Subgroups — C₁₃×#61481 #15747820

Order 3328.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3519	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3337	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3310	C₂	1	2	yes	maximal, complemented
13	D₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
14	D₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3174	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3126	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3123	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
26	C₁₃×#557	—	2	1	no	—
27	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	—	2	1	no	—
30	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#555	C₂²	1	1	yes	characteristic
32	C₁₃×#554	C₂²	1	1	yes	characteristic
33	C₁₃×#553	—	2	1	no	—
34	C₁₃×#553	C₂²	1	2	yes	—
35	C₁₃×#552	—	2	2	no	—
36	C₁₃×#552	C₂²	1	2	yes	complemented
37	C₁₃×#550	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
39	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#546	—	2	1	no	—
41	C₁₃×#546	—	2	2	no	—
42	D₄²×C₁₃	C₂²	1	2	yes	—
43	D₄²×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#541	—	2	2	no	—
45	C₁₃×#541	C₂²	1	2	yes	complemented
46	C₁₃×#540	C₂²	1	2	yes	—
47	C₁₃×#538	—	2	2	no	—
48	C₁₃×#533	—	2	1	no	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#532	C₂²	1	1	yes	characteristic
51	C₁₃×#529	—	2	1	no	—
52	C₁₃×#529	C₂²	1	1	yes	characteristic
53	C₁₃×#525	—	2	1	no	—
54	C₂×C₁₃×#121	—	2	1	no	—
55	C₁₃×#519	C₂²	1	2	yes	complemented
56	C₁₃×#518	C₂²	1	2	yes	—
57	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#499	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#492	C₂²	1	2	yes	complemented
63	C₁₃×#491	C₂²	1	2	yes	complemented
64	C₁₃×#490	C₂²	1	2	yes	complemented
65	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	complemented
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#484	C₂²	1	2	yes	complemented
70	C₁₃×#482	C₂²	1	2	yes	complemented
71	C₁₃×#482	C₂²	1	2	yes	complemented
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×#478	C₂²	1	2	yes	—
76	C₁₃×#478	C₂²	1	2	yes	complemented
77	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#477	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#474	C₂²	1	1	yes	characteristic
80	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#468	C₂²	1	2	yes	complemented
82	C₁₃×#468	C₂²	1	2	yes	complemented
83	C₁₃×#465	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	complemented
85	C₁₃×#465	C₂²	1	2	yes	complemented
86	C₁₃×#465	C₂²	1	2	yes	complemented
87	C₁₃×#461	C₂²	1	1	yes	characteristic
88	C₁₃×#461	C₂²	1	2	yes	—
89	C₁₃×#461	C₂²	1	2	yes	complemented
90	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#460	C₂²	1	2	yes	complemented
93	C₁₃×#460	C₂²	1	2	yes	complemented
94	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#450	C₂²	1	2	yes	—
96	C₁₃×#450	C₂²	1	2	yes	—
97	C₁₃×#450	C₂²	1	2	yes	—
98	C₁₃×#448	C₂²	1	2	yes	complemented
99	C₁₃×#448	C₂²	1	2	yes	complemented
100	C₁₃×#448	C₂²	1	2	yes	complemented
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#440	C₂²	1	2	yes	—
104	C₁₃×#440	C₂²	1	2	yes	—
105	C₁₃×#440	C₂²	1	2	yes	complemented
106	C₁₃×#440	C₂²	1	2	yes	complemented
107	C₁₃×#440	C₂²	1	2	yes	complemented
108	C₁₃×#440	C₂²	1	2	yes	complemented
109	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
111	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
112	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
113	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
116	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
120	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
122	C₁₃×#435	C₂²	1	2	yes	complemented
123	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#432	C₂²	1	1	yes	characteristic, complemented
127	C₁₃×#427	C₂²	1	2	yes	complemented
128	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
129	C₁₃×#419	C₂²	1	2	yes	complemented
130	C₁₃×#418	C₂²	1	2	yes	—
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
139	C₂²×D₄×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	—	2	2	no	—
141	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₂³×C₄×C₁₃	—	2	1	no	—
