Subgroups — C₁₃×#24175 #15710514

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2039	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2007	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2007	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1980	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1859	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	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₁₃×#553	—	2	1	no	—
20	C₁₃×#553	—	2	1	no	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#553	—	2	2	no	—
23	C₁₃×#552	—	2	1	no	—
24	C₁₃×#552	—	2	1	no	—
25	C₁₃×#541	—	2	1	no	—
26	C₁₃×#540	—	2	1	no	—
27	C₁₃×#537	C₂²	1	1	yes	characteristic
28	C₁₃×#537	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#529	—	2	1	no	—
31	C₁₃×#529	—	2	1	no	—
32	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	1	yes	characteristic
34	C₁₃×#520	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×#464	—	2	1	no	—
38	C₁₃×#464	—	2	1	no	—
39	C₁₃×#462	—	2	1	no	—
40	C₁₃×#460	—	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×#423	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
53	C₁₃×#419	C₂²	1	1	yes	characteristic
54	C₁₃×#417	C₂²	1	1	yes	characteristic
55	C₁₃×#417	C₂²	1	1	yes	characteristic
56	C₁₃×#417	C₂²	1	1	yes	characteristic
57	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
58	C₁₃×#398	—	2	2	no	—
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#391	C₂²	1	1	yes	characteristic
61	C₁₃×#387	—	2	2	no	—
62	C₁₃×#384	C₂²	1	1	yes	characteristic
63	C₁₃×#382	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₁₃×#343	C₂²	1	1	yes	characteristic
66	C₁₃×#343	C₂²	1	1	yes	characteristic
67	C₁₃×#343	C₂²	1	1	yes	characteristic
68	C₁₃×#343	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	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#137	—	2	2	no	—
76	C₁₃×#137	—	2	2	no	—
77	C₁₃×#137	—	2	2	no	—
78	C₁₃×#137	—	2	2	no	—
79	C₁₃×#137	—	4	1	no	—
80	C₁₃×#137	—	4	1	no	—
81	C₂×C₁₃×Q₁₆	—	2	1	no	—
82	C₂×C₁₃×Q₁₆	—	2	1	no	—
83	C₂×C₁₃×Q₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	2	1	no	—
86	C₂×C₁₃×SD₁₆	—	2	1	no	—
87	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
92	C₁₃×#127	D₄	1	1	yes	characteristic
93	C₁₃×#126	—	2	2	no	—
94	C₁₃×#126	—	2	2	no	—
95	C₁₃×#126	—	2	2	no	—
96	C₁₃×#126	—	2	2	no	—
97	C₁₃×#125	—	2	2	no	—
98	C₁₃×#125	—	2	2	no	—
99	C₁₃×#125	—	2	1	no	—
100	C₁₃×#125	—	2	1	no	—
101	C₁₃×#125	—	2	1	no	—
102	C₁₃×#125	—	2	1	no	—
103	C₁₃×#124	D₄	1	1	yes	characteristic
104	C₁₃×#124	D₄	1	1	yes	characteristic
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×C₂²⋊Q₈	—	2	1	no	—
110	C₁₃×C₂²⋊Q₈	—	2	1	no	—
111	C₁₃×C₂²⋊Q₈	—	2	1	no	—
112	C₁₃×C₂²⋊Q₈	—	2	1	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	1	no	—
116	C₁₃×#121	—	2	1	no	—
117	C₁₃×#121	—	2	1	no	—
118	C₁₃×#121	—	2	1	no	—
119	C₁₃×#121	—	2	1	no	—
120	C₁₃×#121	—	2	1	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	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	2	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	1	no	—
141	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
142	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
143	C₁₃×#117	—	2	2	no	—
144	C₁₃×#117	—	2	2	no	—
