Subgroups — C₁₃×#61453 #15747792

Order 3328.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3481	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3314	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3299	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3181	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3117	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3110	C₂	1	2	yes	maximal, complemented
21	C₁₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
24	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	C₁₃×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	—	2	1	no	—
29	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#554	—	2	1	no	—
31	C₁₃×#554	—	2	2	no	—
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#554	C₂²	1	1	yes	characteristic
34	C₁₃×#554	C₂²	1	1	yes	characteristic
35	C₁₃×#554	C₂²	1	2	yes	complemented
36	C₁₃×#553	—	2	1	no	—
37	C₁₃×#553	C₂²	1	2	yes	—
38	C₁₃×#551	—	2	2	no	—
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
40	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
41	C₁₃×#546	—	2	1	no	—
42	C₁₃×#546	C₂²	1	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#533	—	2	2	no	—
45	C₁₃×#533	—	2	1	no	—
46	C₁₃×#533	C₂²	1	2	yes	complemented
47	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#529	—	2	1	no	—
50	C₁₃×#529	C₂²	1	2	yes	—
51	C₁₃×#525	—	2	2	no	—
52	C₄×C₁₃×#41	—	2	1	no	—
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
54	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
57	C₂×C₄×D₄×C₁₃	—	2	1	no	—
58	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#497	C₂²	1	2	yes	complemented
62	C₁₃×#492	C₂²	1	1	yes	characteristic
63	C₁₃×#491	C₂²	1	2	yes	complemented
64	C₁₃×#489	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#484	C₂²	1	2	yes	complemented
69	C₁₃×#484	C₂²	1	2	yes	complemented
70	C₁₃×#484	C₂²	1	2	yes	complemented
71	C₁₃×#481	C₂²	1	2	yes	—
72	C₁₃×#480	C₂²	1	2	yes	complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#476	C₂²	1	1	yes	characteristic
79	C₁₃×#474	C₂²	1	2	yes	—
80	C₁₃×#474	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#467	C₂²	1	2	yes	complemented
84	C₁₃×#467	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#461	C₂²	1	2	yes	—
91	C₁₃×#461	C₂²	1	1	yes	characteristic
92	C₁₃×#461	C₂²	1	2	yes	complemented
93	C₁₃×#460	C₂²	1	1	yes	characteristic
94	C₁₃×#460	C₂²	1	1	yes	characteristic
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	2	yes	complemented
97	C₁₃×#450	C₂²	1	2	yes	—
98	C₁₃×#450	C₂²	1	2	yes	—
99	C₁₃×#448	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#441	C₂²	1	2	yes	complemented
104	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
105	C₁₃×#441	C₂²	1	1	yes	characteristic, complemented
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₁₃×#440	C₂²	1	2	yes	—
108	C₁₃×#440	C₂²	1	1	yes	characteristic
109	C₁₃×#440	C₂²	1	2	yes	—
110	C₁₃×#440	C₂²	1	1	yes	characteristic
111	C₁₃×#440	C₂²	1	2	yes	complemented
112	C₁₃×#440	C₂²	1	2	yes	complemented
113	C₁₃×#440	C₂²	1	2	yes	complemented
114	C₁₃×#440	C₂²	1	2	yes	complemented
115	C₁₃×#440	C₂²	1	2	yes	complemented
116	C₁₃×#440	C₂²	1	2	yes	complemented
117	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
121	C₁₃×#435	C₂²	1	2	yes	complemented
122	C₁₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
125	C₁₃×#432	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
129	C₁₃×#419	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#417	C₂²	1	1	yes	characteristic
131	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
132	C₂×C₁₃×#102	C₂²	1	2	yes	—
133	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₁₃	—	2	1	no	—
141	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₁₃	—	2	2	no	—
143	C₁₃×#137	—	2	4	no	—
144	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	—	2	8	no	—
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
157	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
158	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
