Subgroups — C₁₃×#61973 #15748312

Order 3328.

1856 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3311	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3269	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3215	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#3111	C₂	1	2	yes	maximal, complemented
20	C₁₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
22	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₁₃×#559	C₂²	1	1	yes	characteristic
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	C₂²	1	1	yes	characteristic
30	C₁₃×#556	C₂²	1	1	yes	characteristic
31	C₁₃×#556	C₂²	1	2	yes	complemented
32	C₁₃×#555	—	2	1	no	—
33	C₁₃×#552	—	2	1	no	—
34	C₁₃×#552	—	2	2	no	—
35	C₁₃×#551	—	2	2	no	—
36	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#548	—	2	1	no	—
39	C₁₃×#548	C₂²	1	2	yes	—
40	C₁₃×#547	C₂²	1	1	yes	characteristic
41	C₁₃×#547	C₂²	1	2	yes	complemented
42	C₁₃×#546	—	2	1	no	—
43	C₁₃×#546	C₂²	1	2	yes	—
44	D₄²×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#542	—	2	1	no	—
46	C₁₃×#538	—	2	2	no	—
47	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#533	C₂²	1	2	yes	complemented
49	C₁₃×#532	C₂²	1	1	yes	characteristic
50	C₁₃×#529	—	2	1	no	—
51	C₁₃×#529	—	2	2	no	—
52	C₁₃×#529	C₂²	1	1	yes	characteristic
53	C₁₃×#529	C₂²	1	2	yes	—
54	C₂×C₁₃×#124	C₂²	1	2	yes	—
55	C₁₃×#518	—	2	1	no	—
56	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
59	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
60	C₁₃×#497	C₂²	1	2	yes	—
61	C₁₃×#497	C₂²	1	2	yes	complemented
62	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#492	C₂²	1	1	yes	characteristic
64	C₁₃×#489	C₂²	1	2	yes	—
65	C₁₃×#489	C₂²	1	2	yes	complemented
66	C₁₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#486	C₂²	1	1	yes	characteristic
68	C₁₃×#485	C₂²	1	2	yes	complemented
69	C₁₃×#485	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#482	C₂²	1	1	yes	characteristic
71	C₁₃×#482	C₂²	1	2	yes	—
72	C₁₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#479	C₂²	1	2	yes	complemented
74	C₁₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×#477	C₂²	1	2	yes	complemented
76	C₁₃×#476	C₂²	1	2	yes	complemented
77	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#474	C₂²	1	1	yes	characteristic
79	C₁₃×#470	C₂²	1	2	yes	complemented
80	C₁₃×#470	C₂²	1	2	yes	complemented
81	C₁₃×#468	C₂²	1	2	yes	—
82	C₁₃×#468	C₂²	1	2	yes	—
83	C₁₃×#467	C₂²	1	2	yes	complemented
84	C₁₃×#465	C₂²	1	2	yes	—
85	C₁₃×#464	C₂²	1	2	yes	—
86	C₁₃×#464	C₂²	1	2	yes	—
87	C₁₃×#464	C₂²	1	1	yes	characteristic
88	C₁₃×#464	C₂²	1	2	yes	complemented
89	C₁₃×#464	C₂²	1	2	yes	complemented
90	C₁₃×#464	C₂²	1	2	yes	complemented
91	C₁₃×#464	C₂²	1	2	yes	complemented
92	C₁₃×#463	C₂²	1	2	yes	—
93	C₁₃×#463	C₂²	1	1	yes	characteristic
94	C₁₃×#463	C₂²	1	2	yes	complemented
95	C₁₃×#463	C₂²	1	2	yes	complemented
96	C₁₃×#462	C₂²	1	2	yes	complemented
97	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
98	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
99	C₁₃×#461	C₂²	1	1	yes	characteristic
100	C₁₃×#461	C₂²	1	2	yes	complemented
101	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
102	C₁₃×#460	C₂²	1	1	yes	characteristic
103	C₁₃×#459	C₂²	1	1	yes	characteristic
104	C₁₃×#452	C₂²	1	2	yes	complemented
105	C₁₃×#452	C₂²	1	2	yes	complemented
106	C₁₃×#452	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#452	C₂²	1	2	yes	complemented
108	C₁₃×#451	C₂²	1	2	yes	complemented
109	C₁₃×#451	C₂²	1	2	yes	complemented
110	C₁₃×#450	C₂²	1	2	yes	—
111	C₁₃×#450	C₂²	1	2	yes	—
112	C₁₃×#449	C₂²	1	1	yes	characteristic
113	C₁₃×#449	C₂²	1	2	yes	—
114	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₁₃×#446	C₂²	1	1	yes	characteristic, complemented
116	C₁₃×#442	C₂²	1	2	yes	complemented
117	C₁₃×#441	C₂²	1	2	yes	complemented
118	C₁₃×#440	C₂²	1	2	yes	complemented
119	C₁₃×#440	C₂²	1	2	yes	complemented
120	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
122	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
123	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
124	C₁₃×#436	C₂²	1	1	yes	characteristic
125	C₁₃×#436	C₂²	1	1	yes	characteristic
126	C₁₃×#435	C₂²	1	2	yes	complemented
127	C₁₃×#435	C₂²	1	2	yes	complemented
128	C₁₃×#432	C₂²	1	2	yes	complemented
129	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₁₃×#423	C₂²	1	2	yes	complemented
131	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
132	C₁₃×#419	C₂²	1	2	yes	complemented
