	1	6	yes	—
270	C₄×D₅₂	C₂³	1	6	yes	—
271	C₄×D₅₂	C₂³	1	6	yes	—
272	#88126	C₂³	1	12	yes	—
273	#88126	C₂³	1	12	yes	—
274	#88126	C₂³	1	12	yes	—
275	C₄²×D₁₃	C₂³	1	12	yes	—
276	#88124	C₂³	1	2	yes	—
277	#88124	C₂³	1	6	yes	—
278	#88124	C₂³	1	6	yes	—
279	#88123	C₂³	1	3	yes	—
280	#88123	C₂³	1	6	yes	—
281	#88123	C₂³	1	6	yes	—
282	#88123	C₂³	1	6	yes	—
283	#88123	C₂³	1	1	yes	characteristic
284	#88123	C₂³	1	1	yes	characteristic
285	C₄×Dic₂₆	C₂³	1	2	yes	—
286	C₄×Dic₂₆	C₂³	1	2	yes	—
287	C₄×Dic₂₆	C₂³	1	6	yes	—
288	C₄×Dic₂₆	C₂³	1	6	yes	—
289	C₄×Dic₂₆	C₂³	1	6	yes	—
290	C₄×Dic₂₆	C₂³	1	6	yes	—
291	#62800	—	13	1	no	maximal, Sylow
292	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
293	C₂³×D₁₃	C₂⁴	1	12	yes	—
294	C₁₃×#41	—	2	4	no	—
295	C₁₃×#41	—	2	12	no	—
296	C₁₃×#41	—	2	12	no	—
297	C₁₃×#41	#41	1	8	yes	complemented
298	C₂×Q₈×C₁₃	—	2	4	no	—
299	C₂×Q₈×C₁₃	C₂⁴	1	3	yes	—
300	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂×D₄×C₁₃	—	2	12	no	—
302	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
303	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
304	C₂×D₄×C₁₃	C₂⁴	1	3	yes	—
305	C₂²×C₄×C₁₃	—	2	12	no	—
306	C₂²×C₄×C₁₃	—	2	12	no	—
307	C₂²×C₄×C₁₃	—	4	6	no	—
308	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
312	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
313	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
314	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
315	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
316	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
317	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
318	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
319	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
320	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
321	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
322	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
323	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
324	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₁₃	—	4	24	no	—
327	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
328	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
329	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
330	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
331	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
332	#6131	—	2	16	no	—
333	D₄×D₁₃	—	2	48	no	—
334	#6127	—	2	24	no	—
335	#6127	—	2	24	no	—
336	#6127	—	4	24	no	—
337	#6127	—	4	12	no	—
338	#6127	—	4	24	no	—
339	#6127	—	4	24	no	—
340	C₂×D₅₂	—	2	24	no	—
341	C₂×D₅₂	—	4	12	no	—
342	C₂×D₅₂	—	4	12	no	—
343	C₂×D₅₂	C₂⁴	1	6	yes	—
344	C₂×D₅₂	C₂⁴	1	6	yes	—
345	C₂×D₅₂	C₂⁴	1	6	yes	—
346	C₂×D₅₂	C₂⁴	1	12	yes	—
347	C₂×D₅₂	C₂⁴	1	12	yes	—
348	C₂×D₅₂	C₂⁴	1	12	yes	—
349	C₂×C₄×D₁₃	—	4	24	no	—
350	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
351	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
352	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
353	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
354	C₂×Dic₂₆	—	4	12	no	—
355	C₂×Dic₂₆	C₂⁴	1	2	yes	—
356	C₂×Dic₂₆	C₂⁴	1	2	yes	—
357	C₂×Dic₂₆	C₂⁴	1	6	yes	—
358	C₂×Dic₂₆	C₂⁴	1	12	yes	—
359	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
360	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
361	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
362	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
363	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
364	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
