Subgroups — C₁₃×#62020 #15748359

Order 3328.

1772 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3313	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3296	C₂	1	2	yes	maximal, complemented
8	D₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3266	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3258	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3223	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3121	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#137	C₂²	1	2	yes	—
21	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
24	C₁₃×#563	—	2	1	no	—
25	C₁₃×#562	—	2	1	no	—
26	C₁₃×#557	—	2	1	no	—
27	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#556	—	2	1	no	—
30	C₁₃×#556	C₂²	1	2	yes	—
31	C₁₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#552	—	2	2	no	—
33	C₁₃×#552	C₂²	1	2	yes	—
34	C₁₃×#551	—	2	2	no	—
35	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
37	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#548	C₂²	1	2	yes	—
39	C₁₃×#546	C₂²	1	2	yes	—
40	C₁₃×#543	—	2	1	no	—
41	C₁₃×#542	—	2	2	no	—
42	C₁₃×#542	C₂²	1	2	yes	—
43	C₁₃×#541	—	2	2	no	—
44	C₁₃×#541	C₂²	1	2	yes	complemented
45	C₁₃×#538	—	2	1	no	—
46	C₁₃×#536	C₂²	1	2	yes	—
47	C₁₃×#533	—	2	1	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×#124	C₂²	1	1	yes	characteristic
53	C₁₃×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#497	C₂²	1	2	yes	—
56	C₁₃×#497	C₂²	1	2	yes	—
57	C₁₃×#494	C₂²	1	2	yes	complemented
58	C₁₃×#491	C₂²	1	2	yes	complemented
59	C₁₃×#489	C₂²	1	2	yes	—
60	C₁₃×#488	C₂²	1	2	yes	—
61	C₁₃×#485	C₂²	1	2	yes	complemented
62	C₁₃×#483	C₂²	1	2	yes	—
63	C₁₃×#482	C₂²	1	2	yes	—
64	C₁₃×#479	C₂²	1	2	yes	complemented
65	C₁₃×#478	C₂²	1	2	yes	—
66	C₁₃×#477	C₂²	1	2	yes	complemented
67	C₁₃×#477	C₂²	1	2	yes	complemented
68	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#475	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#470	C₂²	1	2	yes	complemented
71	C₁₃×#468	C₂²	1	2	yes	—
72	C₁₃×#467	C₂²	1	2	yes	—
73	C₁₃×#467	C₂²	1	2	yes	—
74	C₁₃×#467	C₂²	1	2	yes	complemented
75	C₁₃×#465	C₂²	1	2	yes	—
76	C₁₃×#464	C₂²	1	2	yes	—
77	C₁₃×#464	C₂²	1	2	yes	—
78	C₁₃×#464	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	—
80	C₁₃×#464	C₂²	1	2	yes	—
81	C₁₃×#464	C₂²	1	2	yes	—
82	C₁₃×#464	C₂²	1	2	yes	—
83	C₁₃×#464	C₂²	1	2	yes	—
84	C₁₃×#462	C₂²	1	2	yes	complemented
85	C₁₃×#462	C₂²	1	2	yes	complemented
86	C₁₃×#462	C₂²	1	2	yes	complemented
87	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#462	C₂²	1	2	yes	complemented
89	C₁₃×#462	C₂²	1	2	yes	complemented
90	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
91	C₁₃×#461	C₂²	1	2	yes	—
92	C₁₃×#452	C₂²	1	2	yes	—
93	C₁₃×#452	C₂²	1	2	yes	—
94	C₁₃×#451	C₂²	1	2	yes	—
95	C₁₃×#451	C₂²	1	2	yes	—
96	C₁₃×#451	C₂²	1	2	yes	complemented
97	C₁₃×#451	C₂²	1	2	yes	complemented
98	C₁₃×#451	C₂²	1	2	yes	complemented
99	C₁₃×#450	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	2	yes	—
101	C₁₃×#446	C₂²	1	2	yes	complemented
102	C₁₃×#441	C₂²	1	2	yes	complemented
103	C₁₃×#441	C₂²	1	2	yes	complemented
104	C₁₃×#441	C₂²	1	2	yes	complemented
105	C₁₃×#440	C₂²	1	2	yes	—
106	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
108	C₁₃×#435	C₂²	1	2	yes	—
109	C₁₃×#435	C₂²	1	2	yes	complemented
110	C₈×D₄×C₁₃	C₂²	1	2	yes	—
111	C₁₃×#433	C₂²	1	2	yes	complemented
112	C₁₃×#432	C₂²	1	1	yes	characteristic
113	C₁₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₁₃×#419	C₂²	1	2	yes	complemented
116	C₁₃×#416	C₂²	1	2	yes	—
117	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
118	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	C₂³	1	2	yes	—
120	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#137	—	4	4	no	—
126	C₂×C₁₃×Q₁₆	—	4	2	no	—
127	C₂×C₁₃×Q₁₆	—	4	4	no	—
128	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
130	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
135	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
136	C₂×C₁₃×SD₁₆	—	4	2	no	—
137	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
142	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
145	C₁₃×C₄⋊Q₈	—	2	1	no	—
146	C₁₃×C₄⋊Q₈	—	2	1	no	—
147	C₁₃×C₄⋊Q₈	—	2	2	no	—
148	C₁₃×C₄⋊Q₈	—	2	2	no	—
