Subgroups — C₁₃×#61672 #15748011

Order 3328.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3321	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3317	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3316	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3271	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3270	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3269	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3216	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3201	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
18	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
19	C₁₃×#2980	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
21	C₂×C₁₃×#137	C₂²	1	2	yes	—
22	C₂×C₁₃×#137	C₂²	1	2	yes	—
23	C₂×C₁₃×#135	C₂²	1	2	yes	—
24	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
25	C₁₃×#562	—	2	2	no	—
26	C₁₃×#555	—	2	1	no	—
27	C₁₃×#555	C₂²	1	1	yes	characteristic
28	C₁₃×#554	C₂²	1	1	yes	characteristic
29	C₁₃×#553	—	2	1	no	—
30	C₁₃×#552	C₂²	1	2	yes	—
31	C₁₃×#550	—	2	1	no	—
32	C₁₃×#550	C₂²	1	2	yes	—
33	D₄×Q₈×C₁₃	—	2	1	no	—
34	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#548	—	2	2	no	—
37	C₁₃×#548	C₂²	1	2	yes	—
38	C₁₃×#548	C₂²	1	2	yes	—
39	C₁₃×#548	C₂²	1	2	yes	—
40	C₁₃×#547	C₂²	1	1	yes	characteristic
41	C₁₃×#544	—	2	1	no	—
42	C₁₃×#542	—	2	2	no	—
43	C₁₃×#540	—	2	1	no	—
44	C₁₃×#537	—	2	1	no	—
45	C₁₃×#537	—	2	1	no	—
46	C₁₃×#537	C₂²	1	2	yes	—
47	C₁₃×#537	C₂²	1	2	yes	—
48	C₁₃×#536	C₂²	1	2	yes	—
49	C₁₃×#533	C₂²	1	1	yes	characteristic
50	C₁₃×#532	—	2	2	no	—
51	C₁₃×#532	C₂²	1	1	yes	characteristic
52	C₁₃×#532	C₂²	1	1	yes	characteristic
53	C₁₃×#529	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#497	C₂²	1	2	yes	—
56	C₁₃×#497	C₂²	1	1	yes	characteristic
57	C₁₃×#496	C₂²	1	1	yes	characteristic
58	C₁₃×#491	C₂²	1	1	yes	characteristic
59	C₁₃×#490	C₂²	1	1	yes	characteristic
60	C₁₃×#489	C₂²	1	2	yes	—
61	C₁₃×#485	C₂²	1	2	yes	—
62	C₁₃×#484	C₂²	1	1	yes	characteristic
63	C₁₃×#483	C₂²	1	2	yes	—
64	C₁₃×#483	C₂²	1	2	yes	—
65	C₁₃×#482	C₂²	1	2	yes	—
66	C₁₃×#481	C₂²	1	2	yes	—
67	C₁₃×#481	C₂²	1	1	yes	characteristic
68	C₁₃×#479	C₂²	1	2	yes	—
69	C₁₃×#475	C₂²	1	2	yes	—
70	C₁₃×#470	C₂²	1	2	yes	—
71	C₁₃×#470	C₂²	1	2	yes	—
72	C₁₃×#469	C₂²	1	2	yes	—
73	C₁₃×#468	C₂²	1	2	yes	—
74	C₁₃×#467	C₂²	1	2	yes	—
75	C₁₃×#465	C₂²	1	2	yes	—
76	C₁₃×#465	C₂²	1	2	yes	—
77	C₁₃×#465	C₂²	1	2	yes	—
78	C₁₃×#464	C₂²	1	2	yes	—
79	C₁₃×#464	C₂²	1	2	yes	—
80	C₁₃×#463	C₂²	1	2	yes	—
81	C₁₃×#462	C₂²	1	2	yes	—
82	C₁₃×#462	C₂²	1	2	yes	—
83	C₁₃×#460	C₂²	1	2	yes	—
84	C₁₃×#452	C₂²	1	2	yes	—
85	C₁₃×#452	C₂²	1	2	yes	—
86	C₁₃×#452	C₂²	1	2	yes	—
87	C₁₃×#452	C₂²	1	2	yes	—
88	C₁₃×#452	C₂²	1	2	yes	—
89	C₁₃×#452	C₂²	1	2	yes	—
90	C₁₃×#452	C₂²	1	2	yes	—
91	C₁₃×#451	C₂²	1	1	yes	characteristic
92	C₁₃×#451	C₂²	1	2	yes	—
93	C₁₃×#451	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	—
97	C₁₃×#449	C₂²	1	2	yes	—
98	C₁₃×#449	C₂²	1	2	yes	—
99	C₁₃×#449	C₂²	1	2	yes	—
100	C₁₃×#448	C₂²	1	1	yes	characteristic
101	C₁₃×#448	C₂²	1	2	yes	—
102	C₁₃×#448	C₂²	1	2	yes	—
103	C₁₃×#441	C₂²	1	2	yes	—
104	C₁₃×#441	C₂²	1	2	yes	—
105	C₁₃×#441	C₂²	1	2	yes	—
106	C₁₃×#440	C₂²	1	2	yes	—
107	C₁₃×#435	C₂²	1	2	yes	—
108	C₁₃×#435	C₂²	1	2	yes	—
109	C₁₃×#435	C₂²	1	2	yes	—
110	C₁₃×#435	C₂²	1	2	yes	—
111	C₁₃×#432	C₂²	1	1	yes	characteristic
112	C₁₃×#432	C₂²	1	1	yes	characteristic
113	C₁₃×#419	C₂²	1	2	yes	—
114	C₁₃×#417	C₂²	1	2	yes	—
115	C₁₃×#416	C₂²	1	2	yes	—
116	C₂×C₁₃×#103	C₂²	1	2	yes	—
117	C₁₃×#408	C₂²	1	2	yes	—
118	C₁₃×#408	C₂²	1	2	yes	—
119	C₁₃×2₋¹⁺⁴	—	4	4	no	—
120	C₁₃×2₋¹⁺⁴	—	4	4	no	—
121	C₂×C₁₃×#41	—	2	2	no	—
122	C₂×C₁₃×#41	—	2	2	no	—
123	C₂×C₁₃×#41	—	2	2	no	—
124	C₂×C₁₃×#41	C₂³	1	2	yes	—
125	C₂×C₁₃×#41	C₂³	1	2	yes	—
126	C₂×C₁₃×#41	C₂³	1	2	yes	—
