Subgroups — C₁₃×#62166 #15748505

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3345	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3335	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3306	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3244	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#563	—	2	1	no	—
21	C₁₃×#562	—	2	1	no	—
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#554	C₂²	1	2	yes	—
24	C₁₃×#554	C₂²	1	2	yes	complemented
25	C₁₃×#553	C₂²	1	2	yes	—
26	C₁₃×#553	C₂²	1	2	yes	complemented
27	C₁₃×#552	—	2	1	no	—
28	C₁₃×#551	—	2	2	no	—
29	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#548	—	2	1	no	—
31	C₁₃×#547	—	2	2	no	—
32	C₁₃×#547	C₂²	1	1	yes	characteristic
33	C₁₃×#547	C₂²	1	1	yes	characteristic
34	C₁₃×#547	C₂²	1	2	yes	—
35	C₁₃×#546	C₂²	1	2	yes	—
36	C₁₃×#544	C₂²	1	2	yes	complemented
37	C₁₃×#542	C₂²	1	2	yes	—
38	C₁₃×#540	C₂²	1	2	yes	complemented
39	C₁₃×#539	—	2	2	no	—
40	C₁₃×#539	—	2	2	no	—
41	C₁₃×#539	—	2	1	no	—
42	C₁₃×#537	—	2	1	no	—
43	C₁₃×#533	C₂²	1	1	yes	characteristic
44	C₁₃×#532	C₂²	1	1	yes	characteristic
45	C₁₃×#529	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
47	C₁₃×#525	—	2	1	no	—
48	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
49	C₁₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#501	C₂²	1	2	yes	complemented
52	C₁₃×#501	C₂²	1	2	yes	complemented
53	C₁₃×#498	C₂²	1	2	yes	complemented
54	C₁₃×#491	C₂²	1	2	yes	complemented
55	C₁₃×#489	C₂²	1	2	yes	—
56	C₁₃×#488	C₂²	1	2	yes	—
57	C₁₃×#485	C₂²	1	2	yes	complemented
58	C₁₃×#484	C₂²	1	2	yes	—
59	C₁₃×#483	C₂²	1	2	yes	—
60	C₁₃×#483	C₂²	1	2	yes	complemented
61	C₁₃×#482	C₂²	1	2	yes	—
62	C₁₃×#481	C₂²	1	2	yes	—
63	C₁₃×#481	C₂²	1	2	yes	—
64	C₁₃×#481	C₂²	1	2	yes	complemented
65	C₁₃×#480	C₂²	1	2	yes	complemented
66	C₁₃×#479	C₂²	1	2	yes	complemented
67	C₁₃×#479	C₂²	1	2	yes	complemented
68	C₁₃×#479	C₂²	1	2	yes	complemented
69	C₁₃×#478	C₂²	1	2	yes	—
70	C₁₃×#478	C₂²	1	2	yes	—
71	C₁₃×#478	C₂²	1	2	yes	—
72	C₁₃×#478	C₂²	1	2	yes	—
73	C₁₃×#478	C₂²	1	2	yes	—
74	C₁₃×#476	C₂²	1	2	yes	—
75	C₁₃×#476	C₂²	1	1	yes	characteristic
76	C₁₃×#476	C₂²	1	1	yes	characteristic
77	C₁₃×#476	C₂²	1	2	yes	complemented
78	C₁₃×#476	C₂²	1	2	yes	complemented
79	C₁₃×#475	C₂²	1	2	yes	complemented
80	C₁₃×#475	C₂²	1	2	yes	complemented
81	C₁₃×#474	C₂²	1	2	yes	complemented
82	C₁₃×#469	C₂²	1	2	yes	—
83	C₁₃×#468	C₂²	1	2	yes	complemented
84	C₁₃×#466	C₂²	1	2	yes	—
85	C₁₃×#465	C₂²	1	2	yes	—
86	C₁₃×#465	C₂²	1	2	yes	—
87	C₁₃×#465	C₂²	1	2	yes	complemented
88	C₁₃×#463	C₂²	1	2	yes	—
89	C₁₃×#463	C₂²	1	2	yes	—
90	C₁₃×#461	C₂²	1	2	yes	complemented
91	C₁₃×#460	C₂²	1	2	yes	complemented
92	C₁₃×#459	C₂²	1	1	yes	characteristic
93	C₁₃×#459	C₂²	1	1	yes	characteristic
94	C₁₃×#449	C₂²	1	2	yes	—
95	C₁₃×#449	C₂²	1	2	yes	—
96	C₁₃×#447	C₂²	1	2	yes	—
97	C₁₃×#446	C₂²	1	2	yes	complemented
98	C₁₃×#442	C₂²	1	2	yes	—
99	C₁₃×#442	C₂²	1	2	yes	—
100	C₁₃×#442	C₂²	1	2	yes	—
101	C₁₃×#440	C₂²	1	2	yes	complemented
102	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
103	C₄×C₁₃×D₈	C₂²	1	2	yes	—
104	C₁₃×#435	C₂²	1	2	yes	—
105	C₁₃×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₁₃	C₂²	1	2	yes	—
107	C₁₃×#433	C₂²	1	2	yes	complemented
108	C₁₃×#432	C₂²	1	1	yes	characteristic
109	C₁₃×#428	C₂²	1	2	yes	complemented
110	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
111	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
112	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
113	C₁₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
115	C₁₃×#417	C₂²	1	2	yes	—
116	C₁₃×#416	C₂²	1	2	yes	—
117	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