149	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₁₃×#126	—	2	2	no	—
156	C₁₃×#126	—	2	2	no	—
157	C₁₃×#126	—	2	2	no	—
158	C₁₃×#126	—	2	2	no	—
159	C₁₃×#126	—	2	2	no	—
160	C₁₃×#126	—	2	2	no	—
161	C₁₃×#126	—	2	2	no	—
162	C₁₃×#126	D₄	1	2	yes	—
163	C₁₃×#125	—	2	1	no	—
164	C₁₃×#125	—	2	2	no	—
165	C₁₃×#125	—	2	2	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	2	no	—
168	C₁₃×#125	—	2	2	no	—
169	C₁₃×#125	—	2	1	no	—
170	C₁₃×#125	—	2	1	no	—
171	C₁₃×#125	D₄	1	1	yes	characteristic
172	C₁₃×#125	C₂³	1	2	yes	—
173	C₁₃×#124	—	2	1	no	—
174	C₁₃×#124	—	2	2	no	—
175	C₁₃×#124	—	2	2	no	—
176	C₁₃×#124	—	2	1	no	—
177	C₁₃×#124	—	2	1	no	—
178	C₁₃×#124	D₄	1	1	yes	characteristic
179	C₁₃×#124	C₂³	1	2	yes	—
180	C₁₃×#124	C₂³	1	2	yes	—
181	C₁₃×#124	C₂³	1	2	yes	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×#123	—	2	2	no	—
184	C₁₃×#123	—	2	2	no	—
185	C₁₃×#123	—	2	2	no	—
186	C₁₃×#123	—	2	2	no	—
187	C₁₃×#123	D₄	1	2	yes	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	1	no	—
190	C₁₃×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
198	C₁₃×C₂²⋊Q₈	—	2	2	no	—
199	C₁₃×C₂²⋊Q₈	—	2	2	no	—
200	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
201	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	D₄	1	1	yes	characteristic
209	C₁₃×#121	C₂³	1	2	yes	—
210	C₁₃×#120	—	2	2	no	—
211	C₄×Q₈×C₁₃	—	2	1	no	—
212	C₄×Q₈×C₁₃	—	2	2	no	—
213	C₄×Q₈×C₁₃	—	2	2	no	—
214	C₄×Q₈×C₁₃	—	2	1	no	—
215	C₄×Q₈×C₁₃	—	2	1	no	—
216	C₄×Q₈×C₁₃	—	2	1	no	—
217	C₄×Q₈×C₁₃	—	2	1	no	—
218	C₄×Q₈×C₁₃	—	2	1	no	—
219	C₄×Q₈×C₁₃	—	2	1	no	—
220	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
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	2	yes	—
229	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₁₃	—	2	2	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	C₂³	1	2	yes	—
235	C₄×D₄×C₁₃	C₂³	1	2	yes	—
236	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
237	C₁₃×#117	—	2	1	no	—
238	C₁₃×#117	—	2	1	no	—
239	C₁₃×#117	—	2	2	no	—
240	C₁₃×#117	—	2	2	no	—
241	C₁₃×#117	—	2	2	no	—
242	C₁₃×#117	—	2	2	no	—
243	C₁₃×#117	C₂³	1	2	yes	—
244	C₁₃×#117	C₂³	1	2	yes	—
245	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
246	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
247	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²×C₁₃	—	2	1	no	—
251	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
252	C₁₃×#107	C₂³	1	2	yes	—
253	C₁₃×#107	C₂³	1	2	yes	—
254	C₁₃×#106	C₂³	1	2	yes	—
255	C₁₃×#106	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
258	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₁₃×#103	C₂³	1	2	yes	—
263	C₁₃×#103	C₂³	1	2	yes	—
264	C₁₃×#103	C₂³	1	2	yes	—
265	C₁₃×#103	C₂³	1	2	yes	—
266	C₁₃×#103	C₂³	1	2	yes	—
267	C₁₃×#103	C₂³	1	2	yes	—
268	C₁₃×#103	C₂³	1	2	yes	—
269	C₁₃×#103	C₂³	1	2	yes	—
270	C₁₃×#103	C₂³	1	2	yes	—
271	C₁₃×#103	C₂³	1	2	yes	—
272	C₁₃×#103	C₂³	1	2	yes	—
273	C₁₃×#103	C₂³	1	2	yes	—
274	C₁₃×#102	C₂³	1	2	yes	—
275	C₁₃×#102	C₂³	1	2	yes	—
276	C₁₃×#102	C₂³	1	2	yes	—
277	C₁₃×#102	C₂³	1	2	yes	—
278	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₁₃×#97	C₂³	1	2	yes	—
282	C₁₃×#97	C₂³	1	2	yes	—
283	C₄×C₈×C₁₃	C₂³	1	2	yes	—
284	#62020	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂⁴×C₁₃	—	2	1	no	—
286	C₁₃×#41	—	4	2	no	—
287	C₁₃×#41	—	4	2	no	—
288	C₂×Q₈×C₁₃	—	2	1	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	1	no	—
291	C₂×Q₈×C₁₃	—	2	1	no	—
292	C₂×Q₈×C₁₃	—	2	2	no	—
293	C₂×Q₈×C₁₃	—	2	1	no	—
294	C₂×Q₈×C₁₃	—	2	2	no	—
295	C₂×Q₈×C₁₃	—	2	4	no	—
296	C₂×Q₈×C₁₃	—	4	1	no	—
297	C₂×Q₈×C₁₃	—	4	2	no	—
298	C₂×Q₈×C₁₃	—	4	1	no	—
299	C₂×Q₈×C₁₃	—	4	2	no	—
300	C₂×Q₈×C₁₃	—	4	1	no	—
301	C₂×Q₈×C₁₃	—	4	2	no	—
302	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
305	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
306	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂×D₄×C₁₃	—	2	2	no	—
309	C₂×D₄×C₁₃	—	2	2	no	—
310	C₂×D₄×C₁₃	—	2	1	no	—
311	C₂×D₄×C₁₃	—	4	1	no	—
312	C₂×D₄×C₁₃	—	4	1	no	—
313	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
314	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
315	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₁₃	—	2	1	no	—
317	C₂²×C₄×C₁₃	—	2	1	no	—
318	C₂²×C₄×C₁₃	—	2	2	no	—
