Subgroups — C₁₃×#61431 #15747770

Order 3328.

2000 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3481	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3361	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3339	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3297	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3280	C₂	1	2	yes	maximal, complemented
10	D₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3106	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3105	C₂	1	4	yes	maximal, complemented
15	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
20	C₁₃×#559	C₂²	1	2	yes	complemented
21	C₁₃×#554	C₂²	1	2	yes	—
22	C₁₃×#554	C₂²	1	2	yes	complemented
23	C₁₃×#553	—	2	2	no	—
24	C₁₃×#553	C₂²	1	4	yes	complemented
25	C₁₃×#551	—	2	4	no	—
26	C₁₃×#546	—	2	2	no	—
27	C₁₃×#546	C₂²	1	4	yes	complemented
28	D₄²×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#532	C₂²	1	2	yes	complemented
30	C₁₃×#529	—	2	2	no	—
31	C₁₃×#529	C₂²	1	4	yes	complemented
32	C₁₃×#525	—	2	4	no	—
33	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₁₃	—	2	2	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
37	C₁₃×#500	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#499	C₂²	1	2	yes	complemented
39	C₁₃×#495	C₂²	1	2	yes	complemented
40	C₁₃×#493	C₂²	1	1	yes	characteristic
41	C₁₃×#488	C₂²	1	4	yes	complemented
42	C₁₃×#486	C₂²	1	2	yes	complemented
43	C₁₃×#484	C₂²	1	4	yes	complemented
44	C₁₃×#482	C₂²	1	4	yes	complemented
45	C₁₃×#481	C₂²	1	4	yes	complemented
46	C₁₃×#478	C₂²	1	4	yes	complemented
47	C₁₃×#478	C₂²	1	4	yes	complemented
48	C₁₃×#477	C₂²	1	2	yes	complemented
49	C₁₃×#476	C₂²	1	2	yes	complemented
50	C₁₃×#467	C₂²	1	2	yes	complemented
51	C₁₃×#466	C₂²	1	2	yes	—
52	C₁₃×#466	C₂²	1	2	yes	complemented
53	C₁₃×#466	C₂²	1	2	yes	complemented
54	C₁₃×#465	C₂²	1	4	yes	complemented
55	C₁₃×#463	C₂²	1	4	yes	complemented
56	C₁₃×#463	C₂²	1	4	yes	complemented
57	C₁₃×#460	C₂²	1	2	yes	complemented
58	C₁₃×#459	C₂²	1	2	yes	—
59	C₁₃×#450	C₂²	1	4	yes	complemented
60	C₁₃×#449	C₂²	1	4	yes	complemented
61	C₁₃×#447	C₂²	1	4	yes	—
62	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
65	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
67	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
68	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
69	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×D₈	C₂²	1	2	yes	—
71	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
73	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
74	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
75	C₄×C₁₃×D₈	C₂²	1	4	yes	complemented
76	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
77	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
78	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
80	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
81	C₁₃×#431	C₂²	1	2	yes	complemented
82	C₁₃×#431	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
85	C₁₃×#416	C₂²	1	2	yes	complemented
86	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
87	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₁₃×#41	—	2	2	no	—
90	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂²×D₄×C₁₃	—	2	2	no	—