365	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
366	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
367	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
368	C₁₃×C₂²⋊C₄	C₂⁴	1	6	yes	—
369	C₄²×C₁₃	C₂⁴	1	3	yes	—
370	C₄²×C₁₃	C₂⁴	1	3	yes	—
371	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
372	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₁₃	C₂⁴	1	3	yes	—
374	C₄²×C₁₃	C₂⁴	1	3	yes	—
375	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₁₃	C₂⁴	1	3	yes	—
377	C₄²×C₁₃	C₂⁴	1	3	yes	—
378	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₃	C₂⁴	1	3	yes	—
380	C₄²×C₁₃	C₂⁴	1	3	yes	—
381	C₄²×C₁₃	C₂⁴	1	3	yes	—
382	C₄²×C₁₃	C₂⁴	1	3	yes	—
383	C₄²×C₁₃	C₂⁴	1	3	yes	—
384	C₄²×C₁₃	C₂⁴	1	3	yes	—
385	C₂²⋊Dic₁₃	C₂⁴	1	12	yes	—
386	C₂²⋊Dic₁₃	C₂⁴	1	12	yes	—
387	C₂²⋊Dic₁₃	C₂⁴	1	4	yes	—
388	#6103	C₂⁴	1	12	yes	—
389	#6103	C₂⁴	1	12	yes	—
390	#6103	C₂⁴	1	12	yes	—
391	#6103	C₂⁴	1	12	yes	—
392	#6103	C₂⁴	1	12	yes	—
393	#6103	C₂⁴	1	12	yes	—
394	#6103	C₂⁴	1	24	yes	—
395	#6103	C₂⁴	1	24	yes	—
396	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
397	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₁₃	C₂⁴	1	6	yes	—
399	C₄⋊Dic₁₃	C₂⁴	1	6	yes	—
400	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
401	C₄⋊Dic₁₃	C₂⁴	1	2	yes	—
402	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
403	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
404	#6101	C₂⁴	1	4	yes	—
405	#6101	C₂⁴	1	4	yes	—
406	#6101	C₂⁴	1	12	yes	—
407	#6101	C₂⁴	1	12	yes	—
408	#6101	C₂⁴	1	12	yes	—
409	#6101	C₂⁴	1	12	yes	—
410	C₄×Dic₁₃	C₂⁴	1	4	yes	—
411	C₄×Dic₁₃	C₂⁴	1	12	yes	—
412	C₄×Dic₁₃	C₂⁴	1	12	yes	—
413	#3522	—	13	2	no	—
414	#3519	—	13	6	no	—
415	#3517	—	13	2	no	—
416	#3514	—	13	6	no	—
417	#3511	—	13	3	no	—
418	#3508	—	13	3	no	—
419	#3503	—	13	1	no	—
420	#3498	—	13	1	no	—
421	#3494	—	13	6	no	—
422	#3488	—	13	2	no	—
423	#3483	—	13	2	no	—
424	#3481	—	13	6	no	—
425	#3480	—	13	2	no	—
426	D₄×#41	—	13	6	no	—
427	#3460	—	13	6	no	—
428	#3444	—	13	3	no	—
429	C₂×#532	—	13	3	no	—
430	C₄×H(5,𝔽₂)	—	13	2	no	—
431	C₂×C₄×#41	D₁₃	1	1	yes	characteristic, complemented
432	C₂³×C₁₃	—	2	6	no	—
433	C₂³×C₁₃	—	2	6	no	—
434	C₂³×C₁₃	—	4	3	no	—
435	C₂³×C₁₃	C₂⁵	1	3	yes	—
436	C₂³×C₁₃	C₂⁵	1	3	yes	—
437	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
438	C₂²×D₁₃	—	2	24	no	—
439	C₂²×D₁₃	—	4	12	no	—
440	C₂²×D₁₃	—	4	12	no	—
441	C₂²×D₁₃	C₂⁵	1	12	yes	—
442	Q₈×C₁₃	—	2	6	no	—
443	Q₈×C₁₃	C₂×#41	1	4	yes	complemented
444	D₄×C₁₃	—	2	12	no	—
445	D₄×C₁₃	—	2	6	no	—
446	D₄×C₁₃	C₂×#41	1	12	yes	complemented
447	C₂×C₄×C₁₃	—	2	6	no	—
448	C₂×C₄×C₁₃	—	2	6	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	2	6	no	—
451	C₂×C₄×C₁₃	—	2	6	no	—
452	C₂×C₄×C₁₃	—	2	6	no	—
453	C₂×C₄×C₁₃	—	2	6	no	—
454	C₂×C₄×C₁₃	—	2	6	no	—
455	C₂×C₄×C₁₃	—	2	6	no	—
456	C₂×C₄×C₁₃	—	2	6	no	—
457	C₂×C₄×C₁₃	—	2	6	no	—
458	C₂×C₄×C₁₃	—	2	6	no	—
459	C₂×C₄×C₁₃	—	2	2	no	—
460	C₂×C₄×C₁₃	—	4	3	no	—
461	C₂×C₄×C₁₃	—	4	3	no	—
462	C₂×C₄×C₁₃	—	4	3	no	—
463	C₂×C₄×C₁₃	C₂×#41	1	12	yes	complemented
464	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
465	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
466	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
467	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
468	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
469	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
470	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
471	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