319	C₂²×C₄×C₁₃	—	2	1	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	2	no	—
323	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
327	C₁₃×Q₁₆	—	2	4	no	—
328	C₁₃×Q₁₆	—	2	4	no	—
329	C₁₃×Q₁₆	—	4	2	no	—
330	C₁₃×Q₁₆	—	4	2	no	—
331	C₁₃×Q₁₆	—	4	2	no	—
332	C₁₃×Q₁₆	—	4	2	no	—
333	C₁₃×Q₁₆	—	4	2	no	—
334	C₁₃×Q₁₆	—	4	2	no	—
335	C₁₃×SD₁₆	—	2	4	no	—
336	C₁₃×SD₁₆	—	4	2	no	—
337	C₁₃×SD₁₆	—	4	2	no	—
338	C₁₃×SD₁₆	—	4	2	no	—
339	C₁₃×M₁₆	—	4	2	no	—
340	C₂×C₈×C₁₃	—	4	1	no	—
341	C₂×C₈×C₁₃	—	4	1	no	—
342	C₂×C₈×C₁₃	—	4	2	no	—
343	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
344	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
345	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
347	C₁₃×C₄⋊C₄	—	2	1	no	—
348	C₁₃×C₄⋊C₄	—	2	1	no	—
349	C₁₃×C₄⋊C₄	—	2	1	no	—
350	C₁₃×C₄⋊C₄	—	2	1	no	—
351	C₁₃×C₄⋊C₄	—	2	1	no	—
352	C₁₃×C₄⋊C₄	—	2	2	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	2	no	—
355	C₁₃×C₄⋊C₄	—	2	2	no	—
356	C₁₃×C₄⋊C₄	—	2	1	no	—
357	C₁₃×C₄⋊C₄	—	2	1	no	—
358	C₁₃×C₄⋊C₄	—	2	2	no	—
359	C₁₃×C₄⋊C₄	—	2	1	no	—
360	C₁₃×C₄⋊C₄	—	2	1	no	—
361	C₁₃×C₄⋊C₄	—	2	2	no	—
362	C₁₃×C₄⋊C₄	—	2	1	no	—
363	C₁₃×C₄⋊C₄	—	2	2	no	—
364	C₁₃×C₄⋊C₄	—	2	2	no	—
365	C₁₃×C₄⋊C₄	—	2	2	no	—
366	C₁₃×C₄⋊C₄	—	2	2	no	—
367	C₁₃×C₄⋊C₄	—	2	1	no	—
368	C₁₃×C₄⋊C₄	—	2	2	no	—
369	C₁₃×C₄⋊C₄	—	2	2	no	—
370	C₁₃×C₄⋊C₄	—	2	2	no	—
371	C₁₃×C₄⋊C₄	—	2	2	no	—
372	C₁₃×C₄⋊C₄	—	2	2	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
375	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
376	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
377	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
378	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
379	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
380	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
381	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
382	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
383	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
384	C₁₃×C₂²⋊C₄	—	2	2	no	—
385	C₁₃×C₂²⋊C₄	—	2	2	no	—
386	C₁₃×C₂²⋊C₄	—	2	2	no	—
387	C₁₃×C₂²⋊C₄	—	2	2	no	—
388	C₁₃×C₂²⋊C₄	—	2	2	no	—
389	C₁₃×C₂²⋊C₄	—	2	2	no	—
390	C₁₃×C₂²⋊C₄	—	2	2	no	—
391	C₁₃×C₂²⋊C₄	—	2	2	no	—
392	C₁₃×C₂²⋊C₄	—	2	2	no	—
393	C₁₃×C₂²⋊C₄	—	2	2	no	—
394	C₁₃×C₂²⋊C₄	—	2	2	no	—
395	C₁₃×C₂²⋊C₄	—	2	2	no	—
396	C₁₃×C₂²⋊C₄	—	2	2	no	—
397	C₁₃×C₂²⋊C₄	—	2	2	no	—
398	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
399	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
400	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
401	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
402	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
403	C₄²×C₁₃	—	2	1	no	—
404	C₄²×C₁₃	—	2	1	no	—
405	C₄²×C₁₃	—	2	1	no	—
406	C₄²×C₁₃	—	2	1	no	—
407	C₄²×C₁₃	—	2	2	no	—
408	C₄²×C₁₃	—	2	2	no	—
409	C₄²×C₁₃	—	2	2	no	—
410	C₄²×C₁₃	—	2	2	no	—
411	C₄²×C₁₃	—	2	2	no	—
412	C₄²×C₁₃	—	2	2	no	—
413	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
414	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
415	C₄²×C₁₃	C₂⁴	1	2	yes	—
416	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
417	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
418	#3561	C₂×C₁₃	1	1	yes	characteristic
419	#3523	C₂×C₁₃	1	1	yes	characteristic, complemented
420	#3398	C₂×C₁₃	1	2	yes	complemented
421	#3377	C₂×C₁₃	1	2	yes	complemented
422	#3313	C₂×C₁₃	1	2	yes	complemented
423	#3312	C₂×C₁₃	1	2	yes	complemented
424	#3296	C₂×C₁₃	1	2	yes	complemented
425	D₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
426	#3270	C₂×C₁₃	1	2	yes	complemented
427	#3266	C₂×C₁₃	1	2	yes	complemented
428	#3258	C₂×C₁₃	1	2	yes	complemented
429	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
430	#3223	C₂×C₁₃	1	2	yes	complemented
431	#3215	C₂×C₁₃	1	1	yes	characteristic, complemented
432	#3121	C₂×C₁₃	1	2	yes	complemented
433	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
434	#3044	C₂×C₁₃	1	2	yes	complemented
435	C₂×#464	C₂×C₁₃	1	1	yes	characteristic, complemented
436	#2992	C₂×C₁₃	1	1	yes	characteristic, complemented
437	C₂³×C₁₃	—	2	2	no	—
438	C₂³×C₁₃	—	4	2	no	—
439	C₂³×C₁₃	—	8	1	no	—
440	C₂³×C₁₃	—	8	1	no	—
441	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