93	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₁₃	—	2	4	no	—
95	C₁₃×#135	—	2	4	no	—
96	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	—	2	8	no	—
100	C₂×C₁₃×D₈	C₂³	1	4	yes	—
101	C₂×C₁₃×D₈	C₂³	1	2	yes	—
102	C₂×C₁₃×D₈	C₂³	1	2	yes	—
103	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
107	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₃×#127	C₂³	1	2	yes	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#126	—	2	4	no	—
112	C₁₃×#125	—	2	2	no	—
113	C₁₃×#125	C₂³	1	4	yes	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#123	—	2	4	no	—
118	C₁₃×#123	—	2	4	no	—
119	C₁₃×#123	—	2	4	no	—
120	C₁₃×#123	—	2	4	no	—
121	C₁₃×C₂²⋊Q₈	—	2	2	no	—
122	C₁₃×C₂²⋊Q₈	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
125	C₁₃×#121	—	2	4	no	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	2	no	—
128	C₁₃×#121	—	2	4	no	—
129	C₁₃×#121	C₂³	1	4	yes	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₁₃×#120	—	2	4	no	—
132	C₁₃×#120	—	2	4	no	—
133	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
134	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
135	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
136	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
137	C₄×D₄×C₁₃	—	2	2	no	—
138	C₄×D₄×C₁₃	—	2	4	no	—
139	C₄×D₄×C₁₃	—	2	2	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	4	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	4	no	—
145	C₄×D₄×C₁₃	—	2	4	no	—
146	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
147	C₄×D₄×C₁₃	D₄	1	2	yes	—
148	C₄×D₄×C₁₃	C₂³	1	2	yes	—
149	C₄×D₄×C₁₃	C₂³	1	4	yes	—
150	C₄×D₄×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	4	yes	—
152	C₄×D₄×C₁₃	C₂³	1	4	yes	—
153	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₁₃	C₂³	1	2	yes	—
155	C₁₃×#117	—	2	2	no	—
156	C₁₃×#117	—	2	4	no	—
157	C₁₃×#117	D₄	1	2	yes	—
158	C₁₃×#117	D₄	1	1	yes	characteristic
159	C₁₃×#117	C₂³	1	2	yes	—
160	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
163	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
164	C₂×C₄²×C₁₃	—	2	2	no	—
165	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₁₃×#107	C₂³	1	1	yes	characteristic
168	C₁₃×#107	C₂³	1	2	yes	—
169	C₁₃×#107	C₂³	1	4	yes	—
170	C₁₃×#107	C₂³	1	1	yes	characteristic
171	C₁₃×#107	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	4	yes	—
174	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₃×#103	C₂³	1	2	yes	—
179	C₁₃×#103	C₂³	1	2	yes	—
180	C₁₃×#103	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	2	yes	—
182	C₁₃×#102	C₂³	1	4	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	2	yes	—
186	C₁₃×#102	C₂³	1	4	yes	—
187	C₁₃×#102	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₃	C₂³	1	2	yes	—
193	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₃	C₂³	1	2	yes	—
197	C₄×C₈×C₁₃	C₂³	1	2	yes	—
198	#61431	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂⁴×C₁₃	—	2	4	no	—
200	C₁₃×#41	—	2	4	no	—
201	C₁₃×#41	—	2	4	no	—
202	C₁₃×#41	—	4	2	no	—
203	C₁₃×#41	—	8	4	no	—
204	C₂×Q₈×C₁₃	—	2	2	no	—
205	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
207	C₂×D₄×C₁₃	—	2	8	no	—