159	C₁₃×C₄⋊Q₈	—	2	1	no	—
160	C₁₃×C₄⋊Q₈	—	2	2	no	—
161	C₁₃×C₄⋊Q₈	—	2	1	no	—
162	C₁₃×C₄⋊Q₈	—	2	2	no	—
163	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₃×#127	C₂³	1	1	yes	characteristic
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#125	—	2	1	no	—
172	C₁₃×#125	—	2	1	no	—
173	C₁₃×#125	—	2	2	no	—
174	C₁₃×#125	—	2	1	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	—	2	1	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	C₂³	1	2	yes	—
179	C₁₃×#124	—	2	1	no	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×C₂²⋊Q₈	—	2	1	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	1	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	—	2	2	no	—
194	C₁₃×C₂²⋊Q₈	—	2	2	no	—
195	C₁₃×C₂²⋊Q₈	—	2	2	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	1	no	—
203	C₁₃×#121	—	2	1	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	C₂³	1	2	yes	—
206	C₁₃×#121	C₂³	1	2	yes	—
207	C₁₃×#120	—	2	2	no	—
208	C₁₃×#120	—	2	2	no	—
209	C₄×Q₈×C₁₃	—	2	1	no	—
210	C₄×Q₈×C₁₃	—	2	1	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	1	no	—
214	C₄×Q₈×C₁₃	—	2	2	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	2	no	—
217	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
218	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₁₃	—	2	1	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	2	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	1	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	—	2	1	no	—
239	C₄×D₄×C₁₃	—	2	2	no	—
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
242	C₄×D₄×C₁₃	D₄	1	2	yes	—
243	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
248	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₁₃×#117	—	2	2	no	—
251	C₁₃×#117	—	2	1	no	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	D₄	1	2	yes	—
255	C₁₃×#117	D₄	1	1	yes	characteristic
256	C₁₃×#117	C₂³	1	1	yes	characteristic
257	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²×C₁₃	—	2	2	no	—
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	2	1	no	—
268	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
269	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	2	yes	—
276	C₁₃×#107	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	2	yes	—
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	1	yes	characteristic
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	1	yes	characteristic
291	C₁₃×#103	C₂³	1	1	yes	characteristic
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	2	yes	—
294	C₁₃×#103	C₂³	1	2	yes	—
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	1	yes	characteristic
298	C₁₃×#102	C₂³	1	2	yes	—
299	C₁₃×#102	C₂³	1	2	yes	—
300	C₁₃×#102	C₂³	1	2	yes	—
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	1	yes	characteristic
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₁₃×#97	C₂³	1	2	yes	—
311	C₁₃×#97	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
314	#61453	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	2	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	4	1	no	—
319	C₁₃×#41	—	8	2	no	—
320	C₂×Q₈×C₁₃	—	2	1	no	—
321	C₂×Q₈×C₁₃	—	2	2	no	—
322	C₂×Q₈×C₁₃	—	2	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	4	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	—	4	2	no	—
328	C₂×Q₈×C₁₃	—	4	1	no	—
329	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
332	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×D₄×C₁₃	—	2	4	no	—
335	C₂×D₄×C₁₃	—	2	1	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	1	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	4	2	no	—
342	C₂×D₄×C₁₃	—	4	4	no	—
343	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
344	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
345	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
346	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	2	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	2	no	—
356	C₂²×C₄×C₁₃	—	2	2	no	—
357	C₂²×C₄×C₁₃	—	2	2	no	—
358	C₂²×C₄×C₁₃	—	8	4	no	—
359	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