127	C₂×C₁₃×#41	C₂³	1	2	yes	—
128	C₂×C₁₃×#41	C₂³	1	2	yes	—
129	C₂²×Q₈×C₁₃	—	2	2	no	—
130	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
132	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
133	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×#137	—	4	4	no	—
135	C₁₃×#137	—	4	4	no	—
136	C₁₃×#135	—	4	4	no	—
137	C₂×C₁₃×Q₁₆	—	4	4	no	—
138	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
139	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
140	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
143	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
144	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
145	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
146	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
147	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
148	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
149	C₂×C₁₃×D₈	C₂³	1	2	yes	—
150	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
151	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
152	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
153	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
154	C₁₃×C₄⋊Q₈	—	2	2	no	—
155	C₁₃×C₄⋊Q₈	—	2	2	no	—
156	C₁₃×C₄⋊Q₈	—	2	1	no	—
157	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×#127	—	2	2	no	—
162	C₁₃×#127	D₄	1	1	yes	characteristic
163	C₁₃×#127	C₂³	1	1	yes	characteristic
164	C₁₃×#126	—	2	2	no	—
165	C₁₃×#126	—	2	1	no	—
166	C₁₃×#125	—	2	2	no	—
167	C₁₃×#125	—	2	1	no	—
168	C₁₃×#125	—	2	1	no	—
169	C₁₃×#125	C₂³	1	1	yes	characteristic
170	C₁₃×#124	—	2	2	no	—
171	C₁₃×#124	—	2	2	no	—
172	C₁₃×#124	—	2	2	no	—
173	C₁₃×#124	—	2	2	no	—
174	C₁₃×#124	—	2	2	no	—
175	C₁₃×#124	D₄	1	2	yes	—
176	C₁₃×#124	C₂³	1	2	yes	—
177	C₁₃×#124	C₂³	1	1	yes	characteristic
178	C₁₃×#123	—	2	2	no	—
179	C₁₃×#123	—	2	2	no	—
180	C₁₃×#123	—	2	2	no	—
181	C₁₃×#123	—	2	1	no	—
182	C₁₃×#123	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	—	2	2	no	—
185	C₁₃×C₂²⋊Q₈	—	2	1	no	—
186	C₁₃×C₂²⋊Q₈	—	2	2	no	—
187	C₁₃×C₂²⋊Q₈	—	2	2	no	—
188	C₁₃×C₂²⋊Q₈	—	2	2	no	—
189	C₁₃×C₂²⋊Q₈	—	2	2	no	—
190	C₁₃×C₂²⋊Q₈	—	2	2	no	—
191	C₁₃×C₂²⋊Q₈	—	2	2	no	—
192	C₁₃×C₂²⋊Q₈	—	2	2	no	—
193	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₁₃×#121	—	2	2	no	—
201	C₁₃×#121	—	2	2	no	—
202	C₁₃×#121	—	2	2	no	—
203	C₁₃×#121	—	2	2	no	—
204	C₁₃×#121	—	2	2	no	—
205	C₁₃×#121	—	2	2	no	—
206	C₁₃×#121	—	2	2	no	—
207	C₁₃×#121	—	2	2	no	—
208	C₁₃×#121	—	2	1	no	—
209	C₁₃×#121	—	2	2	no	—
210	C₁₃×#121	—	2	1	no	—
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	2	yes	—
216	C₁₃×#121	D₄	1	1	yes	characteristic
217	C₁₃×#121	D₄	1	1	yes	characteristic
218	C₁₃×#121	C₂³	1	1	yes	characteristic
219	C₁₃×#121	C₂³	1	2	yes	—
220	C₁₃×#121	C₂³	1	2	yes	—
221	C₁₃×#121	C₂³	1	2	yes	—
222	C₄×Q₈×C₁₃	—	2	1	no	—
223	C₄×Q₈×C₁₃	—	2	1	no	—
224	C₄×Q₈×C₁₃	—	2	1	no	—
225	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
227	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
229	C₄×D₄×C₁₃	—	2	2	no	—
230	C₄×D₄×C₁₃	—	2	1	no	—
231	C₄×D₄×C₁₃	—	2	1	no	—
232	C₄×D₄×C₁₃	—	2	1	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	2	no	—
237	C₄×D₄×C₁₃	—	2	1	no	—
238	C₄×D₄×C₁₃	—	2	1	no	—
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	2	yes	—
243	C₁₃×#117	—	2	1	no	—
244	C₁₃×#117	—	2	1	no	—
245	C₁₃×#117	—	2	2	no	—
246	C₁₃×#117	—	2	1	no	—
247	C₁₃×#117	C₂³	1	2	yes	—
248	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
252	C₂×C₄²×C₁₃	—	2	1	no	—
253	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
254	C₁₃×#107	C₂³	1	2	yes	—
255	C₁₃×#106	C₂³	1	2	yes	—
256	C₁₃×#106	C₂³	1	2	yes	—
257	C₁₃×#106	C₂³	1	2	yes	—
258	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
259	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₁₃×#103	C₂³	1	2	yes	—