208	C₂×D₄×C₁₃	—	2	2	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	4	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	4	4	no	—
215	C₂×D₄×C₁₃	—	4	8	no	—
216	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
217	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
219	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₁₃	—	2	4	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	no	—
224	C₂²×C₄×C₁₃	—	2	4	no	—
225	C₂²×C₄×C₁₃	—	2	4	no	—
226	C₂²×C₄×C₁₃	—	2	4	no	—
227	C₂²×C₄×C₁₃	—	8	8	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₁₃×Q₁₆	—	2	2	no	—
235	C₁₃×SD₁₆	—	2	4	no	—
236	C₁₃×SD₁₆	—	4	4	no	—
237	C₁₃×D₈	—	2	8	no	—
238	C₁₃×D₈	—	2	4	no	—
239	C₁₃×D₈	—	4	2	no	—
240	C₁₃×D₈	#41	1	4	yes	complemented
241	C₂×C₈×C₁₃	—	2	4	no	—
242	C₂×C₈×C₁₃	—	2	2	no	—
243	C₂×C₈×C₁₃	—	4	1	no	—
244	C₂×C₈×C₁₃	—	4	2	no	—
245	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	4	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	4	no	—
257	C₁₃×C₄⋊C₄	—	2	4	no	—
258	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
264	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	4	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	4	no	—
272	C₁₃×C₂²⋊C₄	—	2	4	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	4	no	—
275	C₁₃×C₂²⋊C₄	—	2	4	no	—
276	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
279	C₄²×C₁₃	—	2	2	no	—
280	C₄²×C₁₃	—	2	2	no	—
281	C₄²×C₁₃	—	2	2	no	—
282	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₁₃	C₂×D₄	1	2	yes	—
284	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₁₃	C₂×D₄	1	2	yes	—
286	C₄²×C₁₃	C₂⁴	1	2	yes	—
287	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
288	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
289	#3481	C₂×C₁₃	1	2	yes	complemented
290	#3396	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#3380	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3361	C₂×C₁₃	1	2	yes	complemented
293	#3339	C₂×C₁₃	1	2	yes	complemented
294	#3338	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3297	C₂×C₁₃	1	4	yes	complemented
296	#3295	C₂×C₁₃	1	2	yes	complemented
297	#3280	C₂×C₁₃	1	2	yes	complemented
298	D₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#3168	C₂×C₁₃	1	2	yes	complemented
301	#3106	C₂×C₁₃	1	2	yes	complemented
302	#3105	C₂×C₁₃	1	4	yes	complemented
303	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
304	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
305	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
306	C₂³×C₁₃	—	2	2	no	—
307	C₂³×C₁₃	—	2	4	no	—
308	C₂³×C₁₃	—	4	8	no	—
309	C₂³×C₁₃	—	4	8	no	—
310	C₂³×C₁₃	—	8	4	no	—
311	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
312	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
313	Q₈×C₁₃	—	2	2	no	—
314	Q₈×C₁₃	—	2	2	no	—
315	Q₈×C₁₃	—	2	2	no	—
316	Q₈×C₁₃	—	8	2	no	—
317	D₄×C₁₃	—	2	4	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	2	2	no	—
320	D₄×C₁₃	—	2	4	no	—
321	D₄×C₁₃	—	4	8	no	—
322	D₄×C₁₃	—	4	4	no	—
323	D₄×C₁₃	—	4	8	no	—
324	D₄×C₁₃	—	4	4	no	—
325	D₄×C₁₃	—	8	2	no	—
326	D₄×C₁₃	—	8	4	no	—
327	D₄×C₁₃	#135	1	4	yes	complemented
328	D₄×C₁₃	C₂×#41	1	4	yes	—
329	C₂×C₄×C₁₃	—	2	4	no	—
330	C₂×C₄×C₁₃	—	2	2	no	—
331	C₂×C₄×C₁₃	—	2	4	no	—
332	C₂×C₄×C₁₃	—	2	2	no	—