118	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
119	C₂×C₁₃×#41	—	2	1	no	—
120	C₂×C₁₃×#41	—	2	2	no	—
121	C₂×C₁₃×#41	—	2	1	no	—
122	C₂×C₁₃×#41	C₂³	1	2	yes	—
123	C₂²×Q₈×C₁₃	—	2	1	no	—
124	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₁₃	—	2	1	no	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×D₈	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₁₃×#127	C₂³	1	1	yes	characteristic
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#126	—	2	2	no	—
145	C₁₃×#126	D₄	1	2	yes	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	—	2	1	no	—
149	C₁₃×#125	—	2	1	no	—
150	C₁₃×#125	—	2	1	no	—
151	C₁₃×#125	D₄	1	1	yes	characteristic
152	C₁₃×#125	C₂³	1	2	yes	—
153	C₁₃×#125	C₂³	1	2	yes	—
154	C₁₃×#125	C₂³	1	2	yes	—
155	C₁₃×#124	—	2	2	no	—
156	C₁₃×#124	—	2	1	no	—
157	C₁₃×#124	D₄	1	1	yes	characteristic
158	C₁₃×#124	C₂³	1	2	yes	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×#123	—	2	2	no	—
161	C₁₃×#123	—	2	2	no	—
162	C₁₃×#123	—	2	2	no	—
163	C₁₃×#123	—	2	2	no	—
164	C₁₃×#123	—	2	2	no	—
165	C₁₃×#123	—	2	2	no	—
166	C₁₃×#123	—	2	2	no	—
167	C₁₃×#123	—	2	2	no	—
168	C₁₃×#123	—	2	2	no	—
169	C₁₃×#123	D₄	1	2	yes	—
170	C₁₃×C₂²⋊Q₈	—	2	1	no	—
171	C₁₃×C₂²⋊Q₈	—	2	2	no	—
172	C₁₃×C₂²⋊Q₈	—	2	1	no	—
173	C₁₃×C₂²⋊Q₈	—	2	2	no	—
174	C₁₃×C₂²⋊Q₈	—	2	1	no	—
175	C₁₃×C₂²⋊Q₈	—	2	1	no	—
176	C₁₃×C₂²⋊Q₈	—	2	2	no	—
177	C₁₃×C₂²⋊Q₈	—	2	2	no	—
178	C₁₃×C₂²⋊Q₈	—	2	2	no	—
179	C₁₃×C₂²⋊Q₈	—	2	2	no	—
180	C₁₃×C₂²⋊Q₈	—	2	2	no	—
181	C₁₃×C₂²⋊Q₈	—	2	2	no	—
182	C₁₃×C₂²⋊Q₈	—	2	2	no	—
183	C₁₃×C₂²⋊Q₈	—	2	2	no	—
184	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
185	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
187	C₁₃×#121	—	2	1	no	—
188	C₁₃×#121	—	2	2	no	—
189	C₁₃×#121	—	2	2	no	—
190	C₁₃×#121	—	2	1	no	—
191	C₁₃×#121	—	2	2	no	—
192	C₁₃×#121	—	2	2	no	—
193	C₁₃×#121	—	2	2	no	—
194	C₁₃×#121	D₄	1	1	yes	characteristic
195	C₁₃×#121	C₂³	1	2	yes	—
196	C₁₃×#121	C₂³	1	2	yes	—
197	C₁₃×#121	C₂³	1	2	yes	—
198	C₁₃×#121	C₂³	1	2	yes	—
199	C₁₃×#120	—	2	2	no	—
200	C₄×Q₈×C₁₃	—	2	1	no	—
201	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₁₃	—	2	2	no	—
205	C₄×D₄×C₁₃	—	2	2	no	—
206	C₄×D₄×C₁₃	—	2	2	no	—
207	C₄×D₄×C₁₃	—	2	2	no	—
208	C₄×D₄×C₁₃	—	2	2	no	—
209	C₄×D₄×C₁₃	—	2	1	no	—
210	C₄×D₄×C₁₃	—	2	1	no	—
211	C₄×D₄×C₁₃	—	2	1	no	—
212	C₄×D₄×C₁₃	C₂³	1	2	yes	—
213	C₄×D₄×C₁₃	C₂³	1	2	yes	—
214	C₄×D₄×C₁₃	C₂³	1	2	yes	—
215	C₄×D₄×C₁₃	C₂³	1	2	yes	—
216	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
218	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
219	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
220	C₄×D₄×C₁₃	C₂³	1	2	yes	—
221	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
222	C₁₃×#117	—	2	1	no	—
223	C₁₃×#117	—	2	2	no	—
224	C₁₃×#117	—	2	1	no	—
225	C₁₃×#117	C₂³	1	2	yes	—
226	C₁₃×#117	C₂³	1	2	yes	—
227	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
228	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
229	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
231	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
233	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
234	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
235	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
236	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
237	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
240	C₁₃×#107	C₂³	1	2	yes	—
241	C₁₃×#107	C₂³	1	2	yes	—
242	C₁₃×#107	C₂³	1	2	yes	—
243	C₁₃×#107	C₂³	1	2	yes	—
244	C₁₃×#106	C₂³	1	2	yes	—
245	C₁₃×#106	C₂³	1	2	yes	—
246	C₁₃×#106	C₂³	1	2	yes	—
247	C₁₃×#106	C₂³	1	2	yes	—
248	C₁₃×#106	C₂³	1	2	yes	—
249	C₁₃×#106	C₂³	1	2	yes	—
250	C₁₃×#106	C₂³	1	2	yes	—
251	C₁₃×#106	C₂³	1	2	yes	—
252	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