133	C₁₃×#418	C₂²	1	2	yes	—
134	C₁₃×#416	C₂²	1	2	yes	complemented
135	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
136	C₂×C₁₃×#41	C₂³	1	2	yes	—
137	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
138	C₂×C₁₃×#41	C₂³	1	2	yes	—
139	C₂²×Q₈×C₁₃	—	2	1	no	—
140	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₁₃	—	2	1	no	—
142	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
143	C₁₃×#137	—	4	4	no	—
144	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
145	C₁₃×#135	—	4	4	no	—
146	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₁₃×SD₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
158	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
159	C₂×C₁₃×D₈	C₂³	1	2	yes	—
160	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
161	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
162	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
163	C₁₃×C₄⋊Q₈	—	2	1	no	—
164	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
169	C₁₃×#127	C₂³	1	1	yes	characteristic
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	1	no	—
177	C₁₃×#125	—	2	2	no	—
178	C₁₃×#125	—	2	2	no	—
179	C₁₃×#125	—	2	1	no	—
180	C₁₃×#125	C₂³	1	1	yes	characteristic
181	C₁₃×#124	—	2	1	no	—
182	C₁₃×#124	—	2	1	no	—
183	C₁₃×#124	—	2	2	no	—
184	C₁₃×#124	—	2	2	no	—
185	C₁₃×#124	—	2	2	no	—
186	C₁₃×#124	—	2	2	no	—
187	C₁₃×#124	C₂³	1	1	yes	characteristic
188	C₁₃×#124	C₂³	1	2	yes	—
189	C₁₃×#124	C₂³	1	2	yes	—
190	C₁₃×#124	C₂³	1	2	yes	—
191	C₁₃×#123	—	2	1	no	—
192	C₁₃×#123	—	2	2	no	—
193	C₁₃×#123	—	2	2	no	—
194	C₁₃×#123	—	2	2	no	—
195	C₁₃×#123	—	2	2	no	—
196	C₁₃×#123	—	2	2	no	—
197	C₁₃×#123	—	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	1	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	C₂³	1	2	yes	—
206	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
209	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
210	C₁₃×#121	—	2	1	no	—
211	C₁₃×#121	—	2	2	no	—
212	C₁₃×#121	—	2	2	no	—
213	C₁₃×#121	—	2	1	no	—
214	C₁₃×#121	—	2	1	no	—
215	C₁₃×#121	—	2	1	no	—
216	C₁₃×#121	—	2	2	no	—
217	C₁₃×#121	C₂³	1	1	yes	characteristic
218	C₁₃×#121	C₂³	1	2	yes	—
219	C₁₃×#120	—	2	2	no	—
220	C₁₃×#120	—	2	2	no	—
221	C₄×Q₈×C₁₃	—	2	1	no	—
222	C₄×Q₈×C₁₃	—	2	1	no	—
223	C₄×Q₈×C₁₃	—	2	2	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	—	2	2	no	—
226	C₄×Q₈×C₁₃	D₄	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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	1	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	1	no	—
244	C₄×D₄×C₁₃	—	2	1	no	—
245	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
246	C₄×D₄×C₁₃	D₄	1	2	yes	—
247	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
249	C₄×D₄×C₁₃	C₂³	1	2	yes	—
250	C₄×D₄×C₁₃	C₂³	1	2	yes	—
251	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₁₃	C₂³	1	2	yes	—
253	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
254	C₁₃×#117	—	2	2	no	—
255	C₁₃×#117	—	2	1	no	—
256	C₁₃×#117	—	2	1	no	—
257	C₁₃×#117	—	2	2	no	—
258	C₁₃×#117	—	2	1	no	—
259	C₁₃×#117	—	2	1	no	—
260	C₁₃×#117	—	2	2	no	—
261	C₁₃×#117	D₄	1	2	yes	—
262	C₁₃×#117	D₄	1	1	yes	characteristic
263	C₁₃×#117	C₂³	1	1	yes	characteristic
264	C₁₃×#117	C₂³	1	2	yes	—
265	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
267	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₄²×C₁₃	—	2	1	no	—
271	C₂×C₄²×C₁₃	—	2	2	no	—
272	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
274	C₁₃×#107	C₂³	1	1	yes	characteristic
275	C₁₃×#107	C₂³	1	1	yes	characteristic
276	C₁₃×#107	C₂³	1	2	yes	—
277	C₁₃×#106	C₂³	1	1	yes	characteristic
278	C₁₃×#106	C₂³	1	1	yes	characteristic
279	C₁₃×#106	C₂³	1	2	yes	—
280	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
282	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
285	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
286	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₁₃×#103	C₂³	1	2	yes	—
288	C₁₃×#103	C₂³	1	2	yes	—
289	C₁₃×#103	C₂³	1	1	yes	characteristic
290	C₁₃×#103	C₂³	1	2	yes	—
291	C₁₃×#103	C₂³	1	2	yes	—
292	C₁₃×#103	C₂³	1	1	yes	characteristic
293	C₁₃×#103	C₂³	1	1	yes	characteristic
294	C₁₃×#103	C₂³	1	1	yes	characteristic
295	C₁₃×#103	C₂³	1	2	yes	—
296	C₁₃×#103	C₂³	1	2	yes	—
297	C₁₃×#103	C₂³	1	2	yes	—
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	2	yes	—
302	C₁₃×#102	C₂³	1	2	yes	—
303	C₁₃×#102	C₂³	1	1	yes	characteristic
304	C₁₃×#102	C₂³	1	1	yes	characteristic
305	C₁₃×#102	C₂³	1	1	yes	characteristic
