Subgroups — C₁₃×#61440 #15747779

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3480	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×#3387	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3320	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3172	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3108	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3107	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₁₃×#137	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	—
25	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₁₃×#559	—	2	1	no	—
27	C₁₃×#559	C₂²	1	1	yes	characteristic
28	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#557	—	2	1	no	—
30	C₁₃×#557	C₂²	1	1	yes	characteristic
31	C₁₃×#557	C₂²	1	1	yes	characteristic
32	C₁₃×#556	—	2	1	no	—
33	C₁₃×#556	C₂²	1	1	yes	characteristic
34	C₁₃×#554	—	2	2	no	—
35	C₁₃×#554	—	2	1	no	—
36	C₁₃×#554	C₂²	1	2	yes	—
37	C₁₃×#554	C₂²	1	1	yes	characteristic
38	C₁₃×#553	—	2	2	no	—
39	C₁₃×#553	C₂²	1	2	yes	—
40	C₁₃×#550	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
42	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#548	C₂²	1	2	yes	—
44	C₁₃×#533	—	2	1	no	—
45	C₁₃×#533	—	2	2	no	—
46	C₁₃×#533	C₂²	1	1	yes	characteristic
47	C₁₃×#533	C₂²	1	2	yes	—
48	C₁₃×#532	—	2	1	no	—
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	2	no	—
51	C₁₃×#529	C₂²	1	2	yes	—
52	C₄×C₁₃×#41	—	2	1	no	—
53	C₄×C₁₃×#41	—	2	1	no	—
54	C₄×C₁₃×#41	C₂²	1	2	yes	—
55	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
59	C₁₃×#501	C₂²	1	2	yes	—
60	C₁₃×#498	C₂²	1	1	yes	characteristic
61	C₁₃×#497	C₂²	1	2	yes	—
62	C₁₃×#492	C₂²	1	1	yes	characteristic
63	C₁₃×#491	C₂²	1	2	yes	—
64	C₁₃×#489	C₂²	1	2	yes	—
65	C₁₃×#487	C₂²	1	1	yes	characteristic
66	C₁₃×#486	C₂²	1	1	yes	characteristic
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#485	C₂²	1	2	yes	—
69	C₁₃×#484	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	2	yes	—
71	C₁₃×#481	C₂²	1	2	yes	—
72	C₁₃×#480	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	—
74	C₁₃×#479	C₂²	1	2	yes	—
75	C₁₃×#477	C₂²	1	1	yes	characteristic
76	C₁₃×#477	C₂²	1	1	yes	characteristic
77	C₁₃×#475	C₂²	1	2	yes	—
78	C₁₃×#475	C₂²	1	1	yes	characteristic
79	C₁₃×#475	C₂²	1	1	yes	characteristic
80	C₁₃×#474	C₂²	1	2	yes	—
81	C₁₃×#470	C₂²	1	2	yes	—
82	C₁₃×#470	C₂²	1	2	yes	—
83	C₁₃×#468	C₂²	1	2	yes	—
84	C₁₃×#468	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#464	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	2	yes	—
90	C₁₃×#462	C₂²	1	1	yes	characteristic
91	C₁₃×#462	C₂²	1	1	yes	characteristic
92	C₁₃×#461	C₂²	1	2	yes	—
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×#452	C₂²	1	2	yes	—
97	C₁₃×#451	C₂²	1	2	yes	—
98	C₁₃×#451	C₂²	1	2	yes	—
99	C₁₃×#448	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	1	yes	characteristic
102	C₁₃×#446	C₂²	1	1	yes	characteristic
103	C₁₃×#441	C₂²	1	2	yes	—
104	C₁₃×#441	C₂²	1	2	yes	—
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
108	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
109	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
110	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
116	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
119	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
120	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
121	C₁₃×#436	C₂²	1	1	yes	characteristic
122	C₁₃×#436	C₂²	1	1	yes	characteristic
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₁₃×#435	C₂²	1	2	yes	—
125	C₁₃×#431	C₂²	1	1	yes	characteristic
126	C₁₃×#431	C₂²	1	2	yes	—
127	C₁₃×#428	C₂²	1	2	yes	—
128	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
129	C₁₃×#419	C₂²	1	2	yes	—
130	C₁₃×#417	C₂²	1	2	yes	—
