Subgroups — C₁₃×#24149 #15710488

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2005	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2004	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1967	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1886	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1857	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
17	C₁₃×#559	—	2	1	no	—
18	C₁₃×#559	—	2	1	no	—
19	C₁₃×#556	—	2	1	no	—
20	C₁₃×#556	—	2	1	no	—
21	C₁₃×#551	—	2	2	no	—
22	C₁₃×#551	—	2	2	no	—
23	C₁₃×#542	—	2	1	no	—
24	C₁₃×#542	—	2	1	no	—
25	C₁₃×#536	C₂²	1	1	yes	characteristic
26	C₁₃×#535	C₂²	1	1	yes	characteristic
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₃×#529	—	2	1	no	—
30	C₁₃×#529	—	2	1	no	—
31	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₁₃×#519	C₂²	1	1	yes	characteristic
34	C₁₃×#518	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#479	—	2	1	no	—
38	C₁₃×#479	—	2	1	no	—
39	C₁₃×#477	—	2	1	no	—
40	C₁₃×#475	—	2	1	no	—
41	C₁₃×#441	—	2	1	no	—
42	C₁₃×#440	—	2	1	no	—
43	C₄×C₁₃×Q₁₆	—	2	1	no	—
44	C₄×C₁₃×SD₁₆	—	2	1	no	—
45	C₁₃×#428	C₂²	1	1	yes	characteristic
46	C₁₃×#428	C₂²	1	1	yes	characteristic
47	C₁₃×#428	C₂²	1	1	yes	characteristic
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₁₃×#419	C₂²	1	1	yes	characteristic
52	C₁₃×#419	C₂²	1	1	yes	characteristic
53	C₁₃×#419	C₂²	1	1	yes	characteristic
54	C₁₃×#417	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
59	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
60	C₁₃×#396	—	2	2	no	—
61	C₁₃×#391	C₂²	1	1	yes	characteristic
62	C₁₃×#390	C₂²	1	1	yes	characteristic
63	C₁₃×#388	—	2	2	no	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₁₃×#339	C₂²	1	1	yes	characteristic
68	C₁₃×#339	C₂²	1	1	yes	characteristic
69	C₁₃×#339	C₂²	1	1	yes	characteristic
70	C₁₃×#339	C₂²	1	1	yes	characteristic
71	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#137	—	2	2	no	—
76	C₁₃×#137	—	2	2	no	—
77	C₂×C₁₃×Q₁₆	—	2	1	no	—
78	C₂×C₁₃×SD₁₆	—	2	1	no	—
79	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	2	no	—
85	C₁₃×C₄⋊Q₈	—	4	1	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₃×#127	—	2	1	no	—
89	C₁₃×#126	—	2	2	no	—
90	C₁₃×#126	—	2	2	no	—
91	C₁₃×#126	—	2	2	no	—
92	C₁₃×#126	—	2	2	no	—
93	C₁₃×#125	D₄	1	1	yes	characteristic
94	C₁₃×#125	D₄	1	1	yes	characteristic
95	C₁₃×#124	—	2	2	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	1	no	—
98	C₁₃×#124	—	2	1	no	—
99	C₁₃×#124	—	2	2	no	—
100	C₁₃×#124	—	2	1	no	—
101	C₁₃×#124	—	2	1	no	—
102	C₁₃×#124	—	2	1	no	—
103	C₁₃×#124	—	2	1	no	—
104	C₁₃×#124	—	4	1	no	—
105	C₁₃×#123	—	2	2	no	—
106	C₁₃×#123	—	2	2	no	—
107	C₁₃×#123	—	2	2	no	—
108	C₁₃×#123	—	2	2	no	—
109	C₁₃×#123	—	2	2	no	—
110	C₁₃×C₂²⋊Q₈	—	2	2	no	—
111	C₁₃×C₂²⋊Q₈	—	2	2	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	1	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#120	—	2	2	no	—
119	C₄×Q₈×C₁₃	—	2	1	no	—