306	C₁₃×#102	C₂³	1	2	yes	—
307	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
308	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₁₃×#97	C₂³	1	2	yes	—
312	C₁₃×#97	C₂³	1	2	yes	—
313	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
315	#61973	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂⁴×C₁₃	—	2	2	no	—
317	C₁₃×#41	—	2	2	no	—
318	C₁₃×#41	—	2	4	no	—
319	C₁₃×#41	—	4	2	no	—
320	C₁₃×#41	—	4	2	no	—
321	C₁₃×#41	—	4	1	no	—
322	C₁₃×#41	—	4	2	no	—
323	C₁₃×#41	—	4	2	no	—
324	C₂×Q₈×C₁₃	—	2	2	no	—
325	C₂×Q₈×C₁₃	—	2	1	no	—
326	C₂×Q₈×C₁₃	—	2	2	no	—
327	C₂×Q₈×C₁₃	—	4	2	no	—
328	C₂×Q₈×C₁₃	—	4	2	no	—
329	C₂×Q₈×C₁₃	—	4	4	no	—
330	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
335	C₂×D₄×C₁₃	—	2	2	no	—
336	C₂×D₄×C₁₃	—	2	2	no	—
337	C₂×D₄×C₁₃	—	2	1	no	—
338	C₂×D₄×C₁₃	—	2	1	no	—
339	C₂×D₄×C₁₃	—	2	2	no	—
340	C₂×D₄×C₁₃	—	2	1	no	—
341	C₂×D₄×C₁₃	—	2	1	no	—
342	C₂×D₄×C₁₃	—	2	2	no	—
343	C₂×D₄×C₁₃	—	4	2	no	—
344	C₂×D₄×C₁₃	—	4	2	no	—
345	C₂×D₄×C₁₃	—	4	4	no	—
346	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₁₃	—	2	2	no	—
352	C₂²×C₄×C₁₃	—	2	1	no	—
353	C₂²×C₄×C₁₃	—	2	1	no	—
354	C₂²×C₄×C₁₃	—	2	2	no	—
355	C₂²×C₄×C₁₃	—	2	2	no	—
356	C₂²×C₄×C₁₃	—	2	1	no	—
357	C₂²×C₄×C₁₃	—	2	1	no	—
358	C₂²×C₄×C₁₃	—	2	2	no	—
359	C₂²×C₄×C₁₃	—	2	2	no	—
360	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
362	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
363	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
366	C₁₃×Q₁₆	—	4	1	no	—
367	C₁₃×Q₁₆	—	4	2	no	—
368	C₁₃×Q₁₆	—	4	2	no	—
369	C₁₃×Q₁₆	—	4	2	no	—
370	C₁₃×Q₁₆	—	4	2	no	—
371	C₁₃×SD₁₆	—	2	4	no	—
372	C₁₃×SD₁₆	—	2	2	no	—
373	C₁₃×SD₁₆	—	4	2	no	—
374	C₁₃×SD₁₆	—	4	1	no	—
375	C₁₃×SD₁₆	—	4	2	no	—
376	C₁₃×SD₁₆	—	4	2	no	—
377	C₁₃×SD₁₆	—	4	2	no	—
378	C₁₃×D₈	—	2	4	no	—
379	C₁₃×D₈	—	2	2	no	—
380	C₁₃×M₁₆	—	4	2	no	—
381	C₁₃×M₁₆	—	4	2	no	—
382	C₂×C₈×C₁₃	—	4	2	no	—
383	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
388	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
389	C₁₃×C₄⋊C₄	—	2	2	no	—
390	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
395	C₁₃×C₄⋊C₄	—	2	1	no	—
396	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
407	C₁₃×C₄⋊C₄	—	2	1	no	—
408	C₁₃×C₄⋊C₄	—	2	2	no	—
409	C₁₃×C₄⋊C₄	—	2	1	no	—
410	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
412	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
414	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
415	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
416	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
417	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
418	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	1	no	—
425	C₁₃×C₂²⋊C₄	—	2	1	no	—
426	C₁₃×C₂²⋊C₄	—	2	2	no	—
427	C₁₃×C₂²⋊C₄	—	2	1	no	—
428	C₁₃×C₂²⋊C₄	—	2	1	no	—
429	C₁₃×C₂²⋊C₄	—	2	1	no	—
430	C₁₃×C₂²⋊C₄	—	2	2	no	—
431	C₁₃×C₂²⋊C₄	—	2	2	no	—
432	C₁₃×C₂²⋊C₄	—	2	2	no	—
433	C₁₃×C₂²⋊C₄	—	2	2	no	—
434	C₁₃×C₂²⋊C₄	—	2	2	no	—
435	C₁₃×C₂²⋊C₄	—	2	1	no	—
436	C₁₃×C₂²⋊C₄	—	2	2	no	—
437	C₁₃×C₂²⋊C₄	—	2	1	no	—
438	C₁₃×C₂²⋊C₄	—	2	2	no	—
439	C₁₃×C₂²⋊C₄	—	2	1	no	—
440	C₁₃×C₂²⋊C₄	—	2	2	no	—
441	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
444	C₄²×C₁₃	—	2	1	no	—
445	C₄²×C₁₃	—	2	2	no	—
446	C₄²×C₁₃	—	2	1	no	—
447	C₄²×C₁₃	—	2	2	no	—
448	C₄²×C₁₃	—	2	2	no	—
449	C₄²×C₁₃	—	2	1	no	—
450	C₄²×C₁₃	—	2	2	no	—
451	C₄²×C₁₃	—	2	1	no	—
452	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₁₃	C₂×D₄	1	2	yes	—
454	C₄²×C₁₃	C₂×D₄	1	2	yes	—
455	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
457	C₄²×C₁₃	C₂⁴	1	2	yes	—
458	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
459	#3514	C₂×C₁₃	1	1	yes	characteristic, complemented
460	#3482	C₂×C₁₃	1	1	yes	characteristic, complemented
461	#3400	C₂×C₁₃	1	1	yes	characteristic, complemented
462	#3398	C₂×C₁₃	1	1	yes	characteristic, complemented
463	#3373	C₂×C₁₃	1	1	yes	characteristic, complemented
464	#3367	C₂×C₁₃	1	1	yes	characteristic, complemented
465	#3328	C₂×C₁₃	1	1	yes	characteristic, complemented
466	#3324	C₂×C₁₃	1	1	yes	characteristic, complemented
467	#3313	C₂×C₁₃	1	2	yes	complemented
468	#3311	C₂×C₁₃	1	2	yes	complemented
469	#3276	C₂×C₁₃	1	1	yes	characteristic, complemented
470	#3272	C₂×C₁₃	1	1	yes	characteristic, complemented
471	#3269	C₂×C₁₃	1	2	yes	complemented
472	#3267	C₂×C₁₃	1	2	yes	complemented
473	#3252	C₂×C₁₃	1	2	yes	complemented
474	#3248	C₂×C₁₃	1	1	yes	characteristic, complemented