131	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
132	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
133	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₁₃×#137	—	2	8	no	—
142	C₂×C₁₃×Q₁₆	—	2	4	no	—
143	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
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×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×Q₁₆	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×M₁₆	C₂³	1	2	yes	—
154	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
155	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊Q₈	—	2	1	no	—
158	C₁₃×C₄⋊Q₈	—	2	1	no	—
159	C₁₃×C₄⋊Q₈	—	2	2	no	—
160	C₁₃×C₄⋊Q₈	—	2	1	no	—
161	C₁₃×C₄⋊Q₈	—	2	2	no	—
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
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	—	2	1	no	—
168	C₁₃×#127	C₂³	1	1	yes	characteristic
169	C₁₃×#126	—	2	2	no	—
170	C₁₃×#126	—	2	2	no	—
171	C₁₃×#126	—	2	2	no	—
172	C₁₃×#125	—	2	2	no	—
173	C₁₃×#125	—	2	1	no	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	1	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	C₂³	1	2	yes	—
180	C₁₃×#124	—	2	1	no	—
181	C₁₃×#124	—	2	1	no	—
182	C₁₃×#124	—	2	2	no	—
183	C₁₃×#124	—	2	1	no	—
184	C₁₃×#124	C₂³	1	2	yes	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	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	2	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	C₄×Q₈×C₁₃	—	2	1	no	—
208	C₄×Q₈×C₁₃	—	2	1	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	1	no	—
217	C₄×Q₈×C₁₃	—	2	2	no	—
218	C₄×Q₈×C₁₃	—	2	1	no	—
219	C₄×Q₈×C₁₃	D₄	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	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
225	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	1	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	2	no	—
238	C₄×D₄×C₁₃	—	2	2	no	—
239	C₄×D₄×C₁₃	—	2	2	no	—
240	C₄×D₄×C₁₃	—	2	1	no	—
241	C₄×D₄×C₁₃	—	2	1	no	—
242	C₄×D₄×C₁₃	—	2	2	no	—
243	C₄×D₄×C₁₃	—	2	2	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	D₄	1	2	yes	—
246	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
248	C₄×D₄×C₁₃	C₂³	1	2	yes	—
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	—	2	2	no	—
255	C₁₃×#117	D₄	1	1	yes	characteristic
256	C₁₃×#117	D₄	1	2	yes	—
257	C₁₃×#117	C₂³	1	2	yes	—
258	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₄²×C₁₃	—	2	1	no	—
265	C₂×C₄²×C₁₃	—	2	2	no	—
266	C₂×C₄²×C₁₃	—	2	1	no	—
267	C₂×C₄²×C₁₃	—	2	2	no	—
268	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
270	C₁₃×#107	C₂³	1	1	yes	characteristic
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#107	C₂³	1	1	yes	characteristic
273	C₁₃×#107	C₂³	1	1	yes	characteristic
274	C₁₃×#107	C₂³	1	2	yes	—
275	C₁₃×#107	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	2	yes	—
278	C₁₃×#106	C₂³	1	2	yes	—
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×#103	C₂³	1	1	yes	characteristic
285	C₁₃×#103	C₂³	1	1	yes	characteristic
286	C₁₃×#103	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	1	yes	characteristic
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	2	yes	—
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×#103	C₂³	1	2	yes	—
298	C₁₃×#103	C₂³	1	2	yes	—
299	C₁₃×#103	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	#61440	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₁₃×#41	—	2	4	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	4	2	no	—
318	C₁₃×#41	—	4	4	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	1	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	—	2	4	no	—
328	C₂×Q₈×C₁₃	—	4	1	no	—
329	C₂×Q₈×C₁₃	—	4	1	no	—
330	C₂×Q₈×C₁₃	—	4	2	no	—
331	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