120	C₄×Q₈×C₁₃	—	2	1	no	—
121	C₄×Q₈×C₁₃	—	2	1	no	—
122	C₄×Q₈×C₁₃	—	2	1	no	—
123	C₄×Q₈×C₁₃	—	2	1	no	—
124	C₄×Q₈×C₁₃	—	2	1	no	—
125	C₄×Q₈×C₁₃	—	2	1	no	—
126	C₄×Q₈×C₁₃	—	2	1	no	—
127	C₄×Q₈×C₁₃	—	2	1	no	—
128	C₄×Q₈×C₁₃	—	2	1	no	—
129	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
130	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
131	C₄×D₄×C₁₃	—	2	2	no	—
132	C₄×D₄×C₁₃	—	2	2	no	—
133	C₄×D₄×C₁₃	—	2	1	no	—
134	C₄×D₄×C₁₃	—	2	1	no	—
135	C₄×D₄×C₁₃	—	2	1	no	—
136	C₄×D₄×C₁₃	—	2	1	no	—
137	C₄×D₄×C₁₃	—	2	1	no	—
138	C₄×D₄×C₁₃	—	2	1	no	—
139	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
140	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
141	C₁₃×#117	—	2	2	no	—
142	C₁₃×#117	—	2	2	no	—
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	1	no	—
145	C₁₃×#117	C₂³	1	1	yes	characteristic
146	C₁₃×#117	C₂³	1	1	yes	characteristic
147	C₁₃×#117	C₂³	1	1	yes	characteristic
148	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
156	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
157	C₂×C₄²×C₁₃	—	2	1	no	—
158	C₂×C₄²×C₁₃	—	2	1	no	—
159	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₁₃×#107	—	2	1	no	—
163	C₁₃×#107	—	2	1	no	—
164	C₁₃×#107	—	2	1	no	—
165	C₁₃×#106	—	2	1	no	—
166	C₁₃×#106	—	2	1	no	—
167	C₁₃×#106	—	2	1	no	—
168	C₁₃×C₄⋊C₈	—	2	1	no	—
169	C₁₃×C₄⋊C₈	—	2	1	no	—
170	C₁₃×#104	—	4	1	no	—
171	C₁₃×#104	—	4	1	no	—
172	C₁₃×#103	—	2	1	no	—
173	C₁₃×#103	—	2	1	no	—
174	C₁₃×#103	—	2	1	no	—
175	C₁₃×#103	—	2	1	no	—
176	C₁₃×#103	—	2	1	no	—
177	C₁₃×#103	—	2	1	no	—
178	C₁₃×#103	—	2	1	no	—
179	C₁₃×#102	—	2	1	no	—
180	C₁₃×#101	—	2	2	no	—
181	C₁₃×#101	—	4	1	no	—
182	C₁₃×#100	—	2	2	no	—
183	C₁₃×#100	—	4	1	no	—
184	C₁₃×#97	—	2	1	no	—
185	C₄×C₈×C₁₃	—	2	1	no	—
186	C₁₃×#95	—	2	1	no	—
187	C₁₃×#95	—	2	2	no	—
188	#24149	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
190	C₁₃×#41	—	2	1	no	—
191	C₁₃×#41	—	2	1	no	—
192	C₁₃×#41	—	2	1	no	—
193	C₁₃×#41	—	2	1	no	—
194	C₂×Q₈×C₁₃	—	2	1	no	—
195	C₂×Q₈×C₁₃	—	2	1	no	—
196	C₂×Q₈×C₁₃	—	2	1	no	—
197	C₂×Q₈×C₁₃	—	2	1	no	—
198	C₂×Q₈×C₁₃	—	2	1	no	—
199	C₂×Q₈×C₁₃	—	2	1	no	—
200	C₂×Q₈×C₁₃	—	2	1	no	—
201	C₂×Q₈×C₁₃	—	2	1	no	—
202	C₂×Q₈×C₁₃	—	2	1	no	—
203	C₂×Q₈×C₁₃	—	2	1	no	—
204	C₂×Q₈×C₁₃	—	2	1	no	—
205	C₂×Q₈×C₁₃	—	2	1	no	—
206	C₂×Q₈×C₁₃	—	2	1	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	#41	1	2	yes	—
209	C₂×D₄×C₁₃	—	2	1	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	2	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	1	no	—
214	C₂×D₄×C₁₃	—	2	1	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	—	2	1	no	—
218	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	2	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	2	1	no	—
225	C₂²×C₄×C₁₃	—	2	1	no	—
226	C₂²×C₄×C₁₃	—	2	1	no	—
227	C₂²×C₄×C₁₃	—	2	1	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	1	yes	characteristic
231	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₁₃×Q₁₆	—	2	4	no	—