261	C₁₃×#103	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
272	C₁₃×#102	C₂³	1	2	yes	—
273	C₁₃×#102	C₂³	1	2	yes	—
274	C₁₃×#102	C₂³	1	2	yes	—
275	C₁₃×#102	C₂³	1	2	yes	—
276	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
277	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₁₃×#97	C₂³	1	2	yes	—
284	C₁₃×#97	C₂³	1	1	yes	characteristic
285	C₁₃×#97	C₂³	1	1	yes	characteristic
286	#61672	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₁₃×#41	—	2	4	no	—
288	C₁₃×#41	—	2	4	no	—
289	C₁₃×#41	—	4	2	no	—
290	C₁₃×#41	—	4	2	no	—
291	C₁₃×#41	—	4	2	no	—
292	C₁₃×#41	—	4	2	no	—
293	C₁₃×#41	—	4	2	no	—
294	C₁₃×#41	—	4	2	no	—
295	C₁₃×#41	—	4	8	no	—
296	C₁₃×#41	—	4	8	no	—
297	C₁₃×#41	—	4	2	no	—
298	C₁₃×#41	—	4	2	no	—
299	C₁₃×#41	—	4	8	no	—
300	C₂×Q₈×C₁₃	—	2	4	no	—
301	C₂×Q₈×C₁₃	—	2	1	no	—
302	C₂×Q₈×C₁₃	—	2	2	no	—
303	C₂×Q₈×C₁₃	—	2	2	no	—
304	C₂×Q₈×C₁₃	—	2	1	no	—
305	C₂×Q₈×C₁₃	—	2	2	no	—
306	C₂×Q₈×C₁₃	—	2	4	no	—
307	C₂×Q₈×C₁₃	—	2	4	no	—
308	C₂×Q₈×C₁₃	—	4	2	no	—
309	C₂×Q₈×C₁₃	—	4	2	no	—
310	C₂×Q₈×C₁₃	—	4	2	no	—
311	C₂×Q₈×C₁₃	—	4	2	no	—
312	C₂×Q₈×C₁₃	—	4	8	no	—
313	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
314	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
316	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
317	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
318	C₂×D₄×C₁₃	—	2	2	no	—
319	C₂×D₄×C₁₃	—	2	2	no	—
320	C₂×D₄×C₁₃	—	2	2	no	—
321	C₂×D₄×C₁₃	—	2	1	no	—
322	C₂×D₄×C₁₃	—	2	2	no	—
323	C₂×D₄×C₁₃	—	2	2	no	—
324	C₂×D₄×C₁₃	—	2	2	no	—
325	C₂×D₄×C₁₃	—	2	2	no	—
326	C₂×D₄×C₁₃	—	2	1	no	—
327	C₂×D₄×C₁₃	—	2	1	no	—
328	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
330	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
331	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
332	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
333	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
334	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
335	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
336	C₂²×C₄×C₁₃	—	2	1	no	—
337	C₂²×C₄×C₁₃	—	2	2	no	—
338	C₂²×C₄×C₁₃	—	2	2	no	—
339	C₂²×C₄×C₁₃	—	2	1	no	—
340	C₂²×C₄×C₁₃	—	2	2	no	—
341	C₂²×C₄×C₁₃	—	2	2	no	—
342	C₂²×C₄×C₁₃	—	2	1	no	—
343	C₂²×C₄×C₁₃	—	2	2	no	—
344	C₂²×C₄×C₁₃	—	2	2	no	—
345	C₂²×C₄×C₁₃	—	2	2	no	—
346	C₂²×C₄×C₁₃	—	2	2	no	—
347	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
352	C₁₃×Q₁₆	—	2	4	no	—
353	C₁₃×Q₁₆	—	2	4	no	—
354	C₁₃×Q₁₆	—	2	4	no	—
355	C₁₃×Q₁₆	—	4	2	no	—
356	C₁₃×Q₁₆	—	4	2	no	—
357	C₁₃×Q₁₆	—	4	2	no	—
358	C₁₃×SD₁₆	—	2	4	no	—
359	C₁₃×SD₁₆	—	4	2	no	—
360	C₁₃×SD₁₆	—	4	2	no	—
361	C₁₃×SD₁₆	—	4	2	no	—
362	C₁₃×SD₁₆	—	4	2	no	—
363	C₁₃×D₈	—	4	2	no	—
364	C₁₃×M₁₆	—	4	2	no	—
365	C₁₃×M₁₆	—	4	2	no	—
366	C₂×C₈×C₁₃	—	4	2	no	—
367	C₂×C₈×C₁₃	—	4	2	no	—
368	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
369	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
372	C₁₃×C₄⋊C₄	—	2	1	no	—
373	C₁₃×C₄⋊C₄	—	2	2	no	—
374	C₁₃×C₄⋊C₄	—	2	2	no	—
375	C₁₃×C₄⋊C₄	—	2	2	no	—
376	C₁₃×C₄⋊C₄	—	2	1	no	—
377	C₁₃×C₄⋊C₄	—	2	2	no	—
378	C₁₃×C₄⋊C₄	—	2	1	no	—
379	C₁₃×C₄⋊C₄	—	2	1	no	—
380	C₁₃×C₄⋊C₄	—	2	2	no	—
381	C₁₃×C₄⋊C₄	—	2	1	no	—
382	C₁₃×C₄⋊C₄	—	2	1	no	—
383	C₁₃×C₄⋊C₄	—	2	1	no	—
384	C₁₃×C₄⋊C₄	—	2	1	no	—
385	C₁₃×C₄⋊C₄	—	2	2	no	—
386	C₁₃×C₄⋊C₄	—	2	2	no	—
387	C₁₃×C₄⋊C₄	—	2	2	no	—
388	C₁₃×C₄⋊C₄	—	2	2	no	—
389	C₁₃×C₄⋊C₄	—	2	1	no	—
390	C₁₃×C₄⋊C₄	—	2	2	no	—
391	C₁₃×C₄⋊C₄	—	2	1	no	—
392	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
394	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
395	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
396	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
397	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
398	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
399	C₁₃×C₂²⋊C₄	—	2	2	no	—
