Subgroups — C₁₃×#61866 #15748205

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3555	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3390	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3383	C₂	1	2	yes	maximal, complemented
7	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3364	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3243	C₂	1	2	yes	maximal
16	C₁₃×#3242	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3233	C₂	1	1	yes	maximal, characteristic
18	C₁₃×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3127	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3121	C₂	1	2	yes	maximal
21	C₁₃×#3108	C₂	1	1	yes	maximal, characteristic
22	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	Q₈²×C₁₃	—	2	1	no	—
26	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
28	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#557	—	2	1	no	—
30	C₁₃×#557	—	2	2	no	—
31	C₁₃×#557	C₂²	1	1	yes	characteristic
32	C₁₃×#557	C₂²	1	2	yes	—
33	C₁₃×#557	C₂²	1	1	yes	characteristic
34	C₁₃×#557	C₂²	1	2	yes	—
35	C₁₃×#557	C₂²	1	1	yes	characteristic
36	C₁₃×#557	C₂²	1	2	yes	—
37	C₁₃×#556	—	2	1	no	—
38	C₁₃×#556	C₂²	1	1	yes	characteristic
39	C₁₃×#556	C₂²	1	2	yes	—
40	C₁₃×#554	C₂²	1	1	yes	characteristic
41	C₁₃×#552	—	2	1	no	—
42	C₁₃×#544	—	2	1	no	—
43	C₁₃×#544	—	2	2	no	—
44	C₁₃×#544	C₂²	1	2	yes	—
45	C₁₃×#542	C₂²	1	2	yes	—
46	C₁₃×#541	—	2	1	no	—
47	C₁₃×#541	—	2	2	no	—
48	C₁₃×#541	C₂²	1	2	yes	—
49	C₁₃×#533	—	2	1	no	—
50	C₁₃×#533	—	2	1	no	—
51	C₁₃×#533	C₂²	1	1	yes	characteristic
52	C₁₃×#533	C₂²	1	1	yes	characteristic
53	C₁₃×#533	C₂²	1	1	yes	characteristic
54	C₁₃×#529	C₂²	1	1	yes	characteristic
55	C₁₃×#519	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#501	C₂²	1	2	yes	—
58	C₁₃×#501	C₂²	1	2	yes	—
59	C₁₃×#500	C₂²	1	2	yes	—
60	C₁₃×#500	C₂²	1	1	yes	characteristic
61	C₁₃×#499	C₂²	1	2	yes	—
62	C₁₃×#499	C₂²	1	2	yes	—
63	C₁₃×#498	C₂²	1	1	yes	characteristic
64	C₁₃×#491	C₂²	1	2	yes	—
65	C₁₃×#489	C₂²	1	2	yes	—
66	C₁₃×#488	C₂²	1	2	yes	—
67	C₁₃×#488	C₂²	1	2	yes	—
68	C₁₃×#487	C₂²	1	2	yes	—
69	C₁₃×#487	C₂²	1	1	yes	characteristic
70	C₁₃×#487	C₂²	1	1	yes	characteristic
71	C₁₃×#485	C₂²	1	2	yes	—
72	C₁₃×#485	C₂²	1	2	yes	—
73	C₁₃×#485	C₂²	1	2	yes	—
74	C₁₃×#484	C₂²	1	2	yes	—
75	C₁₃×#483	C₂²	1	1	yes	characteristic
76	C₁₃×#482	C₂²	1	2	yes	—
77	C₁₃×#480	C₂²	1	1	yes	characteristic
78	C₁₃×#479	C₂²	1	1	yes	characteristic
79	C₁₃×#479	C₂²	1	1	yes	characteristic
80	C₁₃×#479	C₂²	1	2	yes	—
81	C₁₃×#479	C₂²	1	2	yes	—
82	C₁₃×#479	C₂²	1	2	yes	—
83	C₁₃×#479	C₂²	1	2	yes	—
84	C₁₃×#479	C₂²	1	2	yes	—
85	C₁₃×#479	C₂²	1	2	yes	—
86	C₁₃×#479	C₂²	1	2	yes	—
87	C₁₃×#478	C₂²	1	2	yes	—
88	C₁₃×#477	C₂²	1	1	yes	characteristic
89	C₁₃×#477	C₂²	1	1	yes	characteristic
90	C₁₃×#477	C₂²	1	1	yes	characteristic
91	C₁₃×#477	C₂²	1	2	yes	—
92	C₁₃×#477	C₂²	1	2	yes	—
93	C₁₃×#477	C₂²	1	2	yes	—
94	C₁₃×#476	C₂²	1	1	yes	characteristic
95	C₁₃×#475	C₂²	1	2	yes	—
96	C₁₃×#475	C₂²	1	1	yes	characteristic
97	C₁₃×#475	C₂²	1	2	yes	—
98	C₁₃×#474	C₂²	1	1	yes	characteristic
99	C₁₃×#474	C₂²	1	2	yes	—
100	C₁₃×#464	C₂²	1	1	yes	characteristic
101	C₁₃×#464	C₂²	1	1	yes	characteristic
102	C₁₃×#464	C₂²	1	2	yes	—
103	C₁₃×#464	C₂²	1	2	yes	—
104	C₁₃×#462	C₂²	1	1	yes	characteristic
105	C₁₃×#462	C₂²	1	1	yes	characteristic
106	C₁₃×#462	C₂²	1	2	yes	—
107	C₁₃×#462	C₂²	1	2	yes	—
108	C₁₃×#451	C₂²	1	2	yes	—
109	C₁₃×#451	C₂²	1	1	yes	characteristic
110	C₁₃×#448	C₂²	1	1	yes	characteristic
111	C₁₃×#446	C₂²	1	1	yes	characteristic
112	C₁₃×#446	C₂²	1	1	yes	characteristic
113	C₁₃×#446	C₂²	1	2	yes	—
114	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
117	C₁₃×#441	C₂²	1	2	yes	—
118	C₁₃×#441	C₂²	1	2	yes	—
119	C₁₃×#441	C₂²	1	2	yes	—