475	#3215	C₂×C₁₃	1	2	yes	complemented
476	#3210	C₂×C₁₃	1	1	yes	characteristic, complemented
477	#3111	C₂×C₁₃	1	2	yes	complemented
478	#3102	C₂×C₁₃	1	1	yes	characteristic, complemented
479	#3040	C₂×C₁₃	1	2	yes	complemented
480	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
481	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
482	C₂³×C₁₃	—	2	1	no	—
483	C₂³×C₁₃	—	2	1	no	—
484	C₂³×C₁₃	—	2	2	no	—
485	C₂³×C₁₃	—	4	4	no	—
486	C₂³×C₁₃	—	8	2	no	—
487	C₂³×C₁₃	—	8	2	no	—
488	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
489	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	Q₈×C₁₃	—	2	2	no	—
491	Q₈×C₁₃	—	2	1	no	—
492	Q₈×C₁₃	—	2	2	no	—
493	Q₈×C₁₃	—	2	1	no	—
494	Q₈×C₁₃	—	2	2	no	—
495	Q₈×C₁₃	—	2	2	no	—
496	Q₈×C₁₃	—	2	1	no	—
497	Q₈×C₁₃	—	2	1	no	—
498	Q₈×C₁₃	—	2	2	no	—
499	Q₈×C₁₃	—	4	4	no	—
500	Q₈×C₁₃	—	4	2	no	—
501	Q₈×C₁₃	—	8	2	no	—
502	D₄×C₁₃	—	2	2	no	—
503	D₄×C₁₃	—	2	1	no	—
504	D₄×C₁₃	—	2	2	no	—
505	D₄×C₁₃	—	2	1	no	—
506	D₄×C₁₃	—	2	1	no	—
507	D₄×C₁₃	—	2	2	no	—
508	D₄×C₁₃	—	4	2	no	—
509	D₄×C₁₃	—	4	4	no	—
510	D₄×C₁₃	—	4	2	no	—
511	D₄×C₁₃	—	4	4	no	—
512	D₄×C₁₃	—	4	2	no	—
513	D₄×C₁₃	—	8	1	no	—
514	D₄×C₁₃	—	8	2	no	—
515	D₄×C₁₃	—	8	1	no	—
516	D₄×C₁₃	—	8	2	no	—
517	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
518	C₂×C₄×C₁₃	—	2	2	no	—
519	C₂×C₄×C₁₃	—	2	1	no	—
520	C₂×C₄×C₁₃	—	2	2	no	—
521	C₂×C₄×C₁₃	—	2	2	no	—
522	C₂×C₄×C₁₃	—	2	1	no	—
523	C₂×C₄×C₁₃	—	2	1	no	—
524	C₂×C₄×C₁₃	—	2	1	no	—
525	C₂×C₄×C₁₃	—	2	2	no	—
526	C₂×C₄×C₁₃	—	2	1	no	—
527	C₂×C₄×C₁₃	—	2	2	no	—
528	C₂×C₄×C₁₃	—	2	1	no	—
529	C₂×C₄×C₁₃	—	2	1	no	—
530	C₂×C₄×C₁₃	—	2	1	no	—
531	C₂×C₄×C₁₃	—	2	2	no	—
532	C₂×C₄×C₁₃	—	4	2	no	—
533	C₂×C₄×C₁₃	—	4	1	no	—
534	C₂×C₄×C₁₃	—	4	2	no	—
535	C₂×C₄×C₁₃	—	4	2	no	—
536	C₂×C₄×C₁₃	—	4	4	no	—
537	C₂×C₄×C₁₃	—	4	2	no	—
538	C₂×C₄×C₁₃	—	4	4	no	—
539	C₂×C₄×C₁₃	—	4	2	no	—
540	C₂×C₄×C₁₃	—	4	2	no	—
541	C₂×C₄×C₁₃	—	8	2	no	—
542	C₂×C₄×C₁₃	—	8	2	no	—
543	C₂×C₄×C₁₃	—	8	2	no	—
544	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
548	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
553	C₈×C₁₃	—	2	2	no	—
554	C₈×C₁₃	—	2	2	no	—
555	C₈×C₁₃	—	2	1	no	—
556	C₈×C₁₃	—	2	1	no	—
557	C₈×C₁₃	—	2	1	no	—
558	C₈×C₁₃	—	2	1	no	—
559	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
560	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
561	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
562	#559	C₂²×C₁₃	1	1	yes	characteristic
563	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
564	#556	C₂²×C₁₃	1	1	yes	characteristic
565	#556	C₂²×C₁₃	1	1	yes	characteristic
566	#556	C₂²×C₁₃	1	2	yes	complemented
567	#555	—	2	1	no	—
568	#552	—	2	1	no	—
569	#552	—	2	2	no	—
570	#551	—	2	2	no	—
571	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
572	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
573	#548	—	2	1	no	—
574	#548	C₂²×C₁₃	1	2	yes	—
575	#547	C₂²×C₁₃	1	1	yes	characteristic
576	#547	C₂²×C₁₃	1	2	yes	complemented
577	#546	—	2	1	no	—
578	#546	C₂²×C₁₃	1	2	yes	—
579	D₄²	C₂²×C₁₃	1	1	yes	characteristic
580	#542	—	2	1	no	—
581	#538	—	2	2	no	—
582	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
583	#533	C₂²×C₁₃	1	2	yes	complemented
584	#532	C₂²×C₁₃	1	1	yes	characteristic
585	#529	—	2	1	no	—
586	#529	—	2	2	no	—
587	#529	C₂²×C₁₃	1	1	yes	characteristic
588	#529	C₂²×C₁₃	1	2	yes	—
589	C₂×#124	C₂²×C₁₃	1	2	yes	—
590	#518	—	2	1	no	—
591	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
592	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
593	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
594	C₂×C₄×Q₈	—	2	1	no	—
595	#497	C₂²×C₁₃	1	2	yes	—
596	#497	C₂²×C₁₃	1	2	yes	complemented
597	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
598	#492	C₂²×C₁₃	1	1	yes	characteristic
599	#489	C₂²×C₁₃	1	2	yes	—
600	#489	C₂²×C₁₃	1	2	yes	complemented
601	#487	C₂²×C₁₃	1	1	yes	characteristic, complemented
602	#486	C₂²×C₁₃	1	1	yes	characteristic
603	#485	C₂²×C₁₃	1	2	yes	complemented
604	#485	C₂²×C₁₃	1	1	yes	characteristic, complemented
605	#482	C₂²×C₁₃	1	1	yes	characteristic
606	#482	C₂²×C₁₃	1	2	yes	—
607	#479	C₂²×C₁₃	1	1	yes	characteristic, complemented
608	#479	C₂²×C₁₃	1	2	yes	complemented
609	#478	C₂²×C₁₃	1	1	yes	characteristic, complemented
610	#477	C₂²×C₁₃	1	2	yes	complemented
611	#476	C₂²×C₁₃	1	2	yes	complemented
612	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
613	#474	C₂²×C₁₃	1	1	yes	characteristic
614	#470	C₂²×C₁₃	1	2	yes	complemented