333	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
334	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₁₃	—	2	2	no	—
338	C₂×D₄×C₁₃	—	2	2	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
343	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
344	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
345	C₂²×C₄×C₁₃	—	2	1	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	1	no	—
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	2	no	—
353	C₂²×C₄×C₁₃	—	2	2	no	—
354	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
355	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
357	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
358	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
360	C₁₃×Q₁₆	—	2	2	no	—
361	C₁₃×Q₁₆	—	2	2	no	—
362	C₁₃×Q₁₆	—	2	4	no	—
363	C₁₃×Q₁₆	—	2	2	no	—
364	C₁₃×Q₁₆	—	4	2	no	—
365	C₁₃×Q₁₆	#41	1	4	yes	complemented
366	C₁₃×SD₁₆	—	2	4	no	—
367	C₁₃×SD₁₆	—	2	4	no	—
368	C₁₃×SD₁₆	—	4	2	no	—
369	C₁₃×SD₁₆	—	4	2	no	—
370	C₁₃×M₁₆	—	2	4	no	—
371	C₁₃×M₁₆	—	4	2	no	—
372	C₂×C₈×C₁₃	—	2	2	no	—
373	C₂×C₈×C₁₃	—	4	1	no	—
374	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
378	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
379	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	—	2	1	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	2	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
385	C₁₃×C₄⋊C₄	—	2	1	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
392	C₁₃×C₄⋊C₄	—	2	1	no	—
393	C₁₃×C₄⋊C₄	—	2	1	no	—
394	C₁₃×C₄⋊C₄	—	2	2	no	—
395	C₁₃×C₄⋊C₄	—	2	2	no	—
396	C₁₃×C₄⋊C₄	—	2	2	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	2	no	—
399	C₁₃×C₄⋊C₄	—	2	1	no	—
400	C₁₃×C₄⋊C₄	—	2	2	no	—
401	C₁₃×C₄⋊C₄	—	2	1	no	—
402	C₁₃×C₄⋊C₄	—	2	2	no	—
403	C₁₃×C₄⋊C₄	—	2	2	no	—
404	C₁₃×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
409	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
411	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂⁴	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×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	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	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	2	no	—
428	C₁₃×C₂²⋊C₄	—	2	2	no	—
429	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
431	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
432	C₄²×C₁₃	—	2	2	no	—
433	C₄²×C₁₃	—	2	2	no	—
434	C₄²×C₁₃	—	2	1	no	—
435	C₄²×C₁₃	—	2	2	no	—
436	C₄²×C₁₃	—	2	1	no	—
437	C₄²×C₁₃	—	2	1	no	—
438	C₄²×C₁₃	—	2	2	no	—
439	C₄²×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
446	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₁₃	C₂×D₄	1	2	yes	—
448	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
450	C₄²×C₁₃	C₂⁴	1	2	yes	—
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	#3480	C₂×C₁₃	1	1	yes	characteristic
453	Q₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3387	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3375	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3374	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3356	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3346	C₂×C₁₃	1	2	yes	complemented
460	#3333	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3320	C₂×C₁₃	1	2	yes	complemented
463	#3316	C₂×C₁₃	1	2	yes	complemented
464	#3278	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3270	C₂×C₁₃	1	2	yes	complemented
466	#3172	C₂×C₁₃	1	2	yes	complemented
467	#3167	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3108	C₂×C₁₃	1	2	yes	complemented
469	#3107	C₂×C₁₃	1	2	yes	complemented
470	#3104	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3103	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#2965	C₂×C₁₃	1	1	yes	characteristic, complemented