144	C₂×C₁₃×SD₁₆	—	2	4	no	—
145	C₂×C₁₃×SD₁₆	—	2	8	no	—
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
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	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
157	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
158	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
159	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	—	2	1	no	—
161	C₁₃×C₄⋊Q₈	—	2	1	no	—
162	C₁₃×C₄⋊Q₈	—	2	2	no	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₁₃×#127	C₂³	1	1	yes	characteristic
168	C₁₃×#127	C₂³	1	2	yes	—
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#126	—	2	2	no	—
173	C₁₃×#126	—	2	2	no	—
174	C₁₃×#126	D₄	1	2	yes	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	2	no	—
180	C₁₃×#125	—	2	2	no	—
181	C₁₃×#125	—	2	1	no	—
182	C₁₃×#125	D₄	1	1	yes	characteristic
183	C₁₃×#125	C₂³	1	2	yes	—
184	C₁₃×#125	C₂³	1	2	yes	—
185	C₁₃×#124	—	2	1	no	—
186	C₁₃×#124	—	2	2	no	—
187	C₁₃×#124	—	2	1	no	—
188	C₁₃×#124	D₄	1	1	yes	characteristic
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	D₄	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	—	2	1	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	no	—
196	C₁₃×C₂²⋊Q₈	—	2	2	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	1	no	—
206	C₁₃×#121	—	2	1	no	—
207	C₁₃×#121	—	2	1	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	2	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	D₄	1	1	yes	characteristic
214	C₁₃×#121	C₂³	1	2	yes	—
215	C₁₃×#121	C₂³	1	2	yes	—
216	C₁₃×#121	C₂³	1	2	yes	—
217	C₁₃×#120	—	2	2	no	—
218	C₁₃×#120	—	2	2	no	—
219	C₁₃×#120	—	2	2	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	—	2	2	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	1	yes	characteristic
231	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₁₃	—	2	2	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	—	2	2	no	—
240	C₄×D₄×C₁₃	—	2	2	no	—
241	C₄×D₄×C₁₃	—	2	1	no	—
242	C₄×D₄×C₁₃	—	2	1	no	—
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
246	C₄×D₄×C₁₃	C₂³	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	2	yes	—
249	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	2	yes	—
252	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
253	C₁₃×#117	—	2	1	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	—	2	2	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	C₂³	1	2	yes	—
259	C₁₃×#117	C₂³	1	2	yes	—
260	C₁₃×#117	C₂³	1	2	yes	—
261	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²×C₁₃	—	2	1	no	—
269	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
270	C₁₃×#107	C₂³	1	2	yes	—
271	C₁₃×#107	C₂³	1	2	yes	—
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#107	C₂³	1	2	yes	—
274	C₁₃×#106	C₂³	1	1	yes	characteristic
275	C₁₃×#106	C₂³	1	1	yes	characteristic
276	C₁₃×#106	C₂³	1	1	yes	characteristic
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	2	yes	—
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	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
308	C₁₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61481	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₁₃×#41	—	8	2	no	—
318	C₁₃×#41	—	8	2	no	—
319	C₂×Q₈×C₁₃	—	2	1	no	—
320	C₂×Q₈×C₁₃	—	2	2	no	—
321	C₂×Q₈×C₁₃	—	2	1	no	—
322	C₂×Q₈×C₁₃	—	2	1	no	—
323	C₂×Q₈×C₁₃	—	2	2	no	—
324	C₂×Q₈×C₁₃	—	2	4	no	—
325	C₂×Q₈×C₁₃	—	4	1	no	—
326	C₂×Q₈×C₁₃	—	4	2	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
330	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	4	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	2	no	—
342	C₂×D₄×C₁₃	—	4	1	no	—
343	C₂×D₄×C₁₃	—	4	2	no	—
344	C₂×D₄×C₁₃	—	8	2	no	—
345	C₂×D₄×C₁₃	—	8	4	no	—
346	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃	—	2	1	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	—	2	1	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	1	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	—	2	2	no	—
361	C₂²×C₄×C₁₃	—	2	1	no	—
362	C₂²×C₄×C₁₃	—	8	2	no	—
363	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
367	C₁₃×SD₁₆	—	2	2	no	—
368	C₁₃×SD₁₆	—	2	4	no	—
369	C₁₃×SD₁₆	—	2	2	no	—
370	C₁₃×SD₁₆	—	2	4	no	—