400	C₁₃×C₂²⋊C₄	—	2	2	no	—
401	C₁₃×C₂²⋊C₄	—	2	2	no	—
402	C₁₃×C₂²⋊C₄	—	2	2	no	—
403	C₁₃×C₂²⋊C₄	—	2	2	no	—
404	C₁₃×C₂²⋊C₄	—	2	2	no	—
405	C₁₃×C₂²⋊C₄	—	2	2	no	—
406	C₁₃×C₂²⋊C₄	—	2	1	no	—
407	C₁₃×C₂²⋊C₄	—	2	1	no	—
408	C₁₃×C₂²⋊C₄	—	2	1	no	—
409	C₁₃×C₂²⋊C₄	—	2	2	no	—
410	C₁₃×C₂²⋊C₄	—	2	2	no	—
411	C₁₃×C₂²⋊C₄	—	2	1	no	—
412	C₁₃×C₂²⋊C₄	—	2	2	no	—
413	C₁₃×C₂²⋊C₄	—	2	2	no	—
414	C₁₃×C₂²⋊C₄	—	2	2	no	—
415	C₁₃×C₂²⋊C₄	—	2	1	no	—
416	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
417	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
418	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
419	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
420	C₄²×C₁₃	—	2	2	no	—
421	C₄²×C₁₃	—	2	2	no	—
422	C₄²×C₁₃	—	2	2	no	—
423	C₄²×C₁₃	—	2	2	no	—
424	C₄²×C₁₃	—	2	1	no	—
425	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
426	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
427	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
428	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
429	#3547	C₂×C₁₃	1	1	yes	characteristic, complemented
430	#3497	C₂×C₁₃	1	1	yes	characteristic, complemented
431	#3321	C₂×C₁₃	1	2	yes	complemented
432	#3317	C₂×C₁₃	1	2	yes	complemented
433	#3316	C₂×C₁₃	1	2	yes	complemented
434	#3312	C₂×C₁₃	1	2	yes	complemented
435	#3271	C₂×C₁₃	1	2	yes	complemented
436	#3270	C₂×C₁₃	1	2	yes	complemented
437	#3270	C₂×C₁₃	1	2	yes	complemented
438	#3269	C₂×C₁₃	1	2	yes	complemented
439	#3219	C₂×C₁₃	1	1	yes	characteristic, complemented
440	#3216	C₂×C₁₃	1	1	yes	characteristic, complemented
441	#3204	C₂×C₁₃	1	2	yes	complemented
442	#3201	C₂×C₁₃	1	2	yes	complemented
443	#3117	C₂×C₁₃	1	1	yes	characteristic, complemented
444	#3113	C₂×C₁₃	1	1	yes	characteristic, complemented
445	#3013	C₂×C₁₃	1	2	yes	complemented
446	#3011	C₂×C₁₃	1	2	yes	complemented
447	#2980	C₂×C₁₃	1	1	yes	characteristic, complemented
448	C₂³×C₁₃	—	2	1	no	—
449	C₂³×C₁₃	—	2	2	no	—
450	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
451	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
453	Q₈×C₁₃	—	2	4	no	—
454	Q₈×C₁₃	—	2	2	no	—
455	Q₈×C₁₃	—	2	2	no	—
456	Q₈×C₁₃	—	2	2	no	—
457	Q₈×C₁₃	—	2	2	no	—
458	Q₈×C₁₃	—	2	2	no	—
459	Q₈×C₁₃	—	2	2	no	—
460	Q₈×C₁₃	—	4	2	no	—
461	Q₈×C₁₃	—	4	4	no	—
462	Q₈×C₁₃	—	4	4	no	—
463	Q₈×C₁₃	—	8	1	no	—
464	Q₈×C₁₃	—	8	2	no	—
465	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	—
466	D₄×C₁₃	—	2	2	no	—
467	D₄×C₁₃	—	2	2	no	—
468	D₄×C₁₃	—	2	2	no	—
469	D₄×C₁₃	—	4	1	no	—
470	D₄×C₁₃	—	4	1	no	—
471	D₄×C₁₃	—	4	2	no	—
472	D₄×C₁₃	—	4	2	no	—
473	D₄×C₁₃	—	4	2	no	—
474	D₄×C₁₃	—	4	2	no	—
475	D₄×C₁₃	—	4	4	no	—
476	D₄×C₁₃	—	4	4	no	—
477	D₄×C₁₃	—	4	2	no	—
478	D₄×C₁₃	—	4	4	no	—
479	D₄×C₁₃	—	8	1	no	—
480	D₄×C₁₃	—	8	1	no	—
481	D₄×C₁₃	—	8	2	no	—
482	D₄×C₁₃	—	8	2	no	—
483	D₄×C₁₃	—	8	2	no	—
484	D₄×C₁₃	—	8	2	no	—
485	C₂×C₄×C₁₃	—	2	4	no	—
486	C₂×C₄×C₁₃	—	2	2	no	—
487	C₂×C₄×C₁₃	—	2	2	no	—
488	C₂×C₄×C₁₃	—	2	2	no	—
489	C₂×C₄×C₁₃	—	2	2	no	—
490	C₂×C₄×C₁₃	—	2	2	no	—
491	C₂×C₄×C₁₃	—	2	2	no	—
492	C₂×C₄×C₁₃	—	2	1	no	—
493	C₂×C₄×C₁₃	—	2	2	no	—
494	C₂×C₄×C₁₃	—	2	2	no	—
495	C₂×C₄×C₁₃	—	2	1	no	—
496	C₂×C₄×C₁₃	—	2	1	no	—
497	C₂×C₄×C₁₃	—	2	2	no	—
498	C₂×C₄×C₁₃	—	2	2	no	—
499	C₂×C₄×C₁₃	—	4	1	no	—
500	C₂×C₄×C₁₃	—	4	1	no	—
501	C₂×C₄×C₁₃	—	4	4	no	—
502	C₂×C₄×C₁₃	—	4	4	no	—
503	C₂×C₄×C₁₃	—	4	4	no	—
504	C₂×C₄×C₁₃	—	4	4	no	—
505	C₂×C₄×C₁₃	—	4	2	no	—
506	C₂×C₄×C₁₃	—	4	4	no	—
507	C₂×C₄×C₁₃	—	8	2	no	—
508	C₂×C₄×C₁₃	—	8	2	no	—
509	C₂×C₄×C₁₃	—	8	1	no	—
510	C₂×C₄×C₁₃	—	8	2	no	—
511	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
516	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
518	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
519	C₈×C₁₃	—	2	2	no	—
520	C₈×C₁₃	—	2	2	no	—
521	C₈×C₁₃	—	2	2	no	—
522	C₈×C₁₃	—	2	2	no	—