145	C₁₃×#117	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	C₂³	1	1	yes	characteristic
149	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
155	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₁₃	—	2	1	no	—
160	C₂×C₄²×C₁₃	—	2	1	no	—
161	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
164	C₁₃×#107	—	2	1	no	—
165	C₁₃×#106	—	2	1	no	—
166	C₁₃×C₄⋊C₈	—	2	1	no	—
167	C₁₃×C₄⋊C₈	—	2	1	no	—
168	C₁₃×#104	—	2	2	no	—
169	C₁₃×#104	—	2	2	no	—
170	C₁₃×#104	—	4	1	no	—
171	C₁₃×#104	—	4	1	no	—
172	C₁₃×#104	—	4	1	no	—
173	C₁₃×#104	—	4	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×#102	—	2	1	no	—
181	C₁₃×#102	—	2	1	no	—
182	C₁₃×#97	—	2	1	no	—
183	C₄×C₈×C₁₃	—	2	1	no	—
184	C₁₃×#95	—	2	1	no	—
185	C₁₃×#95	—	2	2	no	—
186	C₁₃×#95	—	2	2	no	—
187	C₁₃×#95	—	2	2	no	—
188	#24175	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₁₃×#41	—	2	1	no	—
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	C₁₃×#41	—	2	1	no	—
195	C₁₃×#41	—	2	1	no	—
196	C₁₃×#41	—	2	1	no	—
197	C₁₃×#41	—	2	1	no	—
198	C₁₃×#41	—	2	1	no	—
199	C₁₃×#41	—	2	1	no	—
200	C₁₃×#41	—	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	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×Q₈×C₁₃	#41	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	1	no	—
211	C₂×D₄×C₁₃	—	2	1	no	—
212	C₂×D₄×C₁₃	—	2	1	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	2	no	—
215	C₂×D₄×C₁₃	—	2	1	no	—
216	C₂×D₄×C₁₃	—	2	1	no	—
217	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
219	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	2	no	—
223	C₂²×C₄×C₁₃	—	2	2	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	—	2	1	no	—
229	C₂²×C₄×C₁₃	—	2	1	no	—
230	C₂²×C₄×C₁₃	—	2	1	no	—
231	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
232	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₁₃×Q₁₆	—	2	4	no	—
237	C₁₃×Q₁₆	—	4	2	no	—
238	C₁₃×Q₁₆	—	4	2	no	—
239	C₁₃×SD₁₆	—	2	4	no	—
240	C₁₃×SD₁₆	—	4	2	no	—
241	C₁₃×SD₁₆	—	4	2	no	—
242	C₁₃×M₁₆	—	2	1	no	—
243	C₁₃×M₁₆	—	2	1	no	—
244	C₁₃×M₁₆	—	2	1	no	—
245	C₁₃×M₁₆	—	2	1	no	—
246	C₁₃×M₁₆	—	2	1	no	—
247	C₁₃×M₁₆	—	2	1	no	—
248	C₁₃×M₁₆	—	2	1	no	—
249	C₁₃×M₁₆	#41	1	2	yes	—
250	C₂×C₈×C₁₃	—	2	1	no	—
251	C₂×C₈×C₁₃	—	2	1	no	—
252	C₂×C₈×C₁₃	—	2	1	no	—
253	C₂×C₈×C₁₃	—	2	1	no	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	2	no	—
261	C₁₃×C₄⋊C₄	—	2	2	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	1	no	—
264	C₁₃×C₄⋊C₄	—	2	1	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	no	—
267	C₁₃×C₄⋊C₄	—	2	1	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	1	no	—
270	C₁₃×C₄⋊C₄	—	2	1	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	4	2	no	—
273	C₁₃×C₄⋊C₄	—	4	4	no	—
274	C₁₃×C₄⋊C₄	—	4	1	no	—
275	C₁₃×C₄⋊C₄	—	4	1	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
277	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
278	C₁₃×C₂²⋊C₄	—	2	2	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	2	no	—
284	C₁₃×C₂²⋊C₄	—	2	1	no	—
285	C₁₃×C₂²⋊C₄	—	2	1	no	—
286	C₁₃×C₂²⋊C₄	—	2	1	no	—
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	1	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₄²×C₁₃	—	2	2	no	—
292	C₄²×C₁₃	—	2	2	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	—	2	1	no	—
299	C₄²×C₁₃	—	2	1	no	—
300	C₄²×C₁₃	—	4	1	no	—
301	C₄²×C₁₃	—	4	1	no	—