442	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₁₃	—	2	1	no	—
444	Q₈×C₁₃	—	2	1	no	—
445	Q₈×C₁₃	—	2	2	no	—
446	Q₈×C₁₃	—	2	2	no	—
447	Q₈×C₁₃	—	2	2	no	—
448	Q₈×C₁₃	—	2	2	no	—
449	Q₈×C₁₃	—	2	1	no	—
450	Q₈×C₁₃	—	2	2	no	—
451	Q₈×C₁₃	—	2	2	no	—
452	Q₈×C₁₃	—	4	1	no	—
453	Q₈×C₁₃	—	4	4	no	—
454	Q₈×C₁₃	—	4	2	no	—
455	Q₈×C₁₃	—	4	2	no	—
456	Q₈×C₁₃	—	8	1	no	—
457	Q₈×C₁₃	—	8	2	no	—
458	Q₈×C₁₃	—	8	1	no	—
459	Q₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
460	D₄×C₁₃	—	2	4	no	—
461	D₄×C₁₃	—	2	2	no	—
462	D₄×C₁₃	—	2	2	no	—
463	D₄×C₁₃	—	4	1	no	—
464	D₄×C₁₃	—	8	1	no	—
465	D₄×C₁₃	—	8	2	no	—
466	D₄×C₁₃	—	8	2	no	—
467	C₂×C₄×C₁₃	—	2	2	no	—
468	C₂×C₄×C₁₃	—	2	1	no	—
469	C₂×C₄×C₁₃	—	2	1	no	—
470	C₂×C₄×C₁₃	—	2	2	no	—
471	C₂×C₄×C₁₃	—	2	1	no	—
472	C₂×C₄×C₁₃	—	2	2	no	—
473	C₂×C₄×C₁₃	—	2	1	no	—
474	C₂×C₄×C₁₃	—	2	2	no	—
475	C₂×C₄×C₁₃	—	2	2	no	—
476	C₂×C₄×C₁₃	—	2	1	no	—
477	C₂×C₄×C₁₃	—	2	1	no	—
478	C₂×C₄×C₁₃	—	2	2	no	—
479	C₂×C₄×C₁₃	—	2	2	no	—
480	C₂×C₄×C₁₃	—	2	2	no	—
481	C₂×C₄×C₁₃	—	4	1	no	—
482	C₂×C₄×C₁₃	—	4	2	no	—
483	C₂×C₄×C₁₃	—	4	4	no	—
484	C₂×C₄×C₁₃	—	4	2	no	—
485	C₂×C₄×C₁₃	—	8	2	no	—
486	C₂×C₄×C₁₃	—	8	2	no	—
487	C₂×C₄×C₁₃	—	8	2	no	—
488	C₂×C₄×C₁₃	—	8	1	no	—
489	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
498	C₈×C₁₃	—	2	2	no	—
499	C₈×C₁₃	—	2	2	no	—
500	C₈×C₁₃	—	2	2	no	—
501	C₈×C₁₃	—	2	2	no	—
502	C₂×#137	C₂²×C₁₃	1	2	yes	—
503	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
504	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
505	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
506	#563	—	2	1	no	—
507	#562	—	2	1	no	—
508	#557	—	2	1	no	—
509	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#557	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#556	—	2	1	no	—
512	#556	C₂²×C₁₃	1	2	yes	—
513	#556	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	#552	—	2	2	no	—
515	#552	C₂²×C₁₃	1	2	yes	—
516	#551	—	2	2	no	—
517	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
518	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
519	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
520	#548	C₂²×C₁₃	1	2	yes	—
521	#546	C₂²×C₁₃	1	2	yes	—
522	#543	—	2	1	no	—
523	#542	—	2	2	no	—
524	#542	C₂²×C₁₃	1	2	yes	—
525	#541	—	2	2	no	—
526	#541	C₂²×C₁₃	1	2	yes	complemented
527	#538	—	2	1	no	—
528	#536	C₂²×C₁₃	1	2	yes	—
529	#533	—	2	1	no	—
530	#533	C₂²×C₁₃	1	1	yes	characteristic
531	#533	C₂²×C₁₃	1	1	yes	characteristic
532	#529	—	2	1	no	—
533	#529	C₂²×C₁₃	1	1	yes	characteristic
534	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
535	#519	C₂²×C₁₃	1	2	yes	complemented
536	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
537	#497	C₂²×C₁₃	1	2	yes	—
538	#497	C₂²×C₁₃	1	2	yes	—
539	#494	C₂²×C₁₃	1	2	yes	complemented
540	#491	C₂²×C₁₃	1	2	yes	complemented
541	#489	C₂²×C₁₃	1	2	yes	—
542	#488	C₂²×C₁₃	1	2	yes	—
543	#485	C₂²×C₁₃	1	2	yes	complemented
544	#483	C₂²×C₁₃	1	2	yes	—
545	#482	C₂²×C₁₃	1	2	yes	—
546	#479	C₂²×C₁₃	1	2	yes	complemented
547	#478	C₂²×C₁₃	1	2	yes	—
548	#477	C₂²×C₁₃	1	2	yes	complemented
549	#477	C₂²×C₁₃	1	2	yes	complemented
550	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
551	#475	C₂²×C₁₃	1	1	yes	characteristic, complemented
552	#470	C₂²×C₁₃	1	2	yes	complemented
553	#468	C₂²×C₁₃	1	2	yes	—
554	#467	C₂²×C₁₃	1	2	yes	—
555	#467	C₂²×C₁₃	1	2	yes	—
556	#467	C₂²×C₁₃	1	2	yes	complemented
557	#465	C₂²×C₁₃	1	2	yes	—
558	#464	C₂²×C₁₃	1	2	yes	—
559	#464	C₂²×C₁₃	1	2	yes	—
560	#464	C₂²×C₁₃	1	2	yes	—
561	#464	C₂²×C₁₃	1	2	yes	—
562	#464	C₂²×C₁₃	1	2	yes	—
563	#464	C₂²×C₁₃	1	2	yes	—
564	#464	C₂²×C₁₃	1	2	yes	—
565	#464	C₂²×C₁₃	1	2	yes	—
566	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
567	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
568	#462	C₂²×C₁₃	1	2	yes	complemented
569	#462	C₂²×C₁₃	1	2	yes	complemented
570	#462	C₂²×C₁₃	1	2	yes	complemented
571	#462	C₂²×C₁₃	1	2	yes	complemented
572	#462	C₂²×C₁₃	1	2	yes	complemented
573	#461	C₂²×C₁₃	1	2	yes	—
574	#452	C₂²×C₁₃	1	2	yes	—
575	#452	C₂²×C₁₃	1	2	yes	—
576	#451	C₂²×C₁₃	1	2	yes	—
577	#451	C₂²×C₁₃	1	2	yes	—
578	#451	C₂²×C₁₃	1	2	yes	complemented
579	#451	C₂²×C₁₃	1	2	yes	complemented
580	#451	C₂²×C₁₃	1	2	yes	complemented
581	#450	C₂²×C₁₃	1	2	yes	—