360	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
364	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₁₃×Q₁₆	—	2	2	no	—
366	C₁₃×Q₁₆	—	2	2	no	—
367	C₁₃×Q₁₆	—	4	2	no	—
368	C₁₃×SD₁₆	—	2	4	no	—
369	C₁₃×SD₁₆	—	2	4	no	—
370	C₁₃×SD₁₆	—	2	2	no	—
371	C₁₃×SD₁₆	—	2	4	no	—
372	C₁₃×SD₁₆	—	4	2	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	#41	1	4	yes	complemented
375	C₁₃×M₁₆	—	2	2	no	—
376	C₁₃×M₁₆	—	4	1	no	—
377	C₂×C₈×C₁₃	—	2	4	no	—
378	C₂×C₈×C₁₃	—	4	2	no	—
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
383	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	2	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	2	no	—
400	C₁₃×C₄⋊C₄	—	2	1	no	—
401	C₁₃×C₄⋊C₄	—	2	1	no	—
402	C₁₃×C₄⋊C₄	—	2	1	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	2	no	—
405	C₁₃×C₄⋊C₄	—	2	2	no	—
406	C₁₃×C₄⋊C₄	—	2	1	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	2	no	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	2	no	—
423	C₁₃×C₂²⋊C₄	—	2	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
435	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₄²×C₁₃	—	2	1	no	—
438	C₄²×C₁₃	—	2	1	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	1	no	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	2	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	1	no	—
447	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂×D₄	1	2	yes	—
450	C₄²×C₁₃	C₂×D₄	1	2	yes	—
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₁₃	C₂⁴	1	2	yes	—
454	#3481	C₂×C₁₃	1	1	yes	characteristic
455	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3385	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3346	C₂×C₁₃	1	2	yes	complemented
461	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3320	C₂×C₁₃	1	2	yes	complemented
463	#3314	C₂×C₁₃	1	2	yes	complemented
464	#3299	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3295	C₂×C₁₃	1	1	yes	characteristic, complemented
466	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3266	C₂×C₁₃	1	2	yes	complemented
468	#3182	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3181	C₂×C₁₃	1	2	yes	complemented
470	#3117	C₂×C₁₃	1	2	yes	complemented
471	#3116	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#3110	C₂×C₁₃	1	2	yes	complemented
474	#2970	C₂×C₁₃	1	1	yes	characteristic, complemented
475	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
476	C₂×#440	C₂×C₁₃	1	2	yes	complemented
477	C₂³×C₁₃	—	2	1	no	—
478	C₂³×C₁₃	—	2	2	no	—
479	C₂³×C₁₃	—	4	4	no	—
480	C₂³×C₁₃	—	4	4	no	—
481	C₂³×C₁₃	—	8	2	no	—
482	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
484	Q₈×C₁₃	—	2	2	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	2	no	—
487	Q₈×C₁₃	—	2	1	no	—
488	Q₈×C₁₃	—	2	1	no	—
489	Q₈×C₁₃	—	2	1	no	—
490	Q₈×C₁₃	—	2	2	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	4	2	no	—
493	Q₈×C₁₃	—	4	4	no	—
494	Q₈×C₁₃	—	8	2	no	—
495	Q₈×C₁₃	—	8	1	no	—
496	Q₈×C₁₃	—	8	1	no	—
497	Q₈×C₁₃	C₂×#41	1	2	yes	—
498	D₄×C₁₃	—	2	4	no	—
499	D₄×C₁₃	—	2	2	no	—
500	D₄×C₁₃	—	2	1	no	—
501	D₄×C₁₃	—	2	2	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	4	4	no	—
505	D₄×C₁₃	—	4	2	no	—
506	D₄×C₁₃	—	8	1	no	—
507	D₄×C₁₃	—	8	2	no	—
508	D₄×C₁₃	#137	1	4	yes	complemented
509	D₄×C₁₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₁₃	—	2	4	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	2	2	no	—
513	C₂×C₄×C₁₃	—	2	2	no	—
514	C₂×C₄×C₁₃	—	2	1	no	—
515	C₂×C₄×C₁₃	—	2	2	no	—
516	C₂×C₄×C₁₃	—	2	1	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	2	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	4	2	no	—
527	C₂×C₄×C₁₃	—	4	1	no	—
528	C₂×C₄×C₁₃	—	4	4	no	—
529	C₂×C₄×C₁₃	—	4	2	no	—
530	C₂×C₄×C₁₃	—	4	2	no	—
531	C₂×C₄×C₁₃	—	4	2	no	—
532	C₂×C₄×C₁₃	—	4	4	no	—
533	C₂×C₄×C₁₃	—	4	2	no	—
534	C₂×C₄×C₁₃	—	8	2	no	—
535	C₂×C₄×C₁₃	—	8	2	no	—
536	C₂×C₄×C₁₃	—	8	2	no	—
537	C₂×C₄×C₁₃	—	8	1	no	—
538	C₂×C₄×C₁₃	—	8	2	no	—
539	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
545	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