371	C₁₃×SD₁₆	—	2	2	no	—
372	C₁₃×SD₁₆	—	2	4	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	4	2	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	#41	1	4	yes	complemented
377	C₁₃×M₁₆	—	4	2	no	—
378	C₂×C₈×C₁₃	—	2	2	no	—
379	C₂×C₈×C₁₃	—	2	4	no	—
380	C₂×C₈×C₁₃	—	4	1	no	—
381	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
385	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₁₃×C₄⋊C₄	—	2	1	no	—
388	C₁₃×C₄⋊C₄	—	2	1	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
395	C₁₃×C₄⋊C₄	—	2	2	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	2	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	2	no	—
407	C₁₃×C₄⋊C₄	—	2	2	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
413	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
417	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
420	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	1	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	2	no	—
436	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
437	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
438	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
439	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
440	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₄²×C₁₃	—	2	1	no	—
442	C₄²×C₁₃	—	2	1	no	—
443	C₄²×C₁₃	—	2	1	no	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	2	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	—	2	2	no	—
449	C₄²×C₁₃	—	2	2	no	—
450	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₁₃	C₂⁴	1	2	yes	—
455	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3519	C₂×C₁₃	1	1	yes	characteristic
457	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3381	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3372	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3368	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3340	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3337	C₂×C₁₃	1	2	yes	complemented
463	#3329	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3320	C₂×C₁₃	1	2	yes	complemented
466	#3310	C₂×C₁₃	1	2	yes	complemented
467	D₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
468	D₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#3174	C₂×C₁₃	1	2	yes	complemented
470	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3126	C₂×C₁₃	1	2	yes	complemented
472	#3123	C₂×C₁₃	1	2	yes	complemented
473	#3112	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#3110	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#2966	C₂×C₁₃	1	1	yes	characteristic, complemented
476	#2949	C₂×C₁₃	1	2	yes	complemented
477	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
478	C₂³×C₁₃	—	2	1	no	—
479	C₂³×C₁₃	—	2	1	no	—
480	C₂³×C₁₃	—	2	2	no	—
481	C₂³×C₁₃	—	4	2	no	—
482	C₂³×C₁₃	—	4	4	no	—
483	C₂³×C₁₃	—	4	2	no	—
484	C₂³×C₁₃	—	8	1	no	—
485	C₂³×C₁₃	—	8	2	no	—
486	C₂³×C₁₃	—	8	2	no	—
487	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
488	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
489	Q₈×C₁₃	—	2	2	no	—
490	Q₈×C₁₃	—	2	1	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	2	2	no	—
493	Q₈×C₁₃	—	2	2	no	—
494	Q₈×C₁₃	—	2	1	no	—
495	Q₈×C₁₃	—	4	2	no	—
496	Q₈×C₁₃	—	4	4	no	—
497	Q₈×C₁₃	—	4	2	no	—
498	Q₈×C₁₃	—	8	1	no	—
499	Q₈×C₁₃	C₂×#41	1	2	yes	—
500	D₄×C₁₃	—	2	4	no	—
501	D₄×C₁₃	—	2	2	no	—
502	D₄×C₁₃	—	2	1	no	—
503	D₄×C₁₃	—	2	2	no	—
504	D₄×C₁₃	—	2	1	no	—
505	D₄×C₁₃	—	2	1	no	—
506	D₄×C₁₃	—	2	2	no	—
507	D₄×C₁₃	—	4	2	no	—
508	D₄×C₁₃	—	4	4	no	—
509	D₄×C₁₃	—	4	4	no	—
510	D₄×C₁₃	—	4	2	no	—
511	D₄×C₁₃	—	8	2	no	—
512	D₄×C₁₃	—	8	1	no	—
513	D₄×C₁₃	—	8	2	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	—	8	2	no	—
516	D₄×C₁₃	C₂×#41	1	2	yes	—
517	C₂×C₄×C₁₃	—	2	2	no	—
518	C₂×C₄×C₁₃	—	2	1	no	—
519	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	1	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	2	no	—
530	C₂×C₄×C₁₃	—	2	2	no	—
531	C₂×C₄×C₁₃	—	2	1	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	4	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	2	no	—
537	C₂×C₄×C₁₃	—	8	1	no	—
538	C₂×C₄×C₁₃	—	8	1	no	—
539	C₂×C₄×C₁₃	—	8	2	no	—