302	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	#3512	C₂×C₁₃	1	1	yes	characteristic
307	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#2565	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#2007	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#2007	C₂×C₁₃	1	1	yes	characteristic, complemented
314	#1998	C₂×C₁₃	1	1	yes	characteristic, complemented
315	#1980	C₂×C₁₃	1	1	yes	characteristic, complemented
316	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
319	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#1806	C₂×C₁₃	1	1	yes	characteristic, complemented
321	C₂³×C₁₃	—	2	1	no	—
322	C₂³×C₁₃	—	2	1	no	—
323	C₂³×C₁₃	—	2	1	no	—
324	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
325	Q₈×C₁₃	—	2	2	no	—
326	Q₈×C₁₃	—	2	1	no	—
327	Q₈×C₁₃	—	2	1	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	1	no	—
330	Q₈×C₁₃	—	2	1	no	—
331	Q₈×C₁₃	—	2	1	no	—
332	Q₈×C₁₃	—	2	1	no	—
333	Q₈×C₁₃	—	4	1	no	—
334	Q₈×C₁₃	—	4	1	no	—
335	D₄×C₁₃	—	2	1	no	—
336	D₄×C₁₃	—	2	1	no	—
337	D₄×C₁₃	—	2	1	no	—
338	D₄×C₁₃	—	2	1	no	—
339	D₄×C₁₃	—	2	1	no	—
340	D₄×C₁₃	—	2	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	—	4	1	no	—
347	D₄×C₁₃	—	8	1	no	—
348	D₄×C₁₃	—	8	1	no	—
349	D₄×C₁₃	—	8	2	no	—
350	D₄×C₁₃	—	8	2	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	1	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	1	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	2	no	—
373	C₂×C₄×C₁₃	—	4	2	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	—	4	2	no	—
376	C₂×C₄×C₁₃	—	4	1	no	—
377	C₂×C₄×C₁₃	—	4	1	no	—
378	C₂×C₄×C₁₃	—	4	1	no	—
379	C₂×C₄×C₁₃	—	8	1	no	—
380	C₂×C₄×C₁₃	—	8	1	no	—
381	C₂×C₄×C₁₃	—	8	2	no	—
382	C₂×C₄×C₁₃	—	8	2	no	—
383	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
384	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
385	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
386	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
387	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
390	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
391	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
392	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
393	C₈×C₁₃	—	2	2	no	—
394	C₈×C₁₃	—	4	1	no	—
395	C₈×C₁₃	—	4	1	no	—
396	C₈×C₁₃	—	4	1	no	—
397	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
400	#553	—	2	1	no	—
401	#553	—	2	1	no	—
402	#553	—	2	2	no	—
403	#553	—	2	2	no	—
404	#552	—	2	1	no	—
405	#552	—	2	1	no	—
406	#541	—	2	1	no	—
407	#540	—	2	1	no	—
408	#537	C₂²×C₁₃	1	1	yes	characteristic
409	#537	C₂²×C₁₃	1	1	yes	characteristic
410	#532	C₂²×C₁₃	1	1	yes	characteristic
411	#529	—	2	1	no	—
412	#529	—	2	1	no	—
413	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
414	#520	C₂²×C₁₃	1	1	yes	characteristic
415	#520	C₂²×C₁₃	1	1	yes	characteristic
416	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
418	#464	—	2	1	no	—
419	#464	—	2	1	no	—
420	#462	—	2	1	no	—
421	#460	—	2	1	no	—
422	#441	—	2	1	no	—
423	#440	—	2	1	no	—
424	C₄×Q₁₆	—	2	1	no	—
425	C₄×SD₁₆	—	2	1	no	—
426	#428	C₂²×C₁₃	1	1	yes	characteristic
427	#423	C₂²×C₁₃	1	1	yes	characteristic
428	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
429	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