120	C₁₃×#440	C₂²	1	2	yes	—
121	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
122	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
123	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
124	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
125	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
127	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
128	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
129	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
130	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
131	C₁₃×#433	C₂²	1	2	yes	—
132	C₁₃×#433	C₂²	1	2	yes	—
133	C₁₃×#431	C₂²	1	1	yes	characteristic
134	C₁₃×#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
137	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
141	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊Q₈	—	2	1	no	—
143	C₁₃×C₄⋊Q₈	—	2	1	no	—
144	C₁₃×C₄⋊Q₈	—	2	2	no	—
145	C₁₃×C₄⋊Q₈	—	2	2	no	—
146	C₁₃×C₄⋊Q₈	—	2	2	no	—
147	C₁₃×C₄⋊Q₈	—	2	1	no	—
148	C₁₃×C₄⋊Q₈	—	2	1	no	—
149	C₁₃×C₄⋊Q₈	—	2	2	no	—
150	C₁₃×C₄⋊Q₈	—	2	1	no	—
151	C₁₃×C₄⋊Q₈	—	2	2	no	—
152	C₁₃×C₄⋊Q₈	—	2	2	no	—
153	C₁₃×C₄⋊Q₈	—	2	2	no	—
154	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
156	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	1	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	2	no	—
182	C₁₃×#125	—	2	2	no	—
183	C₁₃×#125	—	2	2	no	—
184	C₁₃×#125	—	2	1	no	—
185	C₁₃×#125	D₄	1	2	yes	—
186	C₁₃×#125	C₂³	1	2	yes	—
187	C₁₃×#125	C₂³	1	2	yes	—
188	C₁₃×#125	C₂³	1	2	yes	—
189	C₁₃×#125	C₂³	1	1	yes	characteristic
190	C₁₃×#125	C₂³	1	2	yes	—
191	C₁₃×#124	—	2	2	no	—
192	C₁₃×#124	C₂³	1	1	yes	characteristic
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#123	—	2	1	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	1	no	—
197	C₁₃×C₂²⋊Q₈	—	2	1	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	1	no	—
201	C₁₃×C₂²⋊Q₈	—	2	1	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	2	no	—
206	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
207	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×#121	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₁₃	—	2	1	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	2	no	—
217	C₄×Q₈×C₁₃	—	2	2	no	—
218	C₄×Q₈×C₁₃	—	2	2	no	—
219	C₄×Q₈×C₁₃	—	2	2	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	—	2	1	no	—
222	C₄×Q₈×C₁₃	—	2	2	no	—
223	C₄×Q₈×C₁₃	—	2	1	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	—	2	1	no	—
226	C₄×Q₈×C₁₃	—	2	1	no	—
227	C₄×Q₈×C₁₃	—	2	1	no	—
228	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
234	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₁₃×#117	—	2	1	no	—
248	C₁₃×#117	—	2	2	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	—	2	2	no	—
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	C₂³	1	2	yes	—
254	C₁₃×#117	C₂³	1	2	yes	—
255	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₁₃	—	2	1	no	—
259	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
260	C₁₃×#107	C₂³	1	2	yes	—
261	C₁₃×#107	C₂³	1	2	yes	—
262	C₁₃×#107	C₂³	1	2	yes	—
263	C₁₃×#107	C₂³	1	2	yes	—
264	C₁₃×#107	C₂³	1	2	yes	—
265	C₁₃×#107	C₂³	1	1	yes	characteristic
266	C₁₃×#107	C₂³	1	1	yes	characteristic
267	C₁₃×#107	C₂³	1	2	yes	—
268	C₁₃×#106	C₂³	1	1	yes	characteristic
269	C₁₃×#106	C₂³	1	2	yes	—
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	2	yes	—
274	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×#103	C₂³	1	2	yes	—
283	C₁₃×#103	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	1	yes	characteristic
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	2	yes	—
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
298	C₁₃×#102	C₂³	1	1	yes	characteristic