333	C₂×C₄×C₁₃	—	2	2	no	—
334	C₂×C₄×C₁₃	—	2	1	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	1	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	2	no	—
340	C₂×C₄×C₁₃	—	2	4	no	—
341	C₂×C₄×C₁₃	—	4	4	no	—
342	C₂×C₄×C₁₃	—	4	4	no	—
343	C₂×C₄×C₁₃	—	4	4	no	—
344	C₂×C₄×C₁₃	—	4	8	no	—
345	C₂×C₄×C₁₃	—	8	4	no	—
346	C₂×C₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	—	8	4	no	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
350	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
357	C₈×C₁₃	—	2	2	no	—
358	C₈×C₁₃	—	2	1	no	—
359	C₈×C₁₃	—	2	1	no	—
360	C₈×C₁₃	—	2	1	no	—
361	C₈×C₁₃	—	2	2	no	—
362	C₈×C₁₃	C₂×#41	1	2	yes	—
363	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
364	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
365	#559	C₂²×C₁₃	1	2	yes	complemented
366	#554	C₂²×C₁₃	1	2	yes	—
367	#554	C₂²×C₁₃	1	2	yes	complemented
368	#553	—	2	2	no	—
369	#553	C₂²×C₁₃	1	4	yes	complemented
370	#551	—	2	4	no	—
371	#546	—	2	2	no	—
372	#546	C₂²×C₁₃	1	4	yes	complemented
373	D₄²	C₂²×C₁₃	1	2	yes	—
374	#532	C₂²×C₁₃	1	2	yes	complemented
375	#529	—	2	2	no	—
376	#529	C₂²×C₁₃	1	4	yes	complemented
377	#525	—	2	4	no	—
378	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
379	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
380	C₂×C₄×D₄	—	2	2	no	—
381	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
382	#500	C₂²×C₁₃	1	1	yes	characteristic, complemented
383	#499	C₂²×C₁₃	1	2	yes	complemented
384	#495	C₂²×C₁₃	1	2	yes	complemented
385	#493	C₂²×C₁₃	1	1	yes	characteristic
386	#488	C₂²×C₁₃	1	4	yes	complemented
387	#486	C₂²×C₁₃	1	2	yes	complemented
388	#484	C₂²×C₁₃	1	4	yes	complemented
389	#482	C₂²×C₁₃	1	4	yes	complemented
390	#481	C₂²×C₁₃	1	4	yes	complemented
391	#478	C₂²×C₁₃	1	4	yes	complemented
392	#478	C₂²×C₁₃	1	4	yes	complemented
393	#477	C₂²×C₁₃	1	2	yes	complemented
394	#476	C₂²×C₁₃	1	2	yes	complemented
395	#467	C₂²×C₁₃	1	2	yes	complemented
396	#466	C₂²×C₁₃	1	2	yes	—
397	#466	C₂²×C₁₃	1	2	yes	complemented
398	#466	C₂²×C₁₃	1	2	yes	complemented
399	#465	C₂²×C₁₃	1	4	yes	complemented
400	#463	C₂²×C₁₃	1	4	yes	complemented
401	#463	C₂²×C₁₃	1	4	yes	complemented
402	#460	C₂²×C₁₃	1	2	yes	complemented
403	#459	C₂²×C₁₃	1	2	yes	—
404	#450	C₂²×C₁₃	1	4	yes	complemented
405	#449	C₂²×C₁₃	1	4	yes	complemented
406	#447	C₂²×C₁₃	1	4	yes	—
407	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
408	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
410	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
411	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
412	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
413	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
414	C₄×D₈	C₂²×C₁₃	1	2	yes	—
415	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
417	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
418	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
419	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
420	C₄×D₈	C₂²×C₁₃	1	4	yes	complemented
421	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
422	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
423	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
