Subgroups — C₁₃×#61541 #15747880

Order 3328.

1822 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3344	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3331	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3323	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3283	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3185	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3178	C₂	1	2	yes	maximal, complemented
17	C₁₃×#3125	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3120	C₂	1	2	yes	maximal, complemented
19	C₁₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#2952	C₂	1	2	yes	maximal, complemented
23	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#135	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#556	C₂²	1	1	yes	characteristic
28	C₁₃×#554	C₂²	1	2	yes	—
29	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#553	—	2	1	no	—
32	C₁₃×#552	—	2	2	no	—
33	C₁₃×#552	—	2	1	no	—
34	C₁₃×#552	—	2	1	no	—
35	C₁₃×#552	C₂²	1	2	yes	—
36	C₁₃×#551	—	2	2	no	—
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#548	—	2	1	no	—
39	C₁₃×#547	C₂²	1	1	yes	characteristic
40	C₁₃×#547	C₂²	1	2	yes	—
41	C₁₃×#547	C₂²	1	1	yes	characteristic
42	C₁₃×#547	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#546	C₂²	1	2	yes	—
44	C₁₃×#542	C₂²	1	2	yes	—
45	C₁₃×#541	C₂²	1	2	yes	complemented
46	C₁₃×#539	—	2	2	no	—
47	C₁₃×#539	—	2	2	no	—
48	C₁₃×#533	C₂²	1	1	yes	characteristic
49	C₁₃×#533	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	1	no	—
51	C₁₃×#529	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#125	—	2	1	no	—
53	C₁₃×#525	—	2	1	no	—
54	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
55	C₁₃×#520	C₂²	1	2	yes	—
56	C₁₃×#520	C₂²	1	2	yes	complemented
57	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
59	C₁₃×#501	C₂²	1	2	yes	complemented
60	C₁₃×#498	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#497	C₂²	1	2	yes	—
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#488	C₂²	1	2	yes	—
64	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#487	C₂²	1	2	yes	complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#485	C₂²	1	2	yes	—
68	C₁₃×#484	C₂²	1	2	yes	complemented
69	C₁₃×#483	C₂²	1	2	yes	—
70	C₁₃×#483	C₂²	1	2	yes	complemented
71	C₁₃×#483	C₂²	1	2	yes	complemented
72	C₁₃×#481	C₂²	1	2	yes	—
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	2	yes	—
75	C₁₃×#476	C₂²	1	1	yes	characteristic
76	C₁₃×#476	C₂²	1	1	yes	characteristic
77	C₁₃×#476	C₂²	1	2	yes	complemented
78	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#475	C₂²	1	2	yes	complemented
80	C₁₃×#474	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#470	C₂²	1	2	yes	—
82	C₁₃×#470	C₂²	1	2	yes	—
83	C₁₃×#470	C₂²	1	2	yes	complemented
84	C₁₃×#468	C₂²	1	2	yes	—
85	C₁₃×#467	C₂²	1	2	yes	complemented
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	2	yes	—
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#462	C₂²	1	2	yes	complemented
91	C₁₃×#461	C₂²	1	2	yes	—
92	C₁₃×#461	C₂²	1	1	yes	characteristic
93	C₁₃×#461	C₂²	1	1	yes	characteristic
94	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#452	C₂²	1	2	yes	—
96	C₁₃×#452	C₂²	1	2	yes	—
97	C₁₃×#452	C₂²	1	2	yes	—
98	C₁₃×#452	C₂²	1	2	yes	complemented
99	C₁₃×#450	C₂²	1	2	yes	—
100	C₁₃×#449	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
102	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
103	C₁₃×#442	C₂²	1	2	yes	—
104	C₁₃×#442	C₂²	1	1	yes	characteristic
105	C₁₃×#442	C₂²	1	1	yes	characteristic
106	C₁₃×#441	C₂²	1	2	yes	complemented
107	C₁₃×#441	C₂²	1	2	yes	complemented
108	C₁₃×#441	C₂²	1	2	yes	complemented
109	C₁₃×#440	C₂²	1	1	yes	characteristic
110	C₁₃×#440	C₂²	1	1	yes	characteristic
111	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
112	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
115	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
116	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
117	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
118	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
119	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
120	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
121	C₁₃×#436	C₂²	1	2	yes	—
122	C₁₃×#436	C₂²	1	1	yes	characteristic, complemented