615	#470	C₂²×C₁₃	1	2	yes	complemented
616	#468	C₂²×C₁₃	1	2	yes	—
617	#468	C₂²×C₁₃	1	2	yes	—
618	#467	C₂²×C₁₃	1	2	yes	complemented
619	#465	C₂²×C₁₃	1	2	yes	—
620	#464	C₂²×C₁₃	1	1	yes	characteristic
621	#464	C₂²×C₁₃	1	2	yes	—
622	#464	C₂²×C₁₃	1	2	yes	—
623	#464	C₂²×C₁₃	1	2	yes	complemented
624	#464	C₂²×C₁₃	1	2	yes	complemented
625	#464	C₂²×C₁₃	1	2	yes	complemented
626	#464	C₂²×C₁₃	1	2	yes	complemented
627	#463	C₂²×C₁₃	1	1	yes	characteristic
628	#463	C₂²×C₁₃	1	2	yes	—
629	#463	C₂²×C₁₃	1	2	yes	complemented
630	#463	C₂²×C₁₃	1	2	yes	complemented
631	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
632	#462	C₂²×C₁₃	1	2	yes	complemented
633	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
634	#461	C₂²×C₁₃	1	1	yes	characteristic
635	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
636	#461	C₂²×C₁₃	1	2	yes	complemented
637	#460	C₂²×C₁₃	1	1	yes	characteristic
638	#459	C₂²×C₁₃	1	1	yes	characteristic
639	#452	C₂²×C₁₃	1	1	yes	characteristic, complemented
640	#452	C₂²×C₁₃	1	2	yes	complemented
641	#452	C₂²×C₁₃	1	2	yes	complemented
642	#452	C₂²×C₁₃	1	2	yes	complemented
643	#451	C₂²×C₁₃	1	2	yes	complemented
644	#451	C₂²×C₁₃	1	2	yes	complemented
645	#450	C₂²×C₁₃	1	2	yes	—
646	#450	C₂²×C₁₃	1	2	yes	—
647	#449	C₂²×C₁₃	1	1	yes	characteristic
648	#449	C₂²×C₁₃	1	2	yes	—
649	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
650	#446	C₂²×C₁₃	1	1	yes	characteristic, complemented
651	#442	C₂²×C₁₃	1	2	yes	complemented
652	#441	C₂²×C₁₃	1	2	yes	complemented
653	#440	C₂²×C₁₃	1	2	yes	complemented
654	#440	C₂²×C₁₃	1	2	yes	complemented
655	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
656	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
657	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
658	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
659	#436	C₂²×C₁₃	1	1	yes	characteristic
660	#436	C₂²×C₁₃	1	1	yes	characteristic
661	#435	C₂²×C₁₃	1	2	yes	complemented
662	#435	C₂²×C₁₃	1	2	yes	complemented
663	#432	C₂²×C₁₃	1	2	yes	complemented
664	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
665	#423	C₂²×C₁₃	1	2	yes	complemented
666	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
667	#419	C₂²×C₁₃	1	2	yes	complemented
668	#418	C₂²×C₁₃	1	2	yes	—
669	#416	C₂²×C₁₃	1	2	yes	complemented
670	C₂²×C₁₃	—	2	1	no	—
671	C₂²×C₁₃	—	2	2	no	—
672	C₂²×C₁₃	—	2	2	no	—
673	C₂²×C₁₃	—	2	1	no	—
674	C₂²×C₁₃	—	2	2	no	—
675	C₂²×C₁₃	—	2	1	no	—
676	C₂²×C₁₃	—	2	2	no	—
677	C₂²×C₁₃	—	4	1	no	—
678	C₂²×C₁₃	—	4	1	no	—
679	C₂²×C₁₃	—	4	2	no	—
680	C₂²×C₁₃	—	4	1	no	—
681	C₂²×C₁₃	—	4	2	no	—
682	C₂²×C₁₃	—	4	1	no	—
683	C₂²×C₁₃	—	4	1	no	—
684	C₂²×C₁₃	—	4	2	no	—
685	C₂²×C₁₃	—	16	4	no	—
686	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₁₃	—	2	1	no	—
688	C₄×C₁₃	—	2	2	no	—
689	C₄×C₁₃	—	2	1	no	—
690	C₄×C₁₃	—	2	1	no	—
691	C₄×C₁₃	—	2	2	no	—
692	C₄×C₁₃	—	2	1	no	—
693	C₄×C₁₃	—	2	2	no	—
694	C₄×C₁₃	—	4	1	no	—
695	C₄×C₁₃	—	4	1	no	—
696	C₄×C₁₃	—	4	1	no	—
697	C₄×C₁₃	—	4	2	no	—
698	C₄×C₁₃	—	4	2	no	—
699	C₄×C₁₃	—	4	1	no	—
700	C₄×C₁₃	—	4	1	no	—
701	C₄×C₁₃	—	4	2	no	—
702	C₄×C₁₃	—	4	1	no	—
703	C₄×C₁₃	#575	1	2	yes	—
704	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₄×C₁₃	#585	1	1	yes	characteristic
706	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
707	C₂×#41	C₂³×C₁₃	1	2	yes	—
708	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
709	C₂×#41	C₂³×C₁₃	1	2	yes	—
710	C₂²×Q₈	—	2	1	no	—
711	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
712	C₂²×D₄	—	2	1	no	—
713	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
714	#137	—	4	4	no	—
715	AGL(1,ℤ/8)	—	4	4	no	—
716	#135	—	4	4	no	—
717	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
718	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
719	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
720	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
721	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
722	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
723	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
724	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
725	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
726	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₁₃	1	1	yes	characteristic
728	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
729	C₂×D₈	C₂³×C₁₃	1	2	yes	—
730	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
731	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