233	C₁₃×SD₁₆	—	2	4	no	—
234	C₁₃×M₁₆	—	2	1	no	—
235	C₁₃×M₁₆	—	2	1	no	—
236	C₁₃×M₁₆	—	2	1	no	—
237	C₁₃×M₁₆	—	2	1	no	—
238	C₁₃×M₁₆	—	2	1	no	—
239	C₁₃×M₁₆	—	2	1	no	—
240	C₁₃×M₁₆	—	2	1	no	—
241	C₁₃×M₁₆	#41	1	2	yes	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	2	1	no	—
245	C₂×C₈×C₁₃	—	2	1	no	—
246	C₁₃×C₄⋊C₄	—	2	2	no	—
247	C₁₃×C₄⋊C₄	—	2	2	no	—
248	C₁₃×C₄⋊C₄	—	2	2	no	—
249	C₁₃×C₄⋊C₄	—	2	2	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	1	no	—
259	C₁₃×C₄⋊C₄	—	2	1	no	—
260	C₁₃×C₄⋊C₄	—	4	4	no	—
261	C₁₃×C₄⋊C₄	—	4	2	no	—
262	C₁₃×C₄⋊C₄	—	4	1	no	—
263	C₁₃×C₄⋊C₄	—	4	1	no	—
264	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
265	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
268	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
269	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
270	C₁₃×C₂²⋊C₄	—	2	2	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	—	2	2	no	—
274	C₁₃×C₂²⋊C₄	—	2	2	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	1	no	—
277	C₁₃×C₂²⋊C₄	—	2	1	no	—
278	C₁₃×C₂²⋊C₄	—	2	1	no	—
279	C₁₃×C₂²⋊C₄	—	2	2	no	—
280	C₁₃×C₂²⋊C₄	—	2	2	no	—
281	C₁₃×C₂²⋊C₄	—	2	2	no	—
282	C₁₃×C₂²⋊C₄	—	2	2	no	—
283	C₁₃×C₂²⋊C₄	—	2	1	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	4	4	no	—
286	C₁₃×C₂²⋊C₄	—	4	4	no	—
287	C₄²×C₁₃	—	2	2	no	—
288	C₄²×C₁₃	—	2	2	no	—
289	C₄²×C₁₃	—	2	1	no	—
290	C₄²×C₁₃	—	2	1	no	—
291	C₄²×C₁₃	—	2	1	no	—
292	C₄²×C₁₃	—	2	1	no	—
293	C₄²×C₁₃	—	2	1	no	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	1	no	—
298	C₄²×C₁₃	—	4	1	no	—
299	C₄²×C₁₃	—	4	1	no	—
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	#3510	C₂×C₁₃	1	1	yes	characteristic
305	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
306	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#2545	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#2038	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#2037	C₂×C₁₃	1	1	yes	characteristic
310	#2005	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2004	C₂×C₁₃	1	1	yes	characteristic
312	#1986	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#1967	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#1886	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#1885	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#1857	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
319	C₂³×C₁₃	—	2	2	no	—
320	C₂³×C₁₃	—	2	1	no	—
321	C₂³×C₁₃	—	2	2	no	—
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	—	4	2	no	—
324	C₂³×C₁₃	—	4	2	no	—
325	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	1	no	—
328	Q₈×C₁₃	—	2	1	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	4	1	no	—
331	Q₈×C₁₃	—	4	1	no	—
332	Q₈×C₁₃	—	4	1	no	—
333	Q₈×C₁₃	—	4	1	no	—
334	Q₈×C₁₃	—	4	1	no	—
335	Q₈×C₁₃	—	4	1	no	—
336	Q₈×C₁₃	—	8	1	no	—
337	Q₈×C₁₃	—	8	1	no	—
338	D₄×C₁₃	—	2	1	no	—
339	D₄×C₁₃	—	2	1	no	—
340	D₄×C₁₃	—	4	1	no	—
341	D₄×C₁₃	—	4	1	no	—