123	C₁₃×#435	C₂²	1	2	yes	—
124	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
125	C₁₃×#433	C₂²	1	2	yes	complemented
126	C₁₃×#431	C₂²	1	1	yes	characteristic
127	C₁₃×#428	C₂²	1	1	yes	characteristic
128	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
129	C₁₃×#418	C₂²	1	1	yes	characteristic
130	C₁₃×#417	C₂²	1	2	yes	—
131	C₁₃×#417	C₂²	1	1	yes	characteristic
132	C₁₃×#417	C₂²	1	2	yes	complemented
133	C₁₃×#405	C₂²	1	2	yes	complemented
134	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
135	C₂×C₁₃×#41	—	2	1	no	—
136	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
137	C₂×C₁₃×#41	C₂³	1	2	yes	—
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	—	2	1	no	—
140	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₁₃	—	2	1	no	—
142	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
143	C₁₃×#135	—	2	8	no	—
144	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
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×D₈	C₂³	1	1	yes	characteristic
153	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
157	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	2	no	—
166	C₁₃×#126	—	2	2	no	—
167	C₁₃×#126	—	2	2	no	—
168	C₁₃×#126	—	2	2	no	—
169	C₁₃×#126	D₄	1	2	yes	—
170	C₁₃×#125	—	2	2	no	—
171	C₁₃×#125	—	2	2	no	—
172	C₁₃×#125	—	2	1	no	—
173	C₁₃×#125	—	2	1	no	—
174	C₁₃×#125	—	2	2	no	—
175	C₁₃×#125	—	2	2	no	—
176	C₁₃×#125	—	2	2	no	—
177	C₁₃×#125	—	2	1	no	—
178	C₁₃×#125	—	2	1	no	—
179	C₁₃×#125	D₄	1	1	yes	characteristic
180	C₁₃×#125	C₂³	1	2	yes	—
181	C₁₃×#124	—	2	2	no	—
182	C₁₃×#124	D₄	1	1	yes	characteristic
183	C₁₃×#124	C₂³	1	2	yes	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	—	2	2	no	—
188	C₁₃×#123	—	2	2	no	—
189	C₁₃×#123	—	2	2	no	—
190	C₁₃×#123	—	2	2	no	—
191	C₁₃×#123	—	2	2	no	—
192	C₁₃×#123	D₄	1	2	yes	—
193	C₁₃×C₂²⋊Q₈	—	2	1	no	—
194	C₁₃×C₂²⋊Q₈	—	2	1	no	—
195	C₁₃×C₂²⋊Q₈	—	2	1	no	—
196	C₁₃×C₂²⋊Q₈	—	2	1	no	—
197	C₁₃×C₂²⋊Q₈	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	1	no	—
199	C₁₃×C₂²⋊Q₈	—	2	1	no	—
200	C₁₃×C₂²⋊Q₈	—	2	2	no	—
201	C₁₃×C₂²⋊Q₈	—	2	2	no	—
202	C₁₃×C₂²⋊Q₈	—	2	2	no	—
203	C₁₃×C₂²⋊Q₈	—	2	2	no	—
204	C₁₃×C₂²⋊Q₈	—	2	2	no	—
205	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
206	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₁₃×#121	—	2	1	no	—
212	C₁₃×#121	—	2	1	no	—
213	C₁₃×#121	—	2	2	no	—
214	C₁₃×#121	—	2	2	no	—
215	C₁₃×#121	D₄	1	1	yes	characteristic
216	C₁₃×#121	C₂³	1	2	yes	—
217	C₁₃×#120	—	2	2	no	—
218	C₄×Q₈×C₁₃	—	2	1	no	—
219	C₄×Q₈×C₁₃	—	2	1	no	—
220	C₄×Q₈×C₁₃	—	2	1	no	—
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×D₄×C₁₃	—	2	2	no	—
229	C₄×D₄×C₁₃	—	2	1	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	2	no	—
233	C₄×D₄×C₁₃	—	2	2	no	—
234	C₄×D₄×C₁₃	—	2	2	no	—
235	C₄×D₄×C₁₃	—	2	2	no	—
236	C₄×D₄×C₁₃	—	2	1	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₃	C₂³	1	2	yes	—
244	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
245	C₄×D₄×C₁₃	C₂³	1	2	yes	—
246	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
247	C₄×D₄×C₁₃	C₂³	1	2	yes	—
248	C₁₃×#117	—	2	1	no	—
249	C₁₃×#117	—	2	1	no	—
250	C₁₃×#117	—	2	2	no	—
251	C₁₃×#117	—	2	2	no	—
252	C₁₃×#117	—	2	1	no	—
253	C₁₃×#117	—	2	2	no	—
254	C₁₃×#117	—	2	1	no	—
255	C₁₃×#117	C₂³	1	1	yes	characteristic
256	C₁₃×#117	C₂³	1	2	yes	—
257	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
264	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
265	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
266	C₂×C₁₃×C₂²⋊C₄	—	2	1	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	1	yes	characteristic
271	C₁₃×#107	C₂³	1	1	yes	characteristic
272	C₁₃×#107	C₂³	1	2	yes	—
273	C₁₃×#106	C₂³	1	1	yes	characteristic
274	C₁₃×#106	C₂³	1	2	yes	—
275	C₁₃×#106	C₂³	1	2	yes	—
276	C₁₃×#106	C₂³	1	2	yes	—
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	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×#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×#103	C₂³	1	2	yes	—
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	1	yes	characteristic
301	C₁₃×#102	C₂³	1	1	yes	characteristic
302	C₁₃×#102	C₂³	1	1	yes	characteristic
303	C₁₃×#102	C₂³	1	2	yes	—
304	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₁₃×#97	C₂³	1	1	yes	characteristic
308	C₁₃×#97	C₂³	1	1	yes	characteristic