253	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
257	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₃×#103	C₂³	1	2	yes	—
259	C₁₃×#103	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×#102	C₂³	1	2	yes	—
265	C₁₃×#102	C₂³	1	2	yes	—
266	C₁₃×#102	C₂³	1	2	yes	—
267	C₁₃×#102	C₂³	1	2	yes	—
268	C₁₃×#102	C₂³	1	2	yes	—
269	C₁₃×#102	C₂³	1	2	yes	—
270	C₁₃×#102	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×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₁₃×#97	C₂³	1	2	yes	—
278	C₁₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₁₃	C₂³	1	2	yes	—
280	#62166	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂⁴×C₁₃	—	2	1	no	—
282	C₁₃×#41	—	2	4	no	—
283	C₁₃×#41	—	4	2	no	—
284	C₁₃×#41	—	8	2	no	—
285	C₁₃×#41	—	8	4	no	—
286	C₁₃×#41	—	8	2	no	—
287	C₂×Q₈×C₁₃	—	2	1	no	—
288	C₂×Q₈×C₁₃	—	2	2	no	—
289	C₂×Q₈×C₁₃	—	2	2	no	—
290	C₂×Q₈×C₁₃	—	2	1	no	—
291	C₂×Q₈×C₁₃	—	8	2	no	—
292	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×D₄×C₁₃	—	2	2	no	—
295	C₂×D₄×C₁₃	—	2	2	no	—
296	C₂×D₄×C₁₃	—	2	2	no	—
297	C₂×D₄×C₁₃	—	2	2	no	—
298	C₂×D₄×C₁₃	—	2	2	no	—
299	C₂×D₄×C₁₃	—	2	2	no	—
300	C₂×D₄×C₁₃	—	2	1	no	—
301	C₂×D₄×C₁₃	—	2	1	no	—
302	C₂×D₄×C₁₃	—	2	1	no	—
303	C₂×D₄×C₁₃	—	4	1	no	—
304	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
308	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	—	2	1	no	—
310	C₂²×C₄×C₁₃	—	2	1	no	—
311	C₂²×C₄×C₁₃	—	2	1	no	—
312	C₂²×C₄×C₁₃	—	2	2	no	—
313	C₂²×C₄×C₁₃	—	2	2	no	—
314	C₂²×C₄×C₁₃	—	2	2	no	—
315	C₂²×C₄×C₁₃	—	2	1	no	—
316	C₂²×C₄×C₁₃	—	2	1	no	—
317	C₂²×C₄×C₁₃	—	2	2	no	—
318	C₂²×C₄×C₁₃	—	2	1	no	—
319	C₂²×C₄×C₁₃	—	2	2	no	—
320	C₂²×C₄×C₁₃	—	2	2	no	—
321	C₂²×C₄×C₁₃	—	2	2	no	—
322	C₂²×C₄×C₁₃	—	2	1	no	—
323	C₂²×C₄×C₁₃	—	8	2	no	—
324	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
327	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
328	C₁₃×SD₁₆	—	4	2	no	—
329	C₁₃×SD₁₆	—	4	2	no	—
330	C₁₃×D₈	—	2	4	no	—
331	C₁₃×D₈	—	4	2	no	—
332	C₁₃×M₁₆	—	4	2	no	—
333	C₂×C₈×C₁₃	—	4	1	no	—
334	C₂×C₈×C₁₃	—	4	2	no	—
335	C₂×C₈×C₁₃	—	4	1	no	—
336	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
339	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
340	C₁₃×C₄⋊C₄	—	2	2	no	—
341	C₁₃×C₄⋊C₄	—	2	2	no	—
342	C₁₃×C₄⋊C₄	—	2	1	no	—
343	C₁₃×C₄⋊C₄	—	2	2	no	—
344	C₁₃×C₄⋊C₄	—	2	2	no	—
345	C₁₃×C₄⋊C₄	—	2	2	no	—
346	C₁₃×C₄⋊C₄	—	2	2	no	—
347	C₁₃×C₄⋊C₄	—	2	2	no	—
348	C₁₃×C₄⋊C₄	—	2	2	no	—
349	C₁₃×C₄⋊C₄	—	2	2	no	—
350	C₁₃×C₄⋊C₄	—	2	2	no	—
351	C₁₃×C₄⋊C₄	—	2	1	no	—
352	C₁₃×C₄⋊C₄	—	2	1	no	—
353	C₁₃×C₄⋊C₄	—	2	2	no	—
354	C₁₃×C₄⋊C₄	—	2	1	no	—
355	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
360	C₁₃×C₄⋊C₄	—	2	2	no	—
361	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
362	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
363	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
365	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
366	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
371	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
372	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
373	C₁₃×C₂²⋊C₄	—	2	2	no	—
374	C₁₃×C₂²⋊C₄	—	2	2	no	—
375	C₁₃×C₂²⋊C₄	—	2	2	no	—
376	C₁₃×C₂²⋊C₄	—	2	1	no	—
377	C₁₃×C₂²⋊C₄	—	2	1	no	—
378	C₁₃×C₂²⋊C₄	—	2	1	no	—
379	C₁₃×C₂²⋊C₄	—	2	1	no	—
380	C₁₃×C₂²⋊C₄	—	2	2	no	—
381	C₁₃×C₂²⋊C₄	—	2	2	no	—
382	C₁₃×C₂²⋊C₄	—	2	2	no	—
383	C₁₃×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
391	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
392	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
393	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
394	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
395	C₄²×C₁₃	—	2	2	no	—