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	1	yes	characteristic
301	C₁₃×#102	C₂³	1	2	yes	—
302	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×#97	C₂³	1	2	yes	—
306	C₁₃×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₁₃	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	2	yes	—
311	C₄×C₈×C₁₃	C₂³	1	2	yes	—
312	#61866	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×Q₈×C₁₃	—	2	2	no	—
314	C₂×Q₈×C₁₃	—	2	2	no	—
315	C₂×Q₈×C₁₃	—	2	1	no	—
316	C₂×Q₈×C₁₃	—	2	1	no	—
317	C₂×Q₈×C₁₃	—	2	1	no	—
318	C₂×Q₈×C₁₃	—	2	2	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	2	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
326	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₁₃	—	2	1	no	—
332	C₂²×C₄×C₁₃	—	2	1	no	—
333	C₂²×C₄×C₁₃	—	2	1	no	—
334	C₂²×C₄×C₁₃	—	2	2	no	—
335	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₁₃×Q₁₆	—	2	4	no	—
339	C₁₃×Q₁₆	—	2	2	no	—
340	C₁₃×Q₁₆	—	2	4	no	—
341	C₁₃×Q₁₆	—	2	2	no	—
342	C₁₃×SD₁₆	—	2	2	no	—
343	C₁₃×SD₁₆	—	2	2	no	—
344	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
349	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₁₃×C₄⋊C₄	—	2	1	no	—
351	C₁₃×C₄⋊C₄	—	2	1	no	—
352	C₁₃×C₄⋊C₄	—	2	1	no	—
353	C₁₃×C₄⋊C₄	—	2	1	no	—
354	C₁₃×C₄⋊C₄	—	2	1	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	—	2	2	no	—
362	C₁₃×C₄⋊C₄	—	2	2	no	—
363	C₁₃×C₄⋊C₄	—	2	1	no	—
364	C₁₃×C₄⋊C₄	—	2	1	no	—
365	C₁₃×C₄⋊C₄	—	2	1	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	1	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	2	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	2	no	—
381	C₁₃×C₄⋊C₄	—	2	2	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	2	no	—
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
387	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
388	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
389	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
390	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
391	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
396	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
397	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
402	C₁₃×C₂²⋊C₄	—	2	2	no	—
403	C₁₃×C₂²⋊C₄	—	2	2	no	—
404	C₁₃×C₂²⋊C₄	—	2	1	no	—
405	C₁₃×C₂²⋊C₄	—	2	1	no	—
406	C₁₃×C₂²⋊C₄	—	2	1	no	—
407	C₁₃×C₂²⋊C₄	—	2	1	no	—
408	C₁₃×C₂²⋊C₄	—	2	2	no	—
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	1	no	—
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
413	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
414	C₄²×C₁₃	—	2	1	no	—
415	C₄²×C₁₃	—	2	1	no	—
416	C₄²×C₁₃	—	2	1	no	—
417	C₄²×C₁₃	—	2	1	no	—
418	C₄²×C₁₃	—	2	2	no	—
419	C₄²×C₁₃	—	2	1	no	—
420	C₄²×C₁₃	—	2	2	no	—
421	C₄²×C₁₃	—	2	2	no	—
422	C₄²×C₁₃	—	2	2	no	—
423	C₄²×C₁₃	—	2	2	no	—
424	C₄²×C₁₃	—	2	2	no	—
425	C₄²×C₁₃	—	2	2	no	—
426	C₄²×C₁₃	—	2	2	no	—
427	C₄²×C₁₃	—	2	2	no	—
428	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
429	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
430	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
431	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
432	C₄²×C₁₃	C₂⁴	1	2	yes	—
433	C₄²×C₁₃	C₂⁴	1	2	yes	—
434	#3555	C₂×C₁₃	1	1	yes	characteristic
435	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
436	#3390	C₂×C₁₃	1	2	yes	complemented
437	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
438	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
439	#3383	C₂×C₁₃	1	2	yes	complemented
440	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
442	#3377	C₂×C₁₃	1	2	yes	complemented
443	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3364	C₂×C₁₃	1	1	yes	characteristic, complemented
446	#3364	C₂×C₁₃	1	2	yes	complemented
447	#3363	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3243	C₂×C₁₃	1	2	yes	—