342	D₄×C₁₃	—	4	1	no	—
343	D₄×C₁₃	—	4	1	no	—
344	D₄×C₁₃	—	4	1	no	—
345	D₄×C₁₃	—	4	1	no	—
346	D₄×C₁₃	—	8	2	no	—
347	D₄×C₁₃	—	8	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	no	—
351	C₂×C₄×C₁₃	—	2	1	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	2	1	no	—
356	C₂×C₄×C₁₃	—	2	1	no	—
357	C₂×C₄×C₁₃	—	2	2	no	—
358	C₂×C₄×C₁₃	—	2	2	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	1	no	—
362	C₂×C₄×C₁₃	—	4	1	no	—
363	C₂×C₄×C₁₃	—	4	1	no	—
364	C₂×C₄×C₁₃	—	4	1	no	—
365	C₂×C₄×C₁₃	—	4	1	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	1	no	—
368	C₂×C₄×C₁₃	—	4	2	no	—
369	C₂×C₄×C₁₃	—	4	1	no	—
370	C₂×C₄×C₁₃	—	4	1	no	—
371	C₂×C₄×C₁₃	—	4	1	no	—
372	C₂×C₄×C₁₃	—	4	1	no	—
373	C₂×C₄×C₁₃	—	8	1	no	—
374	C₂×C₄×C₁₃	—	8	1	no	—
375	C₂×C₄×C₁₃	—	8	2	no	—
376	C₂×C₄×C₁₃	—	8	2	no	—
377	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
378	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
379	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
380	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
384	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
385	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
386	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
387	C₈×C₁₃	—	2	2	no	—
388	C₈×C₁₃	—	4	1	no	—
389	C₈×C₁₃	—	4	1	no	—
390	C₈×C₁₃	—	4	1	no	—
391	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
392	#559	—	2	1	no	—
393	#559	—	2	1	no	—
394	#556	—	2	1	no	—
395	#556	—	2	1	no	—
396	#551	—	2	2	no	—
397	#551	—	2	2	no	—
398	#542	—	2	1	no	—
399	#542	—	2	1	no	—
400	#536	C₂²×C₁₃	1	1	yes	characteristic
401	#535	C₂²×C₁₃	1	1	yes	characteristic
402	#533	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
404	#529	—	2	1	no	—
405	#529	—	2	1	no	—
406	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
408	#519	C₂²×C₁₃	1	1	yes	characteristic
409	#518	C₂²×C₁₃	1	1	yes	characteristic
410	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
412	#479	—	2	1	no	—
413	#479	—	2	1	no	—
414	#477	—	2	1	no	—
415	#475	—	2	1	no	—
416	#441	—	2	1	no	—
417	#440	—	2	1	no	—
418	C₄×Q₁₆	—	2	1	no	—
419	C₄×SD₁₆	—	2	1	no	—
420	#428	C₂²×C₁₃	1	1	yes	characteristic
421	#428	C₂²×C₁₃	1	1	yes	characteristic
422	#428	C₂²×C₁₃	1	1	yes	characteristic
423	#423	C₂²×C₁₃	1	1	yes	characteristic
424	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
425	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
426	#419	C₂²×C₁₃	1	1	yes	characteristic
427	#419	C₂²×C₁₃	1	1	yes	characteristic
428	#419	C₂²×C₁₃	1	1	yes	characteristic
429	#417	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
434	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
435	#396	—	2	2	no	—
436	#391	C₂²×C₁₃	1	1	yes	characteristic
437	#390	C₂²×C₁₃	1	1	yes	characteristic
438	#388	—	2	2	no	—
439	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
440	#339	C₂²×C₁₃	1	1	yes	characteristic
441	#339	C₂²×C₁₃	1	1	yes	characteristic
442	#339	C₂²×C₁₃	1	1	yes	characteristic