523	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
524	C₂×#137	C₂²×C₁₃	1	2	yes	—
525	C₂×#137	C₂²×C₁₃	1	2	yes	—
526	C₂×#135	C₂²×C₁₃	1	2	yes	—
527	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
528	#562	—	2	2	no	—
529	#555	—	2	1	no	—
530	#555	C₂²×C₁₃	1	1	yes	characteristic
531	#554	C₂²×C₁₃	1	1	yes	characteristic
532	#553	—	2	1	no	—
533	#552	C₂²×C₁₃	1	2	yes	—
534	#550	—	2	1	no	—
535	#550	C₂²×C₁₃	1	2	yes	—
536	D₄×Q₈	—	2	1	no	—
537	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
538	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
539	#548	—	2	2	no	—
540	#548	C₂²×C₁₃	1	2	yes	—
541	#548	C₂²×C₁₃	1	2	yes	—
542	#548	C₂²×C₁₃	1	2	yes	—
543	#547	C₂²×C₁₃	1	1	yes	characteristic
544	#544	—	2	1	no	—
545	#542	—	2	2	no	—
546	#540	—	2	1	no	—
547	#537	—	2	1	no	—
548	#537	—	2	1	no	—
549	#537	C₂²×C₁₃	1	2	yes	—
550	#537	C₂²×C₁₃	1	2	yes	—
551	#536	C₂²×C₁₃	1	2	yes	—
552	#533	C₂²×C₁₃	1	1	yes	characteristic
553	#532	—	2	2	no	—
554	#532	C₂²×C₁₃	1	1	yes	characteristic
555	#532	C₂²×C₁₃	1	1	yes	characteristic
556	#529	C₂²×C₁₃	1	1	yes	characteristic
557	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
558	#497	C₂²×C₁₃	1	2	yes	—
559	#497	C₂²×C₁₃	1	1	yes	characteristic
560	#496	C₂²×C₁₃	1	1	yes	characteristic
561	#491	C₂²×C₁₃	1	1	yes	characteristic
562	#490	C₂²×C₁₃	1	1	yes	characteristic
563	#489	C₂²×C₁₃	1	2	yes	—
564	#485	C₂²×C₁₃	1	2	yes	—
565	#484	C₂²×C₁₃	1	1	yes	characteristic
566	#483	C₂²×C₁₃	1	2	yes	—
567	#483	C₂²×C₁₃	1	2	yes	—
568	#482	C₂²×C₁₃	1	2	yes	—
569	#481	C₂²×C₁₃	1	1	yes	characteristic
570	#481	C₂²×C₁₃	1	2	yes	—
571	#479	C₂²×C₁₃	1	2	yes	—
572	#475	C₂²×C₁₃	1	2	yes	—
573	#470	C₂²×C₁₃	1	2	yes	—
574	#470	C₂²×C₁₃	1	2	yes	—
575	#469	C₂²×C₁₃	1	2	yes	—
576	#468	C₂²×C₁₃	1	2	yes	—
577	#467	C₂²×C₁₃	1	2	yes	—
578	#465	C₂²×C₁₃	1	2	yes	—
579	#465	C₂²×C₁₃	1	2	yes	—
580	#465	C₂²×C₁₃	1	2	yes	—
581	#464	C₂²×C₁₃	1	2	yes	—
582	#464	C₂²×C₁₃	1	2	yes	—
583	#463	C₂²×C₁₃	1	2	yes	—
584	#462	C₂²×C₁₃	1	2	yes	—
585	#462	C₂²×C₁₃	1	2	yes	—
586	#460	C₂²×C₁₃	1	2	yes	—
587	#452	C₂²×C₁₃	1	2	yes	—
588	#452	C₂²×C₁₃	1	2	yes	—
589	#452	C₂²×C₁₃	1	2	yes	—
590	#452	C₂²×C₁₃	1	2	yes	—
591	#452	C₂²×C₁₃	1	2	yes	—
592	#452	C₂²×C₁₃	1	2	yes	—
593	#452	C₂²×C₁₃	1	2	yes	—
594	#451	C₂²×C₁₃	1	2	yes	—
595	#451	C₂²×C₁₃	1	1	yes	characteristic
596	#451	C₂²×C₁₃	1	2	yes	—
597	#451	C₂²×C₁₃	1	2	yes	—
598	#451	C₂²×C₁₃	1	2	yes	—
599	#451	C₂²×C₁₃	1	2	yes	—
600	#449	C₂²×C₁₃	1	2	yes	—
601	#449	C₂²×C₁₃	1	2	yes	—
602	#449	C₂²×C₁₃	1	2	yes	—
603	#448	C₂²×C₁₃	1	1	yes	characteristic
604	#448	C₂²×C₁₃	1	2	yes	—
605	#448	C₂²×C₁₃	1	2	yes	—
606	#441	C₂²×C₁₃	1	2	yes	—
607	#441	C₂²×C₁₃	1	2	yes	—
608	#441	C₂²×C₁₃	1	2	yes	—
609	#440	C₂²×C₁₃	1	2	yes	—
610	#435	C₂²×C₁₃	1	2	yes	—
611	#435	C₂²×C₁₃	1	2	yes	—
612	#435	C₂²×C₁₃	1	2	yes	—
613	#435	C₂²×C₁₃	1	2	yes	—
614	#432	C₂²×C₁₃	1	1	yes	characteristic
615	#432	C₂²×C₁₃	1	1	yes	characteristic
616	#419	C₂²×C₁₃	1	2	yes	—
617	#417	C₂²×C₁₃	1	2	yes	—
618	#416	C₂²×C₁₃	1	2	yes	—
619	C₂×#103	C₂²×C₁₃	1	2	yes	—
620	#408	C₂²×C₁₃	1	2	yes	—
621	#408	C₂²×C₁₃	1	2	yes	—
622	C₂²×C₁₃	—	2	1	no	—
623	C₂²×C₁₃	—	2	1	no	—
624	C₂²×C₁₃	—	2	2	no	—
625	C₂²×C₁₃	—	2	2	no	—
626	C₂²×C₁₃	—	2	2	no	—
627	C₂²×C₁₃	—	2	2	no	—
628	C₂²×C₁₃	—	2	1	no	—
629	C₂²×C₁₃	—	2	2	no	—
630	C₂²×C₁₃	—	2	2	no	—
631	C₂²×C₁₃	—	4	1	no	—
632	C₂²×C₁₃	—	4	2	no	—
633	C₂²×C₁₃	—	4	2	no	—
634	C₂²×C₁₃	—	4	1	no	—
635	C₂²×C₁₃	—	4	2	no	—
636	C₂²×C₁₃	—	4	1	no	—
637	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
638	C₄×C₁₃	—	2	1	no	—
639	C₄×C₁₃	—	2	1	no	—
640	C₄×C₁₃	—	2	1	no	—
641	C₄×C₁₃	—	2	1	no	—
642	C₄×C₁₃	—	2	4	no	—
643	C₄×C₁₃	—	2	1	no	—
644	C₄×C₁₃	—	2	2	no	—
645	C₄×C₁₃	—	2	2	no	—
646	C₄×C₁₃	—	4	1	no	—
647	C₄×C₁₃	—	4	1	no	—
648	C₄×C₁₃	—	4	2	no	—
649	C₄×C₁₃	—	4	2	no	—
650	C₄×C₁₃	—	4	2	no	—