449	#3242	C₂×C₁₃	1	2	yes	complemented
450	#3233	C₂×C₁₃	1	1	yes	characteristic
451	#3231	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3127	C₂×C₁₃	1	2	yes	complemented
453	#3121	C₂×C₁₃	1	2	yes	—
454	#3108	C₂×C₁₃	1	1	yes	characteristic
455	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
457	C₂³×C₁₃	—	2	1	no	—
458	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
459	Q₈×C₁₃	—	2	4	no	—
460	Q₈×C₁₃	—	2	2	no	—
461	Q₈×C₁₃	—	2	2	no	—
462	Q₈×C₁₃	—	2	1	no	—
463	Q₈×C₁₃	—	2	1	no	—
464	Q₈×C₁₃	—	2	2	no	—
465	Q₈×C₁₃	—	2	1	no	—
466	Q₈×C₁₃	—	2	2	no	—
467	Q₈×C₁₃	—	2	1	no	—
468	Q₈×C₁₃	—	4	2	no	—
469	Q₈×C₁₃	—	4	2	no	—
470	Q₈×C₁₃	—	8	1	no	—
471	Q₈×C₁₃	—	8	1	no	—
472	Q₈×C₁₃	—	8	2	no	—
473	Q₈×C₁₃	—	8	2	no	—
474	Q₈×C₁₃	—	8	2	no	—
475	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
476	Q₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
477	D₄×C₁₃	—	2	1	no	—
478	D₄×C₁₃	—	2	1	no	—
479	D₄×C₁₃	—	8	1	no	—
480	C₂×C₄×C₁₃	—	2	4	no	—
481	C₂×C₄×C₁₃	—	2	1	no	—
482	C₂×C₄×C₁₃	—	2	1	no	—
483	C₂×C₄×C₁₃	—	2	2	no	—
484	C₂×C₄×C₁₃	—	2	1	no	—
485	C₂×C₄×C₁₃	—	2	1	no	—
486	C₂×C₄×C₁₃	—	2	2	no	—
487	C₂×C₄×C₁₃	—	2	1	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	1	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	1	no	—
492	C₂×C₄×C₁₃	—	2	2	no	—
493	C₂×C₄×C₁₃	—	2	1	no	—
494	C₂×C₄×C₁₃	—	2	1	no	—
495	C₂×C₄×C₁₃	—	4	1	no	—
496	C₂×C₄×C₁₃	—	4	2	no	—
497	C₂×C₄×C₁₃	—	8	2	no	—
498	C₂×C₄×C₁₃	—	8	1	no	—
499	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
509	C₈×C₁₃	—	2	1	no	—
510	C₈×C₁₃	—	2	1	no	—
511	C₈×C₁₃	—	2	1	no	—
512	C₈×C₁₃	—	2	2	no	—
513	C₈×C₁₃	—	2	1	no	—
514	C₈×C₁₃	—	2	2	no	—
515	#563	—	2	2	no	—
516	Q₈²	—	2	1	no	—
517	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
518	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
519	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
520	#557	—	2	1	no	—
521	#557	—	2	2	no	—
522	#557	C₂²×C₁₃	1	1	yes	characteristic
523	#557	C₂²×C₁₃	1	1	yes	characteristic
524	#557	C₂²×C₁₃	1	2	yes	—
525	#557	C₂²×C₁₃	1	1	yes	characteristic
526	#557	C₂²×C₁₃	1	2	yes	—
527	#557	C₂²×C₁₃	1	2	yes	—
528	#556	—	2	1	no	—
529	#556	C₂²×C₁₃	1	1	yes	characteristic
530	#556	C₂²×C₁₃	1	2	yes	—
531	#554	C₂²×C₁₃	1	1	yes	characteristic
532	#552	—	2	1	no	—
533	#544	—	2	1	no	—
534	#544	—	2	2	no	—
535	#544	C₂²×C₁₃	1	2	yes	—
536	#542	C₂²×C₁₃	1	2	yes	—
537	#541	—	2	1	no	—
538	#541	—	2	2	no	—
539	#541	C₂²×C₁₃	1	2	yes	—
540	#533	—	2	1	no	—
541	#533	—	2	1	no	—
542	#533	C₂²×C₁₃	1	1	yes	characteristic
543	#533	C₂²×C₁₃	1	1	yes	characteristic
544	#533	C₂²×C₁₃	1	1	yes	characteristic
545	#529	C₂²×C₁₃	1	1	yes	characteristic
546	#519	C₂²×C₁₃	1	2	yes	—
547	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
548	#501	C₂²×C₁₃	1	2	yes	—
549	#501	C₂²×C₁₃	1	2	yes	—
550	#500	C₂²×C₁₃	1	2	yes	—
551	#500	C₂²×C₁₃	1	1	yes	characteristic
552	#499	C₂²×C₁₃	1	2	yes	—
553	#499	C₂²×C₁₃	1	2	yes	—
554	#498	C₂²×C₁₃	1	1	yes	characteristic
555	#491	C₂²×C₁₃	1	2	yes	—
556	#489	C₂²×C₁₃	1	2	yes	—
557	#488	C₂²×C₁₃	1	2	yes	—
558	#488	C₂²×C₁₃	1	2	yes	—
559	#487	C₂²×C₁₃	1	2	yes	—
560	#487	C₂²×C₁₃	1	1	yes	characteristic
561	#487	C₂²×C₁₃	1	1	yes	characteristic
562	#485	C₂²×C₁₃	1	2	yes	—
563	#485	C₂²×C₁₃	1	2	yes	—
564	#485	C₂²×C₁₃	1	2	yes	—
565	#484	C₂²×C₁₃	1	2	yes	—
566	#483	C₂²×C₁₃	1	1	yes	characteristic
567	#482	C₂²×C₁₃	1	2	yes	—
568	#480	C₂²×C₁₃	1	1	yes	characteristic
569	#479	C₂²×C₁₃	1	1	yes	characteristic
570	#479	C₂²×C₁₃	1	1	yes	characteristic
571	#479	C₂²×C₁₃	1	2	yes	—
572	#479	C₂²×C₁₃	1	2	yes	—
573	#479	C₂²×C₁₃	1	2	yes	—
574	#479	C₂²×C₁₃	1	2	yes	—
575	#479	C₂²×C₁₃	1	2	yes	—
576	#479	C₂²×C₁₃	1	2	yes	—
577	#479	C₂²×C₁₃	1	2	yes	—