473	C₄×#137	C₂×C₁₃	1	2	yes	complemented
474	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
475	C₂³×C₁₃	—	2	2	no	—
476	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
477	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
478	Q₈×C₁₃	—	2	2	no	—
479	Q₈×C₁₃	—	2	1	no	—
480	Q₈×C₁₃	—	2	1	no	—
481	Q₈×C₁₃	—	2	2	no	—
482	Q₈×C₁₃	—	2	1	no	—
483	Q₈×C₁₃	—	2	1	no	—
484	Q₈×C₁₃	—	2	1	no	—
485	Q₈×C₁₃	—	2	2	no	—
486	Q₈×C₁₃	—	2	1	no	—
487	Q₈×C₁₃	—	4	4	no	—
488	Q₈×C₁₃	—	4	2	no	—
489	Q₈×C₁₃	—	4	2	no	—
490	Q₈×C₁₃	—	4	2	no	—
491	Q₈×C₁₃	—	8	2	no	—
492	Q₈×C₁₃	—	8	1	no	—
493	Q₈×C₁₃	C₂×#41	1	2	yes	—
494	Q₈×C₁₃	C₂×#41	1	2	yes	—
495	D₄×C₁₃	—	2	4	no	—
496	D₄×C₁₃	—	2	2	no	—
497	D₄×C₁₃	—	2	2	no	—
498	D₄×C₁₃	—	2	2	no	—
499	D₄×C₁₃	—	4	4	no	—
500	D₄×C₁₃	—	4	4	no	—
501	D₄×C₁₃	—	4	2	no	—
502	D₄×C₁₃	—	8	1	no	—
503	D₄×C₁₃	—	8	2	no	—
504	C₂×C₄×C₁₃	—	2	1	no	—
505	C₂×C₄×C₁₃	—	2	1	no	—
506	C₂×C₄×C₁₃	—	2	4	no	—
507	C₂×C₄×C₁₃	—	2	1	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	2	no	—
511	C₂×C₄×C₁₃	—	2	1	no	—
512	C₂×C₄×C₁₃	—	2	1	no	—
513	C₂×C₄×C₁₃	—	2	1	no	—
514	C₂×C₄×C₁₃	—	2	2	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	2	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	4	2	no	—
521	C₂×C₄×C₁₃	—	4	1	no	—
522	C₂×C₄×C₁₃	—	4	4	no	—
523	C₂×C₄×C₁₃	—	4	2	no	—
524	C₂×C₄×C₁₃	—	4	2	no	—
525	C₂×C₄×C₁₃	—	4	4	no	—
526	C₂×C₄×C₁₃	—	4	4	no	—
527	C₂×C₄×C₁₃	—	8	2	no	—
528	C₂×C₄×C₁₃	—	8	1	no	—
529	C₂×C₄×C₁₃	—	8	1	no	—
530	C₂×C₄×C₁₃	—	8	2	no	—
531	C₂×C₄×C₁₃	#137	1	4	yes	complemented
532	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
540	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
541	C₈×C₁₃	—	2	1	no	—
542	C₈×C₁₃	—	2	2	no	—
543	C₈×C₁₃	—	2	1	no	—
544	C₈×C₁₃	—	2	1	no	—
545	C₈×C₁₃	—	2	2	no	—
546	C₈×C₁₃	C₂×#41	1	2	yes	—
547	C₂×#137	C₂²×C₁₃	1	2	yes	—
548	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
549	#559	—	2	1	no	—
550	#559	C₂²×C₁₃	1	1	yes	characteristic
551	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
552	#557	—	2	1	no	—
553	#557	C₂²×C₁₃	1	1	yes	characteristic
554	#557	C₂²×C₁₃	1	1	yes	characteristic
555	#556	—	2	1	no	—
556	#556	C₂²×C₁₃	1	1	yes	characteristic
557	#554	—	2	2	no	—
558	#554	—	2	1	no	—
559	#554	C₂²×C₁₃	1	1	yes	characteristic
560	#554	C₂²×C₁₃	1	2	yes	—
561	#553	—	2	2	no	—
562	#553	C₂²×C₁₃	1	2	yes	—
563	#550	C₂²×C₁₃	1	1	yes	characteristic
564	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
565	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
566	#548	C₂²×C₁₃	1	2	yes	—
567	#533	—	2	1	no	—
568	#533	—	2	2	no	—
569	#533	C₂²×C₁₃	1	1	yes	characteristic
570	#533	C₂²×C₁₃	1	2	yes	—
571	#532	—	2	1	no	—
572	#532	C₂²×C₁₃	1	1	yes	characteristic
573	#529	—	2	2	no	—
574	#529	C₂²×C₁₃	1	2	yes	—
575	C₄×#41	—	2	1	no	—
576	C₄×#41	—	2	1	no	—
577	C₄×#41	C₂²×C₁₃	1	2	yes	—
578	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
579	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
580	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
581	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
582	#501	C₂²×C₁₃	1	2	yes	—
583	#498	C₂²×C₁₃	1	1	yes	characteristic
584	#497	C₂²×C₁₃	1	2	yes	—
585	#492	C₂²×C₁₃	1	1	yes	characteristic
586	#491	C₂²×C₁₃	1	2	yes	—
587	#489	C₂²×C₁₃	1	2	yes	—
588	#487	C₂²×C₁₃	1	1	yes	characteristic
589	#486	C₂²×C₁₃	1	1	yes	characteristic
590	#485	C₂²×C₁₃	1	2	yes	—
591	#485	C₂²×C₁₃	1	2	yes	—
592	#484	C₂²×C₁₃	1	2	yes	—
593	#483	C₂²×C₁₃	1	2	yes	—
594	#481	C₂²×C₁₃	1	2	yes	—
595	#480	C₂²×C₁₃	1	2	yes	—
596	#479	C₂²×C₁₃	1	2	yes	—
597	#479	C₂²×C₁₃	1	2	yes	—
598	#477	C₂²×C₁₃	1	1	yes	characteristic
599	#477	C₂²×C₁₃	1	1	yes	characteristic