548	C₈×C₁₃	—	2	2	no	—
549	C₈×C₁₃	—	2	1	no	—
550	C₈×C₁₃	—	2	1	no	—
551	C₈×C₁₃	—	2	2	no	—
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	C₂×#41	1	2	yes	—
554	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
555	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
556	#559	C₂²×C₁₃	1	1	yes	characteristic
557	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	#557	—	2	1	no	—
559	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
560	#554	—	2	1	no	—
561	#554	—	2	2	no	—
562	#554	C₂²×C₁₃	1	1	yes	characteristic
563	#554	C₂²×C₁₃	1	1	yes	characteristic
564	#554	C₂²×C₁₃	1	1	yes	characteristic
565	#554	C₂²×C₁₃	1	2	yes	complemented
566	#553	—	2	1	no	—
567	#553	C₂²×C₁₃	1	2	yes	—
568	#551	—	2	2	no	—
569	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
570	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
571	#546	—	2	1	no	—
572	#546	C₂²×C₁₃	1	2	yes	—
573	D₄²	C₂²×C₁₃	1	1	yes	characteristic
574	#533	—	2	2	no	—
575	#533	—	2	1	no	—
576	#533	C₂²×C₁₃	1	2	yes	complemented
577	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
578	#532	C₂²×C₁₃	1	1	yes	characteristic
579	#529	—	2	1	no	—
580	#529	C₂²×C₁₃	1	2	yes	—
581	#525	—	2	2	no	—
582	C₄×#41	—	2	1	no	—
583	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
584	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
585	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
586	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
587	C₂×C₄×D₄	—	2	1	no	—
588	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
589	#501	C₂²×C₁₃	1	2	yes	complemented
590	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#497	C₂²×C₁₃	1	2	yes	complemented
592	#492	C₂²×C₁₃	1	1	yes	characteristic
593	#491	C₂²×C₁₃	1	2	yes	complemented
594	#489	C₂²×C₁₃	1	2	yes	complemented
595	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#486	C₂²×C₁₃	1	1	yes	characteristic
597	#485	C₂²×C₁₃	1	2	yes	complemented
598	#484	C₂²×C₁₃	1	2	yes	complemented
599	#484	C₂²×C₁₃	1	2	yes	complemented
600	#484	C₂²×C₁₃	1	2	yes	complemented
601	#481	C₂²×C₁₃	1	2	yes	—
602	#480	C₂²×C₁₃	1	2	yes	complemented
603	#479	C₂²×C₁₃	1	2	yes	complemented
604	#479	C₂²×C₁₃	1	2	yes	complemented
605	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
607	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#476	C₂²×C₁₃	1	1	yes	characteristic
609	#474	C₂²×C₁₃	1	2	yes	—
610	#474	C₂²×C₁₃	1	2	yes	complemented
611	#468	C₂²×C₁₃	1	2	yes	complemented
612	#468	C₂²×C₁₃	1	2	yes	complemented
613	#467	C₂²×C₁₃	1	2	yes	complemented
614	#467	C₂²×C₁₃	1	2	yes	complemented
615	#465	C₂²×C₁₃	1	2	yes	—
616	#465	C₂²×C₁₃	1	2	yes	—
617	#464	C₂²×C₁₃	1	2	yes	complemented
618	#464	C₂²×C₁₃	1	2	yes	complemented
619	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
620	#461	C₂²×C₁₃	1	2	yes	—
621	#461	C₂²×C₁₃	1	1	yes	characteristic
622	#461	C₂²×C₁₃	1	2	yes	complemented
623	#460	C₂²×C₁₃	1	1	yes	characteristic
624	#460	C₂²×C₁₃	1	1	yes	characteristic
625	#452	C₂²×C₁₃	1	2	yes	—
626	#451	C₂²×C₁₃	1	2	yes	complemented
627	#450	C₂²×C₁₃	1	2	yes	—
628	#450	C₂²×C₁₃	1	2	yes	—
629	#448	C₂²×C₁₃	1	2	yes	—
630	#448	C₂²×C₁₃	1	2	yes	complemented
631	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#441	C₂²×C₁₃	1	2	yes	complemented
634	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	#441	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#440	C₂²×C₁₃	1	1	yes	characteristic
637	#440	C₂²×C₁₃	1	2	yes	—
638	#440	C₂²×C₁₃	1	2	yes	—
639	#440	C₂²×C₁₃	1	2	yes	—
640	#440	C₂²×C₁₃	1	1	yes	characteristic
641	#440	C₂²×C₁₃	1	2	yes	complemented
642	#440	C₂²×C₁₃	1	2	yes	complemented
643	#440	C₂²×C₁₃	1	2	yes	complemented
644	#440	C₂²×C₁₃	1	2	yes	complemented
645	#440	C₂²×C₁₃	1	2	yes	complemented
646	#440	C₂²×C₁₃	1	2	yes	complemented
647	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
648	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
650	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
651	#435	C₂²×C₁₃	1	2	yes	complemented
652	#435	C₂²×C₁₃	1	2	yes	complemented