443	#339	C₂²×C₁₃	1	1	yes	characteristic
444	#339	C₂²×C₁₃	1	1	yes	characteristic
445	#339	C₂²×C₁₃	1	1	yes	characteristic
446	C₂²×C₁₃	—	2	1	no	—
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	4	1	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	8	2	no	—
455	C₂²×C₁₃	—	8	2	no	—
456	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
457	C₂²×C₁₃	#546	1	1	yes	characteristic
458	C₂²×C₁₃	#547	1	1	yes	characteristic
459	C₄×C₁₃	—	2	1	no	—
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	1	no	—
462	C₄×C₁₃	—	2	1	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	1	no	—
466	C₄×C₁₃	—	4	2	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	1	no	—
469	C₄×C₁₃	—	4	1	no	—
470	C₄×C₁₃	—	4	1	no	—
471	C₄×C₁₃	—	4	1	no	—
472	C₄×C₁₃	—	4	1	no	—
473	C₄×C₁₃	—	8	1	no	—
474	C₄×C₁₃	—	8	1	no	—
475	C₄×C₁₃	#525	1	1	yes	characteristic
476	C₄×C₁₃	#537	1	1	yes	characteristic
477	C₄×C₁₃	#548	1	1	yes	characteristic
478	C₄×C₁₃	#550	1	1	yes	characteristic
479	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
480	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
483	#137	—	2	2	no	—
484	#137	—	2	2	no	—
485	C₂×Q₁₆	—	2	1	no	—
486	C₂×SD₁₆	—	2	1	no	—
487	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
489	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	—	2	2	no	—
493	C₄⋊Q₈	—	4	1	no	—
494	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
495	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
496	#127	—	2	1	no	—
497	#126	—	2	2	no	—
498	#126	—	2	2	no	—
499	#126	—	2	2	no	—
500	#126	—	2	2	no	—
501	#125	D₄×C₁₃	1	1	yes	characteristic
502	#125	D₄×C₁₃	1	1	yes	characteristic
503	#124	—	2	2	no	—
504	#124	—	2	2	no	—
505	#124	—	2	1	no	—
506	#124	—	2	1	no	—
507	#124	—	2	2	no	—
508	#124	—	2	1	no	—
509	#124	—	2	1	no	—
510	#124	—	2	1	no	—
511	#124	—	2	1	no	—
512	#124	—	4	1	no	—
513	#123	—	2	2	no	—
514	#123	—	2	2	no	—
515	#123	—	2	2	no	—
516	#123	—	2	2	no	—
517	#123	—	2	2	no	—
518	C₂²⋊Q₈	—	2	2	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	1	no	—
521	C₂²⋊Q₈	—	2	1	no	—
522	C₂²⋊Q₈	—	2	1	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	#121	—	2	1	no	—
525	#121	—	2	1	no	—
526	#120	—	2	2	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
538	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	2	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	—	2	1	no	—
547	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
548	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
549	#117	—	2	2	no	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	—	2	1	no	—
553	#117	C₂³×C₁₃	1	1	yes	characteristic
554	#117	C₂³×C₁₃	1	1	yes	characteristic
555	#117	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	—	2	1	no	—
557	C₂×C₄⋊C₄	—	2	2	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	—	2	2	no	—
561	C₂×C₂²⋊C₄	—	2	2	no	—
562	C₂×C₂²⋊C₄	—	2	2	no	—
563	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