732	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
733	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
734	C₄⋊Q₈	—	2	1	no	—
735	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
738	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
740	#127	C₂³×C₁₃	1	1	yes	characteristic
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	1	no	—
747	#125	—	2	1	no	—
748	#125	—	2	2	no	—
749	#125	—	2	2	no	—
750	#125	—	2	1	no	—
751	#125	C₂³×C₁₃	1	1	yes	characteristic
752	#124	—	2	1	no	—
753	#124	—	2	1	no	—
754	#124	—	2	2	no	—
755	#124	—	2	2	no	—
756	#124	—	2	2	no	—
757	#124	—	2	2	no	—
758	#124	C₂³×C₁₃	1	1	yes	characteristic
759	#124	C₂³×C₁₃	1	2	yes	—
760	#124	C₂³×C₁₃	1	2	yes	—
761	#124	C₂³×C₁₃	1	2	yes	—
762	#123	—	2	1	no	—
763	#123	—	2	2	no	—
764	#123	—	2	2	no	—
765	#123	—	2	2	no	—
766	#123	—	2	2	no	—
767	#123	—	2	2	no	—
768	#123	—	2	2	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	1	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	2	1	no	—
773	C₂²⋊Q₈	—	2	2	no	—
774	C₂²⋊Q₈	—	2	2	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
777	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
779	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
780	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
781	#121	—	2	1	no	—
782	#121	—	2	2	no	—
783	#121	—	2	2	no	—
784	#121	—	2	1	no	—
785	#121	—	2	1	no	—
786	#121	—	2	1	no	—
787	#121	—	2	2	no	—
788	#121	C₂³×C₁₃	1	2	yes	—
789	#121	C₂³×C₁₃	1	1	yes	characteristic
790	#120	—	2	2	no	—
791	#120	—	2	2	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	2	2	no	—
797	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
799	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
800	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
802	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
803	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
804	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	2	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	1	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
817	C₄×D₄	D₄×C₁₃	1	2	yes	—
818	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₁₃	1	2	yes	—
821	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
822	C₄×D₄	C₂³×C₁₃	1	2	yes	—
823	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₁₃	1	2	yes	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	—	2	1	no	—
828	#117	—	2	2	no	—
829	#117	—	2	1	no	—
830	#117	—	2	1	no	—
831	#117	—	2	2	no	—
832	#117	D₄×C₁₃	1	2	yes	—
833	#117	D₄×C₁₃	1	1	yes	characteristic
834	#117	C₂³×C₁₃	1	2	yes	—
835	#117	C₂³×C₁₃	1	1	yes	characteristic
836	C₂×C₄⋊C₄	—	2	1	no	—
837	C₂×C₄⋊C₄	—	2	2	no	—
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₂²⋊C₄	—	2	2	no	—
840	C₂×C₂²⋊C₄	—	2	2	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	—	2	2	no	—
843	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
844	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
845	#107	C₂³×C₁₃	1	1	yes	characteristic
846	#107	C₂³×C₁₃	1	1	yes	characteristic
847	#107	C₂³×C₁₃	1	2	yes	—
848	#106	C₂³×C₁₃	1	1	yes	characteristic
849	#106	C₂³×C₁₃	1	1	yes	characteristic
850	#106	C₂³×C₁₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
857	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
858	#103	C₂³×C₁₃	1	2	yes	—
859	#103	C₂³×C₁₃	1	2	yes	—
860	#103	C₂³×C₁₃	1	1	yes	characteristic
861	#103	C₂³×C₁₃	1	2	yes	—
862	#103	C₂³×C₁₃	1	2	yes	—
863	#103	C₂³×C₁₃	1	1	yes	characteristic
864	#103	C₂³×C₁₃	1	1	yes	characteristic
865	#103	C₂³×C₁₃	1	1	yes	characteristic
866	#103	C₂³×C₁₃	1	2	yes	—
867	#103	C₂³×C₁₃	1	2	yes	—
868	#103	C₂³×C₁₃	1	2	yes	—
869	#102	C₂³×C₁₃	1	2	yes	—
870	#102	C₂³×C₁₃	1	2	yes	—
871	#102	C₂³×C₁₃	1	1	yes	characteristic
872	#102	C₂³×C₁₃	1	2	yes	—
873	#102	C₂³×C₁₃	1	2	yes	—
874	#102	C₂³×C₁₃	1	1	yes	characteristic
875	#102	C₂³×C₁₃	1	1	yes	characteristic
876	#102	C₂³×C₁₃	1	1	yes	characteristic
877	#102	C₂³×C₁₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
882	#97	C₂³×C₁₃	1	2	yes	—
883	#97	C₂³×C₁₃	1	2	yes	—
884	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
885	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
886	C₂×C₁₃	—	4	1	no	—
887	C₂×C₁₃	—	4	2	no	—
888	C₂×C₁₃	—	4	2	no	—
889	C₂×C₁₃	—	8	2	no	—
890	C₂×C₁₃	—	8	1	no	—
891	C₂×C₁₃	#3488	1	1	yes	characteristic
892	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
893	C₂×C₁₃	#3586	1	1	yes	characteristic
894	C₂⁴	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	4	no	—