651	C₄×C₁₃	—	4	2	no	—
652	C₄×C₁₃	—	4	1	no	—
653	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
654	2₋¹⁺⁴	—	4	4	no	—
655	2₋¹⁺⁴	—	4	4	no	—
656	C₂×#41	—	2	2	no	—
657	C₂×#41	—	2	2	no	—
658	C₂×#41	—	2	2	no	—
659	C₂×#41	C₂³×C₁₃	1	2	yes	—
660	C₂×#41	C₂³×C₁₃	1	2	yes	—
661	C₂×#41	C₂³×C₁₃	1	2	yes	—
662	C₂×#41	C₂³×C₁₃	1	2	yes	—
663	C₂×#41	C₂³×C₁₃	1	2	yes	—
664	C₂²×Q₈	—	2	2	no	—
665	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
666	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
667	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
668	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
669	#137	—	4	4	no	—
670	#137	—	4	4	no	—
671	#135	—	4	4	no	—
672	C₂×Q₁₆	—	4	4	no	—
673	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
674	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
675	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
676	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
677	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
679	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
683	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
684	C₂×D₈	C₂³×C₁₃	1	2	yes	—
685	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
686	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
687	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
688	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
689	C₄⋊Q₈	—	2	2	no	—
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	1	no	—
692	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
693	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
694	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
695	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
696	#127	—	2	2	no	—
697	#127	D₄×C₁₃	1	1	yes	characteristic
698	#127	C₂³×C₁₃	1	1	yes	characteristic
699	#126	—	2	2	no	—
700	#126	—	2	1	no	—
701	#125	—	2	2	no	—
702	#125	—	2	1	no	—
703	#125	—	2	1	no	—
704	#125	C₂³×C₁₃	1	1	yes	characteristic
705	#124	—	2	2	no	—
706	#124	—	2	2	no	—
707	#124	—	2	2	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	D₄×C₁₃	1	2	yes	—
711	#124	C₂³×C₁₃	1	1	yes	characteristic
712	#124	C₂³×C₁₃	1	2	yes	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	1	no	—
717	#123	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	2	no	—
725	C₂²⋊Q₈	—	2	2	no	—
726	C₂²⋊Q₈	—	2	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
729	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
730	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
731	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
733	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
734	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	—	2	2	no	—
742	#121	—	2	2	no	—
743	#121	—	2	1	no	—
744	#121	—	2	2	no	—
745	#121	—	2	1	no	—
746	#121	—	2	1	no	—
747	#121	—	2	1	no	—
748	#121	—	2	2	no	—
749	#121	—	2	2	no	—
750	#121	D₄×C₁₃	1	2	yes	—
751	#121	D₄×C₁₃	1	1	yes	characteristic
752	#121	D₄×C₁₃	1	1	yes	characteristic
753	#121	C₂³×C₁₃	1	1	yes	characteristic
754	#121	C₂³×C₁₃	1	2	yes	—
755	#121	C₂³×C₁₃	1	2	yes	—
756	#121	C₂³×C₁₃	1	2	yes	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
761	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
762	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
763	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	2	1	no	—
773	C₄×D₄	—	2	1	no	—
774	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
775	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
776	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
777	C₄×D₄	C₂³×C₁₃	1	2	yes	—
778	#117	—	2	1	no	—
779	#117	—	2	1	no	—
780	#117	—	2	2	no	—
781	#117	—	2	1	no	—
782	#117	C₂³×C₁₃	1	2	yes	—
783	C₂×C₄⋊C₄	—	2	1	no	—
784	C₂×C₄⋊C₄	—	2	1	no	—
785	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