396	C₄²×C₁₃	—	2	2	no	—
397	C₄²×C₁₃	—	2	2	no	—
398	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₁₃	C₂⁴	1	2	yes	—
401	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
403	#3559	C₂×C₁₃	1	1	yes	characteristic, complemented
404	#3520	C₂×C₁₃	1	1	yes	characteristic, complemented
405	#3384	C₂×C₁₃	1	2	yes	complemented
406	#3376	C₂×C₁₃	1	2	yes	complemented
407	#3346	C₂×C₁₃	1	2	yes	complemented
408	#3345	C₂×C₁₃	1	2	yes	complemented
409	#3335	C₂×C₁₃	1	2	yes	complemented
410	#3307	C₂×C₁₃	1	2	yes	complemented
411	#3306	C₂×C₁₃	1	2	yes	complemented
412	#3297	C₂×C₁₃	1	2	yes	complemented
413	#3257	C₂×C₁₃	1	2	yes	complemented
414	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
415	#3244	C₂×C₁₃	1	2	yes	complemented
416	#3236	C₂×C₁₃	1	1	yes	characteristic, complemented
417	#3119	C₂×C₁₃	1	2	yes	complemented
418	#3109	C₂×C₁₃	1	1	yes	characteristic, complemented
419	#3084	C₂×C₁₃	1	2	yes	complemented
420	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
421	#2992	C₂×C₁₃	1	1	yes	characteristic, complemented
422	C₂³×C₁₃	—	2	1	no	—
423	C₂³×C₁₃	—	2	1	no	—
424	C₂³×C₁₃	—	2	2	no	—
425	C₂³×C₁₃	—	4	2	no	—
426	C₂³×C₁₃	—	4	2	no	—
427	C₂³×C₁₃	—	8	1	no	—
428	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
429	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	Q₈×C₁₃	—	2	2	no	—
431	Q₈×C₁₃	—	2	2	no	—
432	Q₈×C₁₃	—	4	1	no	—
433	Q₈×C₁₃	—	4	2	no	—
434	Q₈×C₁₃	—	8	2	no	—
435	Q₈×C₁₃	—	8	1	no	—
436	Q₈×C₁₃	—	8	2	no	—
437	D₄×C₁₃	—	2	4	no	—
438	D₄×C₁₃	—	2	2	no	—
439	D₄×C₁₃	—	2	1	no	—
440	D₄×C₁₃	—	2	1	no	—
441	D₄×C₁₃	—	2	1	no	—
442	D₄×C₁₃	—	2	2	no	—
443	D₄×C₁₃	—	4	1	no	—
444	D₄×C₁₃	—	4	2	no	—
445	D₄×C₁₃	—	4	4	no	—
446	D₄×C₁₃	—	4	4	no	—
447	D₄×C₁₃	—	8	1	no	—
448	D₄×C₁₃	—	8	1	no	—
449	D₄×C₁₃	—	8	2	no	—
450	D₄×C₁₃	—	8	2	no	—
451	D₄×C₁₃	—	8	2	no	—
452	D₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
453	C₂×C₄×C₁₃	—	2	2	no	—
454	C₂×C₄×C₁₃	—	2	1	no	—
455	C₂×C₄×C₁₃	—	2	2	no	—
456	C₂×C₄×C₁₃	—	2	1	no	—
457	C₂×C₄×C₁₃	—	2	2	no	—
458	C₂×C₄×C₁₃	—	2	2	no	—
459	C₂×C₄×C₁₃	—	2	1	no	—
460	C₂×C₄×C₁₃	—	2	2	no	—
461	C₂×C₄×C₁₃	—	2	2	no	—
462	C₂×C₄×C₁₃	—	2	2	no	—
463	C₂×C₄×C₁₃	—	2	1	no	—
464	C₂×C₄×C₁₃	—	2	2	no	—
465	C₂×C₄×C₁₃	—	4	1	no	—
466	C₂×C₄×C₁₃	—	4	4	no	—
467	C₂×C₄×C₁₃	—	4	2	no	—
468	C₂×C₄×C₁₃	—	4	2	no	—
469	C₂×C₄×C₁₃	—	4	2	no	—
470	C₂×C₄×C₁₃	—	8	2	no	—
471	C₂×C₄×C₁₃	—	8	1	no	—
472	C₂×C₄×C₁₃	—	8	1	no	—
473	C₂×C₄×C₁₃	—	8	2	no	—
474	C₂×C₄×C₁₃	—	8	2	no	—
475	C₂×C₄×C₁₃	—	8	2	no	—
476	C₂×C₄×C₁₃	—	8	1	no	—
477	C₂×C₄×C₁₃	—	8	1	no	—
478	C₂×C₄×C₁₃	—	8	2	no	—
479	C₂×C₄×C₁₃	—	8	2	no	—
480	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
488	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
489	C₈×C₁₃	—	2	2	no	—
490	C₈×C₁₃	—	2	2	no	—
491	C₈×C₁₃	—	2	2	no	—
492	C₈×C₁₃	—	2	2	no	—
493	#563	—	2	1	no	—
494	#562	—	2	1	no	—
495	#556	C₂²×C₁₃	1	1	yes	characteristic
496	#554	C₂²×C₁₃	1	2	yes	—
497	#554	C₂²×C₁₃	1	2	yes	complemented
498	#553	C₂²×C₁₃	1	2	yes	—
499	#553	C₂²×C₁₃	1	2	yes	complemented
500	#552	—	2	1	no	—
501	#551	—	2	2	no	—
502	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
503	#548	—	2	1	no	—
504	#547	—	2	2	no	—
505	#547	C₂²×C₁₃	1	1	yes	characteristic
506	#547	C₂²×C₁₃	1	2	yes	—
507	#547	C₂²×C₁₃	1	1	yes	characteristic
508	#546	C₂²×C₁₃	1	2	yes	—
509	#544	C₂²×C₁₃	1	2	yes	complemented
510	#542	C₂²×C₁₃	1	2	yes	—
511	#540	C₂²×C₁₃	1	2	yes	complemented
512	#539	—	2	2	no	—
513	#539	—	2	2	no	—
514	#539	—	2	1	no	—
515	#537	—	2	1	no	—
516	#533	C₂²×C₁₃	1	1	yes	characteristic
517	#532	C₂²×C₁₃	1	1	yes	characteristic
518	#529	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
520	#525	—	2	1	no	—
521	C₂×C₂²⋊Q₈	—	2	1	no	—
522	#520	C₂²×C₁₃	1	2	yes	—