424	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
425	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
426	#431	C₂²×C₁₃	1	2	yes	complemented
427	#431	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
430	#416	C₂²×C₁₃	1	2	yes	complemented
431	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
432	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
433	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	2	1	no	—
437	C₂²×C₁₃	—	2	4	no	—
438	C₂²×C₁₃	—	2	1	no	—
439	C₂²×C₁₃	—	2	1	no	—
440	C₂²×C₁₃	—	4	2	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	4	no	—
443	C₂²×C₁₃	—	4	4	no	—
444	C₂²×C₁₃	—	4	4	no	—
445	C₂²×C₁₃	—	8	16	no	—
446	C₂²×C₁₃	C₂×#135	1	4	yes	—
447	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₁₃	—	2	1	no	—
449	C₄×C₁₃	—	2	2	no	—
450	C₄×C₁₃	—	2	1	no	—
451	C₄×C₁₃	—	2	2	no	—
452	C₄×C₁₃	—	2	2	no	—
453	C₄×C₁₃	—	2	1	no	—
454	C₄×C₁₃	—	4	2	no	—
455	C₄×C₁₃	—	4	2	no	—
456	C₄×C₁₃	—	4	2	no	—
457	C₄×C₁₃	—	4	4	no	—
458	C₄×C₁₃	C₂×#135	1	2	yes	—
459	C₄×C₁₃	#576	1	2	yes	—
460	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
461	C₄×C₁₃	#585	1	1	yes	characteristic
462	C₂×#41	—	2	2	no	—
463	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
464	C₂×#41	C₂³×C₁₃	1	2	yes	—
465	C₂²×D₄	—	2	2	no	—
466	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
467	C₂³×C₄	—	2	4	no	—
468	#135	—	2	4	no	—
469	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
471	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
472	C₂×D₈	—	2	8	no	—
473	C₂×D₈	C₂³×C₁₃	1	4	yes	—
474	C₂×D₈	C₂³×C₁₃	1	2	yes	—
475	C₂×D₈	C₂³×C₁₃	1	2	yes	—
476	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
482	#127	C₂³×C₁₃	1	2	yes	—
483	#126	—	2	4	no	—
484	#126	—	2	4	no	—
485	#125	—	2	2	no	—
486	#125	C₂³×C₁₃	1	4	yes	—
487	#124	—	2	2	no	—
488	#124	—	2	2	no	—
489	#124	C₂³×C₁₃	1	4	yes	—
490	#123	—	2	4	no	—
491	#123	—	2	4	no	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	4	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
498	#121	—	2	4	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	4	no	—
502	#121	C₂³×C₁₃	1	4	yes	—
503	#121	C₂³×C₁₃	1	4	yes	—
504	#120	—	2	4	no	—
505	#120	—	2	4	no	—
506	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
507	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
508	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
509	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	4	no	—
512	C₄×D₄	—	2	2	no	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	4	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	4	no	—
518	C₄×D₄	—	2	4	no	—
519	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
520	C₄×D₄	D₄×C₁₃	1	2	yes	—
521	C₄×D₄	C₂³×C₁₃	1	2	yes	—
522	C₄×D₄	C₂³×C₁₃	1	4	yes	—
523	C₄×D₄	C₂³×C₁₃	1	4	yes	—
524	C₄×D₄	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	C₂³×C₁₃	1	2	yes	—
526	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₄×D₄	C₂³×C₁₃	1	2	yes	—
528	#117	—	2	2	no	—
529	#117	—	2	4	no	—
530	#117	D₄×C₁₃	1	2	yes	—
531	#117	D₄×C₁₃	1	1	yes	characteristic
532	#117	C₂³×C₁₃	1	2	yes	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
535	C₂×C₂²⋊C₄	—	2	4	no	—
536	C₂×C₂²⋊C₄	—	2	4	no	—
537	C₂×C₄²	—	2	2	no	—
