Subgroups — C₁₃×#24084 #15710423

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2061	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2037	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1860	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1856	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1826	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#555	—	2	1	no	—
18	C₁₃×#553	—	2	1	no	—
19	C₁₃×#553	—	2	1	no	—
20	C₁₃×#551	—	2	2	no	—
21	C₁₃×#547	—	2	1	no	—
22	C₁₃×#546	—	2	2	no	—
23	C₁₃×#544	C₂²	1	1	yes	characteristic
24	C₁₃×#542	—	2	1	no	—
25	C₁₃×#540	—	2	1	no	—
26	C₁₃×#535	C₂²	1	1	yes	characteristic
27	C₁₃×#532	—	2	1	no	—
28	C₁₃×#529	—	2	1	no	—
29	C₁₃×#525	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
31	C₁₃×#520	C₂²	1	1	yes	characteristic
32	C₁₃×#518	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
35	C₁₃×#485	—	2	1	no	—
36	C₁₃×#485	—	2	1	no	—
37	C₁₃×#482	—	2	1	no	—
38	C₁₃×#482	—	2	1	no	—
39	C₁₃×#428	—	2	1	no	—
40	C₁₃×#428	—	2	1	no	—
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#428	C₂²	1	1	yes	characteristic
43	C₁₃×#428	C₂²	1	1	yes	characteristic
44	C₁₃×#428	C₂²	1	1	yes	characteristic
45	C₁₃×#428	C₂²	1	1	yes	characteristic
46	C₁₃×#428	C₂²	1	1	yes	characteristic
47	C₁₃×#427	—	2	1	no	—
48	C₁₃×#427	—	2	1	no	—
49	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic
52	C₁₃×#417	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
55	C₁₃×#407	C₂²	1	1	yes	characteristic
56	C₁₃×#394	—	2	2	no	—
57	C₁₃×#390	C₂²	1	1	yes	characteristic
58	C₁₃×#390	C₂²	1	1	yes	characteristic
59	C₁₃×#388	—	2	2	no	—
60	C₁₃×#384	C₂²	1	1	yes	characteristic
61	C₁₃×#382	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
63	C₁₃×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#343	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	—	2	2	no	—
72	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	D₄	1	2	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	—	2	1	no	—
77	C₂×C₁₃×M₁₆	—	2	2	no	—
78	C₂×C₁₃×M₁₆	—	2	2	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	C₂²×C₈×C₁₃	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	2	1	no	—
86	C₁₃×#127	—	2	1	no	—
87	C₁₃×#126	—	2	2	no	—
88	C₁₃×#126	—	2	2	no	—
89	C₁₃×#125	—	2	1	no	—
90	C₁₃×#125	—	2	1	no	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	—	2	1	no	—
94	C₁₃×#123	—	2	2	no	—
95	C₁₃×#123	—	2	2	no	—
96	C₁₃×#123	—	2	2	no	—
97	C₁₃×#123	—	2	2	no	—
98	C₁₃×#123	—	2	1	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	—	2	2	no	—
101	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
102	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	—	2	2	no	—
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	—	2	1	no	—
107	C₁₃×#121	—	2	1	no	—
108	C₁₃×#121	—	2	1	no	—
109	C₁₃×#121	—	2	1	no	—
110	C₁₃×#121	—	2	1	no	—
111	C₁₃×#121	—	2	1	no	—
112	C₁₃×#121	D₄	1	1	yes	characteristic
113	C₁₃×#121	D₄	1	1	yes	characteristic
114	C₁₃×#120	—	2	1	no	—
115	C₁₃×#120	—	2	2	no	—
116	C₄×Q₈×C₁₃	—	2	1	no	—
117	C₄×D₄×C₁₃	—	2	2	no	—
118	C₄×D₄×C₁₃	—	2	2	no	—