582	#448	C₂²×C₁₃	1	2	yes	—
583	#446	C₂²×C₁₃	1	2	yes	complemented
584	#441	C₂²×C₁₃	1	2	yes	complemented
585	#441	C₂²×C₁₃	1	2	yes	complemented
586	#441	C₂²×C₁₃	1	2	yes	complemented
587	#440	C₂²×C₁₃	1	2	yes	—
588	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
589	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
590	#435	C₂²×C₁₃	1	2	yes	—
591	#435	C₂²×C₁₃	1	2	yes	complemented
592	C₈×D₄	C₂²×C₁₃	1	2	yes	—
593	#433	C₂²×C₁₃	1	2	yes	complemented
594	#432	C₂²×C₁₃	1	1	yes	characteristic
595	#424	C₂²×C₁₃	1	2	yes	complemented
596	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
597	#419	C₂²×C₁₃	1	2	yes	complemented
598	#416	C₂²×C₁₃	1	2	yes	—
599	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
600	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
601	C₂²×C₁₃	—	2	1	no	—
602	C₂²×C₁₃	—	2	1	no	—
603	C₂²×C₁₃	—	2	2	no	—
604	C₂²×C₁₃	—	2	2	no	—
605	C₂²×C₁₃	—	2	2	no	—
606	C₂²×C₁₃	—	4	2	no	—
607	C₂²×C₁₃	—	4	2	no	—
608	C₂²×C₁₃	—	4	2	no	—
609	C₂²×C₁₃	—	16	2	no	—
610	C₂²×C₁₃	#578	1	2	yes	—
611	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
612	C₄×C₁₃	—	2	1	no	—
613	C₄×C₁₃	—	2	1	no	—
614	C₄×C₁₃	—	2	2	no	—
615	C₄×C₁₃	—	2	2	no	—
616	C₄×C₁₃	—	2	1	no	—
617	C₄×C₁₃	—	2	2	no	—
618	C₄×C₁₃	—	2	1	no	—
619	C₄×C₁₃	—	2	1	no	—
620	C₄×C₁₃	—	2	2	no	—
621	C₄×C₁₃	—	4	2	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	—	4	1	no	—
624	C₄×C₁₃	—	4	2	no	—
625	C₄×C₁₃	—	4	2	no	—
626	C₄×C₁₃	—	4	2	no	—
627	C₄×C₁₃	—	4	1	no	—
628	C₄×C₁₃	—	4	1	no	—
629	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	C₄×C₁₃	#585	1	1	yes	characteristic
631	C₂×#41	C₂³×C₁₃	1	2	yes	—
632	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
633	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
634	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
636	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
637	#137	—	4	4	no	—
638	C₂×Q₁₆	—	4	2	no	—
639	C₂×Q₁₆	—	4	4	no	—
640	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
641	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
642	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
643	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
644	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
645	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
646	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
647	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
648	C₂×SD₁₆	—	4	2	no	—
649	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
650	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
651	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
652	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
653	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
654	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
655	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
656	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
657	C₄⋊Q₈	—	2	1	no	—
658	C₄⋊Q₈	—	2	1	no	—
659	C₄⋊Q₈	—	2	2	no	—
660	C₄⋊Q₈	—	2	2	no	—
661	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
662	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
663	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
664	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
665	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
666	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
667	#126	—	2	2	no	—
668	#126	—	2	2	no	—
669	#126	—	2	2	no	—
670	#126	—	2	2	no	—
671	#126	—	2	2	no	—
672	#126	—	2	2	no	—
673	#126	—	2	2	no	—
674	#126	D₄×C₁₃	1	2	yes	—
675	#125	—	2	1	no	—
676	#125	—	2	2	no	—
677	#125	—	2	2	no	—
678	#125	—	2	2	no	—
679	#125	—	2	2	no	—
680	#125	—	2	2	no	—
681	#125	—	2	1	no	—
682	#125	—	2	1	no	—
683	#125	D₄×C₁₃	1	1	yes	characteristic
684	#125	C₂³×C₁₃	1	2	yes	—
685	#124	—	2	1	no	—
686	#124	—	2	2	no	—
687	#124	—	2	2	no	—
688	#124	—	2	1	no	—
689	#124	—	2	1	no	—
690	#124	D₄×C₁₃	1	1	yes	characteristic
691	#124	C₂³×C₁₃	1	2	yes	—
692	#124	C₂³×C₁₃	1	2	yes	—
693	#124	C₂³×C₁₃	1	2	yes	—
694	#123	—	2	2	no	—
695	#123	—	2	2	no	—
696	#123	—	2	2	no	—
697	#123	—	2	2	no	—
698	#123	—	2	2	no	—
699	#123	D₄×C₁₃	1	2	yes	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	1	no	—