430	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
431	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
432	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
433	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
434	#419	C₂²×C₁₃	1	1	yes	characteristic
435	#417	C₂²×C₁₃	1	1	yes	characteristic
436	#417	C₂²×C₁₃	1	1	yes	characteristic
437	#417	C₂²×C₁₃	1	1	yes	characteristic
438	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
439	#398	—	2	2	no	—
440	#391	C₂²×C₁₃	1	1	yes	characteristic
441	#391	C₂²×C₁₃	1	1	yes	characteristic
442	#387	—	2	2	no	—
443	#384	C₂²×C₁₃	1	1	yes	characteristic
444	#382	C₂²×C₁₃	1	1	yes	characteristic
445	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
446	#343	C₂²×C₁₃	1	1	yes	characteristic
447	#343	C₂²×C₁₃	1	1	yes	characteristic
448	#343	C₂²×C₁₃	1	1	yes	characteristic
449	#343	C₂²×C₁₃	1	1	yes	characteristic
450	#339	C₂²×C₁₃	1	1	yes	characteristic
451	#339	C₂²×C₁₃	1	1	yes	characteristic
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	4	1	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	1	no	—
457	C₂²×C₁₃	—	4	1	no	—
458	C₂²×C₁₃	—	4	1	no	—
459	C₂²×C₁₃	—	4	1	no	—
460	C₂²×C₁₃	—	4	1	no	—
461	C₂²×C₁₃	—	4	1	no	—
462	C₂²×C₁₃	—	4	1	no	—
463	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
464	C₂²×C₁₃	#548	1	1	yes	characteristic
465	C₂²×C₁₃	#550	1	1	yes	characteristic
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	1	no	—
470	C₄×C₁₃	—	4	2	no	—
471	C₄×C₁₃	—	4	1	no	—
472	C₄×C₁₃	—	4	1	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	2	no	—
476	C₄×C₁₃	—	4	1	no	—
477	C₄×C₁₃	—	4	2	no	—
478	C₄×C₁₃	—	4	1	no	—
479	C₄×C₁₃	—	8	1	no	—
480	C₄×C₁₃	—	8	1	no	—
481	C₄×C₁₃	#525	1	1	yes	characteristic
482	C₄×C₁₃	#537	1	1	yes	characteristic
483	C₄×C₁₃	#546	1	1	yes	characteristic
484	C₄×C₁₃	#547	1	1	yes	characteristic
485	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
486	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
489	#137	—	2	2	no	—
490	#137	—	2	2	no	—
491	#137	—	2	2	no	—
492	#137	—	2	2	no	—
493	#137	—	4	1	no	—
494	#137	—	4	1	no	—
495	C₂×Q₁₆	—	2	1	no	—
496	C₂×Q₁₆	—	2	1	no	—
497	C₂×Q₁₆	—	2	1	no	—
498	C₂×SD₁₆	—	2	1	no	—
499	C₂×SD₁₆	—	2	1	no	—
500	C₂×SD₁₆	—	2	1	no	—
501	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
504	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
505	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
506	#127	D₄×C₁₃	1	1	yes	characteristic
507	#126	—	2	2	no	—
508	#126	—	2	2	no	—
509	#126	—	2	2	no	—
510	#126	—	2	2	no	—
511	#125	—	2	2	no	—
512	#125	—	2	2	no	—
513	#125	—	2	1	no	—
514	#125	—	2	1	no	—
515	#125	—	2	1	no	—
516	#125	—	2	1	no	—
517	#124	D₄×C₁₃	1	1	yes	characteristic
518	#124	D₄×C₁₃	1	1	yes	characteristic
519	#123	—	2	2	no	—
520	#123	—	2	2	no	—
521	#123	—	2	2	no	—
522	#123	—	2	2	no	—
523	C₂²⋊Q₈	—	2	1	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	1	no	—
527	#121	—	2	2	no	—
528	#121	—	2	2	no	—
529	#121	—	2	1	no	—
530	#121	—	2	1	no	—
531	#121	—	2	1	no	—
532	#121	—	2	1	no	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	C₄×Q₈	—	2	1	no	—
538	C₄×Q₈	—	2	1	no	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
544	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
545	C₄×D₄	—	2	2	no	—
546	C₄×D₄	—	2	2	no	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