578	#478	C₂²×C₁₃	1	2	yes	—
579	#477	C₂²×C₁₃	1	1	yes	characteristic
580	#477	C₂²×C₁₃	1	1	yes	characteristic
581	#477	C₂²×C₁₃	1	1	yes	characteristic
582	#477	C₂²×C₁₃	1	2	yes	—
583	#477	C₂²×C₁₃	1	2	yes	—
584	#477	C₂²×C₁₃	1	2	yes	—
585	#476	C₂²×C₁₃	1	1	yes	characteristic
586	#475	C₂²×C₁₃	1	2	yes	—
587	#475	C₂²×C₁₃	1	1	yes	characteristic
588	#475	C₂²×C₁₃	1	2	yes	—
589	#474	C₂²×C₁₃	1	1	yes	characteristic
590	#474	C₂²×C₁₃	1	2	yes	—
591	#464	C₂²×C₁₃	1	1	yes	characteristic
592	#464	C₂²×C₁₃	1	1	yes	characteristic
593	#464	C₂²×C₁₃	1	2	yes	—
594	#464	C₂²×C₁₃	1	2	yes	—
595	#462	C₂²×C₁₃	1	1	yes	characteristic
596	#462	C₂²×C₁₃	1	1	yes	characteristic
597	#462	C₂²×C₁₃	1	2	yes	—
598	#462	C₂²×C₁₃	1	2	yes	—
599	#451	C₂²×C₁₃	1	2	yes	—
600	#451	C₂²×C₁₃	1	1	yes	characteristic
601	#448	C₂²×C₁₃	1	1	yes	characteristic
602	#446	C₂²×C₁₃	1	1	yes	characteristic
603	#446	C₂²×C₁₃	1	1	yes	characteristic
604	#446	C₂²×C₁₃	1	2	yes	—
605	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
606	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
607	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
608	#441	C₂²×C₁₃	1	2	yes	—
609	#441	C₂²×C₁₃	1	2	yes	—
610	#441	C₂²×C₁₃	1	2	yes	—
611	#440	C₂²×C₁₃	1	2	yes	—
612	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
613	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
614	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
615	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
616	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
617	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
618	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
619	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
620	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
621	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
622	#433	C₂²×C₁₃	1	2	yes	—
623	#433	C₂²×C₁₃	1	2	yes	—
624	#431	C₂²×C₁₃	1	1	yes	characteristic
625	#431	C₂²×C₁₃	1	1	yes	characteristic
626	C₂²×C₁₃	—	2	1	no	—
627	C₂²×C₁₃	—	2	1	no	—
628	C₂²×C₁₃	—	2	1	no	—
629	C₂²×C₁₃	—	4	1	no	—
630	C₂²×C₁₃	—	4	1	no	—
631	C₂²×C₁₃	—	4	1	no	—
632	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
633	C₄×C₁₃	—	2	1	no	—
634	C₄×C₁₃	—	2	1	no	—
635	C₄×C₁₃	—	2	2	no	—
636	C₄×C₁₃	—	2	2	no	—
637	C₄×C₁₃	—	2	2	no	—
638	C₄×C₁₃	—	2	2	no	—
639	C₄×C₁₃	—	2	1	no	—
640	C₄×C₁₃	—	2	1	no	—
641	C₄×C₁₃	—	2	2	no	—
642	C₄×C₁₃	—	2	2	no	—
643	C₄×C₁₃	—	4	2	no	—
644	C₄×C₁₃	—	4	1	no	—
645	C₄×C₁₃	—	4	1	no	—
646	C₄×C₁₃	—	4	1	no	—
647	C₄×C₁₃	—	4	2	no	—
648	C₄×C₁₃	—	4	2	no	—
649	C₄×C₁₃	—	4	1	no	—
650	C₄×C₁₃	—	4	1	no	—
651	C₄×C₁₃	—	4	2	no	—
652	C₄×C₁₃	#578	1	2	yes	—
653	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
654	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
655	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
656	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
657	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
659	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
660	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
661	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
662	C₄⋊Q₈	—	2	1	no	—
663	C₄⋊Q₈	—	2	1	no	—
664	C₄⋊Q₈	—	2	2	no	—
665	C₄⋊Q₈	—	2	2	no	—
666	C₄⋊Q₈	—	2	2	no	—
667	C₄⋊Q₈	—	2	1	no	—
668	C₄⋊Q₈	—	2	1	no	—
669	C₄⋊Q₈	—	2	2	no	—
670	C₄⋊Q₈	—	2	1	no	—
671	C₄⋊Q₈	—	2	2	no	—
672	C₄⋊Q₈	—	2	2	no	—
673	C₄⋊Q₈	—	2	2	no	—
674	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
675	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
676	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
677	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
678	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
679	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