789	#107	C₂³×C₁₃	1	2	yes	—
790	#106	C₂³×C₁₃	1	2	yes	—
791	#106	C₂³×C₁₃	1	2	yes	—
792	#106	C₂³×C₁₃	1	2	yes	—
793	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
794	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
795	#103	C₂³×C₁₃	1	2	yes	—
796	#103	C₂³×C₁₃	1	2	yes	—
797	#103	C₂³×C₁₃	1	2	yes	—
798	#103	C₂³×C₁₃	1	2	yes	—
799	#103	C₂³×C₁₃	1	2	yes	—
800	#103	C₂³×C₁₃	1	2	yes	—
801	#103	C₂³×C₁₃	1	2	yes	—
802	#103	C₂³×C₁₃	1	2	yes	—
803	#103	C₂³×C₁₃	1	2	yes	—
804	#103	C₂³×C₁₃	1	2	yes	—
805	#103	C₂³×C₁₃	1	2	yes	—
806	#102	C₂³×C₁₃	1	2	yes	—
807	#102	C₂³×C₁₃	1	2	yes	—
808	#102	C₂³×C₁₃	1	2	yes	—
809	#102	C₂³×C₁₃	1	2	yes	—
810	#102	C₂³×C₁₃	1	2	yes	—
811	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
812	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
814	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
815	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
816	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
817	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
818	#97	C₂³×C₁₃	1	2	yes	—
819	#97	C₂³×C₁₃	1	1	yes	characteristic
820	#97	C₂³×C₁₃	1	1	yes	characteristic
821	C₂×C₁₃	—	4	1	no	—
822	C₂×C₁₃	—	4	2	no	—
823	C₂×C₁₃	—	4	2	no	—
824	C₂×C₁₃	—	8	1	no	—
825	C₂×C₁₃	—	8	2	no	—
826	C₂×C₁₃	#3484	1	1	yes	characteristic
827	C₂×C₁₃	#3586	1	1	yes	characteristic
828	C₂×C₁₃	#3586	1	1	yes	characteristic
829	#41	—	2	4	no	—
830	#41	—	2	4	no	—
831	#41	—	4	2	no	—
832	#41	—	4	2	no	—
833	#41	—	4	2	no	—
834	#41	—	4	2	no	—
835	#41	—	4	2	no	—
836	#41	—	4	2	no	—
837	#41	—	4	8	no	—
838	#41	—	4	8	no	—
839	#41	—	4	2	no	—
840	#41	—	4	2	no	—
841	#41	—	4	8	no	—
842	C₂×Q₈	—	2	4	no	—
843	C₂×Q₈	—	2	1	no	—
844	C₂×Q₈	—	2	2	no	—
845	C₂×Q₈	—	2	2	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	2	2	no	—
848	C₂×Q₈	—	2	4	no	—
849	C₂×Q₈	—	2	4	no	—
850	C₂×Q₈	—	4	2	no	—
851	C₂×Q₈	—	4	2	no	—
852	C₂×Q₈	—	4	2	no	—
853	C₂×Q₈	—	4	2	no	—
854	C₂×Q₈	—	4	8	no	—
855	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
856	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
857	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
858	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
859	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	—	2	2	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	2	2	no	—
867	C₂×D₄	—	2	2	no	—
868	C₂×D₄	—	2	1	no	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
871	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
872	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
873	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
874	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
875	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
877	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
890	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
894	Q₁₆	—	2	4	no	—
895	Q₁₆	—	2	4	no	—
896	Q₁₆	—	2	4	no	—
897	Q₁₆	—	4	2	no	—
898	Q₁₆	—	4	2	no	—
899	Q₁₆	—	4	2	no	—
900	SD₁₆	—	2	4	no	—
901	SD₁₆	—	4	2	no	—
902	SD₁₆	—	4	2	no	—
903	SD₁₆	—	4	2	no	—
904	SD₁₆	—	4	2	no	—
905	D₈	—	4	2	no	—
906	M₁₆	—	4	2	no	—
907	M₁₆	—	4	2	no	—
908	C₂×C₈	—	4	2	no	—
909	C₂×C₈	—	4	2	no	—
910	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
911	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
912	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
913	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
937	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
938	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
959	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
960	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
961	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
962	C₄²	—	2	2	no	—
963	C₄²	—	2	2	no	—
964	C₄²	—	2	2	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	1	no	—