556	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
557	#117	—	2	2	no	—
558	#117	—	2	2	no	—
559	#117	—	2	1	no	—
560	#117	—	2	1	no	—
561	#117	—	2	1	no	—
562	#117	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	1	no	—
566	C₂×C₄⋊C₄	—	2	1	no	—
567	C₂×C₄⋊C₄	—	2	2	no	—
568	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
569	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×C₄²	—	2	1	no	—
574	C₂×C₄²	—	2	1	no	—
575	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
578	#107	—	2	1	no	—
579	#106	—	2	1	no	—
580	C₄⋊C₈	—	2	1	no	—
581	C₄⋊C₈	—	2	1	no	—
582	#104	—	2	2	no	—
583	#104	—	2	2	no	—
584	#104	—	4	1	no	—
585	#104	—	4	1	no	—
586	#104	—	4	1	no	—
587	#104	—	4	1	no	—
588	#103	—	2	1	no	—
589	#103	—	2	1	no	—
590	#103	—	2	1	no	—
591	#103	—	2	1	no	—
592	#103	—	2	1	no	—
593	#102	—	2	1	no	—
594	#102	—	2	1	no	—
595	#102	—	2	1	no	—
596	#97	—	2	1	no	—
597	C₄×C₈	—	2	1	no	—
598	#95	—	2	1	no	—
599	#95	—	2	2	no	—
600	#95	—	2	2	no	—
601	#95	—	2	2	no	—
602	C₂×C₁₃	—	2	1	no	—
603	C₂×C₁₃	—	2	1	no	—
604	C₂×C₁₃	—	8	1	no	—
605	C₂×C₁₃	—	8	1	no	—
606	C₂×C₁₃	—	8	1	no	—
607	C₂×C₁₃	#2407	1	1	yes	characteristic
608	C₂×C₁₃	#3018	1	1	yes	characteristic
609	C₂×C₁₃	#3022	1	1	yes	characteristic
610	#41	—	2	1	no	—
611	#41	—	2	1	no	—
612	#41	—	2	1	no	—
613	#41	—	2	1	no	—
614	#41	—	2	1	no	—
615	#41	—	2	1	no	—
616	#41	—	2	1	no	—
617	#41	—	2	1	no	—
618	#41	—	2	1	no	—
619	#41	—	2	1	no	—
620	#41	—	2	1	no	—
621	#41	—	2	1	no	—
622	C₂×Q₈	—	2	1	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
628	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂×Q₈	C₁₃×#41	1	2	yes	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	2	1	no	—
650	C₂²×C₄	—	2	1	no	—
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
654	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	Q₁₆	—	2	4	no	—
658	Q₁₆	—	4	2	no	—
659	Q₁₆	—	4	2	no	—
660	SD₁₆	—	2	4	no	—
661	SD₁₆	—	4	2	no	—
662	SD₁₆	—	4	2	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	C₁₃×#41	1	2	yes	—
671	C₂×C₈	—	2	1	no	—
672	C₂×C₈	—	2	1	no	—
673	C₂×C₈	—	2	1	no	—
674	C₂×C₈	—	2	1	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	2	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	1	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	1	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	4	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	1	no	—
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	1	no	—
715	C₄²	—	2	1	no	—
716	C₄²	—	2	1	no	—
717	C₄²	—	2	1	no	—
718	C₄²	—	2	1	no	—
719	C₄²	—	2	1	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	4	1	no	—
722	C₄²	—	4	1	no	—
723	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
724	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
725	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₁₃	#24175	1	1	yes	characteristic, direct product factor, Sylow
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	Q₈	—	2	2	no	—
733	Q₈	—	2	1	no	—
734	Q₈	—	2	1	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	1	no	—
737	Q₈	—	2	1	no	—
738	Q₈	—	2	1	no	—
739	Q₈	—	2	1	no	—
740	Q₈	—	4	1	no	—
741	Q₈	—	4	1	no	—
742	D₄	—	2	1	no	—
743	D₄	—	2	1	no	—
744	D₄	—	2	1	no	—
745	D₄	—	2	1	no	—
746	D₄	—	2	1	no	—