472	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
473	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
474	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
475	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
476	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
477	C₂²⋊D₁₃	—	2	24	no	—
478	C₂²⋊D₁₃	—	2	24	no	—
479	C₂²⋊D₁₃	—	4	24	no	—
480	C₂²⋊D₁₃	—	4	12	no	—
481	C₂×Dic₁₃	—	4	12	no	—
482	C₂×Dic₁₃	C₂⁵	1	4	yes	—
483	C₂×Dic₁₃	C₂⁵	1	4	yes	—
484	C₂×Dic₁₃	C₂⁵	1	12	yes	—
485	D₅₂	—	2	12	no	—
486	D₅₂	—	2	24	no	—
487	D₅₂	—	2	12	no	—
488	D₅₂	—	2	12	no	—
489	D₅₂	—	4	12	no	—
490	D₅₂	—	4	12	no	—
491	C₄×D₁₃	—	2	24	no	—
492	C₄×D₁₃	—	2	24	no	—
493	C₄×D₁₃	—	4	24	no	—
494	C₄×D₁₃	—	4	12	no	—
495	Dic₂₆	—	2	4	no	—
496	Dic₂₆	—	2	12	no	—
497	Dic₂₆	—	2	4	no	—
498	Dic₂₆	—	4	12	no	—
499	C₂×H(5,𝔽₂)	—	13	2	no	—
500	C₂²×#41	—	13	6	no	—
501	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
502	#559	—	13	6	no	—
503	#559	—	13	6	no	—
504	Q₈²	—	13	2	no	—
505	#557	—	13	2	no	—
506	#556	—	13	6	no	—
507	#555	—	13	6	no	—
508	#555	—	13	12	no	—
509	#554	—	13	6	no	—
510	#554	—	13	6	no	—
511	#553	—	13	12	no	—
512	#553	—	13	12	no	—
513	#553	—	13	12	no	—
514	#551	—	13	24	no	—
515	#550	—	13	4	no	—
516	#550	—	13	2	no	—
517	#550	—	13	2	no	—
518	#550	—	13	6	no	—
519	#550	—	13	6	no	—
520	D₄×Q₈	—	13	6	no	—
521	#548	—	13	4	no	—
522	#548	—	13	12	no	—
523	#547	—	13	6	no	—
524	#547	—	13	12	no	—
525	#546	—	13	12	no	—
526	#546	—	13	12	no	—
527	#546	—	13	12	no	—
528	#546	—	13	24	no	—
529	D₄²	—	13	12	no	—
530	D₄²	—	13	6	no	—
531	D₄²	—	13	6	no	—
532	#544	—	13	6	no	—
533	#542	—	13	12	no	—
534	#542	—	13	12	no	—
535	#540	—	13	12	no	—
536	#540	—	13	12	no	—
537	#538	—	13	24	no	—
538	#537	—	13	6	no	—
539	#535	—	13	6	no	—
540	#535	—	13	6	no	—
541	#533	—	13	1	no	—
542	#533	—	13	3	no	—
543	#533	—	13	3	no	—
544	#532	—	13	12	no	—
545	#532	—	13	3	no	—
546	#532	—	13	6	no	—
547	#532	—	13	6	no	—
548	#532	—	13	6	no	—
549	#532	—	13	6	no	—
550	#532	—	13	6	no	—
551	#532	—	13	6	no	—
552	#532	—	13	6	no	—
553	#532	—	13	3	no	—
554	#532	—	13	3	no	—
555	C₂×C₄⋊Q₈	—	13	3	no	—
556	C₂×#127	—	13	3	no	—
557	#529	—	13	12	no	—
558	#529	—	13	6	no	—
559	#529	—	13	6	no	—
560	#529	—	13	6	no	—
561	#529	—	13	6	no	—
562	#529	—	13	6	no	—
563	#529	—	13	6	no	—
564	C₂×#124	—	13	6	no	—
565	#525	—	13	6	no	—
566	#525	—	13	6	no	—
567	#525	—	13	6	no	—
568	#525	—	13	24	no	—
569	C₂×#121	—	13	6	no	—
570	C₂×#121	—	13	6	no	—
571	#520	—	13	2	no	—
572	#520	—	13	4	no	—
573	#520	—	13	6	no	—
574	#518	—	13	12	no	—
575	#518	—	13	6	no	—
576	C₄×#41	—	13	4	no	—
577	C₄×#41	—	13	6	no	—
578	C₄×#41	—	13	6	no	—
579	C₄×#41	—	13	6	no	—
580	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
581	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
582	C₄×#41	C₂×D₁₃	1	3	yes	complemented
583	C₄×#41	C₂×D₁₃	1	3	yes	complemented
584	C₄×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
585	C₄×#41	C₂×D₁₃	1	3	yes	complemented
586	C₄×#41	C₂×D₁₃	1	3	yes	complemented
587	C₄×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
588	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
589	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
590	C₂×C₄×D₄	—	13	12	no	—
591	C₂×C₄×D₄	—	13	6	no	—
592	C₂×C₄×D₄	—	13	6	no	—
593	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	complemented
594	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	complemented
595	C₂×#117	C₂×D₁₃	1	3	yes	complemented
596	C₂²×C₄²	C₂×D₁₃	1	3	yes	complemented
