Subgroups — C₁₃×#61927 #15748266

Order 3328.

1718 conjugacy classes of subgroups.

The subgroup lattice has 1130 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, complemented
2	C₁₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3401	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3394	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3371	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3224	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3222	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
21	C₁₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×#563	—	2	2	no	—
25	C₁₃×#559	C₂²	1	2	yes	—
26	C₁₃×#559	C₂²	1	2	yes	—
27	Q₈²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#557	C₂²	1	2	yes	complemented
30	C₁₃×#556	—	2	1	no	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic
32	C₁₃×#556	C₂²	1	1	yes	characteristic
33	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#556	C₂²	1	2	yes	complemented
35	C₁₃×#555	—	2	1	no	—
36	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#553	—	2	2	no	—
38	C₁₃×#552	—	2	1	no	—
39	C₁₃×#550	C₂²	1	1	yes	characteristic
40	C₁₃×#550	C₂²	1	1	yes	characteristic
41	C₁₃×#547	—	2	1	no	—
42	C₁₃×#544	—	2	1	no	—
43	C₁₃×#542	C₂²	1	2	yes	—
44	C₁₃×#541	—	2	1	no	—
45	C₁₃×#541	—	2	2	no	—
46	C₁₃×#541	C₂²	1	2	yes	—
47	C₁₃×#538	—	2	2	no	—
48	C₁₃×#535	C₂²	1	2	yes	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic
50	C₁₃×#533	C₂²	1	1	yes	characteristic
51	C₁₃×#532	C₂²	1	1	yes	characteristic
52	C₁₃×#529	C₂²	1	1	yes	characteristic
53	C₁₃×#525	—	2	1	no	—
54	C₁₃×#525	—	2	1	no	—
55	C₁₃×#520	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×#497	C₂²	1	2	yes	—
58	C₁₃×#496	C₂²	1	2	yes	—
59	C₁₃×#495	C₂²	1	2	yes	—
60	C₁₃×#495	C₂²	1	2	yes	complemented
61	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#492	C₂²	1	2	yes	—
63	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#490	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	complemented
68	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#486	C₂²	1	2	yes	—
70	C₁₃×#486	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#484	C₂²	1	1	yes	characteristic
72	C₁₃×#483	C₂²	1	2	yes	—
73	C₁₃×#481	C₂²	1	1	yes	characteristic
74	C₁₃×#479	C₂²	1	2	yes	complemented
75	C₁₃×#478	C₂²	1	1	yes	characteristic
76	C₁₃×#478	C₂²	1	1	yes	characteristic
77	C₁₃×#478	C₂²	1	2	yes	complemented
78	C₁₃×#476	C₂²	1	1	yes	characteristic
79	C₁₃×#476	C₂²	1	1	yes	characteristic
80	C₁₃×#476	C₂²	1	2	yes	complemented
81	C₁₃×#475	C₂²	1	2	yes	complemented
82	C₁₃×#464	C₂²	1	2	yes	—
83	C₁₃×#464	C₂²	1	2	yes	—
84	C₁₃×#464	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	complemented
86	C₁₃×#464	C₂²	1	2	yes	complemented
87	C₁₃×#464	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	1	yes	characteristic
90	C₁₃×#463	C₂²	1	1	yes	characteristic
91	C₁₃×#463	C₂²	1	2	yes	complemented
92	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
93	C₁₃×#462	C₂²	1	2	yes	complemented
94	C₁₃×#461	C₂²	1	1	yes	characteristic
95	C₁₃×#461	C₂²	1	1	yes	characteristic
96	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₁₃×#461	C₂²	1	2	yes	complemented
98	C₁₃×#460	C₂²	1	2	yes	—
99	C₁₃×#460	C₂²	1	2	yes	—
100	C₁₃×#460	C₂²	1	2	yes	—
101	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#459	C₂²	1	2	yes	—
103	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
104	C₁₃×#452	C₂²	1	2	yes	—
105	C₁₃×#452	C₂²	1	2	yes	—
106	C₁₃×#452	C₂²	1	2	yes	—
107	C₁₃×#450	C₂²	1	2	yes	—
108	C₁₃×#450	C₂²	1	1	yes	characteristic
109	C₁₃×#449	C₂²	1	2	yes	—
110	C₁₃×#447	C₂²	1	1	yes	characteristic
111	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
112	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
113	C₁₃×#446	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₁₃	C₂²	1	2	yes	complemented
117	C₁₃×#442	C₂²	1	2	yes	complemented
118	C₁₃×#441	C₂²	1	2	yes	complemented
119	C₁₃×#441	C₂²	1	2	yes	complemented
120	C₁₃×#440	C₂²	1	2	yes	complemented
121	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
122	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
123	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