653	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
654	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
655	#432	C₂²×C₁₃	1	2	yes	complemented
656	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
657	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
659	#419	C₂²×C₁₃	1	1	yes	characteristic, complemented
660	#417	C₂²×C₁₃	1	1	yes	characteristic
661	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
662	C₂×#102	C₂²×C₁₃	1	2	yes	—
663	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
664	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
665	C₂²×C₁₃	—	2	2	no	—
666	C₂²×C₁₃	—	2	2	no	—
667	C₂²×C₁₃	—	2	1	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	4	1	no	—
672	C₂²×C₁₃	—	4	1	no	—
673	C₂²×C₁₃	—	4	2	no	—
674	C₂²×C₁₃	—	4	2	no	—
675	C₂²×C₁₃	—	4	2	no	—
676	C₂²×C₁₃	—	8	8	no	—
677	C₂²×C₁₃	C₂×#137	1	4	yes	—
678	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
679	C₄×C₁₃	—	2	1	no	—
680	C₄×C₁₃	—	2	2	no	—
681	C₄×C₁₃	—	2	1	no	—
682	C₄×C₁₃	—	2	1	no	—
683	C₄×C₁₃	—	2	2	no	—
684	C₄×C₁₃	—	2	2	no	—
685	C₄×C₁₃	—	2	1	no	—
686	C₄×C₁₃	—	2	2	no	—
687	C₄×C₁₃	—	4	1	no	—
688	C₄×C₁₃	—	4	2	no	—
689	C₄×C₁₃	—	4	1	no	—
690	C₄×C₁₃	—	4	2	no	—
691	C₄×C₁₃	—	4	1	no	—
692	C₄×C₁₃	—	4	1	no	—
693	C₄×C₁₃	—	4	2	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	C₂×#137	1	2	yes	—
697	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
698	C₄×C₁₃	#585	1	1	yes	characteristic
699	C₂×#41	—	2	1	no	—
700	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
701	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
702	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
703	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
704	C₂²×D₄	—	2	1	no	—
705	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
706	C₂³×C₄	—	2	2	no	—
707	#137	—	2	4	no	—
708	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
710	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
711	C₂×SD₁₆	—	2	8	no	—
712	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
713	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
714	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
715	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
717	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
720	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
721	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
722	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
728	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
729	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
730	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
732	#127	C₂³×C₁₃	1	1	yes	characteristic
733	#126	—	2	2	no	—
734	#126	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	—	2	2	no	—
738	#125	—	2	1	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	2	no	—
742	#125	C₂³×C₁₃	1	2	yes	—
743	#124	—	2	1	no	—
744	#124	—	2	1	no	—
745	#124	C₂³×C₁₃	1	2	yes	—
746	#123	—	2	2	no	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
762	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
763	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
764	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
765	#121	—	2	2	no	—
766	#121	—	2	1	no	—
767	#121	—	2	1	no	—
768	#121	—	2	2	no	—
769	#121	C₂³×C₁₃	1	2	yes	—
770	#121	C₂³×C₁₃	1	2	yes	—
771	#120	—	2	2	no	—
772	#120	—	2	2	no	—
773	C₄×Q₈	—	2	1	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	2	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
784	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
787	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
790	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
791	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	1	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	2	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
806	C₄×D₄	D₄×C₁₃	1	2	yes	—
807	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
808	C₄×D₄	C₂³×C₁₃	1	2	yes	—