309	C₁₃×#97	C₂³	1	2	yes	—
310	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₁₃	C₂³	1	2	yes	—
313	C₄×C₈×C₁₃	C₂³	1	2	yes	—
314	#61541	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
315	C₂⁴×C₁₃	—	2	1	no	—
316	C₁₃×#41	—	2	4	no	—
317	C₁₃×#41	—	2	4	no	—
318	C₁₃×#41	—	2	2	no	—
319	C₁₃×#41	—	4	1	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	4	2	no	—
322	C₁₃×#41	—	8	2	no	—
323	C₂×Q₈×C₁₃	—	2	1	no	—
324	C₂×Q₈×C₁₃	—	2	1	no	—
325	C₂×Q₈×C₁₃	—	2	2	no	—
326	C₂×Q₈×C₁₃	—	8	2	no	—
327	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
328	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
329	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
331	C₂×D₄×C₁₃	—	2	2	no	—
332	C₂×D₄×C₁₃	—	2	2	no	—
333	C₂×D₄×C₁₃	—	2	1	no	—
334	C₂×D₄×C₁₃	—	2	2	no	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	1	no	—
337	C₂×D₄×C₁₃	—	4	1	no	—
338	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
340	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
342	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₁₃	—	2	1	no	—
344	C₂²×C₄×C₁₃	—	2	2	no	—
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	1	no	—
347	C₂²×C₄×C₁₃	—	2	1	no	—
348	C₂²×C₄×C₁₃	—	2	2	no	—
349	C₂²×C₄×C₁₃	—	2	2	no	—
350	C₂²×C₄×C₁₃	—	2	1	no	—
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	2	no	—
355	C₂²×C₄×C₁₃	—	2	1	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	8	2	no	—
358	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
359	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
360	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
362	C₁₃×Q₁₆	—	2	4	no	—
363	C₁₃×Q₁₆	—	4	2	no	—
364	C₁₃×Q₁₆	—	4	2	no	—
365	C₁₃×SD₁₆	—	2	4	no	—
366	C₁₃×SD₁₆	—	2	4	no	—
367	C₁₃×SD₁₆	—	2	2	no	—
368	C₁₃×SD₁₆	—	2	2	no	—
369	C₁₃×SD₁₆	—	4	2	no	—
370	C₁₃×D₈	—	2	2	no	—
371	C₁₃×D₈	#41	1	4	yes	complemented
372	C₁₃×M₁₆	—	2	2	no	—
373	C₁₃×M₁₆	—	4	2	no	—
374	C₁₃×M₁₆	—	4	1	no	—
375	C₂×C₈×C₁₃	—	2	4	no	—
376	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
378	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
379	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
380	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
382	C₁₃×C₄⋊C₄	—	2	2	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	1	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
397	C₁₃×C₄⋊C₄	—	2	1	no	—
398	C₁₃×C₄⋊C₄	—	2	1	no	—
399	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
406	C₁₃×C₄⋊C₄	—	2	2	no	—
407	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
409	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
414	C₁₃×C₄⋊C₄	C₂⁴	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	1	yes	characteristic
418	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
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	2	no	—
424	C₁₃×C₂²⋊C₄	—	2	2	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	1	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	2	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	1	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	2	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₁₃	C₂⁴	1	2	yes	—
453	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
454	#3515	C₂×C₁₃	1	1	yes	characteristic, complemented
455	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
456	#3384	C₂×C₁₃	1	1	yes	characteristic, complemented
457	#3360	C₂×C₁₃	1	1	yes	characteristic, complemented
458	#3359	C₂×C₁₃	1	1	yes	characteristic, complemented
459	#3344	C₂×C₁₃	1	2	yes	complemented
460	#3335	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3331	C₂×C₁₃	1	2	yes	complemented
462	#3331	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3323	C₂×C₁₃	1	2	yes	complemented
465	#3283	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3267	C₂×C₁₃	1	2	yes	complemented
467	#3185	C₂×C₁₃	1	1	yes	characteristic, complemented
468	#3178	C₂×C₁₃	1	2	yes	complemented
469	#3125	C₂×C₁₃	1	2	yes	complemented
470	#3120	C₂×C₁₃	1	2	yes	complemented
471	#3107	C₂×C₁₃	1	1	yes	characteristic, complemented
472	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
473	#2969	C₂×C₁₃	1	1	yes	characteristic, complemented
474	#2952	C₂×C₁₃	1	2	yes	complemented
475	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
476	C₂³×C₁₃	—	2	1	no	—