682	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
683	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
684	#126	—	2	2	no	—
685	#126	—	2	2	no	—
686	#126	—	2	2	no	—
687	#126	—	2	2	no	—
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	1	no	—
691	#125	—	2	2	no	—
692	#125	—	2	2	no	—
693	#125	—	2	2	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	1	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	2	no	—
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	1	no	—
705	#125	D₄×C₁₃	1	2	yes	—
706	#125	C₂³×C₁₃	1	1	yes	characteristic
707	#125	C₂³×C₁₃	1	2	yes	—
708	#125	C₂³×C₁₃	1	2	yes	—
709	#125	C₂³×C₁₃	1	2	yes	—
710	#125	C₂³×C₁₃	1	2	yes	—
711	#124	—	2	2	no	—
712	#124	C₂³×C₁₃	1	1	yes	characteristic
713	#124	C₂³×C₁₃	1	2	yes	—
714	#123	—	2	1	no	—
715	#123	—	2	2	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	2	1	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	1	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
727	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
728	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
731	#121	C₂³×C₁₃	1	1	yes	characteristic
732	C₄×Q₈	—	2	1	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	2	1	no	—
736	C₄×Q₈	—	2	2	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	2	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	—	2	1	no	—
742	C₄×Q₈	—	2	2	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	2	1	no	—
746	C₄×Q₈	—	2	1	no	—
747	C₄×Q₈	—	2	1	no	—
748	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
749	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
750	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
751	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
752	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
753	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
754	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
755	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
756	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
757	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
758	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
759	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
760	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
761	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
763	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
766	C₄×D₄	C₂³×C₁₃	1	2	yes	—
767	#117	—	2	1	no	—
768	#117	—	2	2	no	—
769	#117	—	2	1	no	—
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	1	no	—
773	#117	C₂³×C₁₃	1	2	yes	—
774	#117	C₂³×C₁₃	1	2	yes	—
775	C₂×C₄⋊C₄	—	2	1	no	—
776	C₂×C₄⋊C₄	—	2	1	no	—
777	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
778	C₂×C₄²	—	2	1	no	—
779	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
780	#107	C₂³×C₁₃	1	2	yes	—
781	#107	C₂³×C₁₃	1	2	yes	—
782	#107	C₂³×C₁₃	1	2	yes	—
783	#107	C₂³×C₁₃	1	2	yes	—
784	#107	C₂³×C₁₃	1	2	yes	—
785	#107	C₂³×C₁₃	1	1	yes	characteristic
786	#107	C₂³×C₁₃	1	1	yes	characteristic
787	#107	C₂³×C₁₃	1	2	yes	—
788	#106	C₂³×C₁₃	1	1	yes	characteristic
789	#106	C₂³×C₁₃	1	2	yes	—
790	#106	C₂³×C₁₃	1	1	yes	characteristic
791	#106	C₂³×C₁₃	1	2	yes	—
792	#106	C₂³×C₁₃	1	2	yes	—
793	#106	C₂³×C₁₃	1	2	yes	—
794	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
795	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
796	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
799	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
800	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
801	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
802	#103	C₂³×C₁₃	1	2	yes	—
803	#103	C₂³×C₁₃	1	1	yes	characteristic
804	#103	C₂³×C₁₃	1	1	yes	characteristic