597	C₂²×C₁₃	—	2	1	no	—
598	C₂²×C₁₃	—	2	3	no	—
599	C₂²×C₁₃	—	2	1	no	—
600	C₂²×C₁₃	—	2	3	no	—
601	C₂²×C₁₃	—	2	3	no	—
602	C₂²×C₁₃	—	2	3	no	—
603	C₂²×C₁₃	—	2	3	no	—
604	C₂²×C₁₃	—	4	12	no	—
605	C₂²×C₁₃	C₂²×#41	1	6	yes	—
606	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
607	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
608	C₂×D₁₃	—	2	12	no	—
609	C₂×D₁₃	—	2	12	no	—
610	C₂×D₁₃	—	2	12	no	—
611	C₂×D₁₃	—	8	24	no	—
612	C₄×C₁₃	—	2	1	no	—
613	C₄×C₁₃	—	2	3	no	—
614	C₄×C₁₃	—	2	3	no	—
615	C₄×C₁₃	—	2	3	no	—
616	C₄×C₁₃	—	2	3	no	—
617	C₄×C₁₃	—	2	3	no	—
618	C₄×C₁₃	—	2	1	no	—
619	C₄×C₁₃	C₂²×#41	1	2	yes	—
620	C₄×C₁₃	C₂²×#41	1	6	yes	—
621	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
622	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
623	C₄×C₁₃	#585	1	2	yes	—
624	Dic₁₃	—	2	4	no	—
625	Dic₁₃	—	2	12	no	—
626	Dic₁₃	—	2	4	no	—
627	H(5,𝔽₂)	—	26	16	no	—
628	C₂×#41	—	2	8	no	—
629	C₂×#41	—	13	4	no	—
630	C₂×#41	—	13	6	no	—
631	C₂×#41	—	13	6	no	—
632	C₂×#41	—	13	6	no	—
633	C₂×#41	—	13	12	no	—
634	C₂×#41	—	13	12	no	—
635	C₂×#41	—	13	12	no	—
636	C₂×#41	—	52	24	no	—
637	C₂×#41	C₂²×D₁₃	1	3	yes	—
638	C₂×#41	C₂²×D₁₃	1	3	yes	—
639	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
640	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
641	C₂²×Q₈	—	13	6	no	—
642	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
643	C₂²×D₄	—	13	12	no	—
644	C₂²×D₄	—	13	12	no	—
645	C₂²×D₄	—	13	6	no	—
646	C₂²×D₄	—	13	6	no	—
647	C₂²×D₄	—	13	6	no	—
648	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
649	C₂³×C₄	—	13	12	no	—
650	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
651	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
652	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
653	C₄⋊Q₈	—	13	12	no	—
654	C₄⋊Q₈	—	13	3	no	—
655	C₄⋊Q₈	—	13	6	no	—
656	C₄⋊Q₈	—	13	6	no	—
657	C₄⋊Q₈	—	13	6	no	—
658	C₄⋊Q₈	—	13	1	no	—
659	C₄⋊Q₈	—	13	1	no	—
660	#127	—	13	12	no	—
661	#127	—	13	3	no	—
662	#127	—	13	6	no	—
663	#127	—	13	6	no	—
664	#127	—	13	6	no	—
665	#126	—	13	24	no	—
666	#126	—	13	12	no	—
667	#126	—	13	12	no	—
668	#125	—	13	12	no	—
669	#125	—	13	2	no	—
670	#125	—	13	6	no	—
671	#125	—	13	6	no	—
672	#124	—	13	12	no	—
673	#124	—	13	24	no	—
674	#124	—	13	6	no	—
675	#124	—	13	12	no	—
676	#124	—	13	12	no	—
677	#124	—	13	12	no	—
678	#124	—	13	6	no	—
679	#124	—	13	6	no	—
680	#123	—	13	12	no	—
681	#123	—	13	12	no	—
682	#123	—	13	12	no	—
683	#123	—	13	24	no	—
684	#123	—	13	24	no	—
685	#123	—	13	24	no	—
686	C₂²⋊Q₈	—	13	12	no	—
687	C₂²⋊Q₈	—	13	2	no	—
688	C₂²⋊Q₈	—	13	2	no	—
689	C₂²⋊Q₈	—	13	6	no	—
690	C₂²⋊Q₈	—	13	6	no	—
691	C₂²⋊Q₈	—	13	6	no	—
692	C₂²⋊Q₈	—	13	6	no	—
693	C₂²⋊Q₈	—	13	24	no	—
694	C₂²⋊Q₈	—	13	24	no	—
695	#121	—	13	24	no	—
696	#121	—	13	12	no	—
697	#121	—	13	6	no	—
698	#121	—	13	6	no	—
699	#121	—	13	12	no	—
700	#121	—	13	12	no	—
701	#121	—	13	12	no	—
702	#121	—	13	12	no	—
703	#121	—	13	12	no	—
704	#121	—	13	12	no	—
705	#121	—	13	6	no	—
706	#121	—	13	6	no	—
707	#121	—	13	6	no	—
708	#121	—	13	6	no	—
709	#121	—	13	12	no	—
710	#121	—	13	12	no	—
711	#121	—	13	24	no	—
712	#121	—	13	24	no	—
713	#120	—	13	12	no	—
714	#120	—	13	24	no	—
715	#120	—	13	24	no	—
716	C₄×Q₈	—	13	4	no	—
717	C₄×Q₈	—	13	2	no	—
718	C₄×Q₈	—	13	2	no	—
719	C₄×Q₈	—	13	6	no	—
720	C₄×Q₈	—	13	6	no	—
721	C₄×Q₈	—	13	6	no	—
722	C₄×Q₈	—	13	6	no	—
723	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
724	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
725	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