124	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
125	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
126	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
129	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
130	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
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	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	—	2	1	no	—
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₁₃	—	2	1	no	—
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×D₈	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	—	2	1	no	—
157	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#127	C₂³	1	2	yes	—
165	C₁₃×#127	C₂³	1	1	yes	characteristic
166	C₁₃×#127	C₂³	1	2	yes	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
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	—	2	2	no	—
175	C₁₃×#126	—	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	—	2	1	no	—
183	C₁₃×#125	D₄	1	2	yes	—
184	C₁₃×#125	C₂³	1	1	yes	characteristic
185	C₁₃×#125	C₂³	1	2	yes	—
186	C₁₃×#124	—	2	2	no	—
187	C₁₃×#124	—	2	2	no	—
188	C₁₃×#124	—	2	2	no	—
189	C₁₃×#124	C₂³	1	1	yes	characteristic
190	C₁₃×#124	C₂³	1	2	yes	—
191	C₁₃×#124	C₂³	1	2	yes	—
192	C₁₃×#124	C₂³	1	2	yes	—
193	C₁₃×#124	C₂³	1	2	yes	—
194	C₁₃×#123	—	2	1	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	2	2	no	—
198	C₁₃×#123	—	2	2	no	—
199	C₁₃×#123	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	—	2	1	no	—
201	C₁₃×C₂²⋊Q₈	—	2	1	no	—
202	C₁₃×C₂²⋊Q₈	—	2	1	no	—
203	C₁₃×C₂²⋊Q₈	—	2	1	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	—	2	1	no	—
206	C₁₃×C₂²⋊Q₈	—	2	2	no	—
207	C₁₃×C₂²⋊Q₈	—	2	2	no	—
208	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
211	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	1	no	—
217	C₁₃×#121	—	2	2	no	—
218	C₁₃×#121	—	2	2	no	—
219	C₁₃×#121	—	2	2	no	—
220	C₁₃×#121	—	2	2	no	—
221	C₁₃×#121	C₂³	1	1	yes	characteristic
222	C₁₃×#120	—	2	2	no	—
223	C₁₃×#120	—	2	2	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	—	2	1	no	—
226	C₄×Q₈×C₁₃	—	2	2	no	—
227	C₄×Q₈×C₁₃	—	2	1	no	—
228	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
230	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	—	2	2	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	—	2	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	—	2	1	no	—
246	C₄×D₄×C₁₃	—	2	1	no	—
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	2	yes	—
254	C₄×D₄×C₁₃	C₂³	1	2	yes	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	2	no	—
257	C₁₃×#117	—	2	1	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	2	no	—
260	C₁₃×#117	—	2	1	no	—
261	C₁₃×#117	—	2	1	no	—
262	C₁₃×#117	C₂³	1	2	yes	—
263	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
264	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
266	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
268	C₁₃×#107	C₂³	1	1	yes	characteristic
269	C₁₃×#107	C₂³	1	1	yes	characteristic
270	C₁₃×#106	C₂³	1	1	yes	characteristic
271	C₁₃×#106	C₂³	1	2	yes	—
272	C₁₃×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
283	C₁₃×#103	C₂³	1	2	yes	—
284	C₁₃×#103	C₂³	1	2	yes	—
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	2	yes	—
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	2	yes	—
290	C₁₃×#102	C₂³	1	1	yes	characteristic
291	C₁₃×#102	C₂³	1	1	yes	characteristic
292	C₁₃×#102	C₂³	1	1	yes	characteristic
293	C₁₃×#102	C₂³	1	1	yes	characteristic
294	C₁₃×#102	C₂³	1	1	yes	characteristic
295	C₁₃×#102	C₂³	1	1	yes	characteristic
296	C₁₃×#102	C₂³	1	2	yes	—
297	C₁₃×#102	C₂³	1	2	yes	—
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×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	#61927	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂⁴×C₁₃	—	2	1	no	—
314	C₁₃×#41	—	4	2	no	—
315	C₁₃×#41	—	4	2	no	—
316	C₁₃×#41	—	8	2	no	—
317	C₁₃×#41	—	8	2	no	—
318	C₂×Q₈×C₁₃	—	2	1	no	—
319	C₂×Q₈×C₁₃	—	2	2	no	—
320	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
323	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
326	C₂×D₄×C₁₃	—	2	2	no	—
327	C₂×D₄×C₁₃	—	2	1	no	—
328	C₂×D₄×C₁₃	—	2	1	no	—
329	C₂×D₄×C₁₃	—	2	1	no	—
330	C₂×D₄×C₁₃	—	2	2	no	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	1	no	—