805	#103	C₂³×C₁₃	1	1	yes	characteristic
806	#103	C₂³×C₁₃	1	2	yes	—
807	#103	C₂³×C₁₃	1	1	yes	characteristic
808	#103	C₂³×C₁₃	1	2	yes	—
809	#103	C₂³×C₁₃	1	2	yes	—
810	#103	C₂³×C₁₃	1	2	yes	—
811	#103	C₂³×C₁₃	1	2	yes	—
812	#103	C₂³×C₁₃	1	2	yes	—
813	#103	C₂³×C₁₃	1	1	yes	characteristic
814	#103	C₂³×C₁₃	1	1	yes	characteristic
815	#103	C₂³×C₁₃	1	2	yes	—
816	#103	C₂³×C₁₃	1	2	yes	—
817	#103	C₂³×C₁₃	1	2	yes	—
818	#102	C₂³×C₁₃	1	1	yes	characteristic
819	#102	C₂³×C₁₃	1	2	yes	—
820	#102	C₂³×C₁₃	1	1	yes	characteristic
821	#102	C₂³×C₁₃	1	2	yes	—
822	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
825	#97	C₂³×C₁₃	1	2	yes	—
826	#97	C₂³×C₁₃	1	2	yes	—
827	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
828	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
829	C₄×C₈	C₂³×C₁₃	1	2	yes	—
830	C₄×C₈	C₂³×C₁₃	1	2	yes	—
831	C₄×C₈	C₂³×C₁₃	1	2	yes	—
832	C₂×C₁₃	—	4	1	no	—
833	C₂×C₁₃	—	8	1	no	—
834	C₂×C₁₃	#3486	1	1	yes	characteristic
835	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
836	C₂×C₁₃	#3584	1	1	yes	characteristic
837	C₂×Q₈	—	2	2	no	—
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	2	1	no	—
840	C₂×Q₈	—	2	1	no	—
841	C₂×Q₈	—	2	1	no	—
842	C₂×Q₈	—	2	2	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
847	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
848	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
849	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
850	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
851	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
852	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
855	C₂²×C₄	—	2	1	no	—
856	C₂²×C₄	—	2	1	no	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
860	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
862	Q₁₆	—	2	4	no	—
863	Q₁₆	—	2	2	no	—
864	Q₁₆	—	2	4	no	—
865	Q₁₆	—	2	2	no	—
866	SD₁₆	—	2	2	no	—
867	SD₁₆	—	2	2	no	—
868	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
869	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
870	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
871	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
872	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
873	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	1	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	1	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
911	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
912	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
914	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
915	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
916	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
917	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
918	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
919	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
922	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	1	no	—
929	C₂²⋊C₄	—	2	1	no	—
930	C₂²⋊C₄	—	2	1	no	—
931	C₂²⋊C₄	—	2	1	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	1	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
937	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
938	C₄²	—	2	1	no	—
939	C₄²	—	2	1	no	—
940	C₄²	—	2	1	no	—
941	C₄²	—	2	1	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	1	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	2	2	no	—
947	C₄²	—	2	2	no	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	2	no	—
950	C₄²	—	2	2	no	—
951	C₄²	—	2	2	no	—
952	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
953	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
954	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
956	C₄²	C₂⁴×C₁₃	1	2	yes	—
957	C₄²	C₂⁴×C₁₃	1	2	yes	—