477	C₂³×C₁₃	—	2	1	no	—
478	C₂³×C₁₃	—	2	1	no	—
479	C₂³×C₁₃	—	4	2	no	—
480	C₂³×C₁₃	—	4	2	no	—
481	C₂³×C₁₃	—	8	1	no	—
482	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
483	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
484	Q₈×C₁₃	—	2	2	no	—
485	Q₈×C₁₃	—	2	1	no	—
486	Q₈×C₁₃	—	2	2	no	—
487	Q₈×C₁₃	—	2	2	no	—
488	Q₈×C₁₃	—	2	2	no	—
489	Q₈×C₁₃	—	2	2	no	—
490	Q₈×C₁₃	—	2	1	no	—
491	Q₈×C₁₃	—	4	2	no	—
492	Q₈×C₁₃	—	8	1	no	—
493	Q₈×C₁₃	—	8	2	no	—
494	D₄×C₁₃	—	2	2	no	—
495	D₄×C₁₃	—	2	1	no	—
496	D₄×C₁₃	—	2	1	no	—
497	D₄×C₁₃	—	2	1	no	—
498	D₄×C₁₃	—	2	1	no	—
499	D₄×C₁₃	—	4	2	no	—
500	D₄×C₁₃	—	4	2	no	—
501	D₄×C₁₃	—	4	4	no	—
502	D₄×C₁₃	—	4	4	no	—
503	D₄×C₁₃	—	4	2	no	—
504	D₄×C₁₃	—	8	2	no	—
505	D₄×C₁₃	C₂×#41	1	2	yes	—
506	D₄×C₁₃	C₂×#41	1	2	yes	—
507	C₂×C₄×C₁₃	—	2	2	no	—
508	C₂×C₄×C₁₃	—	2	2	no	—
509	C₂×C₄×C₁₃	—	2	1	no	—
510	C₂×C₄×C₁₃	—	2	1	no	—
511	C₂×C₄×C₁₃	—	2	2	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	1	no	—
516	C₂×C₄×C₁₃	—	2	2	no	—
517	C₂×C₄×C₁₃	—	2	1	no	—
518	C₂×C₄×C₁₃	—	2	2	no	—
519	C₂×C₄×C₁₃	—	2	2	no	—
520	C₂×C₄×C₁₃	—	2	1	no	—
521	C₂×C₄×C₁₃	—	4	1	no	—
522	C₂×C₄×C₁₃	—	4	4	no	—
523	C₂×C₄×C₁₃	—	4	4	no	—
524	C₂×C₄×C₁₃	—	4	2	no	—
525	C₂×C₄×C₁₃	—	4	2	no	—
526	C₂×C₄×C₁₃	—	4	2	no	—
527	C₂×C₄×C₁₃	—	4	2	no	—
528	C₂×C₄×C₁₃	—	8	1	no	—
529	C₂×C₄×C₁₃	—	8	2	no	—
530	C₂×C₄×C₁₃	—	8	1	no	—
531	C₂×C₄×C₁₃	—	8	1	no	—
532	C₂×C₄×C₁₃	—	8	2	no	—
533	C₂×C₄×C₁₃	—	8	2	no	—
534	C₂×C₄×C₁₃	—	8	1	no	—
535	C₂×C₄×C₁₃	—	8	2	no	—
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	2	yes	—
540	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
541	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
545	C₈×C₁₃	—	2	2	no	—
546	C₈×C₁₃	—	2	1	no	—
547	C₈×C₁₃	—	2	1	no	—
548	C₈×C₁₃	—	2	2	no	—
549	C₈×C₁₃	—	2	1	no	—
550	C₈×C₁₃	C₂×#41	1	2	yes	—
551	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
552	C₂×#135	C₂²×C₁₃	1	2	yes	—
553	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
554	#556	C₂²×C₁₃	1	1	yes	characteristic
555	#554	C₂²×C₁₃	1	2	yes	—
556	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
557	#554	C₂²×C₁₃	1	1	yes	characteristic, complemented
558	#553	—	2	1	no	—
559	#552	—	2	2	no	—
560	#552	—	2	1	no	—
561	#552	—	2	1	no	—
562	#552	C₂²×C₁₃	1	2	yes	—
563	#551	—	2	2	no	—
564	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
565	#548	—	2	1	no	—
566	#547	C₂²×C₁₃	1	2	yes	—
567	#547	C₂²×C₁₃	1	1	yes	characteristic
568	#547	C₂²×C₁₃	1	1	yes	characteristic
569	#547	C₂²×C₁₃	1	1	yes	characteristic, complemented
570	#546	C₂²×C₁₃	1	2	yes	—
571	#542	C₂²×C₁₃	1	2	yes	—
572	#541	C₂²×C₁₃	1	2	yes	complemented
573	#539	—	2	2	no	—
574	#539	—	2	2	no	—
575	#533	C₂²×C₁₃	1	1	yes	characteristic
576	#533	C₂²×C₁₃	1	1	yes	characteristic
577	#529	—	2	1	no	—
578	#529	C₂²×C₁₃	1	1	yes	characteristic
579	C₂×#125	—	2	1	no	—
580	#525	—	2	1	no	—
581	C₂×C₂²⋊Q₈	—	2	1	no	—
582	#520	C₂²×C₁₃	1	2	yes	—
583	#520	C₂²×C₁₃	1	2	yes	complemented
584	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
586	#501	C₂²×C₁₃	1	2	yes	complemented
587	#498	C₂²×C₁₃	1	1	yes	characteristic, complemented
588	#497	C₂²×C₁₃	1	2	yes	—
589	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
590	#488	C₂²×C₁₃	1	2	yes	—
591	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
592	#487	C₂²×C₁₃	1	2	yes	complemented
593	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
594	#485	C₂²×C₁₃	1	2	yes	—
595	#484	C₂²×C₁₃	1	2	yes	complemented
596	#483	C₂²×C₁₃	1	2	yes	—
597	#483	C₂²×C₁₃	1	2	yes	complemented
598	#483	C₂²×C₁₃	1	2	yes	complemented
599	#481	C₂²×C₁₃	1	2	yes	—
600	#479	C₂²×C₁₃	1	2	yes	complemented
601	#478	C₂²×C₁₃	1	2	yes	—
602	#476	C₂²×C₁₃	1	1	yes	characteristic
603	#476	C₂²×C₁₃	1	1	yes	characteristic
604	#476	C₂²×C₁₃	1	2	yes	complemented
605	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
606	#475	C₂²×C₁₃	1	2	yes	complemented
607	#474	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#470	C₂²×C₁₃	1	2	yes	—
609	#470	C₂²×C₁₃	1	2	yes	—
610	#470	C₂²×C₁₃	1	2	yes	complemented
611	#468	C₂²×C₁₃	1	2	yes	—
612	#467	C₂²×C₁₃	1	2	yes	complemented
613	#465	C₂²×C₁₃	1	2	yes	—
614	#464	C₂²×C₁₃	1	2	yes	—
615	#463	C₂²×C₁₃	1	2	yes	—
616	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
617	#462	C₂²×C₁₃	1	2	yes	complemented