747	D₄	—	2	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	4	1	no	—
751	D₄	—	4	1	no	—
752	D₄	—	4	1	no	—
753	D₄	—	4	1	no	—
754	D₄	—	8	1	no	—
755	D₄	—	8	1	no	—
756	D₄	—	8	2	no	—
757	D₄	—	8	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	1	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	1	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	1	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	—	4	1	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	4	2	no	—
780	C₂×C₄	—	4	2	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	8	1	no	—
787	C₂×C₄	—	8	1	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	2	no	—
790	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
791	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
792	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
793	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
796	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
797	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
798	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
799	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
800	C₈	—	2	2	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₈	—	4	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	1	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
816	C₂²	C₁₃×#548	1	1	yes	characteristic
817	C₂²	C₁₃×#550	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	1	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	2	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	8	1	no	—
832	C₄	—	8	1	no	—
833	C₄	C₁₃×#525	1	1	yes	characteristic
834	C₄	C₁₃×#537	1	1	yes	characteristic
835	C₄	C₁₃×#546	1	1	yes	characteristic
836	C₄	C₁₃×#547	1	1	yes	characteristic
837	C₂	—	2	1	no	—
838	C₂	—	2	1	no	—
839	C₂	—	8	1	no	—
840	C₂	—	8	1	no	—
841	C₂	—	8	1	no	—
842	C₂	C₁₃×#2407	1	1	yes	characteristic
843	C₂	C₁₃×#3018	1	1	yes	characteristic
844	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×#3512	C₂
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×#3037	C₂	semidirect
3. C₄×C₁₃×#137	C₂	semidirect
4. C₁₃×#2565	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2039	C₂	semidirect
7. C₁₃×#2007	C₂	semidirect
8. C₁₃×#2007	C₂	semidirect
9. C₁₃×#1998	C₂	semidirect
10. C₁₃×#1980	C₂	semidirect
11. C₁₃×#1882	C₂	semidirect
12. C₁₃×#1882	C₂	semidirect
13. C₁₃×#1860	C₂	semidirect
14. C₁₃×#1859	C₂	semidirect
15. C₁₃×#1806	C₂	semidirect
188. #24175	C₁₃	direct (N × H)
307. #3037	C₂×C₁₃	semidirect
308. C₄×#137	C₂×C₁₃	semidirect
309. #2565	C₂×C₁₃	semidirect
310. #2040	C₂×C₁₃	semidirect
311. #2039	C₂×C₁₃	semidirect
312. #2007	C₂×C₁₃	semidirect
313. #2007	C₂×C₁₃	semidirect
314. #1998	C₂×C₁₃	semidirect
315. #1980	C₂×C₁₃	semidirect
316. #1882	C₂×C₁₃	semidirect
317. #1882	C₂×C₁₃	semidirect
318. #1860	C₂×C₁₃	semidirect
319. #1859	C₂×C₁₃	semidirect
320. #1806	C₂×C₁₃	semidirect
727. C₁₃	#24175	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×#3512	2
C₁₃×#3037	2
C₄×C₁₃×#137	2
C₁₃×#2565	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#2007	2
C₁₃×#1998	2
C₁₃×#1980	2
C₁₃×#1882	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1806	2
#24175	13

Subgroups — C13×#24175 #15710514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24175 #15710514