726	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
727	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
728	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
729	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
730	C₄×Q₈	C₂²×D₁₃	1	3	yes	—
731	C₄×D₄	—	13	12	no	—
732	C₄×D₄	—	13	12	no	—
733	C₄×D₄	—	13	12	no	—
734	C₄×D₄	—	13	12	no	—
735	C₄×D₄	—	13	12	no	—
736	C₄×D₄	—	13	12	no	—
737	C₄×D₄	—	13	12	no	—
738	C₄×D₄	—	13	12	no	—
739	C₄×D₄	—	13	12	no	—
740	C₄×D₄	—	13	24	no	—
741	C₄×D₄	—	13	12	no	—
742	C₄×D₄	—	13	6	no	—
743	C₄×D₄	—	13	6	no	—
744	C₄×D₄	—	13	12	no	—
745	C₄×D₄	—	13	12	no	—
746	C₄×D₄	—	13	12	no	—
747	C₄×D₄	—	13	12	no	—
748	C₄×D₄	—	13	12	no	—
749	C₄×D₄	—	13	6	no	—
750	C₄×D₄	—	13	6	no	—
751	C₄×D₄	—	13	6	no	—
752	C₄×D₄	—	13	6	no	—
753	C₄×D₄	C₂²×D₁₃	1	3	yes	—
754	C₄×D₄	C₂²×D₁₃	1	3	yes	—
755	C₄×D₄	C₂²×D₁₃	1	3	yes	—
756	C₄×D₄	C₂²×D₁₃	1	3	yes	—
757	C₄×D₄	C₂²×D₁₃	1	6	yes	—
758	C₄×D₄	C₂²×D₁₃	1	3	yes	—
759	C₄×D₄	C₂²×D₁₃	1	6	yes	—
760	C₄×D₄	C₂²×D₁₃	1	3	yes	—
761	C₄×D₄	C₂²×D₁₃	1	6	yes	—
762	C₄×D₄	C₂²×D₁₃	1	6	yes	—
763	C₄×D₄	C₂²×D₁₃	1	3	yes	—
764	C₄×D₄	C₂²×D₁₃	1	3	yes	—
765	#117	—	13	2	no	—
766	#117	—	13	6	no	—
767	#117	—	13	6	no	—
768	#117	—	13	12	no	—
769	#117	—	13	12	no	—
770	#117	—	13	12	no	—
771	#117	—	13	12	no	—
772	#117	C₂²×D₁₃	1	3	yes	—
773	#117	C₂²×D₁₃	1	3	yes	—
774	#117	C₂²×D₁₃	1	6	yes	—
775	#117	C₂²×D₁₃	1	6	yes	—
776	#117	C₂²×D₁₃	1	3	yes	—
777	#117	C₂²×D₁₃	1	3	yes	—
778	C₂×C₄⋊C₄	—	13	6	no	—
779	C₂×C₄⋊C₄	—	13	6	no	—
780	C₂×C₄⋊C₄	—	13	12	no	—
781	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
782	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
783	C₂×C₂²⋊C₄	—	13	12	no	—
784	C₂×C₂²⋊C₄	—	13	12	no	—
785	C₂×C₂²⋊C₄	—	13	24	no	—
786	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
787	C₂×C₄²	—	13	12	no	—
788	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
789	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
790	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
791	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
792	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
793	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
794	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
795	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
796	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
797	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
798	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
799	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
800	C₂×C₁₃	—	2	6	no	—
801	C₂×C₁₃	—	2	2	no	—
802	C₂×C₁₃	—	4	3	no	—
803	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
804	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
805	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
806	D₁₃	—	4	12	no	—
807	C₂⁴	—	13	12	no	—
808	C₂⁴	C₂³×D₁₃	1	3	yes	—
809	#41	—	2	4	no	—
810	#41	—	2	12	no	—
811	#41	—	2	12	no	—
812	#41	—	26	16	no	—
813	#41	—	26	24	no	—
814	#41	—	26	24	no	—
815	#41	—	52	24	no	—
816	#41	—	52	24	no	—
817	#41	—	52	24	no	—
818	#41	—	52	12	no	—
819	#41	#6127	1	8	yes	complemented
820	C₂×Q₈	—	2	4	no	—
821	C₂×Q₈	—	13	2	no	—
822	C₂×Q₈	—	13	2	no	—
823	C₂×Q₈	—	13	6	no	—
824	C₂×Q₈	—	13	12	no	—
825	C₂×Q₈	—	52	12	no	—
826	C₂×Q₈	C₂³×D₁₃	1	3	yes	—
827	C₂×Q₈	C₂³×D₁₃	1	1	yes	characteristic
828	C₂×D₄	—	2	12	no	—
829	C₂×D₄	—	13	12	no	—
830	C₂×D₄	—	13	12	no	—
831	C₂×D₄	—	13	12	no	—
832	C₂×D₄	—	13	24	no	—
833	C₂×D₄	—	13	12	no	—
834	C₂×D₄	—	13	6	no	—
835	C₂×D₄	—	13	6	no	—