600	#475	C₂²×C₁₃	1	1	yes	characteristic
601	#475	C₂²×C₁₃	1	1	yes	characteristic
602	#475	C₂²×C₁₃	1	2	yes	—
603	#474	C₂²×C₁₃	1	2	yes	—
604	#470	C₂²×C₁₃	1	2	yes	—
605	#470	C₂²×C₁₃	1	2	yes	—
606	#468	C₂²×C₁₃	1	2	yes	—
607	#468	C₂²×C₁₃	1	2	yes	—
608	#465	C₂²×C₁₃	1	2	yes	—
609	#465	C₂²×C₁₃	1	2	yes	—
610	#464	C₂²×C₁₃	1	2	yes	—
611	#464	C₂²×C₁₃	1	2	yes	—
612	#462	C₂²×C₁₃	1	1	yes	characteristic
613	#462	C₂²×C₁₃	1	1	yes	characteristic
614	#462	C₂²×C₁₃	1	2	yes	—
615	#461	C₂²×C₁₃	1	2	yes	—
616	#460	C₂²×C₁₃	1	1	yes	characteristic
617	#460	C₂²×C₁₃	1	1	yes	characteristic
618	#452	C₂²×C₁₃	1	2	yes	—
619	#452	C₂²×C₁₃	1	2	yes	—
620	#451	C₂²×C₁₃	1	2	yes	—
621	#451	C₂²×C₁₃	1	2	yes	—
622	#448	C₂²×C₁₃	1	2	yes	—
623	#448	C₂²×C₁₃	1	2	yes	—
624	#446	C₂²×C₁₃	1	1	yes	characteristic
625	#446	C₂²×C₁₃	1	1	yes	characteristic
626	#441	C₂²×C₁₃	1	2	yes	—
627	#441	C₂²×C₁₃	1	2	yes	—
628	#440	C₂²×C₁₃	1	2	yes	—
629	#440	C₂²×C₁₃	1	2	yes	—
630	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
631	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
632	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
633	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
634	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
635	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
636	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
637	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
639	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
640	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
641	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
642	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
643	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
644	#436	C₂²×C₁₃	1	1	yes	characteristic
645	#436	C₂²×C₁₃	1	1	yes	characteristic
646	#435	C₂²×C₁₃	1	2	yes	—
647	#435	C₂²×C₁₃	1	2	yes	—
648	#431	C₂²×C₁₃	1	1	yes	characteristic
649	#431	C₂²×C₁₃	1	2	yes	—
650	#428	C₂²×C₁₃	1	2	yes	—
651	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
652	#419	C₂²×C₁₃	1	2	yes	—
653	#417	C₂²×C₁₃	1	2	yes	—
654	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
655	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
656	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
657	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
658	C₂²×C₁₃	—	2	1	no	—
659	C₂²×C₁₃	—	2	1	no	—
660	C₂²×C₁₃	—	2	2	no	—
661	C₂²×C₁₃	—	2	2	no	—
662	C₂²×C₁₃	—	2	2	no	—
663	C₂²×C₁₃	—	4	2	no	—
664	C₂²×C₁₃	—	4	2	no	—
665	C₂²×C₁₃	—	4	2	no	—
666	C₂²×C₁₃	C₂×#137	1	2	yes	—
667	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
668	C₄×C₁₃	—	2	1	no	—
669	C₄×C₁₃	—	2	2	no	—
670	C₄×C₁₃	—	2	1	no	—
671	C₄×C₁₃	—	2	2	no	—
672	C₄×C₁₃	—	2	1	no	—
673	C₄×C₁₃	—	2	2	no	—
674	C₄×C₁₃	—	2	2	no	—
675	C₄×C₁₃	—	2	2	no	—
676	C₄×C₁₃	—	4	1	no	—
677	C₄×C₁₃	—	4	1	no	—
678	C₄×C₁₃	—	4	1	no	—
679	C₄×C₁₃	—	4	1	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	C₂×#137	1	2	yes	—
686	C₄×C₁₃	C₂×#137	1	2	yes	—
687	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
688	C₄×C₁₃	#585	1	1	yes	characteristic
689	C₂×#41	—	2	1	no	—
690	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
691	C₂×#41	C₂³×C₁₃	1	2	yes	—
692	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
693	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
694	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
695	#137	—	2	8	no	—
696	C₂×Q₁₆	—	2	4	no	—
697	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
698	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
699	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
701	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
702	C₂×Q₁₆	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×M₁₆	C₂³×C₁₃	1	2	yes	—