809	C₄×D₄	C₂³×C₁₃	1	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	2	yes	—
811	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
812	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
813	C₄×D₄	C₂³×C₁₃	1	2	yes	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	1	no	—
817	#117	—	2	2	no	—
818	#117	D₄×C₁₃	1	2	yes	—
819	#117	D₄×C₁₃	1	1	yes	characteristic
820	#117	C₂³×C₁₃	1	1	yes	characteristic
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
825	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
826	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
827	C₂×C₂²⋊C₄	—	2	2	no	—
828	C₂×C₂²⋊C₄	—	2	2	no	—
829	C₂×C₄²	—	2	2	no	—
830	C₂×C₄²	—	2	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
833	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
834	#107	C₂³×C₁₃	1	1	yes	characteristic
835	#107	C₂³×C₁₃	1	2	yes	—
836	#107	C₂³×C₁₃	1	2	yes	—
837	#107	C₂³×C₁₃	1	2	yes	—
838	#107	C₂³×C₁₃	1	1	yes	characteristic
839	#107	C₂³×C₁₃	1	2	yes	—
840	#107	C₂³×C₁₃	1	2	yes	—
841	#106	C₂³×C₁₃	1	1	yes	characteristic
842	#106	C₂³×C₁₃	1	1	yes	characteristic
843	#106	C₂³×C₁₃	1	2	yes	—
844	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
847	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
848	#103	C₂³×C₁₃	1	1	yes	characteristic
849	#103	C₂³×C₁₃	1	2	yes	—
850	#103	C₂³×C₁₃	1	2	yes	—
851	#103	C₂³×C₁₃	1	2	yes	—
852	#103	C₂³×C₁₃	1	1	yes	characteristic
853	#103	C₂³×C₁₃	1	1	yes	characteristic
854	#103	C₂³×C₁₃	1	1	yes	characteristic
855	#103	C₂³×C₁₃	1	1	yes	characteristic
856	#103	C₂³×C₁₃	1	1	yes	characteristic
857	#103	C₂³×C₁₃	1	2	yes	—
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	2	yes	—
861	#102	C₂³×C₁₃	1	1	yes	characteristic
862	#102	C₂³×C₁₃	1	2	yes	—
863	#102	C₂³×C₁₃	1	2	yes	—
864	#102	C₂³×C₁₃	1	2	yes	—
865	#102	C₂³×C₁₃	1	1	yes	characteristic
866	#102	C₂³×C₁₃	1	2	yes	—
867	#102	C₂³×C₁₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
871	#97	C₂³×C₁₃	1	1	yes	characteristic
872	#97	C₂³×C₁₃	1	2	yes	—
873	#97	C₂³×C₁₃	1	2	yes	—
874	#97	C₂³×C₁₃	1	2	yes	—
875	#97	C₂³×C₁₃	1	1	yes	characteristic
876	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
877	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
878	C₂×C₁₃	—	2	4	no	—
879	C₂×C₁₃	—	4	1	no	—
880	C₂×C₁₃	—	4	2	no	—
881	C₂×C₁₃	—	8	2	no	—
882	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
883	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
884	C₂×C₁₃	#3585	1	1	yes	characteristic
885	C₂⁴	—	2	2	no	—
886	#41	—	2	4	no	—
887	#41	—	2	2	no	—
888	#41	—	4	1	no	—
889	#41	—	8	2	no	—
890	C₂×Q₈	—	2	1	no	—
891	C₂×Q₈	—	2	2	no	—
892	C₂×Q₈	—	2	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	4	no	—
896	C₂×Q₈	—	2	2	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	4	1	no	—
899	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
903	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂×D₄	—	2	4	no	—
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	2	no	—
908	C₂×D₄	—	2	2	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	4	2	no	—
912	C₂×D₄	—	4	4	no	—
913	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
914	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
915	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
916	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	—	2	2	no	—
928	C₂²×C₄	—	8	4	no	—
929	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
930	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
932	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
933	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
934	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	2	2	no	—
937	Q₁₆	—	4	2	no	—
938	SD₁₆	—	2	4	no	—
939	SD₁₆	—	2	4	no	—
940	SD₁₆	—	2	2	no	—
941	SD₁₆	—	2	4	no	—
942	SD₁₆	—	4	2	no	—
943	SD₁₆	—	4	2	no	—
944	SD₁₆	C₁₃×#41	1	4	yes	complemented
945	M₁₆	—	2	2	no	—
946	M₁₆	—	4	1	no	—
947	C₂×C₈	—	2	4	no	—
948	C₂×C₈	—	4	2	no	—
949	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
950	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