333	C₂×D₄×C₁₃	—	2	2	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	4	1	no	—
336	C₂×D₄×C₁₃	—	4	1	no	—
337	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
338	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂²×C₄×C₁₃	—	2	1	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	—	2	1	no	—
345	C₂²×C₄×C₁₃	—	2	1	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	—	2	2	no	—
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	1	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	8	2	no	—
352	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₁₃×Q₁₆	—	4	2	no	—
356	C₁₃×Q₁₆	—	4	2	no	—
357	C₁₃×Q₁₆	—	4	2	no	—
358	C₁₃×SD₁₆	—	4	2	no	—
359	C₁₃×SD₁₆	—	4	2	no	—
360	C₁₃×SD₁₆	—	4	2	no	—
361	C₁₃×SD₁₆	—	4	1	no	—
362	C₁₃×SD₁₆	—	4	2	no	—
363	C₁₃×SD₁₆	—	4	2	no	—
364	C₁₃×SD₁₆	—	4	2	no	—
365	C₁₃×SD₁₆	—	4	1	no	—
366	C₁₃×D₈	—	4	1	no	—
367	C₁₃×D₈	—	4	2	no	—
368	C₁₃×D₈	—	4	1	no	—
369	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
372	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
374	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₁₃×C₄⋊C₄	—	2	1	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	2	no	—
379	C₁₃×C₄⋊C₄	—	2	2	no	—
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	2	no	—
383	C₁₃×C₄⋊C₄	—	2	1	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
392	C₁₃×C₄⋊C₄	—	2	2	no	—
393	C₁₃×C₄⋊C₄	—	2	2	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	1	no	—
397	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
404	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
405	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
406	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
411	C₁₃×C₂²⋊C₄	—	2	2	no	—
412	C₁₃×C₂²⋊C₄	—	2	1	no	—
413	C₁₃×C₂²⋊C₄	—	2	1	no	—
414	C₁₃×C₂²⋊C₄	—	2	1	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	—	2	1	no	—
417	C₁₃×C₂²⋊C₄	—	2	1	no	—
418	C₁₃×C₂²⋊C₄	—	2	2	no	—
419	C₁₃×C₂²⋊C₄	—	2	2	no	—
420	C₁₃×C₂²⋊C₄	—	2	2	no	—
421	C₁₃×C₂²⋊C₄	—	2	2	no	—
422	C₁₃×C₂²⋊C₄	—	2	1	no	—
423	C₁₃×C₂²⋊C₄	—	2	1	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	2	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	1	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
433	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
434	C₄²×C₁₃	—	2	2	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	2	no	—
437	C₄²×C₁₃	—	2	1	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	2	no	—
440	C₄²×C₁₃	—	2	2	no	—
441	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
442	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
443	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
444	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
445	C₄²×C₁₃	C₂⁴	1	2	yes	—
446	C₄²×C₁₃	C₂⁴	1	2	yes	—
447	#3555	C₂×C₁₃	1	1	yes	characteristic, complemented
448	#3506	C₂×C₁₃	1	1	yes	characteristic, complemented
449	#3401	C₂×C₁₃	1	2	yes	complemented
450	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
451	#3397	C₂×C₁₃	1	1	yes	characteristic, complemented
452	#3394	C₂×C₁₃	1	2	yes	complemented
453	#3393	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3392	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3371	C₂×C₁₃	1	2	yes	complemented
456	#3369	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3366	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3365	C₂×C₁₃	1	2	yes	complemented
459	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3224	C₂×C₁₃	1	2	yes	complemented
462	#3222	C₂×C₁₃	1	2	yes	complemented
463	#3212	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3125	C₂×C₁₃	1	2	yes	complemented
466	#3120	C₂×C₁₃	1	2	yes	complemented
467	#3105	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
469	#2986	C₂×C₁₃	1	1	yes	characteristic, complemented
470	C₂³×C₁₃	—	2	1	no	—
471	C₂³×C₁₃	—	2	1	no	—
472	C₂³×C₁₃	—	2	1	no	—
473	C₂³×C₁₃	—	2	2	no	—
474	C₂³×C₁₃	—	4	2	no	—
475	C₂³×C₁₃	—	8	1	no	—
476	C₂³×C₁₃	—	8	1	no	—
477	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	2	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	2	2	no	—
482	Q₈×C₁₃	—	2	2	no	—
483	Q₈×C₁₃	—	2	1	no	—
484	Q₈×C₁₃	—	2	2	no	—
485	Q₈×C₁₃	—	2	2	no	—