618	#461	C₂²×C₁₃	1	1	yes	characteristic
619	#461	C₂²×C₁₃	1	1	yes	characteristic
620	#461	C₂²×C₁₃	1	2	yes	—
621	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
622	#452	C₂²×C₁₃	1	2	yes	—
623	#452	C₂²×C₁₃	1	2	yes	—
624	#452	C₂²×C₁₃	1	2	yes	—
625	#452	C₂²×C₁₃	1	2	yes	complemented
626	#450	C₂²×C₁₃	1	2	yes	—
627	#449	C₂²×C₁₃	1	2	yes	—
628	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
629	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
630	#442	C₂²×C₁₃	1	1	yes	characteristic
631	#442	C₂²×C₁₃	1	2	yes	—
632	#442	C₂²×C₁₃	1	1	yes	characteristic
633	#441	C₂²×C₁₃	1	2	yes	complemented
634	#441	C₂²×C₁₃	1	2	yes	complemented
635	#441	C₂²×C₁₃	1	2	yes	complemented
636	#440	C₂²×C₁₃	1	1	yes	characteristic
637	#440	C₂²×C₁₃	1	1	yes	characteristic
638	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
639	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
640	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
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	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
645	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
646	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
647	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
648	#436	C₂²×C₁₃	1	2	yes	—
649	#436	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#435	C₂²×C₁₃	1	2	yes	—
651	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
652	#433	C₂²×C₁₃	1	2	yes	complemented
653	#431	C₂²×C₁₃	1	1	yes	characteristic
654	#428	C₂²×C₁₃	1	1	yes	characteristic
655	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
656	#418	C₂²×C₁₃	1	1	yes	characteristic
657	#417	C₂²×C₁₃	1	1	yes	characteristic
658	#417	C₂²×C₁₃	1	2	yes	—
659	#417	C₂²×C₁₃	1	2	yes	complemented
660	#405	C₂²×C₁₃	1	2	yes	complemented
661	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
662	C₂²×C₁₃	—	2	1	no	—
663	C₂²×C₁₃	—	2	2	no	—
664	C₂²×C₁₃	—	2	2	no	—
665	C₂²×C₁₃	—	2	1	no	—
666	C₂²×C₁₃	—	2	2	no	—
667	C₂²×C₁₃	—	2	2	no	—
668	C₂²×C₁₃	—	2	1	no	—
669	C₂²×C₁₃	—	2	2	no	—
670	C₂²×C₁₃	—	4	1	no	—
671	C₂²×C₁₃	—	4	1	no	—
672	C₂²×C₁₃	—	4	1	no	—
673	C₂²×C₁₃	—	4	1	no	—
674	C₂²×C₁₃	—	4	1	no	—
675	C₂²×C₁₃	—	4	1	no	—
676	C₂²×C₁₃	—	4	1	no	—
677	C₂²×C₁₃	—	8	4	no	—
678	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
679	C₄×C₁₃	—	2	1	no	—
680	C₄×C₁₃	—	2	1	no	—
681	C₄×C₁₃	—	2	2	no	—
682	C₄×C₁₃	—	2	2	no	—
683	C₄×C₁₃	—	2	1	no	—
684	C₄×C₁₃	—	2	1	no	—
685	C₄×C₁₃	—	2	2	no	—
686	C₄×C₁₃	—	4	1	no	—
687	C₄×C₁₃	—	4	2	no	—
688	C₄×C₁₃	—	4	2	no	—
689	C₄×C₁₃	—	4	1	no	—
690	C₄×C₁₃	—	4	2	no	—
691	C₄×C₁₃	—	4	1	no	—
692	C₄×C₁₃	—	4	1	no	—
693	C₄×C₁₃	—	4	1	no	—
694	C₄×C₁₃	—	4	2	no	—
695	C₄×C₁₃	#577	1	2	yes	—
696	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
697	C₄×C₁₃	#585	1	1	yes	characteristic
698	C₂×#41	—	2	1	no	—
699	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
700	C₂×#41	C₂³×C₁₃	1	2	yes	—
701	C₂×#41	C₂³×C₁₃	1	2	yes	—
702	C₂²×Q₈	—	2	1	no	—
703	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
704	C₂³×C₄	—	2	1	no	—
705	AGL(1,ℤ/8)	—	2	4	no	—
706	#135	—	2	8	no	—
707	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
708	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
709	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
710	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
711	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
712	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
713	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
715	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
716	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
717	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
718	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
719	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
724	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
725	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
726	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
727	#126	—	2	2	no	—
728	#126	—	2	2	no	—
729	#126	—	2	2	no	—
730	#126	—	2	2	no	—
731	#126	—	2	2	no	—
732	#126	D₄×C₁₃	1	2	yes	—
733	#125	—	2	2	no	—
734	#125	—	2	2	no	—
735	#125	—	2	1	no	—
736	#125	—	2	1	no	—
737	#125	—	2	2	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	1	no	—