540	C₂×C₄×C₁₃	—	8	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	1	no	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
546	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
552	C₈×C₁₃	—	2	1	no	—
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	—	2	1	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	2	no	—
557	C₈×C₁₃	C₂×#41	1	2	yes	—
558	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
559	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
560	#557	—	2	1	no	—
561	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
562	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
563	#556	—	2	1	no	—
564	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
565	#555	C₂²×C₁₃	1	1	yes	characteristic
566	#554	C₂²×C₁₃	1	1	yes	characteristic
567	#553	—	2	1	no	—
568	#553	C₂²×C₁₃	1	2	yes	—
569	#552	—	2	2	no	—
570	#552	C₂²×C₁₃	1	2	yes	complemented
571	#550	C₂²×C₁₃	1	1	yes	characteristic
572	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
574	#546	—	2	1	no	—
575	#546	—	2	2	no	—
576	D₄²	C₂²×C₁₃	1	2	yes	—
577	D₄²	C₂²×C₁₃	1	1	yes	characteristic
578	#541	—	2	2	no	—
579	#541	C₂²×C₁₃	1	2	yes	complemented
580	#540	C₂²×C₁₃	1	2	yes	—
581	#538	—	2	2	no	—
582	#533	—	2	1	no	—
583	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#532	C₂²×C₁₃	1	1	yes	characteristic
585	#529	—	2	1	no	—
586	#529	C₂²×C₁₃	1	1	yes	characteristic
587	#525	—	2	1	no	—
588	C₂×#121	—	2	1	no	—
589	#519	C₂²×C₁₃	1	2	yes	complemented
590	#518	C₂²×C₁₃	1	2	yes	—
591	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
593	#499	C₂²×C₁₃	1	2	yes	complemented
594	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
595	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
596	#492	C₂²×C₁₃	1	2	yes	complemented
597	#491	C₂²×C₁₃	1	2	yes	complemented
598	#490	C₂²×C₁₃	1	2	yes	complemented
599	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
600	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
601	#485	C₂²×C₁₃	1	2	yes	complemented
602	#485	C₂²×C₁₃	1	2	yes	complemented
603	#484	C₂²×C₁₃	1	2	yes	complemented
604	#482	C₂²×C₁₃	1	2	yes	complemented
605	#482	C₂²×C₁₃	1	2	yes	complemented
606	#480	C₂²×C₁₃	1	2	yes	complemented
607	#479	C₂²×C₁₃	1	2	yes	complemented
608	#479	C₂²×C₁₃	1	2	yes	complemented
609	#478	C₂²×C₁₃	1	2	yes	—
610	#478	C₂²×C₁₃	1	2	yes	complemented
611	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
612	#477	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#474	C₂²×C₁₃	1	1	yes	characteristic
614	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
615	#468	C₂²×C₁₃	1	2	yes	complemented
616	#468	C₂²×C₁₃	1	2	yes	complemented
617	#465	C₂²×C₁₃	1	2	yes	complemented
618	#465	C₂²×C₁₃	1	2	yes	complemented
619	#465	C₂²×C₁₃	1	2	yes	complemented
620	#465	C₂²×C₁₃	1	2	yes	complemented
621	#461	C₂²×C₁₃	1	1	yes	characteristic
622	#461	C₂²×C₁₃	1	2	yes	—
623	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#461	C₂²×C₁₃	1	2	yes	complemented
625	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
626	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
627	#460	C₂²×C₁₃	1	2	yes	complemented
628	#460	C₂²×C₁₃	1	2	yes	complemented
629	#450	C₂²×C₁₃	1	2	yes	—
630	#450	C₂²×C₁₃	1	2	yes	—
631	#450	C₂²×C₁₃	1	2	yes	—
632	#448	C₂²×C₁₃	1	2	yes	complemented
633	#448	C₂²×C₁₃	1	2	yes	complemented
634	#448	C₂²×C₁₃	1	2	yes	complemented
635	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
637	#440	C₂²×C₁₃	1	2	yes	—
638	#440	C₂²×C₁₃	1	2	yes	—
639	#440	C₂²×C₁₃	1	2	yes	complemented
640	#440	C₂²×C₁₃	1	2	yes	complemented
641	#440	C₂²×C₁₃	1	2	yes	complemented
642	#440	C₂²×C₁₃	1	2	yes	complemented
643	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
644	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
645	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
646	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
647	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
648	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
649	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
650	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
652	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