564	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
565	C₂×C₄²	—	2	1	no	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
570	#107	—	2	1	no	—
571	#107	—	2	1	no	—
572	#107	—	2	1	no	—
573	#106	—	2	1	no	—
574	#106	—	2	1	no	—
575	#106	—	2	1	no	—
576	C₄⋊C₈	—	2	1	no	—
577	C₄⋊C₈	—	2	1	no	—
578	#104	—	4	1	no	—
579	#104	—	4	1	no	—
580	#103	—	2	1	no	—
581	#103	—	2	1	no	—
582	#103	—	2	1	no	—
583	#103	—	2	1	no	—
584	#103	—	2	1	no	—
585	#103	—	2	1	no	—
586	#103	—	2	1	no	—
587	#102	—	2	1	no	—
588	#101	—	2	2	no	—
589	#101	—	4	1	no	—
590	#100	—	2	2	no	—
591	#100	—	4	1	no	—
592	#97	—	2	1	no	—
593	C₄×C₈	—	2	1	no	—
594	#95	—	2	1	no	—
595	#95	—	2	2	no	—
596	C₂×C₁₃	—	2	1	no	—
597	C₂×C₁₃	—	2	1	no	—
598	C₂×C₁₃	—	8	1	no	—
599	C₂×C₁₃	—	8	2	no	—
600	C₂×C₁₃	#2407	1	1	yes	characteristic
601	C₂×C₁₃	#3018	1	1	yes	characteristic
602	C₂×C₁₃	#3022	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
604	#41	—	2	1	no	—
605	#41	—	2	1	no	—
606	#41	—	2	1	no	—
607	#41	—	2	1	no	—
608	C₂×Q₈	—	2	1	no	—
609	C₂×Q₈	—	2	1	no	—
610	C₂×Q₈	—	2	1	no	—
611	C₂×Q₈	—	2	1	no	—
612	C₂×Q₈	—	2	1	no	—
613	C₂×Q₈	—	2	1	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂×Q₈	C₁₃×#41	1	2	yes	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	2	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
646	Q₁₆	—	2	4	no	—
647	SD₁₆	—	2	4	no	—
648	M₁₆	—	2	1	no	—
649	M₁₆	—	2	1	no	—
650	M₁₆	—	2	1	no	—
651	M₁₆	—	2	1	no	—
652	M₁₆	—	2	1	no	—
653	M₁₆	—	2	1	no	—
654	M₁₆	—	2	1	no	—
655	M₁₆	C₁₃×#41	1	2	yes	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	2	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	2	1	no	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	1	no	—
674	C₄⋊C₄	—	4	4	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
679	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
680	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
681	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
684	C₂²⋊C₄	—	2	2	no	—
685	C₂²⋊C₄	—	2	2	no	—
686	C₂²⋊C₄	—	2	2	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	2	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	1	no	—
698	C₂²⋊C₄	—	2	1	no	—
699	C₂²⋊C₄	—	4	4	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	—	2	2	no	—
703	C₄²	—	2	1	no	—
704	C₄²	—	2	1	no	—
705	C₄²	—	2	1	no	—
706	C₄²	—	2	1	no	—
707	C₄²	—	2	1	no	—
708	C₄²	—	2	1	no	—
709	C₄²	—	2	1	no	—
710	C₄²	—	2	1	no	—
711	C₄²	—	2	1	no	—
712	C₄²	—	4	1	no	—
713	C₄²	—	4	1	no	—
714	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
718	C₁₃	#24149	1	1	yes	characteristic, direct product factor, Sylow
719	C₂³	—	2	2	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	2	no	—
724	C₂³	—	4	2	no	—
725	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	Q₈	—	2	2	no	—
727	Q₈	—	2	1	no	—
728	Q₈	—	2	1	no	—
729	Q₈	—	2	2	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	Q₈	—	4	1	no	—
733	Q₈	—	4	1	no	—
734	Q₈	—	4	1	no	—