952	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
953	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
954	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	1	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
984	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1007	C₄²	—	2	1	no	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	2	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1018	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1020	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1021	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1023	C₄²	C₂⁴×C₁₃	1	2	yes	—
1024	C₁₃	#61453	1	1	yes	characteristic, direct product factor, Sylow
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	2	no	—
1027	C₂³	—	4	4	no	—
1028	C₂³	—	4	4	no	—
1029	C₂³	—	8	2	no	—
1030	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	2	no	—
1039	Q₈	—	2	1	no	—
1040	Q₈	—	4	2	no	—
1041	Q₈	—	4	4	no	—
1042	Q₈	—	8	1	no	—
1043	Q₈	—	8	2	no	—
1044	Q₈	—	8	1	no	—
1045	Q₈	C₂×C₁₃×#41	1	2	yes	—
1046	D₄	—	2	4	no	—
1047	D₄	—	2	2	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	2	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	4	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	2	no	—
1056	D₄	C₁₃×#137	1	4	yes	complemented
1057	D₄	C₂×C₁₃×#41	1	2	yes	—
1058	C₂×C₄	—	2	4	no	—
1059	C₂×C₄	—	2	1	no	—
1060	C₂×C₄	—	2	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	2	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	1	no	—
1076	C₂×C₄	—	4	4	no	—
1077	C₂×C₄	—	4	2	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	4	no	—
1081	C₂×C₄	—	4	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1091	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1092	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1093	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1094	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1095	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	—	2	1	no	—
1101	C₈	C₂×C₁₃×#41	1	2	yes	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	2	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	8	8	no	—
1114	C₂²	C₂×C₁₃×#137	1	4	yes	—
1115	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	—	4	1	no	—
1133	C₄	C₂×C₁₃×#137	1	2	yes	—
1134	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1135	C₄	C₁₃×#585	1	1	yes	characteristic
1136	C₂	—	2	4	no	—
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	2	no	—
1140	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1141	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
1142	C₂	C₁₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3481	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₃×#41	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3385	C₂	semidirect
5. C₁₃×#3375	C₂	semidirect
6. C₁₃×#3372	C₂	semidirect
7. C₁₃×#3346	C₂	semidirect
8. C₁₃×#3338	C₂	semidirect
9. C₁₃×#3320	C₂	semidirect
10. C₁₃×#3314	C₂	semidirect
11. C₁₃×#3299	C₂	semidirect
12. C₁₃×#3295	C₂	semidirect
13. D₄×C₁₃×SD₁₆	C₂	semidirect
14. C₁₃×#3266	C₂	semidirect
15. C₁₃×#3182	C₂	semidirect
16. C₁₃×#3181	C₂	semidirect
17. C₁₃×#3117	C₂	semidirect
18. C₁₃×#3116	C₂	semidirect
19. C₁₃×#3112	C₂	semidirect
20. C₁₃×#3110	C₂	semidirect
21. C₁₃×#2970	C₂	semidirect
22. C₄×C₁₃×#137	C₂	semidirect
23. C₂×C₁₃×#440	C₂	semidirect
27. Q₈²×C₁₃	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
35. C₁₃×#554	C₂²	semidirect
40. D₄×Q₈×C₁₃	C₂²	semidirect
46. C₁₃×#533	C₂²	semidirect
47. C₁₃×#533	C₂²	semidirect
55. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
56. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#500	C₂²	semidirect
61. C₁₃×#497	C₂²	semidirect
63. C₁₃×#491	C₂²	semidirect
64. C₁₃×#489	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#484	C₂²	semidirect
69. C₁₃×#484	C₂²	semidirect
70. C₁₃×#484	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#477	C₂²	semidirect
77. C₁₃×#477	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#467	C₂²	semidirect