653	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
654	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
655	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	#435	C₂²×C₁₃	1	2	yes	complemented
657	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
658	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
659	#433	C₂²×C₁₃	1	2	yes	complemented
660	#432	C₂²×C₁₃	1	1	yes	characteristic, complemented
661	#427	C₂²×C₁₃	1	2	yes	complemented
662	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
663	#419	C₂²×C₁₃	1	2	yes	complemented
664	#418	C₂²×C₁₃	1	2	yes	—
665	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
666	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
667	#405	C₂²×C₁₃	1	2	yes	complemented
668	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
669	C₂²×C₁₃	—	2	1	no	—
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	2	no	—
673	C₂²×C₁₃	—	2	2	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	4	1	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	2	no	—
679	C₂²×C₁₃	—	4	1	no	—
680	C₂²×C₁₃	—	4	2	no	—
681	C₂²×C₁₃	—	4	2	no	—
682	C₂²×C₁₃	—	4	1	no	—
683	C₂²×C₁₃	—	8	4	no	—
684	C₂²×C₁₃	—	16	4	no	—
685	C₂²×C₁₃	#577	1	2	yes	—
686	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	2	2	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	1	no	—
692	C₄×C₁₃	—	2	1	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	2	2	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	2	no	—
697	C₄×C₁₃	—	4	1	no	—
698	C₄×C₁₃	—	4	1	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	2	no	—
702	C₄×C₁₃	—	4	2	no	—
703	C₄×C₁₃	#577	1	2	yes	—
704	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
705	C₄×C₁₃	#585	1	1	yes	characteristic
706	C₂×#41	—	2	1	no	—
707	C₂×#41	—	2	1	no	—
708	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
710	C₂²×D₄	—	2	1	no	—
711	C₂²×D₄	—	2	2	no	—
712	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
713	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
714	C₂³×C₄	—	2	1	no	—
715	C₂×SD₁₆	—	2	4	no	—
716	C₂×SD₁₆	—	2	8	no	—
717	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
720	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
721	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
724	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
727	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
728	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
730	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
736	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
738	#127	C₂³×C₁₃	1	1	yes	characteristic
739	#127	C₂³×C₁₃	1	2	yes	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	D₄×C₁₃	1	2	yes	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	2	no	—
752	#125	—	2	1	no	—
753	#125	D₄×C₁₃	1	1	yes	characteristic
754	#125	C₂³×C₁₃	1	2	yes	—
755	#125	C₂³×C₁₃	1	2	yes	—
756	#124	—	2	1	no	—
757	#124	—	2	2	no	—
758	#124	—	2	1	no	—
759	#124	D₄×C₁₃	1	1	yes	characteristic
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	D₄×C₁₃	1	2	yes	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	1	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
772	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
774	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
775	#121	—	2	2	no	—
776	#121	—	2	1	no	—
777	#121	—	2	1	no	—
778	#121	—	2	1	no	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	2	2	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	D₄×C₁₃	1	1	yes	characteristic
785	#121	C₂³×C₁₃	1	2	yes	—
786	#121	C₂³×C₁₃	1	2	yes	—
787	#121	C₂³×C₁₃	1	2	yes	—
788	#120	—	2	2	no	—
789	#120	—	2	2	no	—
790	#120	—	2	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	1	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	1	no	—
797	C₄×Q₈	—	2	1	no	—
798	C₄×Q₈	—	2	1	no	—
799	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
804	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
805	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
806	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	2	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	1	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₁₃	1	2	yes	—