702	C₂²⋊Q₈	—	2	1	no	—
703	C₂²⋊Q₈	—	2	2	no	—
704	C₂²⋊Q₈	—	2	2	no	—
705	C₂²⋊Q₈	—	2	2	no	—
706	C₂²⋊Q₈	—	2	2	no	—
707	C₂²⋊Q₈	—	2	2	no	—
708	C₂²⋊Q₈	—	2	2	no	—
709	C₂²⋊Q₈	—	2	2	no	—
710	C₂²⋊Q₈	—	2	2	no	—
711	C₂²⋊Q₈	—	2	2	no	—
712	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
713	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
714	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
715	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
716	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
717	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
718	#121	—	2	2	no	—
719	#121	—	2	2	no	—
720	#121	D₄×C₁₃	1	1	yes	characteristic
721	#121	C₂³×C₁₃	1	2	yes	—
722	#120	—	2	2	no	—
723	C₄×Q₈	—	2	1	no	—
724	C₄×Q₈	—	2	2	no	—
725	C₄×Q₈	—	2	2	no	—
726	C₄×Q₈	—	2	1	no	—
727	C₄×Q₈	—	2	1	no	—
728	C₄×Q₈	—	2	1	no	—
729	C₄×Q₈	—	2	1	no	—
730	C₄×Q₈	—	2	1	no	—
731	C₄×Q₈	—	2	1	no	—
732	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
733	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
734	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
735	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
736	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
737	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
738	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
739	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
740	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
741	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
742	C₄×D₄	—	2	2	no	—
743	C₄×D₄	—	2	1	no	—
744	C₄×D₄	—	2	2	no	—
745	C₄×D₄	—	2	2	no	—
746	C₄×D₄	C₂³×C₁₃	1	2	yes	—
747	C₄×D₄	C₂³×C₁₃	1	2	yes	—
748	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
749	#117	—	2	1	no	—
750	#117	—	2	1	no	—
751	#117	—	2	2	no	—
752	#117	—	2	2	no	—
753	#117	—	2	2	no	—
754	#117	—	2	2	no	—
755	#117	C₂³×C₁₃	1	2	yes	—
756	#117	C₂³×C₁₃	1	2	yes	—
757	C₂×C₄⋊C₄	—	2	1	no	—
758	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	—	2	1	no	—
760	C₂×C₂²⋊C₄	—	2	1	no	—
761	C₂×C₂²⋊C₄	—	2	2	no	—
762	C₂×C₄²	—	2	1	no	—
763	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
764	#107	C₂³×C₁₃	1	2	yes	—
765	#107	C₂³×C₁₃	1	2	yes	—
766	#106	C₂³×C₁₃	1	2	yes	—
767	#106	C₂³×C₁₃	1	2	yes	—
768	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
769	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
770	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
772	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
773	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
774	#103	C₂³×C₁₃	1	2	yes	—
775	#103	C₂³×C₁₃	1	2	yes	—
776	#103	C₂³×C₁₃	1	2	yes	—
777	#103	C₂³×C₁₃	1	2	yes	—
778	#103	C₂³×C₁₃	1	2	yes	—
779	#103	C₂³×C₁₃	1	2	yes	—
780	#103	C₂³×C₁₃	1	2	yes	—
781	#103	C₂³×C₁₃	1	2	yes	—
782	#103	C₂³×C₁₃	1	2	yes	—
783	#103	C₂³×C₁₃	1	2	yes	—
784	#103	C₂³×C₁₃	1	2	yes	—
785	#103	C₂³×C₁₃	1	2	yes	—
786	#102	C₂³×C₁₃	1	2	yes	—
787	#102	C₂³×C₁₃	1	2	yes	—
788	#102	C₂³×C₁₃	1	2	yes	—
789	#102	C₂³×C₁₃	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
793	#97	C₂³×C₁₃	1	2	yes	—
794	#97	C₂³×C₁₃	1	2	yes	—
795	C₄×C₈	C₂³×C₁₃	1	2	yes	—
796	C₂×C₁₃	—	2	2	no	—
797	C₂×C₁₃	—	4	2	no	—
798	C₂×C₁₃	—	8	2	no	—
799	C₂×C₁₃	#3488	1	1	yes	characteristic
800	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
801	C₂×C₁₃	#3586	1	1	yes	characteristic
802	C₂⁴	—	2	1	no	—
803	#41	—	4	2	no	—
804	#41	—	4	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	2	2	no	—
807	C₂×Q₈	—	2	1	no	—
808	C₂×Q₈	—	2	1	no	—
809	C₂×Q₈	—	2	2	no	—
810	C₂×Q₈	—	2	1	no	—
811	C₂×Q₈	—	2	2	no	—
812	C₂×Q₈	—	2	4	no	—
813	C₂×Q₈	—	4	1	no	—
814	C₂×Q₈	—	4	2	no	—
815	C₂×Q₈	—	4	1	no	—
816	C₂×Q₈	—	4	2	no	—
817	C₂×Q₈	—	4	1	no	—
818	C₂×Q₈	—	4	2	no	—
819	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
821	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
822	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
823	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
824	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	2	no	—
827	C₂×D₄	—	2	1	no	—
828	C₂×D₄	—	4	1	no	—
829	C₂×D₄	—	4	1	no	—
830	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