84. C₁₃×#467	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
92. C₁₃×#461	C₂²	semidirect
96. C₁₃×#451	C₂²	semidirect
100. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#446	C₂²	semidirect
103. C₁₃×#441	C₂²	semidirect
104. C₁₃×#441	C₂²	semidirect
105. C₁₃×#441	C₂²	semidirect
111. C₁₃×#440	C₂²	semidirect
112. C₁₃×#440	C₂²	semidirect
113. C₁₃×#440	C₂²	semidirect
114. C₁₃×#440	C₂²	semidirect
115. C₁₃×#440	C₂²	semidirect
116. C₁₃×#440	C₂²	semidirect
117. C₄×C₁₃×Q₁₆	C₂²	semidirect
118. C₄×C₁₃×Q₁₆	C₂²	semidirect
121. C₁₃×#435	C₂²	semidirect
122. C₁₃×#435	C₂²	semidirect
125. C₁₃×#432	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
127. C₁₃×#428	C₂²	semidirect
128. C₂×C₁₃×#107	C₂²	semidirect
129. C₁₃×#419	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
133. C₄×C₁₃×M₁₆	C₂²	semidirect
134. C₂×C₁₃×#97	C₂²	semidirect
314. #61453	C₁₃	direct (N × H)
374. C₁₃×SD₁₆	#41	semidirect
455. Q₈×#41	C₂×C₁₃	semidirect
456. #3400	C₂×C₁₃	semidirect
457. #3385	C₂×C₁₃	semidirect
458. #3375	C₂×C₁₃	semidirect
459. #3372	C₂×C₁₃	semidirect
460. #3346	C₂×C₁₃	semidirect
461. #3338	C₂×C₁₃	semidirect
462. #3320	C₂×C₁₃	semidirect
463. #3314	C₂×C₁₃	semidirect
464. #3299	C₂×C₁₃	semidirect
465. #3295	C₂×C₁₃	semidirect
466. D₄×SD₁₆	C₂×C₁₃	semidirect
467. #3266	C₂×C₁₃	semidirect
468. #3182	C₂×C₁₃	semidirect
469. #3181	C₂×C₁₃	semidirect
470. #3117	C₂×C₁₃	semidirect
471. #3116	C₂×C₁₃	semidirect
472. #3112	C₂×C₁₃	semidirect
473. #3110	C₂×C₁₃	semidirect
474. #2970	C₂×C₁₃	semidirect
475. C₄×#137	C₂×C₁₃	semidirect
476. C₂×#440	C₂×C₁₃	semidirect
508. D₄×C₁₃	#137	semidirect
557. Q₈²	C₂²×C₁₃	semidirect
559. #557	C₂²×C₁₃	semidirect
565. #554	C₂²×C₁₃	semidirect
570. D₄×Q₈	C₂²×C₁₃	semidirect
576. #533	C₂²×C₁₃	semidirect
577. #533	C₂²×C₁₃	semidirect
585. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
586. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
589. #501	C₂²×C₁₃	semidirect
590. #500	C₂²×C₁₃	semidirect
591. #497	C₂²×C₁₃	semidirect
593. #491	C₂²×C₁₃	semidirect
594. #489	C₂²×C₁₃	semidirect
595. #487	C₂²×C₁₃	semidirect
597. #485	C₂²×C₁₃	semidirect
598. #484	C₂²×C₁₃	semidirect
599. #484	C₂²×C₁₃	semidirect
600. #484	C₂²×C₁₃	semidirect
602. #480	C₂²×C₁₃	semidirect
603. #479	C₂²×C₁₃	semidirect
604. #479	C₂²×C₁₃	semidirect
605. #477	C₂²×C₁₃	semidirect
606. #477	C₂²×C₁₃	semidirect
607. #477	C₂²×C₁₃	semidirect
610. #474	C₂²×C₁₃	semidirect
611. #468	C₂²×C₁₃	semidirect
612. #468	C₂²×C₁₃	semidirect
613. #467	C₂²×C₁₃	semidirect
614. #467	C₂²×C₁₃	semidirect
617. #464	C₂²×C₁₃	semidirect
618. #464	C₂²×C₁₃	semidirect
619. #462	C₂²×C₁₃	semidirect
622. #461	C₂²×C₁₃	semidirect
626. #451	C₂²×C₁₃	semidirect
630. #448	C₂²×C₁₃	semidirect
631. #446	C₂²×C₁₃	semidirect
632. #446	C₂²×C₁₃	semidirect
633. #441	C₂²×C₁₃	semidirect
634. #441	C₂²×C₁₃	semidirect
635. #441	C₂²×C₁₃	semidirect
641. #440	C₂²×C₁₃	semidirect
642. #440	C₂²×C₁₃	semidirect
643. #440	C₂²×C₁₃	semidirect
644. #440	C₂²×C₁₃	semidirect
645. #440	C₂²×C₁₃	semidirect
646. #440	C₂²×C₁₃	semidirect
647. C₄×Q₁₆	C₂²×C₁₃	semidirect
648. C₄×Q₁₆	C₂²×C₁₃	semidirect
651. #435	C₂²×C₁₃	semidirect
652. #435	C₂²×C₁₃	semidirect
655. #432	C₂²×C₁₃	semidirect
656. #432	C₂²×C₁₃	semidirect
657. #428	C₂²×C₁₃	semidirect
658. C₂×#107	C₂²×C₁₃	semidirect
659. #419	C₂²×C₁₃	semidirect
661. C₂×#103	C₂²×C₁₃	semidirect
663. C₄×M₁₆	C₂²×C₁₃	semidirect
664. C₂×#97	C₂²×C₁₃	semidirect
944. SD₁₆	C₁₃×#41	semidirect
1024. C₁₃	#61453	direct (N × H)
1056. D₄	C₁₃×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3481	2
Q₈×C₁₃×#41	2
C₁₃×#3400	2
C₁₃×#3385	2
C₁₃×#3375	2
C₁₃×#3372	2
C₁₃×#3346	2
C₁₃×#3338	2
C₁₃×#3320	2
C₁₃×#3314	2
C₁₃×#3299	2
C₁₃×#3295	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3266	2
C₁₃×#3182	2
C₁₃×#3181	2
C₁₃×#3117	2
C₁₃×#3116	2
C₁₃×#3112	2
C₁₃×#3110	2
C₁₃×#2970	2
C₄×C₁₃×#137	2
C₂×C₁₃×#440	2
#61453	13

Subgroups — C13×#61453 #15747792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61453 #15747792