820	C₄×D₄	C₂³×C₁₃	1	2	yes	—
821	C₄×D₄	C₂³×C₁₃	1	2	yes	—
822	C₄×D₄	C₂³×C₁₃	1	2	yes	—
823	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	2	no	—
827	#117	—	2	2	no	—
828	#117	—	2	2	no	—
829	#117	C₂³×C₁₃	1	2	yes	—
830	#117	C₂³×C₁₃	1	2	yes	—
831	#117	C₂³×C₁₃	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	1	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
835	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
836	C₂×C₂²⋊C₄	—	2	1	no	—
837	C₂×C₂²⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₄²	—	2	1	no	—
840	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
841	#107	C₂³×C₁₃	1	2	yes	—
842	#107	C₂³×C₁₃	1	2	yes	—
843	#107	C₂³×C₁₃	1	2	yes	—
844	#107	C₂³×C₁₃	1	2	yes	—
845	#106	C₂³×C₁₃	1	1	yes	characteristic
846	#106	C₂³×C₁₃	1	1	yes	characteristic
847	#106	C₂³×C₁₃	1	1	yes	characteristic
848	#106	C₂³×C₁₃	1	1	yes	characteristic
849	#106	C₂³×C₁₃	1	2	yes	—
850	#106	C₂³×C₁₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
852	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	1	yes	characteristic
856	#103	C₂³×C₁₃	1	1	yes	characteristic
857	#103	C₂³×C₁₃	1	1	yes	characteristic
858	#103	C₂³×C₁₃	1	1	yes	characteristic
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	2	yes	—
861	#103	C₂³×C₁₃	1	2	yes	—
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	2	yes	—
864	#103	C₂³×C₁₃	1	2	yes	—
865	#102	C₂³×C₁₃	1	1	yes	characteristic
866	#102	C₂³×C₁₃	1	1	yes	characteristic
867	#102	C₂³×C₁₃	1	1	yes	characteristic
868	#102	C₂³×C₁₃	1	1	yes	characteristic
869	#102	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	2	yes	—
871	#102	C₂³×C₁₃	1	2	yes	—
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
878	#97	C₂³×C₁₃	1	2	yes	—
879	#97	C₂³×C₁₃	1	2	yes	—
880	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
881	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
882	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
883	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
884	C₄×C₈	C₂³×C₁₃	1	2	yes	—
885	C₂×C₁₃	—	2	2	no	—
886	C₂×C₁₃	—	4	2	no	—
887	C₂×C₁₃	—	4	2	no	—
888	C₂×C₁₃	—	8	1	no	—
889	C₂×C₁₃	—	8	2	no	—
890	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
891	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
892	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
893	C₂⁴	—	2	1	no	—
894	C₂⁴	—	2	2	no	—
895	#41	—	8	2	no	—
896	#41	—	8	2	no	—
897	C₂×Q₈	—	2	1	no	—
898	C₂×Q₈	—	2	2	no	—
899	C₂×Q₈	—	2	1	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	4	no	—
903	C₂×Q₈	—	4	1	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
906	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
907	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
908	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
909	C₂×D₄	—	2	2	no	—
910	C₂×D₄	—	2	4	no	—
911	C₂×D₄	—	2	2	no	—
912	C₂×D₄	—	2	2	no	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	4	1	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	8	2	no	—
923	C₂×D₄	—	8	4	no	—
924	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
925	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
926	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
928	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₂²×C₄	—	2	1	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	8	2	no	—
941	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
945	SD₁₆	—	2	2	no	—
946	SD₁₆	—	2	4	no	—
947	SD₁₆	—	2	2	no	—
948	SD₁₆	—	2	4	no	—
949	SD₁₆	—	2	2	no	—
950	SD₁₆	—	2	4	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	C₁₃×#41	1	4	yes	complemented
955	M₁₆	—	4	2	no	—
956	C₂×C₈	—	2	2	no	—
957	C₂×C₈	—	2	4	no	—
958	C₂×C₈	—	4	1	no	—
959	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
960	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
961	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
963	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
964	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	2	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	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
990	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