735	Q₈	—	4	1	no	—
736	Q₈	—	8	1	no	—
737	Q₈	—	8	1	no	—
738	D₄	—	2	1	no	—
739	D₄	—	2	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	4	1	no	—
744	D₄	—	4	1	no	—
745	D₄	—	4	1	no	—
746	D₄	—	8	2	no	—
747	D₄	—	8	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	2	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	8	1	no	—
774	C₂×C₄	—	8	1	no	—
775	C₂×C₄	—	8	2	no	—
776	C₂×C₄	—	8	2	no	—
777	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
778	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
779	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
780	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
783	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
784	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
785	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
786	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
787	C₈	—	2	2	no	—
788	C₈	—	4	1	no	—
789	C₈	—	4	1	no	—
790	C₈	—	4	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	8	2	no	—
800	C₂²	—	8	2	no	—
801	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
802	C₂²	C₁₃×#546	1	1	yes	characteristic
803	C₂²	C₁₃×#547	1	1	yes	characteristic
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	1	no	—
811	C₄	—	4	1	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	1	no	—
817	C₄	—	4	2	no	—
818	C₄	—	8	1	no	—
819	C₄	—	8	1	no	—
820	C₄	C₁₃×#525	1	1	yes	characteristic
821	C₄	C₁₃×#537	1	1	yes	characteristic
822	C₄	C₁₃×#548	1	1	yes	characteristic
823	C₄	C₁₃×#550	1	1	yes	characteristic
824	C₂	—	2	1	no	—
825	C₂	—	2	1	no	—
826	C₂	—	8	2	no	—
827	C₂	—	8	1	no	—
828	C₂	C₁₃×#2407	1	1	yes	characteristic
829	C₂	C₁₃×#3018	1	1	yes	characteristic
830	C₂	C₁₃×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#535	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3078	C₂	semidirect
3. C₄×C₁₃×#137	C₂	semidirect
4. C₁₃×#2545	C₂	semidirect
5. C₁₃×#2038	C₂	semidirect
7. C₁₃×#2005	C₂	semidirect
9. C₁₃×#1986	C₂	semidirect
10. C₁₃×#1967	C₂	semidirect
11. C₁₃×#1886	C₂	semidirect
12. C₁₃×#1885	C₂	semidirect
13. C₁₃×#1857	C₂	semidirect
14. C₁₃×#1856	C₂	semidirect
15. C₁₃×#1806	C₂	semidirect
188. #24149	C₁₃	direct (N × H)
305. #3078	C₂×C₁₃	semidirect
306. C₄×#137	C₂×C₁₃	semidirect
307. #2545	C₂×C₁₃	semidirect
308. #2038	C₂×C₁₃	semidirect
310. #2005	C₂×C₁₃	semidirect
312. #1986	C₂×C₁₃	semidirect
313. #1967	C₂×C₁₃	semidirect
314. #1886	C₂×C₁₃	semidirect
315. #1885	C₂×C₁₃	semidirect
316. #1857	C₂×C₁₃	semidirect
317. #1856	C₂×C₁₃	semidirect
318. #1806	C₂×C₁₃	semidirect
718. C₁₃	#24149	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×#3510	2
C₁₃×#3078	2
C₄×C₁₃×#137	2
C₁₃×#2545	2
C₁₃×#2038	2
C₁₃×#2037	2
C₁₃×#2005	2
C₁₃×#2004	2
C₁₃×#1986	2
C₁₃×#1967	2
C₁₃×#1886	2
C₁₃×#1885	2
C₁₃×#1857	2
C₁₃×#1856	2
C₁₃×#1806	2
#24149	13

Subgroups — C13×#24149 #15710488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24149 #15710488