486	Q₈×C₁₃	—	4	2	no	—
487	Q₈×C₁₃	—	8	1	no	—
488	Q₈×C₁₃	—	8	2	no	—
489	D₄×C₁₃	—	2	1	no	—
490	D₄×C₁₃	—	2	1	no	—
491	D₄×C₁₃	—	2	1	no	—
492	D₄×C₁₃	—	2	1	no	—
493	D₄×C₁₃	—	2	2	no	—
494	D₄×C₁₃	—	2	1	no	—
495	D₄×C₁₃	—	2	1	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	4	2	no	—
498	D₄×C₁₃	—	4	4	no	—
499	D₄×C₁₃	—	4	2	no	—
500	D₄×C₁₃	—	8	1	no	—
501	D₄×C₁₃	—	8	2	no	—
502	D₄×C₁₃	—	8	2	no	—
503	D₄×C₁₃	—	8	2	no	—
504	D₄×C₁₃	—	8	2	no	—
505	D₄×C₁₃	—	8	1	no	—
506	C₂×C₄×C₁₃	—	2	2	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	1	no	—
509	C₂×C₄×C₁₃	—	2	2	no	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	2	2	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	2	1	no	—
515	C₂×C₄×C₁₃	—	2	1	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	4	1	no	—
518	C₂×C₄×C₁₃	—	4	4	no	—
519	C₂×C₄×C₁₃	—	4	2	no	—
520	C₂×C₄×C₁₃	—	4	2	no	—
521	C₂×C₄×C₁₃	—	4	2	no	—
522	C₂×C₄×C₁₃	—	8	2	no	—
523	C₂×C₄×C₁₃	—	8	1	no	—
524	C₂×C₄×C₁₃	—	8	1	no	—
525	C₂×C₄×C₁₃	—	8	2	no	—
526	C₂×C₄×C₁₃	—	8	2	no	—
527	C₂×C₄×C₁₃	—	8	1	no	—
528	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
532	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
538	C₈×C₁₃	—	2	1	no	—
539	C₈×C₁₃	—	2	2	no	—
540	C₈×C₁₃	—	2	1	no	—
541	C₈×C₁₃	—	2	2	no	—
542	C₈×C₁₃	—	2	1	no	—
543	C₈×C₁₃	—	2	1	no	—
544	#563	—	2	2	no	—
545	#559	C₂²×C₁₃	1	2	yes	—
546	#559	C₂²×C₁₃	1	2	yes	—
547	Q₈²	C₂²×C₁₃	1	1	yes	characteristic, complemented
548	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
549	#557	C₂²×C₁₃	1	2	yes	complemented
550	#556	—	2	1	no	—
551	#556	C₂²×C₁₃	1	1	yes	characteristic
552	#556	C₂²×C₁₃	1	1	yes	characteristic
553	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	#556	C₂²×C₁₃	1	2	yes	complemented
555	#555	—	2	1	no	—
556	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
557	#553	—	2	2	no	—
558	#552	—	2	1	no	—
559	#550	C₂²×C₁₃	1	1	yes	characteristic
560	#550	C₂²×C₁₃	1	1	yes	characteristic
561	#547	—	2	1	no	—
562	#544	—	2	1	no	—
563	#542	C₂²×C₁₃	1	2	yes	—
564	#541	—	2	1	no	—
565	#541	—	2	2	no	—
566	#541	C₂²×C₁₃	1	2	yes	—
567	#538	—	2	2	no	—
568	#535	C₂²×C₁₃	1	2	yes	—
569	#533	C₂²×C₁₃	1	1	yes	characteristic
570	#533	C₂²×C₁₃	1	1	yes	characteristic
571	#532	C₂²×C₁₃	1	1	yes	characteristic
572	#529	C₂²×C₁₃	1	1	yes	characteristic
573	#525	—	2	1	no	—
574	#525	—	2	1	no	—
575	#520	C₂²×C₁₃	1	2	yes	—
576	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
577	#497	C₂²×C₁₃	1	2	yes	—
578	#496	C₂²×C₁₃	1	2	yes	—
579	#495	C₂²×C₁₃	1	2	yes	—
580	#495	C₂²×C₁₃	1	2	yes	complemented
581	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
582	#492	C₂²×C₁₃	1	2	yes	—
583	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
584	#490	C₂²×C₁₃	1	2	yes	—
585	#489	C₂²×C₁₃	1	2	yes	—
586	#488	C₂²×C₁₃	1	2	yes	—
587	#488	C₂²×C₁₃	1	2	yes	complemented
588	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
589	#486	C₂²×C₁₃	1	2	yes	—
590	#486	C₂²×C₁₃	1	1	yes	characteristic, complemented
591	#484	C₂²×C₁₃	1	1	yes	characteristic
592	#483	C₂²×C₁₃	1	2	yes	—
593	#481	C₂²×C₁₃	1	1	yes	characteristic
594	#479	C₂²×C₁₃	1	2	yes	complemented
595	#478	C₂²×C₁₃	1	1	yes	characteristic
596	#478	C₂²×C₁₃	1	1	yes	characteristic
597	#478	C₂²×C₁₃	1	2	yes	complemented
598	#476	C₂²×C₁₃	1	1	yes	characteristic
599	#476	C₂²×C₁₃	1	1	yes	characteristic
600	#476	C₂²×C₁₃	1	2	yes	complemented
601	#475	C₂²×C₁₃	1	2	yes	complemented
602	#464	C₂²×C₁₃	1	2	yes	—
603	#464	C₂²×C₁₃	1	2	yes	—
604	#464	C₂²×C₁₃	1	2	yes	—
605	#464	C₂²×C₁₃	1	2	yes	complemented
606	#464	C₂²×C₁₃	1	2	yes	complemented
607	#464	C₂²×C₁₃	1	2	yes	complemented
608	#463	C₂²×C₁₃	1	2	yes	—
609	#463	C₂²×C₁₃	1	1	yes	characteristic
610	#463	C₂²×C₁₃	1	1	yes	characteristic
611	#463	C₂²×C₁₃	1	2	yes	complemented
612	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#462	C₂²×C₁₃	1	2	yes	complemented
614	#461	C₂²×C₁₃	1	1	yes	characteristic
615	#461	C₂²×C₁₃	1	1	yes	characteristic
616	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	#461	C₂²×C₁₃	1	2	yes	complemented
618	#460	C₂²×C₁₃	1	2	yes	—
619	#460	C₂²×C₁₃	1	2	yes	—
620	#460	C₂²×C₁₃	1	2	yes	—
621	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#459	C₂²×C₁₃	1	2	yes	—