958	C₁₃	#61866	1	1	yes	characteristic, direct product factor, Sylow
959	C₂³	—	2	1	no	—
960	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
961	Q₈	—	2	4	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	2	no	—
964	Q₈	—	2	1	no	—
965	Q₈	—	2	1	no	—
966	Q₈	—	2	2	no	—
967	Q₈	—	2	1	no	—
968	Q₈	—	2	2	no	—
969	Q₈	—	2	1	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	1	no	—
974	Q₈	—	8	2	no	—
975	Q₈	—	8	2	no	—
976	Q₈	—	8	2	no	—
977	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
978	Q₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
979	D₄	—	2	1	no	—
980	D₄	—	2	1	no	—
981	D₄	—	8	1	no	—
982	C₂×C₄	—	2	4	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	2	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	8	1	no	—
1001	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1004	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1005	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1006	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1007	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1008	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1009	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1010	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1011	C₈	—	2	1	no	—
1012	C₈	—	2	1	no	—
1013	C₈	—	2	1	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	1	no	—
1016	C₈	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1024	C₄	—	2	1	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	—	2	1	no	—
1028	C₄	—	2	1	no	—
1029	C₄	—	2	2	no	—
1030	C₄	—	2	2	no	—
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	4	1	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	2	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	1	no	—
1043	C₄	C₁₃×#578	1	2	yes	—
1044	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1045	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	1	no	—
1048	C₂	C₁₃×#3486	1	1	yes	characteristic
1049	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1050	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#121	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3390	C₂	semidirect
4. C₁₃×#3387	C₂	semidirect
5. C₁₃×#3385	C₂	semidirect
6. C₁₃×#3383	C₂	semidirect
7. Q₈×C₁₃×Q₁₆	C₂	semidirect
8. C₁₃×#3381	C₂	semidirect
9. C₁₃×#3377	C₂	semidirect
10. C₁₃×#3374	C₂	semidirect
11. C₁₃×#3369	C₂	semidirect
12. C₁₃×#3364	C₂	semidirect
13. C₁₃×#3364	C₂	semidirect
14. C₁₃×#3363	C₂	semidirect
16. C₁₃×#3242	C₂	semidirect
18. C₁₃×#3231	C₂	semidirect
19. C₁₃×#3127	C₂	semidirect
22. C₁₃×#3104	C₂	semidirect
23. C₁₃×#2986	C₂	semidirect
312. #61866	C₁₃	direct (N × H)
435. #3502	C₂×C₁₃	semidirect
436. #3390	C₂×C₁₃	semidirect
437. #3387	C₂×C₁₃	semidirect
438. #3385	C₂×C₁₃	semidirect
439. #3383	C₂×C₁₃	semidirect
440. Q₈×Q₁₆	C₂×C₁₃	semidirect
441. #3381	C₂×C₁₃	semidirect
442. #3377	C₂×C₁₃	semidirect
443. #3374	C₂×C₁₃	semidirect
444. #3369	C₂×C₁₃	semidirect
445. #3364	C₂×C₁₃	semidirect
446. #3364	C₂×C₁₃	semidirect
447. #3363	C₂×C₁₃	semidirect
449. #3242	C₂×C₁₃	semidirect
451. #3231	C₂×C₁₃	semidirect
452. #3127	C₂×C₁₃	semidirect
455. #3104	C₂×C₁₃	semidirect
456. #2986	C₂×C₁₃	semidirect
958. C₁₃	#61866	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3555	2
C₁₃×#3502	2
C₁₃×#3390	2
C₁₃×#3387	2
C₁₃×#3385	2
C₁₃×#3383	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3381	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3369	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3243	2
C₁₃×#3242	2
C₁₃×#3233	2
C₁₃×#3231	2
C₁₃×#3127	2
C₁₃×#3121	2
C₁₃×#3108	2
C₁₃×#3104	2
C₁₃×#2986	2
#61866	13

Subgroups — C13×#61866 #15748205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61866 #15748205