708	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
709	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
711	C₄⋊Q₈	—	2	1	no	—
712	C₄⋊Q₈	—	2	1	no	—
713	C₄⋊Q₈	—	2	2	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
717	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
718	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
719	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
721	#127	—	2	1	no	—
722	#127	C₂³×C₁₃	1	1	yes	characteristic
723	#126	—	2	2	no	—
724	#126	—	2	2	no	—
725	#126	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	1	no	—
728	#125	—	2	2	no	—
729	#125	—	2	1	no	—
730	#125	—	2	2	no	—
731	#125	—	2	2	no	—
732	#125	—	2	1	no	—
733	#125	C₂³×C₁₃	1	2	yes	—
734	#124	—	2	1	no	—
735	#124	—	2	1	no	—
736	#124	—	2	2	no	—
737	#124	—	2	1	no	—
738	#124	C₂³×C₁₃	1	2	yes	—
739	#123	—	2	2	no	—
740	#123	—	2	2	no	—
741	#123	—	2	2	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
754	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
755	#121	—	2	2	no	—
756	#121	—	2	2	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	C₂³×C₁₃	1	2	yes	—
760	#121	C₂³×C₁₃	1	2	yes	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	2	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	—	2	1	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	2	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
779	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
782	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
787	C₄×D₄	—	2	2	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	2	1	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	2	no	—
793	C₄×D₄	—	2	2	no	—
794	C₄×D₄	—	2	1	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	D₄×C₁₃	1	2	yes	—
800	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
801	C₄×D₄	C₂³×C₁₃	1	2	yes	—
802	C₄×D₄	C₂³×C₁₃	1	2	yes	—
803	C₄×D₄	C₂³×C₁₃	1	2	yes	—
804	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
805	#117	—	2	2	no	—
806	#117	—	2	1	no	—
807	#117	—	2	2	no	—
808	#117	—	2	2	no	—
809	#117	D₄×C₁₃	1	1	yes	characteristic
810	#117	D₄×C₁₃	1	2	yes	—
811	#117	C₂³×C₁₃	1	2	yes	—
812	C₂×C₄⋊C₄	—	2	1	no	—
813	C₂×C₄⋊C₄	—	2	1	no	—
814	C₂×C₄⋊C₄	—	2	2	no	—
815	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
816	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
817	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
818	C₂×C₄²	—	2	1	no	—
819	C₂×C₄²	—	2	2	no	—
820	C₂×C₄²	—	2	1	no	—
821	C₂×C₄²	—	2	2	no	—
822	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
823	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
824	#107	C₂³×C₁₃	1	1	yes	characteristic
825	#107	C₂³×C₁₃	1	1	yes	characteristic
826	#107	C₂³×C₁₃	1	1	yes	characteristic
827	#107	C₂³×C₁₃	1	1	yes	characteristic
828	#107	C₂³×C₁₃	1	2	yes	—
829	#107	C₂³×C₁₃	1	2	yes	—
830	#106	C₂³×C₁₃	1	2	yes	—
831	#106	C₂³×C₁₃	1	2	yes	—
832	#106	C₂³×C₁₃	1	2	yes	—
833	#106	C₂³×C₁₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
836	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
837	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
838	#103	C₂³×C₁₃	1	1	yes	characteristic
839	#103	C₂³×C₁₃	1	1	yes	characteristic
840	#103	C₂³×C₁₃	1	1	yes	characteristic
841	#103	C₂³×C₁₃	1	1	yes	characteristic
842	#103	C₂³×C₁₃	1	1	yes	characteristic
843	#103	C₂³×C₁₃	1	1	yes	characteristic
844	#103	C₂³×C₁₃	1	1	yes	characteristic
845	#103	C₂³×C₁₃	1	1	yes	characteristic
846	#103	C₂³×C₁₃	1	2	yes	—
847	#103	C₂³×C₁₃	1	2	yes	—
848	#103	C₂³×C₁₃	1	2	yes	—
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	2	yes	—
853	#103	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	2	yes	—
859	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