523	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
524	#501	C₂²×C₁₃	1	2	yes	complemented
525	#501	C₂²×C₁₃	1	2	yes	complemented
526	#498	C₂²×C₁₃	1	2	yes	complemented
527	#491	C₂²×C₁₃	1	2	yes	complemented
528	#489	C₂²×C₁₃	1	2	yes	—
529	#488	C₂²×C₁₃	1	2	yes	—
530	#485	C₂²×C₁₃	1	2	yes	complemented
531	#484	C₂²×C₁₃	1	2	yes	—
532	#483	C₂²×C₁₃	1	2	yes	—
533	#483	C₂²×C₁₃	1	2	yes	complemented
534	#482	C₂²×C₁₃	1	2	yes	—
535	#481	C₂²×C₁₃	1	2	yes	—
536	#481	C₂²×C₁₃	1	2	yes	—
537	#481	C₂²×C₁₃	1	2	yes	complemented
538	#480	C₂²×C₁₃	1	2	yes	complemented
539	#479	C₂²×C₁₃	1	2	yes	complemented
540	#479	C₂²×C₁₃	1	2	yes	complemented
541	#479	C₂²×C₁₃	1	2	yes	complemented
542	#478	C₂²×C₁₃	1	2	yes	—
543	#478	C₂²×C₁₃	1	2	yes	—
544	#478	C₂²×C₁₃	1	2	yes	—
545	#478	C₂²×C₁₃	1	2	yes	—
546	#478	C₂²×C₁₃	1	2	yes	—
547	#476	C₂²×C₁₃	1	1	yes	characteristic
548	#476	C₂²×C₁₃	1	2	yes	—
549	#476	C₂²×C₁₃	1	1	yes	characteristic
550	#476	C₂²×C₁₃	1	2	yes	complemented
551	#476	C₂²×C₁₃	1	2	yes	complemented
552	#475	C₂²×C₁₃	1	2	yes	complemented
553	#475	C₂²×C₁₃	1	2	yes	complemented
554	#474	C₂²×C₁₃	1	2	yes	complemented
555	#469	C₂²×C₁₃	1	2	yes	—
556	#468	C₂²×C₁₃	1	2	yes	complemented
557	#466	C₂²×C₁₃	1	2	yes	—
558	#465	C₂²×C₁₃	1	2	yes	—
559	#465	C₂²×C₁₃	1	2	yes	—
560	#465	C₂²×C₁₃	1	2	yes	complemented
561	#463	C₂²×C₁₃	1	2	yes	—
562	#463	C₂²×C₁₃	1	2	yes	—
563	#461	C₂²×C₁₃	1	2	yes	complemented
564	#460	C₂²×C₁₃	1	2	yes	complemented
565	#459	C₂²×C₁₃	1	1	yes	characteristic
566	#459	C₂²×C₁₃	1	1	yes	characteristic
567	#449	C₂²×C₁₃	1	2	yes	—
568	#449	C₂²×C₁₃	1	2	yes	—
569	#447	C₂²×C₁₃	1	2	yes	—
570	#446	C₂²×C₁₃	1	2	yes	complemented
571	#442	C₂²×C₁₃	1	2	yes	—
572	#442	C₂²×C₁₃	1	2	yes	—
573	#442	C₂²×C₁₃	1	2	yes	—
574	#440	C₂²×C₁₃	1	2	yes	complemented
575	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
576	C₄×D₈	C₂²×C₁₃	1	2	yes	—
577	#435	C₂²×C₁₃	1	2	yes	—
578	#435	C₂²×C₁₃	1	2	yes	complemented
579	C₈×D₄	C₂²×C₁₃	1	2	yes	—
580	#433	C₂²×C₁₃	1	2	yes	complemented
581	#432	C₂²×C₁₃	1	1	yes	characteristic
582	#428	C₂²×C₁₃	1	2	yes	complemented
583	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
584	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
585	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
586	#424	C₂²×C₁₃	1	2	yes	complemented
587	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
588	#417	C₂²×C₁₃	1	2	yes	—
589	#416	C₂²×C₁₃	1	2	yes	—
590	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
591	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
592	C₂²×C₁₃	—	2	1	no	—
593	C₂²×C₁₃	—	2	1	no	—
594	C₂²×C₁₃	—	2	2	no	—
595	C₂²×C₁₃	—	2	2	no	—
596	C₂²×C₁₃	—	2	2	no	—
597	C₂²×C₁₃	—	2	2	no	—
598	C₂²×C₁₃	—	4	1	no	—
599	C₂²×C₁₃	—	4	1	no	—
600	C₂²×C₁₃	—	4	1	no	—
601	C₂²×C₁₃	—	4	2	no	—
602	C₂²×C₁₃	—	4	1	no	—
603	C₂²×C₁₃	—	4	2	no	—
604	C₂²×C₁₃	—	4	2	no	—
605	C₂²×C₁₃	—	4	1	no	—
606	C₂²×C₁₃	—	8	4	no	—
607	C₂²×C₁₃	#577	1	2	yes	—
608	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
609	C₄×C₁₃	—	2	1	no	—
610	C₄×C₁₃	—	2	1	no	—
611	C₄×C₁₃	—	2	2	no	—
612	C₄×C₁₃	—	2	2	no	—
613	C₄×C₁₃	—	2	1	no	—
614	C₄×C₁₃	—	2	1	no	—
615	C₄×C₁₃	—	2	1	no	—
616	C₄×C₁₃	—	2	2	no	—
617	C₄×C₁₃	—	4	1	no	—
618	C₄×C₁₃	—	4	1	no	—
619	C₄×C₁₃	—	4	2	no	—
620	C₄×C₁₃	—	4	2	no	—
621	C₄×C₁₃	—	4	2	no	—
622	C₄×C₁₃	—	4	2	no	—
623	C₄×C₁₃	—	4	2	no	—
624	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
625	C₄×C₁₃	#585	1	1	yes	characteristic
626	C₂×#41	—	2	1	no	—
627	C₂×#41	—	2	2	no	—
628	C₂×#41	—	2	1	no	—
629	C₂×#41	C₂³×C₁₃	1	2	yes	—
630	C₂²×Q₈	—	2	1	no	—
631	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
632	C₂³×C₄	—	2	1	no	—
633	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