836	C₂×D₄	—	13	6	no	—
837	C₂×D₄	—	13	12	no	—
838	C₂×D₄	—	13	12	no	—
839	C₂×D₄	—	26	48	no	—
840	C₂×D₄	—	26	24	no	—
841	C₂×D₄	—	52	12	no	—
842	C₂×D₄	—	52	12	no	—
843	C₂×D₄	—	52	24	no	—
844	C₂×D₄	C₂³×D₁₃	1	6	yes	—
845	C₂×D₄	C₂³×D₁₃	1	3	yes	—
846	C₂×D₄	C₂³×D₁₃	1	3	yes	—
847	C₂²×C₄	—	2	12	no	—
848	C₂²×C₄	—	2	12	no	—
849	C₂²×C₄	—	4	6	no	—
850	C₂²×C₄	—	13	12	no	—
851	C₂²×C₄	—	13	12	no	—
852	C₂²×C₄	—	13	12	no	—
853	C₂²×C₄	—	13	12	no	—
854	C₂²×C₄	—	13	24	no	—
855	C₂²×C₄	—	52	24	no	—
856	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
857	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
858	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
859	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
860	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
861	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
862	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
863	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
864	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
865	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
866	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
867	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
868	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
869	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
870	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
871	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
872	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
873	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
874	C₄⋊C₄	—	13	12	no	—
875	C₄⋊C₄	—	13	6	no	—
876	C₄⋊C₄	—	13	6	no	—
877	C₄⋊C₄	—	13	12	no	—
878	C₄⋊C₄	—	13	12	no	—
879	C₄⋊C₄	—	13	2	no	—
880	C₄⋊C₄	—	13	2	no	—
881	C₄⋊C₄	—	13	4	no	—
882	C₄⋊C₄	—	13	4	no	—
883	C₄⋊C₄	—	13	2	no	—
884	C₄⋊C₄	—	13	2	no	—
885	C₄⋊C₄	—	13	12	no	—
886	C₄⋊C₄	—	13	12	no	—
887	C₄⋊C₄	—	13	12	no	—
888	C₄⋊C₄	C₂³×D₁₃	1	3	yes	—
889	C₄⋊C₄	C₂³×D₁₃	1	3	yes	—
890	C₄⋊C₄	C₂³×D₁₃	1	3	yes	—
891	C₄⋊C₄	C₂³×D₁₃	1	3	yes	—
892	C₄⋊C₄	C₂³×D₁₃	1	6	yes	—
893	C₄⋊C₄	C₂³×D₁₃	1	6	yes	—
894	C₂²⋊C₄	—	13	12	no	—
895	C₂²⋊C₄	—	13	4	no	—
896	C₂²⋊C₄	—	13	12	no	—
897	C₂²⋊C₄	—	13	12	no	—
898	C₂²⋊C₄	—	13	24	no	—
899	C₂²⋊C₄	—	13	12	no	—
900	C₂²⋊C₄	—	13	12	no	—
901	C₂²⋊C₄	—	13	24	no	—
902	C₂²⋊C₄	—	13	12	no	—
903	C₂²⋊C₄	—	13	12	no	—
904	C₂²⋊C₄	—	13	12	no	—
905	C₂²⋊C₄	C₂³×D₁₃	1	6	yes	—
906	C₂²⋊C₄	C₂³×D₁₃	1	6	yes	—
907	C₂²⋊C₄	C₂³×D₁₃	1	6	yes	—
908	C₂²⋊C₄	C₂³×D₁₃	1	6	yes	—
909	C₄²	—	13	12	no	—
910	C₄²	—	13	12	no	—
911	C₄²	—	13	4	no	—
912	C₄²	C₂³×D₁₃	1	1	yes	characteristic
913	C₄²	C₂³×D₁₃	1	1	yes	characteristic
914	C₄²	C₂³×D₁₃	1	3	yes	—
915	C₄²	C₂³×D₁₃	1	3	yes	—
916	C₄²	C₂³×D₁₃	1	3	yes	—
917	C₄²	C₂³×D₁₃	1	3	yes	—
918	C₄²	C₂³×D₁₃	1	3	yes	—
919	C₄²	C₂³×D₁₃	1	3	yes	—
920	C₄²	C₂³×D₁₃	1	3	yes	—
921	C₄²	C₂³×D₁₃	1	3	yes	—
922	C₄²	C₂³×D₁₃	1	3	yes	—
923	C₄²	C₂³×D₁₃	1	3	yes	—
924	C₄²	C₂³×D₁₃	1	3	yes	—
925	C₄²	C₂³×D₁₃	1	1	yes	characteristic
926	C₄²	C₂³×D₁₃	1	1	yes	characteristic
927	C₄²	C₂³×D₁₃	1	3	yes	—
928	C₁₃	#62800	1	1	yes	characteristic, complemented, Sylow
929	C₂³	—	2	6	no	—
930	C₂³	—	2	6	no	—
931	C₂³	—	4	3	no	—
932	C₂³	—	13	12	no	—
933	C₂³	—	26	24	no	—
934	C₂³	—	52	12	no	—
935	C₂³	—	52	12	no	—
936	C₂³	C₂⁴×D₁₃	1	3	yes	—
937	C₂³	C₂⁴×D₁₃	1	3	yes	—
938	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
939	Q₈	—	2	6	no	—
940	Q₈	—	26	4	no	—
941	Q₈	—	26	12	no	—
942	Q₈	—	26	4	no	—
943	Q₈	—	52	12	no	—
944	Q₈	C₂×#6127	1	4	yes	complemented
945	D₄	—	2	12	no	—
946	D₄	—	2	6	no	—
947	D₄	—	26	24	no	—