538	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
539	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
540	#107	C₂³×C₁₃	1	1	yes	characteristic
541	#107	C₂³×C₁₃	1	2	yes	—
542	#107	C₂³×C₁₃	1	4	yes	—
543	#107	C₂³×C₁₃	1	1	yes	characteristic
544	#107	C₂³×C₁₃	1	2	yes	—
545	#106	C₂³×C₁₃	1	2	yes	—
546	#106	C₂³×C₁₃	1	4	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
548	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
549	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
550	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
551	#103	C₂³×C₁₃	1	2	yes	—
552	#103	C₂³×C₁₃	1	2	yes	—
553	#103	C₂³×C₁₃	1	4	yes	—
554	#102	C₂³×C₁₃	1	2	yes	—
555	#102	C₂³×C₁₃	1	4	yes	—
556	#102	C₂³×C₁₃	1	4	yes	—
557	#102	C₂³×C₁₃	1	4	yes	—
558	#102	C₂³×C₁₃	1	2	yes	—
559	#102	C₂³×C₁₃	1	4	yes	—
560	#102	C₂³×C₁₃	1	4	yes	—
561	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
562	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
563	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
564	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
565	C₄×C₈	C₂³×C₁₃	1	2	yes	—
566	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
567	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₁₃	1	2	yes	—
570	C₄×C₈	C₂³×C₁₃	1	2	yes	—
571	C₂×C₁₃	—	2	4	no	—
572	C₂×C₁₃	—	4	1	no	—
573	C₂×C₁₃	—	4	4	no	—
574	C₂×C₁₃	—	8	4	no	—
575	C₂×C₁₃	D₄×#41	1	1	yes	characteristic
576	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
577	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
578	C₂⁴	—	2	4	no	—
579	#41	—	2	4	no	—
580	#41	—	2	4	no	—
581	#41	—	4	2	no	—
582	#41	—	8	4	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
585	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
586	C₂×D₄	—	2	8	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	4	4	no	—
594	C₂×D₄	—	4	8	no	—
595	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
596	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
598	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
599	C₂²×C₄	—	2	4	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	4	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	8	8	no	—
607	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
608	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
613	Q₁₆	—	2	2	no	—
614	SD₁₆	—	2	4	no	—
615	SD₁₆	—	4	4	no	—
616	D₈	—	2	8	no	—
617	D₈	—	2	4	no	—
618	D₈	—	4	2	no	—
619	D₈	C₁₃×#41	1	4	yes	complemented
620	C₂×C₈	—	2	4	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	4	1	no	—
623	C₂×C₈	—	4	2	no	—
624	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
627	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
628	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
629	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
639	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
656	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₁₃	1	2	yes	—
664	C₄²	C₂×D₄×C₁₃	1	2	yes	—
665	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
666	C₄²	C₂⁴×C₁₃	1	2	yes	—
667	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
668	C₁₃	#61431	1	1	yes	characteristic, direct product factor, Sylow