897	#41	—	4	2	no	—
898	#41	—	4	2	no	—
899	#41	—	4	1	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	1	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	4	no	—
908	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
909	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
910	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
911	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
913	C₂×D₄	—	2	2	no	—
914	C₂×D₄	—	2	2	no	—
915	C₂×D₄	—	2	1	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	1	no	—
919	C₂×D₄	—	2	1	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	4	2	no	—
922	C₂×D₄	—	4	2	no	—
923	C₂×D₄	—	4	4	no	—
924	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
925	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
926	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
928	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	2	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
939	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
940	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
941	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
944	Q₁₆	—	4	2	no	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	1	no	—
948	Q₁₆	—	4	2	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	2	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	1	no	—
956	D₈	—	2	4	no	—
957	D₈	—	2	2	no	—
958	M₁₆	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	C₂×C₈	—	4	2	no	—
961	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
962	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
966	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
990	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
992	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	2	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1020	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1021	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	2	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1031	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1032	C₄²	C₂×D₄×C₁₃	1	2	yes	—
1033	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
1034	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₁₃	1	2	yes	—
1036	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
1037	C₁₃	#61973	1	1	yes	characteristic, direct product factor, Sylow
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
1045	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	2	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	2	2	no	—
1055	Q₈	—	4	4	no	—
1056	Q₈	—	4	2	no	—
1057	Q₈	—	8	2	no	—
1058	D₄	—	2	2	no	—
1059	D₄	—	2	1	no	—
1060	D₄	—	2	2	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	4	2	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	4	2	no	—
1067	D₄	—	4	4	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	8	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	4	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1109	C₈	—	2	2	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	1	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	1	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	2	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	2	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₁₃×#575	1	2	yes	—
1149	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1150	C₄	C₁₃×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	1	no	—
1155	C₂	—	8	2	no	—
1156	C₂	C₁₃×#3488	1	1	yes	characteristic
1157	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
1158	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3514	C₂	semidirect
2. C₁₃×#3482	C₂	semidirect
3. C₁₃×#3400	C₂	semidirect
4. C₁₃×#3398	C₂	semidirect
5. C₁₃×#3373	C₂	semidirect
6. C₁₃×#3367	C₂	semidirect
7. C₁₃×#3328	C₂	semidirect
8. C₁₃×#3324	C₂	semidirect
9. C₁₃×#3313	C₂	semidirect
10. C₁₃×#3311	C₂	semidirect
11. C₁₃×#3276	C₂	semidirect
12. C₁₃×#3272	C₂	semidirect
13. C₁₃×#3269	C₂	semidirect
14. C₁₃×#3267	C₂	semidirect
15. C₁₃×#3252	C₂	semidirect
16. C₁₃×#3248	C₂	semidirect
17. C₁₃×#3215	C₂	semidirect
18. C₁₃×#3210	C₂	semidirect
19. C₁₃×#3111	C₂	semidirect
20. C₁₃×#3102	C₂	semidirect
21. C₁₃×#3040	C₂	semidirect
22. C₁₃×#3035	C₂	semidirect
23. C₁₃×#2989	C₂	semidirect
24. C₂×C₁₃×#137	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#547	C₂²	semidirect
47. C₁₃×#533	C₂²	semidirect
48. C₁₃×#533	C₂²	semidirect
57. C₄×C₁₃×#41	C₂²	semidirect