742	#125	D₄×C₁₃	1	1	yes	characteristic
743	#125	C₂³×C₁₃	1	2	yes	—
744	#124	—	2	2	no	—
745	#124	D₄×C₁₃	1	1	yes	characteristic
746	#124	C₂³×C₁₃	1	2	yes	—
747	#123	—	2	2	no	—
748	#123	—	2	2	no	—
749	#123	—	2	2	no	—
750	#123	—	2	2	no	—
751	#123	—	2	2	no	—
752	#123	—	2	2	no	—
753	#123	—	2	2	no	—
754	#123	—	2	2	no	—
755	#123	D₄×C₁₃	1	2	yes	—
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	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
769	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
771	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
772	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
773	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
774	#121	—	2	1	no	—
775	#121	—	2	1	no	—
776	#121	—	2	2	no	—
777	#121	—	2	2	no	—
778	#121	D₄×C₁₃	1	1	yes	characteristic
779	#121	C₂³×C₁₃	1	2	yes	—
780	#120	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	1	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
786	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
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	C₂³×C₁₃	1	1	yes	characteristic
802	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
810	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	2	no	—
814	#117	—	2	2	no	—
815	#117	—	2	1	no	—
816	#117	—	2	2	no	—
817	#117	—	2	1	no	—
818	#117	C₂³×C₁₃	1	1	yes	characteristic
819	#117	C₂³×C₁₃	1	2	yes	—
820	C₂×C₄⋊C₄	—	2	2	no	—
821	C₂×C₄⋊C₄	—	2	2	no	—
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	2	no	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	—	2	1	no	—
826	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
828	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
829	C₂×C₂²⋊C₄	—	2	1	no	—
830	C₂×C₂²⋊C₄	—	2	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
833	#107	C₂³×C₁₃	1	1	yes	characteristic
834	#107	C₂³×C₁₃	1	1	yes	characteristic
835	#107	C₂³×C₁₃	1	2	yes	—
836	#106	C₂³×C₁₃	1	1	yes	characteristic
837	#106	C₂³×C₁₃	1	2	yes	—
838	#106	C₂³×C₁₃	1	2	yes	—
839	#106	C₂³×C₁₃	1	2	yes	—
840	#106	C₂³×C₁₃	1	1	yes	characteristic
841	#106	C₂³×C₁₃	1	2	yes	—
842	#106	C₂³×C₁₃	1	2	yes	—
843	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
844	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
845	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
846	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
847	#103	C₂³×C₁₃	1	1	yes	characteristic
848	#103	C₂³×C₁₃	1	1	yes	characteristic
849	#103	C₂³×C₁₃	1	2	yes	—
850	#103	C₂³×C₁₃	1	2	yes	—
851	#103	C₂³×C₁₃	1	2	yes	—
852	#103	C₂³×C₁₃	1	2	yes	—
853	#103	C₂³×C₁₃	1	2	yes	—
854	#103	C₂³×C₁₃	1	2	yes	—
855	#103	C₂³×C₁₃	1	2	yes	—
856	#103	C₂³×C₁₃	1	2	yes	—
857	#103	C₂³×C₁₃	1	2	yes	—
858	#102	C₂³×C₁₃	1	1	yes	characteristic
859	#102	C₂³×C₁₃	1	1	yes	characteristic
860	#102	C₂³×C₁₃	1	1	yes	characteristic
861	#102	C₂³×C₁₃	1	2	yes	—
862	#102	C₂³×C₁₃	1	2	yes	—
863	#102	C₂³×C₁₃	1	1	yes	characteristic
864	#102	C₂³×C₁₃	1	1	yes	characteristic
865	#102	C₂³×C₁₃	1	1	yes	characteristic
866	#102	C₂³×C₁₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
870	#97	C₂³×C₁₃	1	1	yes	characteristic
871	#97	C₂³×C₁₃	1	1	yes	characteristic
872	#97	C₂³×C₁₃	1	2	yes	—
873	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
874	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
875	C₄×C₈	C₂³×C₁₃	1	2	yes	—
876	C₄×C₈	C₂³×C₁₃	1	2	yes	—
877	C₂×C₁₃	—	4	2	no	—
878	C₂×C₁₃	—	4	1	no	—
879	C₂×C₁₃	—	4	2	no	—
880	C₂×C₁₃	—	4	2	no	—
881	C₂×C₁₃	—	8	1	no	—
882	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
883	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
884	C₂×C₁₃	#3586	1	1	yes	characteristic
885	C₂⁴	—	2	1	no	—
886	#41	—	2	4	no	—
887	#41	—	2	4	no	—
888	#41	—	2	2	no	—
889	#41	—	4	1	no	—
890	#41	—	4	2	no	—
891	#41	—	4	2	no	—
892	#41	—	8	2	no	—
893	C₂×Q₈	—	2	1	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	8	2	no	—
897	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
899	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
900	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
901	C₂×D₄	—	2	2	no	—
902	C₂×D₄	—	2	2	no	—
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	4	1	no	—
908	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
909	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