623	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
624	#452	C₂²×C₁₃	1	2	yes	—
625	#452	C₂²×C₁₃	1	2	yes	—
626	#452	C₂²×C₁₃	1	2	yes	—
627	#450	C₂²×C₁₃	1	2	yes	—
628	#450	C₂²×C₁₃	1	1	yes	characteristic
629	#449	C₂²×C₁₃	1	2	yes	—
630	#447	C₂²×C₁₃	1	1	yes	characteristic
631	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
633	#446	C₂²×C₁₃	1	2	yes	complemented
634	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
635	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	C₈×Q₈	C₂²×C₁₃	1	2	yes	complemented
637	#442	C₂²×C₁₃	1	2	yes	complemented
638	#441	C₂²×C₁₃	1	2	yes	complemented
639	#441	C₂²×C₁₃	1	2	yes	complemented
640	#440	C₂²×C₁₃	1	2	yes	complemented
641	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
642	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
643	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
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	complemented
647	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
648	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
649	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
650	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
651	#433	C₂²×C₁₃	1	2	yes	—
652	#433	C₂²×C₁₃	1	2	yes	—
653	#431	C₂²×C₁₃	1	1	yes	characteristic
654	#431	C₂²×C₁₃	1	1	yes	characteristic
655	C₂²×C₁₃	—	2	1	no	—
656	C₂²×C₁₃	—	2	1	no	—
657	C₂²×C₁₃	—	2	1	no	—
658	C₂²×C₁₃	—	4	1	no	—
659	C₂²×C₁₃	—	4	2	no	—
660	C₂²×C₁₃	—	4	1	no	—
661	C₂²×C₁₃	—	4	1	no	—
662	C₂²×C₁₃	—	4	2	no	—
663	C₂²×C₁₃	—	4	1	no	—
664	C₂²×C₁₃	—	4	1	no	—
665	C₂²×C₁₃	—	4	1	no	—
666	C₂²×C₁₃	—	4	1	no	—
667	C₂²×C₁₃	—	4	1	no	—
668	C₂²×C₁₃	—	4	1	no	—
669	C₂²×C₁₃	—	4	2	no	—
670	C₂²×C₁₃	—	8	4	no	—
671	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
672	C₄×C₁₃	—	2	1	no	—
673	C₄×C₁₃	—	2	1	no	—
674	C₄×C₁₃	—	2	2	no	—
675	C₄×C₁₃	—	2	2	no	—
676	C₄×C₁₃	—	2	1	no	—
677	C₄×C₁₃	—	2	1	no	—
678	C₄×C₁₃	—	2	2	no	—
679	C₄×C₁₃	—	2	2	no	—
680	C₄×C₁₃	—	4	2	no	—
681	C₄×C₁₃	—	4	1	no	—
682	C₄×C₁₃	—	4	2	no	—
683	C₄×C₁₃	—	4	1	no	—
684	C₄×C₁₃	—	4	2	no	—
685	C₄×C₁₃	—	4	1	no	—
686	C₄×C₁₃	—	4	1	no	—
687	C₄×C₁₃	—	4	1	no	—
688	C₄×C₁₃	#577	1	2	yes	—
689	C₄×C₁₃	#585	1	1	yes	characteristic
690	C₄×C₁₃	#585	1	1	yes	characteristic
691	C₂×#41	—	2	1	no	—
692	C₂×#41	—	2	1	no	—
693	C₂×#41	C₂³×C₁₃	1	2	yes	—
694	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
695	C₂³×C₄	—	2	1	no	—
696	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
697	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
698	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
699	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
701	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
702	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
704	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
705	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
706	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
707	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
708	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×D₈	C₂³×C₁₃	1	2	yes	—
710	C₄⋊Q₈	—	2	2	no	—
711	C₄⋊Q₈	—	2	2	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
714	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
717	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
720	#127	C₂³×C₁₃	1	1	yes	characteristic
721	#127	C₂³×C₁₃	1	2	yes	—
722	#127	C₂³×C₁₃	1	2	yes	—
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#126	—	2	2	no	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	1	no	—
732	#125	—	2	2	no	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	2	no	—
736	#125	—	2	2	no	—
737	#125	—	2	1	no	—
738	#125	—	2	1	no	—
739	#125	D₄×C₁₃	1	2	yes	—
740	#125	C₂³×C₁₃	1	1	yes	characteristic
741	#125	C₂³×C₁₃	1	2	yes	—
742	#124	—	2	2	no	—
743	#124	—	2	2	no	—
744	#124	—	2	2	no	—
745	#124	C₂³×C₁₃	1	1	yes	characteristic
746	#124	C₂³×C₁₃	1	2	yes	—
747	#124	C₂³×C₁₃	1	2	yes	—
748	#124	C₂³×C₁₃	1	2	yes	—
749	#124	C₂³×C₁₃	1	2	yes	—
750	#123	—	2	1	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	—	2	2	no	—
756	C₂²⋊Q₈	—	2	1	no	—
757	C₂²⋊Q₈	—	2	1	no	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	2	1	no	—
760	C₂²⋊Q₈	—	2	2	no	—