635	C₂×D₈	C₂³×C₁₃	1	2	yes	—
636	C₂×D₈	C₂³×C₁₃	1	2	yes	—
637	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
638	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
640	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
644	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
646	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
647	#127	C₂³×C₁₃	1	1	yes	characteristic
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	D₄×C₁₃	1	2	yes	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	1	no	—
656	#125	—	2	1	no	—
657	#125	—	2	1	no	—
658	#125	D₄×C₁₃	1	1	yes	characteristic
659	#125	C₂³×C₁₃	1	2	yes	—
660	#125	C₂³×C₁₃	1	2	yes	—
661	#125	C₂³×C₁₃	1	2	yes	—
662	#124	—	2	2	no	—
663	#124	—	2	1	no	—
664	#124	D₄×C₁₃	1	1	yes	characteristic
665	#124	C₂³×C₁₃	1	2	yes	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	—	2	2	no	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	D₄×C₁₃	1	2	yes	—
677	C₂²⋊Q₈	—	2	1	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	1	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	1	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
694	#121	—	2	1	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	D₄×C₁₃	1	1	yes	characteristic
702	#121	C₂³×C₁₃	1	2	yes	—
703	#121	C₂³×C₁₃	1	2	yes	—
704	#121	C₂³×C₁₃	1	2	yes	—
705	#121	C₂³×C₁₃	1	2	yes	—
706	#120	—	2	2	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
709	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
710	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	2	no	—
714	C₄×D₄	—	2	2	no	—
715	C₄×D₄	—	2	2	no	—
716	C₄×D₄	—	2	1	no	—
717	C₄×D₄	—	2	1	no	—
718	C₄×D₄	—	2	1	no	—
719	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
720	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
721	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
722	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
723	C₄×D₄	C₂³×C₁₃	1	2	yes	—
724	C₄×D₄	C₂³×C₁₃	1	2	yes	—
725	C₄×D₄	C₂³×C₁₃	1	2	yes	—
726	C₄×D₄	C₂³×C₁₃	1	2	yes	—
727	C₄×D₄	C₂³×C₁₃	1	2	yes	—
728	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
729	#117	—	2	1	no	—
730	#117	—	2	2	no	—
731	#117	—	2	1	no	—
732	#117	C₂³×C₁₃	1	2	yes	—
733	#117	C₂³×C₁₃	1	2	yes	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	1	no	—
736	C₂×C₄⋊C₄	—	2	2	no	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	—	2	2	no	—
739	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
742	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
743	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
744	C₂×C₂²⋊C₄	—	2	1	no	—
745	C₂×C₂²⋊C₄	—	2	2	no	—
746	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
747	#107	C₂³×C₁₃	1	2	yes	—
748	#107	C₂³×C₁₃	1	2	yes	—
749	#107	C₂³×C₁₃	1	2	yes	—
750	#107	C₂³×C₁₃	1	2	yes	—
751	#106	C₂³×C₁₃	1	2	yes	—
752	#106	C₂³×C₁₃	1	2	yes	—
753	#106	C₂³×C₁₃	1	2	yes	—
754	#106	C₂³×C₁₃	1	2	yes	—
755	#106	C₂³×C₁₃	1	2	yes	—
756	#106	C₂³×C₁₃	1	2	yes	—
757	#106	C₂³×C₁₃	1	2	yes	—
758	#106	C₂³×C₁₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
760	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
761	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
762	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
763	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
764	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
765	#103	C₂³×C₁₃	1	2	yes	—
766	#103	C₂³×C₁₃	1	2	yes	—
767	#103	C₂³×C₁₃	1	2	yes	—
768	#103	C₂³×C₁₃	1	2	yes	—
769	#103	C₂³×C₁₃	1	2	yes	—
770	#103	C₂³×C₁₃	1	2	yes	—
771	#102	C₂³×C₁₃	1	2	yes	—
772	#102	C₂³×C₁₃	1	2	yes	—
773	#102	C₂³×C₁₃	1	2	yes	—
774	#102	C₂³×C₁₃	1	2	yes	—
775	#102	C₂³×C₁₃	1	2	yes	—
776	#102	C₂³×C₁₃	1	2	yes	—