948	D₄	—	26	24	no	—
949	D₄	—	26	12	no	—
950	D₄	—	26	24	no	—
951	D₄	—	26	12	no	—
952	D₄	—	26	12	no	—
953	D₄	—	52	12	no	—
954	D₄	—	52	12	no	—
955	D₄	—	52	24	no	—
956	D₄	—	52	12	no	—
957	D₄	C₂×#6127	1	12	yes	complemented
958	C₂×C₄	—	2	6	no	—
959	C₂×C₄	—	2	6	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	6	no	—
962	C₂×C₄	—	2	6	no	—
963	C₂×C₄	—	2	6	no	—
964	C₂×C₄	—	2	6	no	—
965	C₂×C₄	—	2	6	no	—
966	C₂×C₄	—	2	6	no	—
967	C₂×C₄	—	2	6	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	6	no	—
970	C₂×C₄	—	2	6	no	—
971	C₂×C₄	—	4	3	no	—
972	C₂×C₄	—	4	3	no	—
973	C₂×C₄	—	4	3	no	—
974	C₂×C₄	—	13	4	no	—
975	C₂×C₄	—	13	4	no	—
976	C₂×C₄	—	13	12	no	—
977	C₂×C₄	—	26	24	no	—
978	C₂×C₄	—	26	24	no	—
979	C₂×C₄	—	52	24	no	—
980	C₂×C₄	—	52	12	no	—
981	C₂×C₄	—	52	12	no	—
982	C₂×C₄	C₂×#6127	1	12	yes	complemented
983	C₂×C₄	#88256	1	4	yes	complemented
984	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
985	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
986	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
987	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
988	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
989	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
990	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
991	C₂×C₄	C₂⁴×D₁₃	1	3	yes	—
992	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
993	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
994	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
996	C₂²	—	2	1	no	—
997	C₂²	—	2	3	no	—
998	C₂²	—	2	1	no	—
999	C₂²	—	2	3	no	—
1000	C₂²	—	2	3	no	—
1001	C₂²	—	2	3	no	—
1002	C₂²	—	2	3	no	—
1003	C₂²	—	4	12	no	—
1004	C₂²	—	26	12	no	—
1005	C₂²	—	26	12	no	—
1006	C₂²	—	26	12	no	—
1007	C₂²	—	104	24	no	—
1008	C₂²	C₂²×#6127	1	6	yes	—
1009	C₂²	C₂×#88256	1	2	yes	—
1010	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
1011	C₄	—	2	1	no	—
1012	C₄	—	2	3	no	—
1013	C₄	—	2	3	no	—
1014	C₄	—	2	3	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	3	no	—
1017	C₄	—	2	3	no	—
1018	C₄	—	26	4	no	—
1019	C₄	—	26	12	no	—
1020	C₄	—	26	4	no	—
1021	C₄	C₂²×#6127	1	2	yes	—
1022	C₄	C₂²×#6127	1	6	yes	—
1023	C₄	C₂×#88256	1	2	yes	—
1024	C₄	C₂×#88256	1	2	yes	—
1025	C₄	#11719648	1	2	yes	—
1026	C₂	—	2	2	no	—
1027	C₂	—	2	6	no	—
1028	C₂	—	4	3	no	—
1029	C₂	—	52	12	no	—
1030	C₂	C₂³×#6127	1	1	yes	characteristic
1031	C₂	C₂²×#88256	1	1	yes	characteristic
1032	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₄×C₁₃×#41	C₂
hypercenter	C₂×C₄×#41	D₁₃
hypocenter	C₁₃	#62800
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. #13128921	C₂	semidirect
2. #13128868	C₂	semidirect
3. #13128842	C₂	semidirect
4. #13128797	C₂	semidirect
5. #13128747	C₂	semidirect
6. #13128712	C₂	semidirect
7. #13128655	C₂	semidirect
8. #13128614	C₂	semidirect
9. #13128571	C₂	semidirect
10. #13128505	C₂	semidirect
11. #13128462	C₂	semidirect
12. #13128446	C₂	semidirect
13. #13128431	C₂	semidirect
14. D₄×#6127	C₂	semidirect
15. #13128252	C₂	semidirect
16. #13128132	C₂	semidirect
17. C₂×#11719182	C₂	semidirect
18. C₄×#88256	C₂	semidirect
19. C₂×C₄×C₁₃×#41	C₂	semidirect
22. C₂²×#6127	C₂²	semidirect
25. C₄×C₁₃×#41	C₂²	semidirect
26. C₄×C₁₃×#41	C₂²	semidirect
27. C₄×C₁₃×#41	C₂²	semidirect
28. C₄×C₁₃×#41	C₂²	semidirect
29. C₄×C₁₃×#41	C₂²	semidirect
30. C₄×C₁₃×#41	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
32. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₁₃×#117	C₂²	semidirect
36. C₂²×C₄²×C₁₃	C₂²	semidirect