58. C₄×C₁₃×#41	C₂²	semidirect
61. C₁₃×#497	C₂²	semidirect
62. C₁₃×#494	C₂²	semidirect
65. C₁₃×#489	C₂²	semidirect
66. C₁₃×#487	C₂²	semidirect
68. C₁₃×#485	C₂²	semidirect
69. C₁₃×#485	C₂²	semidirect
72. C₁₃×#479	C₂²	semidirect
73. C₁₃×#479	C₂²	semidirect
74. C₁₃×#478	C₂²	semidirect
75. C₁₃×#477	C₂²	semidirect
76. C₁₃×#476	C₂²	semidirect
77. C₁₃×#475	C₂²	semidirect
79. C₁₃×#470	C₂²	semidirect
80. C₁₃×#470	C₂²	semidirect
83. C₁₃×#467	C₂²	semidirect
88. C₁₃×#464	C₂²	semidirect
89. C₁₃×#464	C₂²	semidirect
90. C₁₃×#464	C₂²	semidirect
91. C₁₃×#464	C₂²	semidirect
94. C₁₃×#463	C₂²	semidirect
95. C₁₃×#463	C₂²	semidirect
96. C₁₃×#462	C₂²	semidirect
97. C₁₃×#462	C₂²	semidirect
98. C₁₃×#462	C₂²	semidirect
100. C₁₃×#461	C₂²	semidirect
101. C₁₃×#461	C₂²	semidirect
104. C₁₃×#452	C₂²	semidirect
105. C₁₃×#452	C₂²	semidirect
106. C₁₃×#452	C₂²	semidirect
107. C₁₃×#452	C₂²	semidirect
108. C₁₃×#451	C₂²	semidirect
109. C₁₃×#451	C₂²	semidirect
114. C₁₃×#446	C₂²	semidirect
115. C₁₃×#446	C₂²	semidirect
116. C₁₃×#442	C₂²	semidirect
117. C₁₃×#441	C₂²	semidirect
118. C₁₃×#440	C₂²	semidirect
119. C₁₃×#440	C₂²	semidirect
120. C₄×C₁₃×Q₁₆	C₂²	semidirect
122. C₄×C₁₃×SD₁₆	C₂²	semidirect
126. C₁₃×#435	C₂²	semidirect
127. C₁₃×#435	C₂²	semidirect
128. C₁₃×#432	C₂²	semidirect
129. C₁₃×#431	C₂²	semidirect
130. C₁₃×#423	C₂²	semidirect
131. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
132. C₁₃×#419	C₂²	semidirect
134. C₁₃×#416	C₂²	semidirect
315. #61973	C₁₃	direct (N × H)
459. #3514	C₂×C₁₃	semidirect
460. #3482	C₂×C₁₃	semidirect
461. #3400	C₂×C₁₃	semidirect
462. #3398	C₂×C₁₃	semidirect
463. #3373	C₂×C₁₃	semidirect
464. #3367	C₂×C₁₃	semidirect
465. #3328	C₂×C₁₃	semidirect
466. #3324	C₂×C₁₃	semidirect
467. #3313	C₂×C₁₃	semidirect
468. #3311	C₂×C₁₃	semidirect
469. #3276	C₂×C₁₃	semidirect
470. #3272	C₂×C₁₃	semidirect
471. #3269	C₂×C₁₃	semidirect
472. #3267	C₂×C₁₃	semidirect
473. #3252	C₂×C₁₃	semidirect
474. #3248	C₂×C₁₃	semidirect
475. #3215	C₂×C₁₃	semidirect
476. #3210	C₂×C₁₃	semidirect
477. #3111	C₂×C₁₃	semidirect
478. #3102	C₂×C₁₃	semidirect
479. #3040	C₂×C₁₃	semidirect
480. #3035	C₂×C₁₃	semidirect
481. #2989	C₂×C₁₃	semidirect
559. C₂×#137	C₂²×C₁₃	semidirect
561. C₂×#135	C₂²×C₁₃	semidirect
563. #557	C₂²×C₁₃	semidirect
566. #556	C₂²×C₁₃	semidirect
572. D₄×Q₈	C₂²×C₁₃	semidirect
576. #547	C₂²×C₁₃	semidirect
582. #533	C₂²×C₁₃	semidirect
583. #533	C₂²×C₁₃	semidirect
592. C₄×#41	C₂²×C₁₃	semidirect
593. C₄×#41	C₂²×C₁₃	semidirect
596. #497	C₂²×C₁₃	semidirect
597. #494	C₂²×C₁₃	semidirect
600. #489	C₂²×C₁₃	semidirect
601. #487	C₂²×C₁₃	semidirect
603. #485	C₂²×C₁₃	semidirect
604. #485	C₂²×C₁₃	semidirect
607. #479	C₂²×C₁₃	semidirect
608. #479	C₂²×C₁₃	semidirect
609. #478	C₂²×C₁₃	semidirect
610. #477	C₂²×C₁₃	semidirect
611. #476	C₂²×C₁₃	semidirect
612. #475	C₂²×C₁₃	semidirect
614. #470	C₂²×C₁₃	semidirect
615. #470	C₂²×C₁₃	semidirect
618. #467	C₂²×C₁₃	semidirect
623. #464	C₂²×C₁₃	semidirect
624. #464	C₂²×C₁₃	semidirect
625. #464	C₂²×C₁₃	semidirect
626. #464	C₂²×C₁₃	semidirect
629. #463	C₂²×C₁₃	semidirect
630. #463	C₂²×C₁₃	semidirect
631. #462	C₂²×C₁₃	semidirect
632. #462	C₂²×C₁₃	semidirect
633. #462	C₂²×C₁₃	semidirect
635. #461	C₂²×C₁₃	semidirect
636. #461	C₂²×C₁₃	semidirect
639. #452	C₂²×C₁₃	semidirect
640. #452	C₂²×C₁₃	semidirect
641. #452	C₂²×C₁₃	semidirect
642. #452	C₂²×C₁₃	semidirect
643. #451	C₂²×C₁₃	semidirect
644. #451	C₂²×C₁₃	semidirect
649. #446	C₂²×C₁₃	semidirect
650. #446	C₂²×C₁₃	semidirect
651. #442	C₂²×C₁₃	semidirect
652. #441	C₂²×C₁₃	semidirect
653. #440	C₂²×C₁₃	semidirect
654. #440	C₂²×C₁₃	semidirect
655. C₄×Q₁₆	C₂²×C₁₃	semidirect
657. C₄×SD₁₆	C₂²×C₁₃	semidirect
661. #435	C₂²×C₁₃	semidirect
662. #435	C₂²×C₁₃	semidirect
663. #432	C₂²×C₁₃	semidirect
664. #431	C₂²×C₁₃	semidirect
665. #423	C₂²×C₁₃	semidirect
666. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
667. #419	C₂²×C₁₃	semidirect
669. #416	C₂²×C₁₃	semidirect
1037. C₁₃	#61973	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×#3514	2
C₁₃×#3482	2
C₁₃×#3400	2
C₁₃×#3398	2
C₁₃×#3373	2
C₁₃×#3367	2
C₁₃×#3328	2
C₁₃×#3324	2
C₁₃×#3313	2
C₁₃×#3311	2
C₁₃×#3276	2
C₁₃×#3272	2
C₁₃×#3269	2
C₁₃×#3267	2
C₁₃×#3252	2
C₁₃×#3248	2
C₁₃×#3215	2
C₁₃×#3210	2
C₁₃×#3111	2
C₁₃×#3102	2
C₁₃×#3040	2
C₁₃×#3035	2
C₁₃×#2989	2
#61973	13

Subgroups — C13×#61973 #15748312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61973 #15748312