831	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	1	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	2	2	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
841	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
844	Q₁₆	—	2	4	no	—
845	Q₁₆	—	2	4	no	—
846	Q₁₆	—	4	2	no	—
847	Q₁₆	—	4	2	no	—
848	Q₁₆	—	4	2	no	—
849	Q₁₆	—	4	2	no	—
850	Q₁₆	—	4	2	no	—
851	Q₁₆	—	4	2	no	—
852	SD₁₆	—	2	4	no	—
853	SD₁₆	—	4	2	no	—
854	SD₁₆	—	4	2	no	—
855	SD₁₆	—	4	2	no	—
856	M₁₆	—	4	2	no	—
857	C₂×C₈	—	4	1	no	—
858	C₂×C₈	—	4	1	no	—
859	C₂×C₈	—	4	2	no	—
860	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
861	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
862	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
863	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	1	no	—
874	C₄⋊C₄	—	2	1	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	1	no	—
877	C₄⋊C₄	—	2	1	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	2	no	—
883	C₄⋊C₄	—	2	2	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	2	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	2	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
892	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
893	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
894	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
895	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
896	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
897	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
898	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
899	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
900	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	2	2	no	—
909	C₂²⋊C₄	—	2	2	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
916	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
917	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
918	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
919	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
920	C₄²	—	2	1	no	—
921	C₄²	—	2	1	no	—
922	C₄²	—	2	1	no	—
923	C₄²	—	2	1	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
931	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
932	C₄²	C₂⁴×C₁₃	1	2	yes	—
933	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
934	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
935	C₁₃	#62020	1	1	yes	characteristic, direct product factor, Sylow
936	C₂³	—	2	2	no	—
937	C₂³	—	4	2	no	—
938	C₂³	—	8	1	no	—
939	C₂³	—	8	1	no	—
940	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
941	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
942	Q₈	—	2	1	no	—
943	Q₈	—	2	1	no	—
944	Q₈	—	2	2	no	—
945	Q₈	—	2	2	no	—
946	Q₈	—	2	2	no	—
947	Q₈	—	2	2	no	—
948	Q₈	—	2	1	no	—
949	Q₈	—	2	2	no	—
950	Q₈	—	2	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	4	4	no	—
953	Q₈	—	4	2	no	—
954	Q₈	—	4	2	no	—
955	Q₈	—	8	2	no	—
956	Q₈	—	8	1	no	—
957	Q₈	—	8	1	no	—
958	Q₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
959	D₄	—	2	4	no	—
960	D₄	—	2	2	no	—
961	D₄	—	2	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	8	1	no	—
964	D₄	—	8	2	no	—
965	D₄	—	8	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	4	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	8	2	no	—
985	C₂×C₄	—	8	2	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	1	no	—
988	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
989	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
990	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
991	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
992	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
993	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
994	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
995	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
996	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
997	C₈	—	2	2	no	—
998	C₈	—	2	2	no	—
999	C₈	—	2	2	no	—
1000	C₈	—	2	2	no	—
1001	C₂²	—	2	1	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	2	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	16	2	no	—
1010	C₂²	C₁₃×#578	1	2	yes	—
1011	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	2	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	2	1	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	2	no	—