669	C₂³	—	2	2	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	8	no	—
673	C₂³	—	8	4	no	—
674	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
675	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	8	2	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	4	no	—
682	D₄	—	2	2	no	—
683	D₄	—	2	4	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	8	no	—
687	D₄	—	4	4	no	—
688	D₄	—	8	2	no	—
689	D₄	—	8	4	no	—
690	D₄	C₁₃×#135	1	4	yes	complemented
691	D₄	C₂×C₁₃×#41	1	4	yes	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	8	no	—
708	C₂×C₄	—	8	4	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
714	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
715	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
716	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
717	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
719	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
720	C₈	—	2	2	no	—
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	2	1	no	—
724	C₈	—	2	2	no	—
725	C₈	C₂×C₁₃×#41	1	2	yes	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	8	16	no	—
738	C₂²	C₂×C₁₃×#135	1	4	yes	—
739	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	2	no	—
743	C₄	—	2	1	no	—
744	C₄	—	2	1	no	—
745	C₄	—	2	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	—	4	4	no	—
749	C₄	—	4	2	no	—
750	C₄	C₂×C₁₃×#135	1	2	yes	—
751	C₄	C₁₃×#576	1	2	yes	—
752	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
753	C₄	C₁₃×#585	1	1	yes	characteristic
754	C₂	—	2	4	no	—
755	C₂	—	4	1	no	—
756	C₂	—	4	4	no	—
757	C₂	—	8	4	no	—
758	C₂	D₄×C₁₃×#41	1	1	yes	characteristic
759	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
760	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3481	C₂	semidirect
2. C₁₃×#3396	C₂	semidirect
3. C₁₃×#3380	C₂	semidirect
4. C₁₃×#3361	C₂	semidirect
5. C₁₃×#3339	C₂	semidirect
6. C₁₃×#3338	C₂	semidirect
7. C₁₃×#3297	C₂	semidirect
8. C₁₃×#3295	C₂	semidirect
9. C₁₃×#3280	C₂	semidirect
10. D₄×C₁₃×D₈	C₂	semidirect
11. C₁₃×#3169	C₂	semidirect
12. C₁₃×#3168	C₂	semidirect
13. C₁₃×#3106	C₂	semidirect
14. C₁₃×#3105	C₂	semidirect
15. C₈×C₁₃×#41	C₂	semidirect
16. C₄×C₁₃×#135	C₂	semidirect
17. C₂×C₄×C₁₃×D₈	C₂	semidirect
20. C₁₃×#559	C₂²	semidirect
22. C₁₃×#554	C₂²	semidirect
24. C₁₃×#553	C₂²	semidirect
27. C₁₃×#546	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
31. C₁₃×#529	C₂²	semidirect
34. C₄×C₁₃×#41	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#500	C₂²	semidirect
38. C₁₃×#499	C₂²	semidirect
39. C₁₃×#495	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#486	C₂²	semidirect
43. C₁₃×#484	C₂²	semidirect
44. C₁₃×#482	C₂²	semidirect
45. C₁₃×#481	C₂²	semidirect
46. C₁₃×#478	C₂²	semidirect
47. C₁₃×#478	C₂²	semidirect
48. C₁₃×#477	C₂²	semidirect
49. C₁₃×#476	C₂²	semidirect
50. C₁₃×#467	C₂²	semidirect
52. C₁₃×#466	C₂²	semidirect
53. C₁₃×#466	C₂²	semidirect
54. C₁₃×#465	C₂²	semidirect
55. C₁₃×#463	C₂²	semidirect
56. C₁₃×#463	C₂²	semidirect
57. C₁₃×#460	C₂²	semidirect
59. C₁₃×#450	C₂²	semidirect
60. C₁₃×#449	C₂²	semidirect
62. C₈×Q₈×C₁₃	C₂²	semidirect
63. C₈×Q₈×C₁₃	C₂²	semidirect
64. C₄×C₁₃×Q₁₆	C₂²	semidirect
65. C₄×C₁₃×Q₁₆	C₂²	semidirect