910	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
911	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	1	no	—
917	C₂²×C₄	—	2	1	no	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	1	no	—
926	C₂²×C₄	—	2	1	no	—
927	C₂²×C₄	—	8	2	no	—
928	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
929	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
930	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
931	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
932	Q₁₆	—	2	4	no	—
933	Q₁₆	—	4	2	no	—
934	Q₁₆	—	4	2	no	—
935	SD₁₆	—	2	4	no	—
936	SD₁₆	—	2	4	no	—
937	SD₁₆	—	2	2	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	4	2	no	—
940	D₈	—	2	2	no	—
941	D₈	C₁₃×#41	1	4	yes	complemented
942	M₁₆	—	2	2	no	—
943	M₁₆	—	4	2	no	—
944	M₁₆	—	4	1	no	—
945	C₂×C₈	—	2	4	no	—
946	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
947	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
948	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
950	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
951	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	2	2	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
979	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
980	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
982	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
983	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
985	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	2	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1009	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1010	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	2	2	no	—
1017	C₄²	—	2	2	no	—
1018	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1019	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1020	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1021	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1022	C₄²	C₂⁴×C₁₃	1	2	yes	—
1023	C₁₃	#61541	1	1	yes	characteristic, direct product factor, Sylow
1024	C₂³	—	2	1	no	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	2	no	—
1029	C₂³	—	8	1	no	—
1030	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1031	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1032	Q₈	—	2	2	no	—
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	4	2	no	—
1040	Q₈	—	8	2	no	—
1041	Q₈	—	8	1	no	—
1042	D₄	—	2	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	2	1	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	4	2	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	4	no	—
1050	D₄	—	4	4	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	8	2	no	—
1053	D₄	C₂×C₁₃×#41	1	2	yes	—
1054	D₄	C₂×C₁₃×#41	1	2	yes	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	1	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	4	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	2	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	8	1	no	—
1077	C₂×C₄	—	8	1	no	—
1078	C₂×C₄	—	8	1	no	—
1079	C₂×C₄	—	8	2	no	—
1080	C₂×C₄	—	8	2	no	—
1081	C₂×C₄	—	8	1	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1088	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1089	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1090	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1091	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1092	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1093	C₈	—	2	2	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	C₂×C₁₃×#41	1	2	yes	—
1099	C₂²	—	2	1	no	—
1100	C₂²	—	2	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	1	no	—
1112	C₂²	—	4	1	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	—	8	4	no	—
1115	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	2	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	2	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	2	no	—
1132	C₄	C₁₃×#577	1	2	yes	—
1133	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
1134	C₄	C₁₃×#585	1	1	yes	characteristic
1135	C₂	—	4	1	no	—
1136	C₂	—	4	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
1141	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1142	C₂	C₁₃×#3586	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3520	C₂	semidirect
2. C₁₃×#3515	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3384	C₂	semidirect