1021	C₄	—	4	1	no	—
1022	C₄	—	4	1	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	2	no	—
1025	C₄	—	4	1	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
1030	C₄	C₁₃×#585	1	1	yes	characteristic
1031	C₂	—	2	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	8	2	no	—
1034	C₂	C₁₃×#3488	1	1	yes	characteristic
1035	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
1036	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3561	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3523	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3377	C₂	semidirect
5. C₁₃×#3313	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3296	C₂	semidirect
8. D₄×C₁₃×Q₁₆	C₂	semidirect
9. C₁₃×#3270	C₂	semidirect
10. C₁₃×#3266	C₂	semidirect
11. C₁₃×#3258	C₂	semidirect
12. C₁₃×#3249	C₂	semidirect
13. C₁₃×#3223	C₂	semidirect
14. C₁₃×#3215	C₂	semidirect
15. C₁₃×#3121	C₂	semidirect
16. C₁₃×#3113	C₂	semidirect
17. C₁₃×#3044	C₂	semidirect
18. C₂×C₁₃×#464	C₂	semidirect
19. C₁₃×#2992	C₂	semidirect
22. C₂²×C₁₃×Q₁₆	C₂²	semidirect
27. C₁₃×#557	C₂²	semidirect
28. C₁₃×#557	C₂²	semidirect
31. C₁₃×#556	C₂²	semidirect
37. D₄×Q₈×C₁₃	C₂²	semidirect
44. C₁₃×#541	C₂²	semidirect
53. C₁₃×#519	C₂²	semidirect
57. C₁₃×#494	C₂²	semidirect
58. C₁₃×#491	C₂²	semidirect
61. C₁₃×#485	C₂²	semidirect
64. C₁₃×#479	C₂²	semidirect
66. C₁₃×#477	C₂²	semidirect
67. C₁₃×#477	C₂²	semidirect
68. C₁₃×#475	C₂²	semidirect
69. C₁₃×#475	C₂²	semidirect
70. C₁₃×#470	C₂²	semidirect
74. C₁₃×#467	C₂²	semidirect
84. C₁₃×#462	C₂²	semidirect
85. C₁₃×#462	C₂²	semidirect
86. C₁₃×#462	C₂²	semidirect
87. C₁₃×#462	C₂²	semidirect
88. C₁₃×#462	C₂²	semidirect
89. C₁₃×#462	C₂²	semidirect
90. C₁₃×#462	C₂²	semidirect
96. C₁₃×#451	C₂²	semidirect
97. C₁₃×#451	C₂²	semidirect
98. C₁₃×#451	C₂²	semidirect
101. C₁₃×#446	C₂²	semidirect
102. C₁₃×#441	C₂²	semidirect
103. C₁₃×#441	C₂²	semidirect
104. C₁₃×#441	C₂²	semidirect
106. C₄×C₁₃×Q₁₆	C₂²	semidirect
109. C₁₃×#435	C₂²	semidirect
111. C₁₃×#433	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
115. C₁₃×#419	C₂²	semidirect
284. #62020	C₁₃	direct (N × H)
419. #3523	C₂×C₁₃	semidirect
420. #3398	C₂×C₁₃	semidirect
421. #3377	C₂×C₁₃	semidirect
422. #3313	C₂×C₁₃	semidirect
423. #3312	C₂×C₁₃	semidirect
424. #3296	C₂×C₁₃	semidirect
425. D₄×Q₁₆	C₂×C₁₃	semidirect
426. #3270	C₂×C₁₃	semidirect
427. #3266	C₂×C₁₃	semidirect
428. #3258	C₂×C₁₃	semidirect
429. #3249	C₂×C₁₃	semidirect
430. #3223	C₂×C₁₃	semidirect
431. #3215	C₂×C₁₃	semidirect
432. #3121	C₂×C₁₃	semidirect
433. #3113	C₂×C₁₃	semidirect
434. #3044	C₂×C₁₃	semidirect
435. C₂×#464	C₂×C₁₃	semidirect
436. #2992	C₂×C₁₃	semidirect
504. C₂²×Q₁₆	C₂²×C₁₃	semidirect
509. #557	C₂²×C₁₃	semidirect
510. #557	C₂²×C₁₃	semidirect
513. #556	C₂²×C₁₃	semidirect
519. D₄×Q₈	C₂²×C₁₃	semidirect
526. #541	C₂²×C₁₃	semidirect
535. #519	C₂²×C₁₃	semidirect
539. #494	C₂²×C₁₃	semidirect
540. #491	C₂²×C₁₃	semidirect
543. #485	C₂²×C₁₃	semidirect
546. #479	C₂²×C₁₃	semidirect
548. #477	C₂²×C₁₃	semidirect
549. #477	C₂²×C₁₃	semidirect
550. #475	C₂²×C₁₃	semidirect
551. #475	C₂²×C₁₃	semidirect
552. #470	C₂²×C₁₃	semidirect
556. #467	C₂²×C₁₃	semidirect
566. #462	C₂²×C₁₃	semidirect
567. #462	C₂²×C₁₃	semidirect
568. #462	C₂²×C₁₃	semidirect
569. #462	C₂²×C₁₃	semidirect
570. #462	C₂²×C₁₃	semidirect
571. #462	C₂²×C₁₃	semidirect
572. #462	C₂²×C₁₃	semidirect
578. #451	C₂²×C₁₃	semidirect
579. #451	C₂²×C₁₃	semidirect
580. #451	C₂²×C₁₃	semidirect
583. #446	C₂²×C₁₃	semidirect
584. #441	C₂²×C₁₃	semidirect
585. #441	C₂²×C₁₃	semidirect
586. #441	C₂²×C₁₃	semidirect
588. C₄×Q₁₆	C₂²×C₁₃	semidirect
591. #435	C₂²×C₁₃	semidirect
593. #433	C₂²×C₁₃	semidirect
595. #424	C₂²×C₁₃	semidirect
597. #419	C₂²×C₁₃	semidirect
935. C₁₃	#62020	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×#3561	2
C₁₃×#3523	2
C₁₃×#3398	2
C₁₃×#3377	2
C₁₃×#3313	2
C₁₃×#3312	2
C₁₃×#3296	2
D₄×C₁₃×Q₁₆	2
C₁₃×#3270	2
C₁₃×#3266	2
C₁₃×#3258	2
C₁₃×#3249	2
C₁₃×#3223	2
C₁₃×#3215	2
C₁₃×#3121	2
C₁₃×#3113	2
C₁₃×#3044	2
C₂×C₁₃×#464	2
C₁₃×#2992	2
#62020	13

Subgroups — C13×#62020 #15748359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62020 #15748359