66. C₄×C₁₃×SD₁₆	C₂²	semidirect
67. C₄×C₁₃×SD₁₆	C₂²	semidirect
68. C₄×C₁₃×SD₁₆	C₂²	semidirect
72. C₄×C₁₃×D₈	C₂²	semidirect
73. C₄×C₁₃×D₈	C₂²	semidirect
74. C₄×C₁₃×D₈	C₂²	semidirect
75. C₄×C₁₃×D₈	C₂²	semidirect
76. C₄×C₁₃×D₈	C₂²	semidirect
79. C₈×D₄×C₁₃	C₂²	semidirect
80. C₈×D₄×C₁₃	C₂²	semidirect
81. C₁₃×#431	C₂²	semidirect
82. C₁₃×#431	C₂²	semidirect
83. C₁₃×#427	C₂²	semidirect
84. C₂×C₁₃×#107	C₂²	semidirect
85. C₁₃×#416	C₂²	semidirect
86. C₂×C₁₃×#102	C₂²	semidirect
87. C₂×C₄×C₈×C₁₃	C₂²	semidirect
88. C₂×C₄×C₈×C₁₃	C₂²	semidirect
198. #61431	C₁₃	direct (N × H)
240. C₁₃×D₈	#41	semidirect
289. #3481	C₂×C₁₃	semidirect
290. #3396	C₂×C₁₃	semidirect
291. #3380	C₂×C₁₃	semidirect
292. #3361	C₂×C₁₃	semidirect
293. #3339	C₂×C₁₃	semidirect
294. #3338	C₂×C₁₃	semidirect
295. #3297	C₂×C₁₃	semidirect
296. #3295	C₂×C₁₃	semidirect
297. #3280	C₂×C₁₃	semidirect
298. D₄×D₈	C₂×C₁₃	semidirect
299. #3169	C₂×C₁₃	semidirect
300. #3168	C₂×C₁₃	semidirect
301. #3106	C₂×C₁₃	semidirect
302. #3105	C₂×C₁₃	semidirect
303. C₈×#41	C₂×C₁₃	semidirect
304. C₄×#135	C₂×C₁₃	semidirect
305. C₂×C₄×D₈	C₂×C₁₃	semidirect
327. D₄×C₁₃	#135	semidirect
365. #559	C₂²×C₁₃	semidirect
367. #554	C₂²×C₁₃	semidirect
369. #553	C₂²×C₁₃	semidirect
372. #546	C₂²×C₁₃	semidirect
374. #532	C₂²×C₁₃	semidirect
376. #529	C₂²×C₁₃	semidirect
379. C₄×#41	C₂²×C₁₃	semidirect
381. C₂×C₄×D₄	C₂²×C₁₃	semidirect
382. #500	C₂²×C₁₃	semidirect
383. #499	C₂²×C₁₃	semidirect
384. #495	C₂²×C₁₃	semidirect
386. #488	C₂²×C₁₃	semidirect
387. #486	C₂²×C₁₃	semidirect
388. #484	C₂²×C₁₃	semidirect
389. #482	C₂²×C₁₃	semidirect
390. #481	C₂²×C₁₃	semidirect
391. #478	C₂²×C₁₃	semidirect
392. #478	C₂²×C₁₃	semidirect
393. #477	C₂²×C₁₃	semidirect
394. #476	C₂²×C₁₃	semidirect
395. #467	C₂²×C₁₃	semidirect
397. #466	C₂²×C₁₃	semidirect
398. #466	C₂²×C₁₃	semidirect
399. #465	C₂²×C₁₃	semidirect
400. #463	C₂²×C₁₃	semidirect
401. #463	C₂²×C₁₃	semidirect
402. #460	C₂²×C₁₃	semidirect
404. #450	C₂²×C₁₃	semidirect
405. #449	C₂²×C₁₃	semidirect
407. C₈×Q₈	C₂²×C₁₃	semidirect
408. C₈×Q₈	C₂²×C₁₃	semidirect
409. C₄×Q₁₆	C₂²×C₁₃	semidirect
410. C₄×Q₁₆	C₂²×C₁₃	semidirect
411. C₄×SD₁₆	C₂²×C₁₃	semidirect
412. C₄×SD₁₆	C₂²×C₁₃	semidirect
413. C₄×SD₁₆	C₂²×C₁₃	semidirect
417. C₄×D₈	C₂²×C₁₃	semidirect
418. C₄×D₈	C₂²×C₁₃	semidirect
419. C₄×D₈	C₂²×C₁₃	semidirect
420. C₄×D₈	C₂²×C₁₃	semidirect
421. C₄×D₈	C₂²×C₁₃	semidirect
424. C₈×D₄	C₂²×C₁₃	semidirect
425. C₈×D₄	C₂²×C₁₃	semidirect
426. #431	C₂²×C₁₃	semidirect
427. #431	C₂²×C₁₃	semidirect
428. #427	C₂²×C₁₃	semidirect
429. C₂×#107	C₂²×C₁₃	semidirect
430. #416	C₂²×C₁₃	semidirect
431. C₂×#102	C₂²×C₁₃	semidirect
432. C₂×C₄×C₈	C₂²×C₁₃	semidirect
433. C₂×C₄×C₈	C₂²×C₁₃	semidirect
619. D₈	C₁₃×#41	semidirect
668. C₁₃	#61431	direct (N × H)
690. D₄	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3481	2
C₁₃×#3396	2
C₁₃×#3380	2
C₁₃×#3361	2
C₁₃×#3339	2
C₁₃×#3338	2
C₁₃×#3297	2
C₁₃×#3295	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3169	2
C₁₃×#3168	2
C₁₃×#3106	2
C₁₃×#3105	2
C₈×C₁₃×#41	2
C₄×C₁₃×#135	2
C₂×C₄×C₁₃×D₈	2
#61431	13

Subgroups — C13×#61431 #15747770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61431 #15747770