967	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
968	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
969	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
970	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
971	C₁₃	#61672	1	1	yes	characteristic, direct product factor, Sylow
972	C₂³	—	2	1	no	—
973	C₂³	—	2	2	no	—
974	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
975	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
976	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
977	Q₈	—	2	4	no	—
978	Q₈	—	2	2	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	2	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	2	2	no	—
983	Q₈	—	2	2	no	—
984	Q₈	—	4	2	no	—
985	Q₈	—	4	4	no	—
986	Q₈	—	4	4	no	—
987	Q₈	—	8	2	no	—
988	Q₈	—	8	1	no	—
989	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	—
990	D₄	—	2	2	no	—
991	D₄	—	2	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	4	1	no	—
994	D₄	—	4	1	no	—
995	D₄	—	4	2	no	—
996	D₄	—	4	2	no	—
997	D₄	—	4	2	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	4	2	no	—
1002	D₄	—	4	4	no	—
1003	D₄	—	8	1	no	—
1004	D₄	—	8	1	no	—
1005	D₄	—	8	2	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	2	no	—
1008	D₄	—	8	2	no	—
1009	C₂×C₄	—	2	4	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	4	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	4	4	no	—
1028	C₂×C₄	—	4	4	no	—
1029	C₂×C₄	—	4	2	no	—
1030	C₂×C₄	—	4	4	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1037	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1039	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
1042	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
1043	C₈	—	2	2	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	2	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	4	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	2	no	—
1077	C₄	—	4	1	no	—
1078	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
1079	C₂	—	4	1	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	—	8	1	no	—
1083	C₂	—	8	2	no	—
1084	C₂	C₁₃×#3484	1	1	yes	characteristic
1085	C₂	C₁₃×#3586	1	1	yes	characteristic
1086	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3547	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3321	C₂	semidirect
4. C₁₃×#3317	C₂	semidirect
5. C₁₃×#3316	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3271	C₂	semidirect
8. C₁₃×#3270	C₂	semidirect
9. C₁₃×#3270	C₂	semidirect
10. C₁₃×#3269	C₂	semidirect
11. C₁₃×#3219	C₂	semidirect
12. C₁₃×#3216	C₂	semidirect
13. C₁₃×#3204	C₂	semidirect
14. C₁₃×#3201	C₂	semidirect
15. C₁₃×#3117	C₂	semidirect
16. C₁₃×#3113	C₂	semidirect
17. C₁₃×#3013	C₂	semidirect
18. C₁₃×#3011	C₂	semidirect
19. C₁₃×#2980	C₂	semidirect
286. #61672	C₁₃	direct (N × H)
429. #3547	C₂×C₁₃	semidirect
430. #3497	C₂×C₁₃	semidirect
431. #3321	C₂×C₁₃	semidirect
432. #3317	C₂×C₁₃	semidirect
433. #3316	C₂×C₁₃	semidirect
434. #3312	C₂×C₁₃	semidirect
435. #3271	C₂×C₁₃	semidirect
436. #3270	C₂×C₁₃	semidirect
437. #3270	C₂×C₁₃	semidirect
438. #3269	C₂×C₁₃	semidirect
439. #3219	C₂×C₁₃	semidirect
440. #3216	C₂×C₁₃	semidirect
441. #3204	C₂×C₁₃	semidirect
442. #3201	C₂×C₁₃	semidirect
443. #3117	C₂×C₁₃	semidirect
444. #3113	C₂×C₁₃	semidirect
445. #3013	C₂×C₁₃	semidirect
446. #3011	C₂×C₁₃	semidirect
447. #2980	C₂×C₁₃	semidirect
971. C₁₃	#61672	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×#3547	2
C₁₃×#3497	2
C₁₃×#3321	2
C₁₃×#3317	2
C₁₃×#3316	2
C₁₃×#3312	2
C₁₃×#3271	2
C₁₃×#3270	2
C₁₃×#3269	2
C₁₃×#3219	2
C₁₃×#3216	2
C₁₃×#3204	2
C₁₃×#3201	2
C₁₃×#3117	2
C₁₃×#3113	2
C₁₃×#3013	2
C₁₃×#3011	2
C₁₃×#2980	2
#61672	13

Subgroups — C13×#61672 #15748011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61672 #15748011