5. C₁₃×#3360	C₂	semidirect
6. C₁₃×#3359	C₂	semidirect
7. C₁₃×#3344	C₂	semidirect
8. C₁₃×#3335	C₂	semidirect
9. C₁₃×#3331	C₂	semidirect
10. C₁₃×#3331	C₂	semidirect
11. C₁₃×#3330	C₂	semidirect
12. C₁₃×#3323	C₂	semidirect
13. C₁₃×#3283	C₂	semidirect
14. C₁₃×#3267	C₂	semidirect
15. C₁₃×#3185	C₂	semidirect
16. C₁₃×#3178	C₂	semidirect
17. C₁₃×#3125	C₂	semidirect
18. C₁₃×#3120	C₂	semidirect
19. C₁₃×#3107	C₂	semidirect
20. C₁₃×#3101	C₂	semidirect
21. C₁₃×#2969	C₂	semidirect
22. C₁₃×#2952	C₂	semidirect
23. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
26. C₁₃×#557	C₂²	semidirect
29. C₁₃×#554	C₂²	semidirect
30. C₁₃×#554	C₂²	semidirect
42. C₁₃×#547	C₂²	semidirect
45. C₁₃×#541	C₂²	semidirect
56. C₁₃×#520	C₂²	semidirect
59. C₁₃×#501	C₂²	semidirect
60. C₁₃×#498	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
64. C₁₃×#487	C₂²	semidirect
65. C₁₃×#487	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
68. C₁₃×#484	C₂²	semidirect
70. C₁₃×#483	C₂²	semidirect
71. C₁₃×#483	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#475	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
80. C₁₃×#474	C₂²	semidirect
83. C₁₃×#470	C₂²	semidirect
85. C₁₃×#467	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
94. C₁₃×#461	C₂²	semidirect
98. C₁₃×#452	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₈×Q₈×C₁₃	C₂²	semidirect
106. C₁₃×#441	C₂²	semidirect
107. C₁₃×#441	C₂²	semidirect
108. C₁₃×#441	C₂²	semidirect
111. C₄×C₁₃×Q₁₆	C₂²	semidirect
117. C₄×C₁₃×SD₁₆	C₂²	semidirect
118. C₄×C₁₃×SD₁₆	C₂²	semidirect
122. C₁₃×#436	C₂²	semidirect
124. C₈×D₄×C₁₃	C₂²	semidirect
125. C₁₃×#433	C₂²	semidirect
128. C₂×C₁₃×#106	C₂²	semidirect
132. C₁₃×#417	C₂²	semidirect
133. C₁₃×#405	C₂²	semidirect
314. #61541	C₁₃	direct (N × H)
371. C₁₃×D₈	#41	semidirect
453. #3520	C₂×C₁₃	semidirect
454. #3515	C₂×C₁₃	semidirect
455. #3398	C₂×C₁₃	semidirect
456. #3384	C₂×C₁₃	semidirect
457. #3360	C₂×C₁₃	semidirect
458. #3359	C₂×C₁₃	semidirect
459. #3344	C₂×C₁₃	semidirect
460. #3335	C₂×C₁₃	semidirect
461. #3331	C₂×C₁₃	semidirect
462. #3331	C₂×C₁₃	semidirect
463. #3330	C₂×C₁₃	semidirect
464. #3323	C₂×C₁₃	semidirect
465. #3283	C₂×C₁₃	semidirect
466. #3267	C₂×C₁₃	semidirect
467. #3185	C₂×C₁₃	semidirect
468. #3178	C₂×C₁₃	semidirect
469. #3125	C₂×C₁₃	semidirect
470. #3120	C₂×C₁₃	semidirect
471. #3107	C₂×C₁₃	semidirect
472. #3101	C₂×C₁₃	semidirect
473. #2969	C₂×C₁₃	semidirect
474. #2952	C₂×C₁₃	semidirect
475. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
553. #557	C₂²×C₁₃	semidirect
556. #554	C₂²×C₁₃	semidirect
557. #554	C₂²×C₁₃	semidirect
569. #547	C₂²×C₁₃	semidirect
572. #541	C₂²×C₁₃	semidirect
583. #520	C₂²×C₁₃	semidirect
586. #501	C₂²×C₁₃	semidirect
587. #498	C₂²×C₁₃	semidirect
589. #494	C₂²×C₁₃	semidirect
591. #487	C₂²×C₁₃	semidirect
592. #487	C₂²×C₁₃	semidirect
593. #487	C₂²×C₁₃	semidirect
595. #484	C₂²×C₁₃	semidirect
597. #483	C₂²×C₁₃	semidirect
598. #483	C₂²×C₁₃	semidirect
600. #479	C₂²×C₁₃	semidirect
604. #476	C₂²×C₁₃	semidirect
605. #475	C₂²×C₁₃	semidirect
606. #475	C₂²×C₁₃	semidirect
607. #474	C₂²×C₁₃	semidirect
610. #470	C₂²×C₁₃	semidirect
612. #467	C₂²×C₁₃	semidirect
616. #462	C₂²×C₁₃	semidirect
617. #462	C₂²×C₁₃	semidirect
621. #461	C₂²×C₁₃	semidirect
625. #452	C₂²×C₁₃	semidirect
628. #446	C₂²×C₁₃	semidirect
629. C₈×Q₈	C₂²×C₁₃	semidirect
633. #441	C₂²×C₁₃	semidirect
634. #441	C₂²×C₁₃	semidirect
635. #441	C₂²×C₁₃	semidirect
638. C₄×Q₁₆	C₂²×C₁₃	semidirect
644. C₄×SD₁₆	C₂²×C₁₃	semidirect
645. C₄×SD₁₆	C₂²×C₁₃	semidirect
649. #436	C₂²×C₁₃	semidirect
651. C₈×D₄	C₂²×C₁₃	semidirect
652. #433	C₂²×C₁₃	semidirect
655. C₂×#106	C₂²×C₁₃	semidirect
659. #417	C₂²×C₁₃	semidirect
660. #405	C₂²×C₁₃	semidirect
941. D₈	C₁₃×#41	semidirect
1023. C₁₃	#61541	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×#3520	2
C₁₃×#3515	2
C₁₃×#3398	2
C₁₃×#3384	2
C₁₃×#3360	2
C₁₃×#3359	2
C₁₃×#3344	2
C₁₃×#3335	2
C₁₃×#3331	2
C₁₃×#3330	2
C₁₃×#3323	2
C₁₃×#3283	2
C₁₃×#3267	2
C₁₃×#3185	2
C₁₃×#3178	2
C₁₃×#3125	2
C₁₃×#3120	2
C₁₃×#3107	2
C₁₃×#3101	2
C₁₃×#2969	2
C₁₃×#2952	2
C₄×C₁₃×AGL(1,ℤ/8)	2
#61541	13

Subgroups — C13×#61541 #15747880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61541 #15747880