993	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
996	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1015	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1018	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1029	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1030	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1031	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1032	C₄²	C₂⁴×C₁₃	1	2	yes	—
1033	C₁₃	#61481	1	1	yes	characteristic, direct product factor, Sylow
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	2	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	4	4	no	—
1039	C₂³	—	4	2	no	—
1040	C₂³	—	8	1	no	—
1041	C₂³	—	8	2	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1044	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	4	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	8	1	no	—
1055	Q₈	C₂×C₁₃×#41	1	2	yes	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	4	4	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	8	2	no	—
1068	D₄	—	8	1	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	2	no	—
1071	D₄	—	8	2	no	—
1072	D₄	C₂×C₁₃×#41	1	2	yes	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	2	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	4	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	1	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	1	no	—
1099	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1102	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	2	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	C₂×C₁₃×#41	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	2	no	—
1124	C₂²	—	4	2	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	8	4	no	—
1129	C₂²	—	16	4	no	—
1130	C₂²	C₁₃×#577	1	2	yes	—
1131	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	2	no	—
1148	C₄	C₁₃×#577	1	2	yes	—
1149	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1150	C₄	C₁₃×#585	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	2	no	—
1156	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1157	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1158	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3519	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3523	C₂	semidirect
3. C₁₃×#3392	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. C₁₃×#3372	C₂	semidirect
6. C₁₃×#3368	C₂	semidirect
7. C₁₃×#3340	C₂	semidirect
8. C₁₃×#3337	C₂	semidirect
9. C₁₃×#3329	C₂	semidirect
10. C₁₃×#3324	C₂	semidirect
11. C₁₃×#3320	C₂	semidirect
12. C₁₃×#3310	C₂	semidirect
13. D₄×C₁₃×SD₁₆	C₂	semidirect
14. D₄×C₁₃×SD₁₆	C₂	semidirect
15. C₁₃×#3174	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3126	C₂	semidirect
18. C₁₃×#3123	C₂	semidirect
19. C₁₃×#3112	C₂	semidirect
20. C₁₃×#3110	C₂	semidirect
21. C₁₃×#2966	C₂	semidirect
22. C₁₃×#2949	C₂	semidirect
23. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
30. C₁₃×#556	C₂²	semidirect
36. C₁₃×#552	C₂²	semidirect
38. D₄×Q₈×C₁₃	C₂²	semidirect
39. D₄×Q₈×C₁₃	C₂²	semidirect
45. C₁₃×#541	C₂²	semidirect
49. C₁₃×#533	C₂²	semidirect
55. C₁₃×#519	C₂²	semidirect
57. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
59. C₁₃×#499	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
61. C₁₃×#492	C₂²	semidirect
62. C₁₃×#492	C₂²	semidirect
63. C₁₃×#491	C₂²	semidirect
64. C₁₃×#490	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#486	C₂²	semidirect
67. C₁₃×#485	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#484	C₂²	semidirect
70. C₁₃×#482	C₂²	semidirect
71. C₁₃×#482	C₂²	semidirect
72. C₁₃×#480	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
76. C₁₃×#478	C₂²	semidirect
77. C₁₃×#477	C₂²	semidirect
78. C₁₃×#477	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
81. C₁₃×#468	C₂²	semidirect
82. C₁₃×#468	C₂²	semidirect
83. C₁₃×#465	C₂²	semidirect
84. C₁₃×#465	C₂²	semidirect
85. C₁₃×#465	C₂²	semidirect
86. C₁₃×#465	C₂²	semidirect
89. C₁₃×#461	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
92. C₁₃×#460	C₂²	semidirect
93. C₁₃×#460	C₂²	semidirect
94. C₁₃×#460	C₂²	semidirect
98. C₁₃×#448	C₂²	semidirect
99. C₁₃×#448	C₂²	semidirect