860	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
866	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
867	C₄×C₈	C₂³×C₁₃	1	2	yes	—
868	C₂×C₁₃	—	2	2	no	—
869	C₂×C₁₃	—	4	2	no	—
870	C₂×C₁₃	—	8	2	no	—
871	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
872	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
873	C₂×C₁₃	#3584	1	1	yes	characteristic
874	#41	—	2	4	no	—
875	#41	—	2	4	no	—
876	#41	—	4	2	no	—
877	#41	—	4	4	no	—
878	C₂×Q₈	—	2	1	no	—
879	C₂×Q₈	—	2	2	no	—
880	C₂×Q₈	—	2	1	no	—
881	C₂×Q₈	—	2	1	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	2	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	4	no	—
887	C₂×Q₈	—	4	1	no	—
888	C₂×Q₈	—	4	1	no	—
889	C₂×Q₈	—	4	2	no	—
890	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
891	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
893	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
894	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
895	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
896	C₂×D₄	—	2	2	no	—
897	C₂×D₄	—	2	2	no	—
898	C₂×D₄	—	2	2	no	—
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
902	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
903	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	2	1	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	2	no	—
912	C₂²×C₄	—	2	2	no	—
913	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
914	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
915	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
916	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
917	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
919	Q₁₆	—	2	2	no	—
920	Q₁₆	—	2	2	no	—
921	Q₁₆	—	2	4	no	—
922	Q₁₆	—	2	2	no	—
923	Q₁₆	—	4	2	no	—
924	Q₁₆	C₁₃×#41	1	4	yes	complemented
925	SD₁₆	—	2	4	no	—
926	SD₁₆	—	2	4	no	—
927	SD₁₆	—	4	2	no	—
928	SD₁₆	—	4	2	no	—
929	M₁₆	—	2	4	no	—
930	M₁₆	—	4	2	no	—
931	C₂×C₈	—	2	2	no	—
932	C₂×C₈	—	4	1	no	—
933	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
936	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
937	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
938	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	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	2	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	1	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	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
970	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
971	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
973	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
975	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	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	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
989	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
990	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	2	no	—
997	C₄²	—	2	2	no	—
998	C₄²	—	2	1	no	—
999	C₄²	—	2	2	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1005	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1006	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1007	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1008	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1009	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1010	C₄²	C₂⁴×C₁₃	1	2	yes	—
1011	C₁₃	#61440	1	1	yes	characteristic, direct product factor, Sylow
1012	C₂³	—	2	2	no	—
1013	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1014	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	2	1	no	—
1022	Q₈	—	2	2	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	4	4	no	—
1025	Q₈	—	4	2	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	8	1	no	—