777	#102	C₂³×C₁₃	1	2	yes	—
778	#102	C₂³×C₁₃	1	2	yes	—
779	#102	C₂³×C₁₃	1	2	yes	—
780	#102	C₂³×C₁₃	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
784	#97	C₂³×C₁₃	1	2	yes	—
785	#97	C₂³×C₁₃	1	2	yes	—
786	C₄×C₈	C₂³×C₁₃	1	2	yes	—
787	C₂×C₁₃	—	2	2	no	—
788	C₂×C₁₃	—	4	2	no	—
789	C₂×C₁₃	—	4	2	no	—
790	C₂×C₁₃	—	8	2	no	—
791	C₂×C₁₃	—	8	1	no	—
792	C₂×C₁₃	#3489	1	1	yes	characteristic
793	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
794	C₂×C₁₃	#3585	1	1	yes	characteristic
795	C₂⁴	—	2	1	no	—
796	#41	—	2	4	no	—
797	#41	—	4	2	no	—
798	#41	—	8	2	no	—
799	#41	—	8	4	no	—
800	#41	—	8	2	no	—
801	C₂×Q₈	—	2	1	no	—
802	C₂×Q₈	—	2	2	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	1	no	—
805	C₂×Q₈	—	8	2	no	—
806	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
808	C₂×D₄	—	2	2	no	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	1	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	4	1	no	—
818	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
821	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
822	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	2	no	—
832	C₂²×C₄	—	2	1	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	1	no	—
837	C₂²×C₄	—	8	2	no	—
838	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
839	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
842	SD₁₆	—	4	2	no	—
843	SD₁₆	—	4	2	no	—
844	D₈	—	2	4	no	—
845	D₈	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	C₂×C₈	—	4	1	no	—
848	C₂×C₈	—	4	2	no	—
849	C₂×C₈	—	4	1	no	—
850	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
851	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
853	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	1	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	2	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
876	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
877	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
878	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
880	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
881	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
885	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	1	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
905	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
909	C₄²	—	2	2	no	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
913	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
914	C₄²	C₂⁴×C₁₃	1	2	yes	—
915	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
916	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
917	C₁₃	#62166	1	1	yes	characteristic, direct product factor, Sylow
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	8	1	no	—
924	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
925	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	1	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	8	2	no	—
931	Q₈	—	8	1	no	—
932	Q₈	—	8	2	no	—
933	D₄	—	2	4	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	1	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	—	8	1	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	2	no	—
976	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
984	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	2	no	—
998	C₂²	—	4	1	no	—
999	C₂²	—	4	1	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	C₁₃×#577	1	2	yes	—
1005	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	2	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	1	no	—
1011	C₄	—	2	2	no	—
1012	C₄	—	2	2	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
1022	C₄	C₁₃×#585	1	1	yes	characteristic
1023	C₂	—	2	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	2	no	—