761	C₂²⋊Q₈	—	2	1	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
765	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
766	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
767	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
768	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
769	#121	—	2	1	no	—
770	#121	—	2	1	no	—
771	#121	—	2	1	no	—
772	#121	—	2	1	no	—
773	#121	—	2	2	no	—
774	#121	—	2	2	no	—
775	#121	—	2	2	no	—
776	#121	—	2	2	no	—
777	#121	C₂³×C₁₃	1	1	yes	characteristic
778	#120	—	2	2	no	—
779	#120	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
785	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
788	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
789	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
790	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
791	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
792	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
793	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	2	no	—
798	C₄×D₄	—	2	2	no	—
799	C₄×D₄	—	2	1	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
804	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
805	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
806	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
807	C₄×D₄	C₂³×C₁₃	1	2	yes	—
808	C₄×D₄	C₂³×C₁₃	1	2	yes	—
809	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
810	C₄×D₄	C₂³×C₁₃	1	2	yes	—
811	#117	—	2	1	no	—
812	#117	—	2	2	no	—
813	#117	—	2	1	no	—
814	#117	—	2	1	no	—
815	#117	—	2	2	no	—
816	#117	—	2	1	no	—
817	#117	—	2	1	no	—
818	#117	C₂³×C₁₃	1	2	yes	—
819	C₂×C₄⋊C₄	—	2	2	no	—
820	C₂×C₄⋊C₄	—	2	1	no	—
821	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
822	C₂×C₂²⋊C₄	—	2	1	no	—
823	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
824	#107	C₂³×C₁₃	1	1	yes	characteristic
825	#107	C₂³×C₁₃	1	1	yes	characteristic
826	#106	C₂³×C₁₃	1	1	yes	characteristic
827	#106	C₂³×C₁₃	1	2	yes	—
828	#106	C₂³×C₁₃	1	1	yes	characteristic
829	#106	C₂³×C₁₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
834	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
837	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
838	#103	C₂³×C₁₃	1	1	yes	characteristic
839	#103	C₂³×C₁₃	1	2	yes	—
840	#103	C₂³×C₁₃	1	2	yes	—
841	#103	C₂³×C₁₃	1	1	yes	characteristic
842	#103	C₂³×C₁₃	1	2	yes	—
843	#103	C₂³×C₁₃	1	2	yes	—
844	#103	C₂³×C₁₃	1	2	yes	—
845	#103	C₂³×C₁₃	1	2	yes	—
846	#102	C₂³×C₁₃	1	1	yes	characteristic
847	#102	C₂³×C₁₃	1	1	yes	characteristic
848	#102	C₂³×C₁₃	1	1	yes	characteristic
849	#102	C₂³×C₁₃	1	1	yes	characteristic
850	#102	C₂³×C₁₃	1	1	yes	characteristic
851	#102	C₂³×C₁₃	1	1	yes	characteristic
852	#102	C₂³×C₁₃	1	2	yes	—
853	#102	C₂³×C₁₃	1	2	yes	—
854	#102	C₂³×C₁₃	1	2	yes	—
855	#102	C₂³×C₁₃	1	2	yes	—
856	#102	C₂³×C₁₃	1	2	yes	—
857	#102	C₂³×C₁₃	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
861	#97	C₂³×C₁₃	1	2	yes	—
862	#97	C₂³×C₁₃	1	2	yes	—
863	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
864	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
865	C₄×C₈	C₂³×C₁₃	1	2	yes	—
866	C₄×C₈	C₂³×C₁₃	1	2	yes	—
867	C₄×C₈	C₂³×C₁₃	1	2	yes	—
868	C₂×C₁₃	—	4	1	no	—
869	C₂×C₁₃	—	8	1	no	—
870	C₂×C₁₃	—	8	2	no	—
871	C₂×C₁₃	—	8	1	no	—
872	C₂×C₁₃	—	8	1	no	—
873	C₂×C₁₃	#3487	1	1	yes	characteristic
874	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
875	C₂×C₁₃	#3584	1	1	yes	characteristic
876	C₂⁴	—	2	1	no	—
877	#41	—	4	2	no	—
878	#41	—	4	2	no	—
879	#41	—	8	2	no	—
880	#41	—	8	2	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
884	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
885	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
886	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
887	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
888	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
889	C₂×D₄	—	2	2	no	—
890	C₂×D₄	—	2	1	no	—
891	C₂×D₄	—	2	1	no	—
892	C₂×D₄	—	2	1	no	—
893	C₂×D₄	—	2	2	no	—
894	C₂×D₄	—	2	2	no	—
895	C₂×D₄	—	2	1	no	—
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	4	1	no	—
899	C₂×D₄	—	4	1	no	—
900	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