1030	Q₈	C₂×C₁₃×#41	1	2	yes	—
1031	Q₈	C₂×C₁₃×#41	1	2	yes	—
1032	D₄	—	2	4	no	—
1033	D₄	—	2	2	no	—
1034	D₄	—	2	2	no	—
1035	D₄	—	2	2	no	—
1036	D₄	—	4	4	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	2	no	—
1039	D₄	—	8	1	no	—
1040	D₄	—	8	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	4	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	2	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	4	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	4	no	—
1063	C₂×C₄	—	4	4	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	8	1	no	—
1066	C₂×C₄	—	8	1	no	—
1067	C₂×C₄	—	8	2	no	—
1068	C₂×C₄	C₁₃×#137	1	4	yes	complemented
1069	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
1073	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₂⁵×C₁₃	1	1	yes	characteristic
1078	C₈	—	2	1	no	—
1079	C₈	—	2	2	no	—
1080	C₈	—	2	1	no	—
1081	C₈	—	2	1	no	—
1082	C₈	—	2	2	no	—
1083	C₈	C₂×C₁₃×#41	1	2	yes	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	2	no	—
1087	C₂²	—	2	2	no	—
1088	C₂²	—	2	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	C₂×C₁₃×#137	1	2	yes	—
1093	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1094	C₄	—	2	2	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	C₂×C₁₃×#137	1	2	yes	—
1112	C₄	C₂×C₁₃×#137	1	2	yes	—
1113	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1114	C₄	C₁₃×#585	1	1	yes	characteristic
1115	C₂	—	2	2	no	—
1116	C₂	—	4	2	no	—
1117	C₂	—	8	2	no	—
1118	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1119	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
1120	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₁₃×#3480	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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×#3387	C₂	semidirect
5. C₁₃×#3375	C₂	semidirect
6. C₁₃×#3374	C₂	semidirect
7. C₁₃×#3356	C₂	semidirect
8. C₁₃×#3346	C₂	semidirect
9. C₁₃×#3333	C₂	semidirect
10. C₁₃×#3328	C₂	semidirect
11. C₁₃×#3320	C₂	semidirect
12. C₁₃×#3316	C₂	semidirect
13. C₁₃×#3278	C₂	semidirect
14. C₁₃×#3270	C₂	semidirect
15. C₁₃×#3172	C₂	semidirect
16. C₁₃×#3167	C₂	semidirect
17. C₁₃×#3108	C₂	semidirect
18. C₁₃×#3107	C₂	semidirect
19. C₁₃×#3104	C₂	semidirect
20. C₁₃×#3103	C₂	semidirect
21. C₁₃×#2965	C₂	semidirect
22. C₄×C₁₃×#137	C₂	semidirect
23. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
314. #61440	C₁₃	direct (N × H)
365. C₁₃×Q₁₆	#41	semidirect
453. Q₈×#41	C₂×C₁₃	semidirect
454. #3400	C₂×C₁₃	semidirect
455. #3387	C₂×C₁₃	semidirect
456. #3375	C₂×C₁₃	semidirect
457. #3374	C₂×C₁₃	semidirect
458. #3356	C₂×C₁₃	semidirect
459. #3346	C₂×C₁₃	semidirect
460. #3333	C₂×C₁₃	semidirect
461. #3328	C₂×C₁₃	semidirect
462. #3320	C₂×C₁₃	semidirect
463. #3316	C₂×C₁₃	semidirect
464. #3278	C₂×C₁₃	semidirect
465. #3270	C₂×C₁₃	semidirect
466. #3172	C₂×C₁₃	semidirect
467. #3167	C₂×C₁₃	semidirect
468. #3108	C₂×C₁₃	semidirect
469. #3107	C₂×C₁₃	semidirect
470. #3104	C₂×C₁₃	semidirect
471. #3103	C₂×C₁₃	semidirect
472. #2965	C₂×C₁₃	semidirect
473. C₄×#137	C₂×C₁₃	semidirect
474. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
531. C₂×C₄×C₁₃	#137	semidirect
924. Q₁₆	C₁₃×#41	semidirect
1011. C₁₃	#61440	direct (N × H)
1068. C₂×C₄	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×#3480	2
Q₈×C₁₃×#41	2
C₁₃×#3400	2
C₁₃×#3387	2
C₁₃×#3375	2
C₁₃×#3374	2
C₁₃×#3356	2
C₁₃×#3346	2
C₁₃×#3333	2
C₁₃×#3328	2
C₁₃×#3320	2
C₁₃×#3316	2
C₁₃×#3278	2
C₁₃×#3270	2
C₁₃×#3172	2
C₁₃×#3167	2
C₁₃×#3108	2
C₁₃×#3107	2
C₁₃×#3104	2
C₁₃×#3103	2
C₁₃×#2965	2
C₄×C₁₃×#137	2
C₂×C₄×C₁₃×Q₁₆	2
#61440	13

Subgroups — C13×#61440 #15747779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61440 #15747779