1026	C₂	—	8	1	no	—
1027	C₂	—	8	2	no	—
1028	C₂	C₁₃×#3489	1	1	yes	characteristic
1029	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
1030	C₂	C₁₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3559	C₂	semidirect
2. C₁₃×#3520	C₂	semidirect
3. C₁₃×#3384	C₂	semidirect
4. C₁₃×#3376	C₂	semidirect
5. C₁₃×#3346	C₂	semidirect
6. C₁₃×#3345	C₂	semidirect
7. C₁₃×#3335	C₂	semidirect
8. C₁₃×#3307	C₂	semidirect
9. C₁₃×#3306	C₂	semidirect
10. C₁₃×#3297	C₂	semidirect
11. C₁₃×#3257	C₂	semidirect
12. C₁₃×#3246	C₂	semidirect
13. C₁₃×#3244	C₂	semidirect
14. C₁₃×#3236	C₂	semidirect
15. C₁₃×#3119	C₂	semidirect
16. C₁₃×#3109	C₂	semidirect
17. C₁₃×#3084	C₂	semidirect
18. C₂×C₁₃×#478	C₂	semidirect
19. C₁₃×#2992	C₂	semidirect
24. C₁₃×#554	C₂²	semidirect
26. C₁₃×#553	C₂²	semidirect
36. C₁₃×#544	C₂²	semidirect
38. C₁₃×#540	C₂²	semidirect
51. C₁₃×#501	C₂²	semidirect
52. C₁₃×#501	C₂²	semidirect
53. C₁₃×#498	C₂²	semidirect
54. C₁₃×#491	C₂²	semidirect
57. C₁₃×#485	C₂²	semidirect
60. C₁₃×#483	C₂²	semidirect
64. C₁₃×#481	C₂²	semidirect
65. C₁₃×#480	C₂²	semidirect
66. C₁₃×#479	C₂²	semidirect
67. C₁₃×#479	C₂²	semidirect
68. C₁₃×#479	C₂²	semidirect
77. C₁₃×#476	C₂²	semidirect
78. C₁₃×#476	C₂²	semidirect
79. C₁₃×#475	C₂²	semidirect
80. C₁₃×#475	C₂²	semidirect
81. C₁₃×#474	C₂²	semidirect
83. C₁₃×#468	C₂²	semidirect
87. C₁₃×#465	C₂²	semidirect
90. C₁₃×#461	C₂²	semidirect
91. C₁₃×#460	C₂²	semidirect
97. C₁₃×#446	C₂²	semidirect
101. C₁₃×#440	C₂²	semidirect
102. C₄×C₁₃×SD₁₆	C₂²	semidirect
105. C₁₃×#435	C₂²	semidirect
107. C₁₃×#433	C₂²	semidirect
109. C₁₃×#428	C₂²	semidirect
112. C₂×C₁₃×#106	C₂²	semidirect
113. C₁₃×#424	C₂²	semidirect
280. #62166	C₁₃	direct (N × H)
403. #3559	C₂×C₁₃	semidirect
404. #3520	C₂×C₁₃	semidirect
405. #3384	C₂×C₁₃	semidirect
406. #3376	C₂×C₁₃	semidirect
407. #3346	C₂×C₁₃	semidirect
408. #3345	C₂×C₁₃	semidirect
409. #3335	C₂×C₁₃	semidirect
410. #3307	C₂×C₁₃	semidirect
411. #3306	C₂×C₁₃	semidirect
412. #3297	C₂×C₁₃	semidirect
413. #3257	C₂×C₁₃	semidirect
414. #3246	C₂×C₁₃	semidirect
415. #3244	C₂×C₁₃	semidirect
416. #3236	C₂×C₁₃	semidirect
417. #3119	C₂×C₁₃	semidirect
418. #3109	C₂×C₁₃	semidirect
419. #3084	C₂×C₁₃	semidirect
420. C₂×#478	C₂×C₁₃	semidirect
421. #2992	C₂×C₁₃	semidirect
497. #554	C₂²×C₁₃	semidirect
499. #553	C₂²×C₁₃	semidirect
509. #544	C₂²×C₁₃	semidirect
511. #540	C₂²×C₁₃	semidirect
524. #501	C₂²×C₁₃	semidirect
525. #501	C₂²×C₁₃	semidirect
526. #498	C₂²×C₁₃	semidirect
527. #491	C₂²×C₁₃	semidirect
530. #485	C₂²×C₁₃	semidirect
533. #483	C₂²×C₁₃	semidirect
537. #481	C₂²×C₁₃	semidirect
538. #480	C₂²×C₁₃	semidirect
539. #479	C₂²×C₁₃	semidirect
540. #479	C₂²×C₁₃	semidirect
541. #479	C₂²×C₁₃	semidirect
550. #476	C₂²×C₁₃	semidirect
551. #476	C₂²×C₁₃	semidirect
552. #475	C₂²×C₁₃	semidirect
553. #475	C₂²×C₁₃	semidirect
554. #474	C₂²×C₁₃	semidirect
556. #468	C₂²×C₁₃	semidirect
560. #465	C₂²×C₁₃	semidirect
563. #461	C₂²×C₁₃	semidirect
564. #460	C₂²×C₁₃	semidirect
570. #446	C₂²×C₁₃	semidirect
574. #440	C₂²×C₁₃	semidirect
575. C₄×SD₁₆	C₂²×C₁₃	semidirect
578. #435	C₂²×C₁₃	semidirect
580. #433	C₂²×C₁₃	semidirect
582. #428	C₂²×C₁₃	semidirect
585. C₂×#106	C₂²×C₁₃	semidirect
586. #424	C₂²×C₁₃	semidirect
917. C₁₃	#62166	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×#3559	2
C₁₃×#3520	2
C₁₃×#3384	2
C₁₃×#3376	2
C₁₃×#3346	2
C₁₃×#3345	2
C₁₃×#3335	2
C₁₃×#3307	2
C₁₃×#3306	2
C₁₃×#3297	2
C₁₃×#3257	2
C₁₃×#3246	2
C₁₃×#3244	2
C₁₃×#3236	2
C₁₃×#3119	2
C₁₃×#3109	2
C₁₃×#3084	2
C₂×C₁₃×#478	2
C₁₃×#2992	2
#62166	13

Subgroups — C13×#62166 #15748505

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62166 #15748505