100. C₁₃×#448	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
105. C₁₃×#440	C₂²	semidirect
106. C₁₃×#440	C₂²	semidirect
107. C₁₃×#440	C₂²	semidirect
108. C₁₃×#440	C₂²	semidirect
114. C₄×C₁₃×SD₁₆	C₂²	semidirect
115. C₄×C₁₃×SD₁₆	C₂²	semidirect
116. C₄×C₁₃×SD₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
119. C₄×C₁₃×SD₁₆	C₂²	semidirect
120. C₄×C₁₃×SD₁₆	C₂²	semidirect
121. C₁₃×#436	C₂²	semidirect
122. C₁₃×#435	C₂²	semidirect
123. C₈×D₄×C₁₃	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
126. C₁₃×#432	C₂²	semidirect
127. C₁₃×#427	C₂²	semidirect
128. C₂×C₁₃×#106	C₂²	semidirect
129. C₁₃×#419	C₂²	semidirect
131. C₂×C₁₃×#103	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₁₃	C₂²	semidirect
314. #61481	C₁₃	direct (N × H)
376. C₁₃×SD₁₆	#41	semidirect
455. #3523	C₂×C₁₃	semidirect
457. #3392	C₂×C₁₃	semidirect
458. #3381	C₂×C₁₃	semidirect
459. #3372	C₂×C₁₃	semidirect
460. #3368	C₂×C₁₃	semidirect
461. #3340	C₂×C₁₃	semidirect
462. #3337	C₂×C₁₃	semidirect
463. #3329	C₂×C₁₃	semidirect
464. #3324	C₂×C₁₃	semidirect
465. #3320	C₂×C₁₃	semidirect
466. #3310	C₂×C₁₃	semidirect
467. D₄×SD₁₆	C₂×C₁₃	semidirect
468. D₄×SD₁₆	C₂×C₁₃	semidirect
469. #3174	C₂×C₁₃	semidirect
470. #3167	C₂×C₁₃	semidirect
471. #3126	C₂×C₁₃	semidirect
472. #3123	C₂×C₁₃	semidirect
473. #3112	C₂×C₁₃	semidirect
474. #3110	C₂×C₁₃	semidirect
475. #2966	C₂×C₁₃	semidirect
476. #2949	C₂×C₁₃	semidirect
477. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
561. #557	C₂²×C₁₃	semidirect
562. #557	C₂²×C₁₃	semidirect
564. #556	C₂²×C₁₃	semidirect
570. #552	C₂²×C₁₃	semidirect
572. D₄×Q₈	C₂²×C₁₃	semidirect
573. D₄×Q₈	C₂²×C₁₃	semidirect
579. #541	C₂²×C₁₃	semidirect
583. #533	C₂²×C₁₃	semidirect
589. #519	C₂²×C₁₃	semidirect
591. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
593. #499	C₂²×C₁₃	semidirect
594. #498	C₂²×C₁₃	semidirect
595. #492	C₂²×C₁₃	semidirect
596. #492	C₂²×C₁₃	semidirect
597. #491	C₂²×C₁₃	semidirect
598. #490	C₂²×C₁₃	semidirect
599. #487	C₂²×C₁₃	semidirect
600. #486	C₂²×C₁₃	semidirect
601. #485	C₂²×C₁₃	semidirect
602. #485	C₂²×C₁₃	semidirect
603. #484	C₂²×C₁₃	semidirect
604. #482	C₂²×C₁₃	semidirect
605. #482	C₂²×C₁₃	semidirect
606. #480	C₂²×C₁₃	semidirect
607. #479	C₂²×C₁₃	semidirect
608. #479	C₂²×C₁₃	semidirect
610. #478	C₂²×C₁₃	semidirect
611. #477	C₂²×C₁₃	semidirect
612. #477	C₂²×C₁₃	semidirect
614. #474	C₂²×C₁₃	semidirect
615. #468	C₂²×C₁₃	semidirect
616. #468	C₂²×C₁₃	semidirect
617. #465	C₂²×C₁₃	semidirect
618. #465	C₂²×C₁₃	semidirect
619. #465	C₂²×C₁₃	semidirect
620. #465	C₂²×C₁₃	semidirect
623. #461	C₂²×C₁₃	semidirect
624. #461	C₂²×C₁₃	semidirect
625. #460	C₂²×C₁₃	semidirect
626. #460	C₂²×C₁₃	semidirect
627. #460	C₂²×C₁₃	semidirect
628. #460	C₂²×C₁₃	semidirect
632. #448	C₂²×C₁₃	semidirect
633. #448	C₂²×C₁₃	semidirect
634. #448	C₂²×C₁₃	semidirect
635. #446	C₂²×C₁₃	semidirect
636. C₈×Q₈	C₂²×C₁₃	semidirect
639. #440	C₂²×C₁₃	semidirect
640. #440	C₂²×C₁₃	semidirect
641. #440	C₂²×C₁₃	semidirect
642. #440	C₂²×C₁₃	semidirect
648. C₄×SD₁₆	C₂²×C₁₃	semidirect
649. C₄×SD₁₆	C₂²×C₁₃	semidirect
650. C₄×SD₁₆	C₂²×C₁₃	semidirect
651. C₄×SD₁₆	C₂²×C₁₃	semidirect
652. C₄×SD₁₆	C₂²×C₁₃	semidirect
653. C₄×SD₁₆	C₂²×C₁₃	semidirect
654. C₄×SD₁₆	C₂²×C₁₃	semidirect
655. #436	C₂²×C₁₃	semidirect
656. #435	C₂²×C₁₃	semidirect
657. C₈×D₄	C₂²×C₁₃	semidirect
658. C₈×D₄	C₂²×C₁₃	semidirect
659. #433	C₂²×C₁₃	semidirect
660. #432	C₂²×C₁₃	semidirect
661. #427	C₂²×C₁₃	semidirect
662. C₂×#106	C₂²×C₁₃	semidirect
663. #419	C₂²×C₁₃	semidirect
665. C₂×#103	C₂²×C₁₃	semidirect
667. #405	C₂²×C₁₃	semidirect
668. C₂×C₄×C₈	C₂²×C₁₃	semidirect
954. SD₁₆	C₁₃×#41	semidirect
1033. C₁₃	#61481	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×#3523	2
C₁₃×#3519	2
C₁₃×#3392	2
C₁₃×#3381	2
C₁₃×#3372	2
C₁₃×#3368	2
C₁₃×#3340	2
C₁₃×#3337	2
C₁₃×#3329	2
C₁₃×#3324	2
C₁₃×#3320	2
C₁₃×#3310	2
D₄×C₁₃×SD₁₆	2
C₁₃×#3174	2
C₁₃×#3167	2
C₁₃×#3126	2
C₁₃×#3123	2
C₁₃×#3112	2
C₁₃×#3110	2
C₁₃×#2966	2
C₁₃×#2949	2
C₂×C₄×C₁₃×SD₁₆	2
#61481	13

Subgroups — C13×#61481 #15747820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61481 #15747820