901	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
902	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
903	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	2	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	2	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	8	2	no	—
915	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
916	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
918	Q₁₆	—	4	2	no	—
919	Q₁₆	—	4	2	no	—
920	Q₁₆	—	4	2	no	—
921	SD₁₆	—	4	2	no	—
922	SD₁₆	—	4	2	no	—
923	SD₁₆	—	4	2	no	—
924	SD₁₆	—	4	1	no	—
925	SD₁₆	—	4	2	no	—
926	SD₁₆	—	4	2	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	1	no	—
929	D₈	—	4	1	no	—
930	D₈	—	4	2	no	—
931	D₈	—	4	1	no	—
932	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
933	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
935	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	1	no	—
960	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
961	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
962	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
963	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
964	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
965	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
966	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
967	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
968	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
970	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₂²⋊C₄	—	2	2	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	2	1	no	—
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	1	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
996	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1005	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1007	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₁₃	1	2	yes	—
1009	C₄²	C₂⁴×C₁₃	1	2	yes	—
1010	C₁₃	#61927	1	1	yes	characteristic, direct product factor, Sylow
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	—	2	1	no	—
1014	C₂³	—	2	2	no	—
1015	C₂³	—	4	2	no	—
1016	C₂³	—	8	1	no	—
1017	C₂³	—	8	1	no	—
1018	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1019	Q₈	—	2	2	no	—
1020	Q₈	—	2	2	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	8	2	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	1	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	2	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	4	4	no	—
1040	D₄	—	4	2	no	—
1041	D₄	—	8	1	no	—
1042	D₄	—	8	2	no	—
1043	D₄	—	8	2	no	—
1044	D₄	—	8	2	no	—
1045	D₄	—	8	2	no	—
1046	D₄	—	8	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	4	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	—	8	1	no	—
1065	C₂×C₄	—	8	2	no	—
1066	C₂×C₄	—	8	2	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	—	8	1	no	—
1069	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1070	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1071	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1072	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1073	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1074	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1075	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1076	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1077	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1079	C₈	—	2	1	no	—
1080	C₈	—	2	2	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	2	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	8	4	no	—
1101	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	2	no	—
1104	C₄	—	2	2	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	C₁₃×#577	1	2	yes	—
1119	C₄	C₁₃×#585	1	1	yes	characteristic
1120	C₄	C₁₃×#585	1	1	yes	characteristic
1121	C₂	—	4	1	no	—
1122	C₂	—	8	1	no	—
1123	C₂	—	8	1	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	8	2	no	—
1126	C₂	C₁₃×#3487	1	1	yes	characteristic
1127	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1128	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
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
1. C₁₃×#3555	C₂	semidirect
2. C₁₃×#3506	C₂	semidirect