37. #11719539	C₂²	semidirect
38. #11719538	C₂²	semidirect
39. #11719535	C₂²	semidirect
40. #11719534	C₂²	semidirect
42. #11719522	C₂²	semidirect
43. D₄×C₂²⋊D₁₃	C₂²	semidirect
44. #11719496	C₂²	semidirect
45. #11719496	C₂²	semidirect
46. #11719496	C₂²	semidirect
47. C₂×#88184	C₂²	semidirect
48. C₂×#88184	C₂²	semidirect
49. #11719290	C₂²	semidirect
50. #11719290	C₂²	semidirect
51. #11719289	C₂²	semidirect
52. #11719287	C₂²	semidirect
53. #11719285	C₂²	semidirect
54. #11719284	C₂²	semidirect
55. #11719282	C₂²	semidirect
56. #11719282	C₂²	semidirect
57. #11719279	C₂²	semidirect
58. C₄×#6131	C₂²	semidirect
59. #11719275	C₂²	semidirect
60. Q₈×Dic₂₆	C₂²	semidirect
61. #11719270	C₂²	semidirect
62. #11719268	C₂²	semidirect
63. #11719267	C₂²	semidirect
64. #11719265	C₂²	semidirect
65. #11719258	C₂²	semidirect
66. #11719258	C₂²	semidirect
67. #11719257	C₂²	semidirect
68. #11719256	C₂²	semidirect
69. #11719255	C₂²	semidirect
70. #11719255	C₂²	semidirect
71. D₄×D₅₂	C₂²	semidirect
72. D₄×D₅₂	C₂²	semidirect
73. #11719253	C₂²	semidirect
74. #11719252	C₂²	semidirect
75. #11719250	C₂²	semidirect
76. C₄×D₄×D₁₃	C₂²	semidirect
77. #11719248	C₂²	semidirect
78. D₄×Dic₂₆	C₂²	semidirect
79. #11719240	C₂²	semidirect
80. #11719239	C₂²	semidirect
81. #11719237	C₂²	semidirect
82. #11719235	C₂²	semidirect
83. #11719232	C₂²	semidirect
84. #11719230	C₂²	semidirect
85. #11719228	C₂²	semidirect
86. #11719226	C₂²	semidirect
87. #11719224	C₂²	semidirect
88. #11719219	C₂²	semidirect
89. #11719212	C₂²	semidirect
90. #11719195	C₂²	semidirect
91. #11719184	C₂²	semidirect
92. #11719184	C₂²	semidirect
93. #11719184	C₂²	semidirect
94. #11719184	C₂²	semidirect
95. #11719184	C₂²	semidirect
96. #11719184	C₂²	semidirect
97. #11719182	C₂²	semidirect
98. #11719182	C₂²	semidirect
99. #11719182	C₂²	semidirect
100. #11719182	C₂²	semidirect
101. #11719182	C₂²	semidirect
102. #11719182	C₂²	semidirect
103. #11719182	C₂²	semidirect
104. #11719182	C₂²	semidirect
105. #11719182	C₂²	semidirect
106. #11719182	C₂²	semidirect
107. C₂×#88129	C₂²	semidirect
108. C₂×#88128	C₂²	semidirect
109. C₄×#6127	C₂²	semidirect
110. C₄×#6127	C₂²	semidirect
111. C₄×#6127	C₂²	semidirect
112. C₂×C₄×D₅₂	C₂²	semidirect
113. C₂×C₄×D₅₂	C₂²	semidirect
114. #11719175	C₂²	semidirect
115. #11719175	C₂²	semidirect
116. #11719175	C₂²	semidirect
117. C₂×#88123	C₂²	semidirect
297. C₁₃×#41	#41	semidirect
431. C₂×C₄×#41	D₁₃	semidirect
443. Q₈×C₁₃	C₂×#41	semidirect
446. D₄×C₁₃	C₂×#41	semidirect
463. C₂×C₄×C₁₃	C₂×#41	semidirect
464. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
582. C₄×#41	C₂×D₁₃	semidirect
583. C₄×#41	C₂×D₁₃	semidirect
584. C₄×#41	C₂×D₁₃	semidirect
585. C₄×#41	C₂×D₁₃	semidirect
586. C₄×#41	C₂×D₁₃	semidirect
587. C₄×#41	C₂×D₁₃	semidirect
588. C₂×C₄×Q₈	C₂×D₁₃	semidirect
589. C₂×C₄×Q₈	C₂×D₁₃	semidirect
593. C₂×C₄×D₄	C₂×D₁₃	semidirect
594. C₂×C₄×D₄	C₂×D₁₃	semidirect
595. C₂×#117	C₂×D₁₃	semidirect
596. C₂²×C₄²	C₂×D₁₃	semidirect
819. #41	#6127	semidirect
928. C₁₃	#62800	semidirect
944. Q₈	C₂×#6127	semidirect
957. D₄	C₂×#6127	semidirect
982. C₂×C₄	C₂×#6127	semidirect
983. C₂×C₄	#88256	semidirect

Maximal subgroups

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

subgroup	index
#13128921	2
#13128868	2
#13128842	2
#13128797	2
#13128747	2
#13128712	2
#13128655	2
#13128614	2
#13128571	2
#13128505	2
#13128462	2
#13128446	2
#13128431	2
D₄×#6127	2
#13128252	2
#13128132	2
C₂×#11719182	2
C₄×#88256	2
C₂×C₄×C₁₃×#41	2
#62800	13