3. C₁₃×#3401	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3397	C₂	semidirect
6. C₁₃×#3394	C₂	semidirect
7. C₁₃×#3393	C₂	semidirect
8. C₁₃×#3392	C₂	semidirect
9. C₁₃×#3371	C₂	semidirect
10. C₁₃×#3369	C₂	semidirect
11. C₁₃×#3366	C₂	semidirect
12. C₁₃×#3365	C₂	semidirect
13. C₁₃×#3362	C₂	semidirect
14. C₁₃×#3360	C₂	semidirect
15. C₁₃×#3224	C₂	semidirect
16. C₁₃×#3222	C₂	semidirect
17. C₁₃×#3212	C₂	semidirect
18. C₁₃×#3210	C₂	semidirect
19. C₁₃×#3125	C₂	semidirect
20. C₁₃×#3120	C₂	semidirect
21. C₁₃×#3105	C₂	semidirect
22. C₁₃×#3101	C₂	semidirect
23. C₁₃×#2986	C₂	semidirect
27. Q₈²×C₁₃	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
29. C₁₃×#557	C₂²	semidirect
33. C₁₃×#556	C₂²	semidirect
34. C₁₃×#556	C₂²	semidirect
36. C₁₃×#554	C₂²	semidirect
60. C₁₃×#495	C₂²	semidirect
61. C₁₃×#494	C₂²	semidirect
63. C₁₃×#492	C₂²	semidirect
67. C₁₃×#488	C₂²	semidirect
68. C₁₃×#487	C₂²	semidirect
70. C₁₃×#486	C₂²	semidirect
74. C₁₃×#479	C₂²	semidirect
77. C₁₃×#478	C₂²	semidirect
80. C₁₃×#476	C₂²	semidirect
81. C₁₃×#475	C₂²	semidirect
85. C₁₃×#464	C₂²	semidirect
86. C₁₃×#464	C₂²	semidirect
87. C₁₃×#464	C₂²	semidirect
91. C₁₃×#463	C₂²	semidirect
92. C₁₃×#462	C₂²	semidirect
93. C₁₃×#462	C₂²	semidirect
96. C₁₃×#461	C₂²	semidirect
97. C₁₃×#461	C₂²	semidirect
101. C₁₃×#460	C₂²	semidirect
103. C₁₃×#459	C₂²	semidirect
111. C₁₃×#446	C₂²	semidirect
112. C₁₃×#446	C₂²	semidirect
113. C₁₃×#446	C₂²	semidirect
114. C₈×Q₈×C₁₃	C₂²	semidirect
115. C₈×Q₈×C₁₃	C₂²	semidirect
116. C₈×Q₈×C₁₃	C₂²	semidirect
117. C₁₃×#442	C₂²	semidirect
118. C₁₃×#441	C₂²	semidirect
119. C₁₃×#441	C₂²	semidirect
120. C₁₃×#440	C₂²	semidirect
121. C₄×C₁₃×Q₁₆	C₂²	semidirect
126. C₄×C₁₃×SD₁₆	C₂²	semidirect
127. C₄×C₁₃×SD₁₆	C₂²	semidirect
128. C₄×C₁₃×SD₁₆	C₂²	semidirect
312. #61927	C₁₃	direct (N × H)
447. #3555	C₂×C₁₃	semidirect
448. #3506	C₂×C₁₃	semidirect
449. #3401	C₂×C₁₃	semidirect
450. #3398	C₂×C₁₃	semidirect
451. #3397	C₂×C₁₃	semidirect
452. #3394	C₂×C₁₃	semidirect
453. #3393	C₂×C₁₃	semidirect
454. #3392	C₂×C₁₃	semidirect
455. #3371	C₂×C₁₃	semidirect
456. #3369	C₂×C₁₃	semidirect
457. #3366	C₂×C₁₃	semidirect
458. #3365	C₂×C₁₃	semidirect
459. #3362	C₂×C₁₃	semidirect
460. #3360	C₂×C₁₃	semidirect
461. #3224	C₂×C₁₃	semidirect
462. #3222	C₂×C₁₃	semidirect
463. #3212	C₂×C₁₃	semidirect
464. #3210	C₂×C₁₃	semidirect
465. #3125	C₂×C₁₃	semidirect
466. #3120	C₂×C₁₃	semidirect
467. #3105	C₂×C₁₃	semidirect
468. #3101	C₂×C₁₃	semidirect
469. #2986	C₂×C₁₃	semidirect
547. Q₈²	C₂²×C₁₃	semidirect
548. #557	C₂²×C₁₃	semidirect
549. #557	C₂²×C₁₃	semidirect
553. #556	C₂²×C₁₃	semidirect
554. #556	C₂²×C₁₃	semidirect
556. #554	C₂²×C₁₃	semidirect
580. #495	C₂²×C₁₃	semidirect
581. #494	C₂²×C₁₃	semidirect
583. #492	C₂²×C₁₃	semidirect
587. #488	C₂²×C₁₃	semidirect
588. #487	C₂²×C₁₃	semidirect
590. #486	C₂²×C₁₃	semidirect
594. #479	C₂²×C₁₃	semidirect
597. #478	C₂²×C₁₃	semidirect
600. #476	C₂²×C₁₃	semidirect
601. #475	C₂²×C₁₃	semidirect
605. #464	C₂²×C₁₃	semidirect
606. #464	C₂²×C₁₃	semidirect
607. #464	C₂²×C₁₃	semidirect
611. #463	C₂²×C₁₃	semidirect
612. #462	C₂²×C₁₃	semidirect
613. #462	C₂²×C₁₃	semidirect
616. #461	C₂²×C₁₃	semidirect
617. #461	C₂²×C₁₃	semidirect
621. #460	C₂²×C₁₃	semidirect
623. #459	C₂²×C₁₃	semidirect
631. #446	C₂²×C₁₃	semidirect
632. #446	C₂²×C₁₃	semidirect
633. #446	C₂²×C₁₃	semidirect
634. C₈×Q₈	C₂²×C₁₃	semidirect
635. C₈×Q₈	C₂²×C₁₃	semidirect
636. C₈×Q₈	C₂²×C₁₃	semidirect
637. #442	C₂²×C₁₃	semidirect
638. #441	C₂²×C₁₃	semidirect
639. #441	C₂²×C₁₃	semidirect
640. #440	C₂²×C₁₃	semidirect
641. C₄×Q₁₆	C₂²×C₁₃	semidirect
646. C₄×SD₁₆	C₂²×C₁₃	semidirect
647. C₄×SD₁₆	C₂²×C₁₃	semidirect
648. C₄×SD₁₆	C₂²×C₁₃	semidirect
1010. C₁₃	#61927	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×#3506	2
C₁₃×#3401	2
C₁₃×#3398	2
C₁₃×#3397	2
C₁₃×#3394	2
C₁₃×#3393	2
C₁₃×#3392	2
C₁₃×#3371	2
C₁₃×#3369	2
C₁₃×#3366	2
C₁₃×#3365	2
C₁₃×#3362	2
C₁₃×#3360	2
C₁₃×#3224	2
C₁₃×#3222	2
C₁₃×#3212	2
C₁₃×#3210	2
C₁₃×#3125	2
C₁₃×#3120	2
C₁₃×#3105	2
C₁₃×#3101	2
C₁₃×#2986	2
#61927	13

Subgroups — C13×#61927 #15748266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61927 #15748266