119	C₄×D₄×C₁₃	—	2	1	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	—	2	1	no	—
122	C₄×D₄×C₁₃	—	2	1	no	—
123	C₄×D₄×C₁₃	—	2	1	no	—
124	C₄×D₄×C₁₃	—	2	1	no	—
125	C₄×D₄×C₁₃	—	2	1	no	—
126	C₄×D₄×C₁₃	—	2	1	no	—
127	C₁₃×#117	—	2	2	no	—
128	C₁₃×#117	—	2	1	no	—
129	C₁₃×#117	—	2	1	no	—
130	C₁₃×#117	—	2	1	no	—
131	C₁₃×#117	—	2	1	no	—
132	C₁₃×#117	—	2	1	no	—
133	C₁₃×#117	—	2	1	no	—
134	C₁₃×#117	—	2	1	no	—
135	C₁₃×#117	D₄	1	1	yes	characteristic
136	C₁₃×#117	D₄	1	1	yes	characteristic
137	C₁₃×#117	C₂³	1	1	yes	characteristic
138	C₁₃×#117	C₂³	1	1	yes	characteristic
139	C₁₃×#117	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
143	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
144	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
149	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
151	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
154	C₂×C₄²×C₁₃	—	2	1	no	—
155	C₂×C₄²×C₁₃	—	2	1	no	—
156	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₁₃×#107	—	2	1	no	—
159	C₁₃×#107	—	2	1	no	—
160	C₁₃×#107	—	2	1	no	—
161	C₁₃×#107	—	2	1	no	—
162	C₁₃×#107	—	2	1	no	—
163	C₁₃×#107	—	2	1	no	—
164	C₁₃×#106	—	2	1	no	—
165	C₁₃×#106	—	2	1	no	—
166	C₁₃×#106	—	2	1	no	—
167	C₁₃×#106	—	2	1	no	—
168	C₁₃×#106	—	2	1	no	—
169	C₁₃×#106	—	2	1	no	—
170	C₁₃×#104	—	2	2	no	—
171	C₁₃×#104	—	2	2	no	—
172	C₁₃×#103	—	2	1	no	—
173	C₁₃×#103	—	2	1	no	—
174	C₁₃×#102	—	2	1	no	—
175	C₁₃×#102	—	2	1	no	—
176	C₁₃×#100	—	2	2	no	—
177	C₁₃×#100	—	2	2	no	—
178	C₁₃×C₂²⋊C₈	—	2	1	no	—
179	C₁₃×C₂²⋊C₈	—	2	1	no	—
180	C₁₃×#95	—	2	1	no	—
181	C₁₃×#95	—	2	2	no	—
182	#24084	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
184	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₁₃×#41	—	2	1	no	—
186	C₁₃×#41	—	2	1	no	—
187	C₁₃×#41	—	2	1	no	—
188	C₁₃×#41	—	2	1	no	—
189	C₁₃×#41	—	8	4	no	—
190	C₂×Q₈×C₁₃	—	2	2	no	—
191	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₂×D₄×C₁₃	—	2	1	no	—
193	C₂×D₄×C₁₃	—	2	2	no	—
194	C₂×D₄×C₁₃	—	2	1	no	—
195	C₂×D₄×C₁₃	—	2	2	no	—
196	C₂×D₄×C₁₃	—	2	2	no	—
197	C₂×D₄×C₁₃	—	2	1	no	—
198	C₂×D₄×C₁₃	—	2	2	no	—
199	C₂×D₄×C₁₃	—	2	1	no	—
200	C₂×D₄×C₁₃	—	2	1	no	—
201	C₂×D₄×C₁₃	—	2	1	no	—
202	C₂×D₄×C₁₃	—	2	1	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	8	2	no	—
206	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₁₃	—	2	1	no	—
208	C₂²×C₄×C₁₃	—	2	1	no	—
209	C₂²×C₄×C₁₃	—	2	1	no	—
210	C₂²×C₄×C₁₃	—	2	1	no	—
211	C₂²×C₄×C₁₃	—	2	1	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	2	no	—
214	C₂²×C₄×C₁₃	—	2	2	no	—
215	C₂²×C₄×C₁₃	—	2	2	no	—
216	C₂²×C₄×C₁₃	—	2	1	no	—
217	C₂²×C₄×C₁₃	—	2	1	no	—
218	C₂²×C₄×C₁₃	—	2	1	no	—
219	C₂²×C₄×C₁₃	—	2	1	no	—
220	C₂²×C₄×C₁₃	—	2	1	no	—
221	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₁₃×M₁₆	—	2	4	no	—
229	C₁₃×M₁₆	—	2	1	no	—
230	C₁₃×M₁₆	—	2	1	no	—
231	C₁₃×M₁₆	—	2	1	no	—
232	C₁₃×M₁₆	—	2	1	no	—
233	C₁₃×M₁₆	—	2	1	no	—
234	C₁₃×M₁₆	—	2	1	no	—
235	C₁₃×M₁₆	#41	1	2	yes	complemented
236	C₁₃×M₁₆	#41	1	2	yes	complemented
237	C₂×C₈×C₁₃	—	2	4	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₁₃×C₄⋊C₄	—	2	2	no	—
243	C₁₃×C₄⋊C₄	—	2	2	no	—
244	C₁₃×C₄⋊C₄	—	2	2	no	—
245	C₁₃×C₄⋊C₄	—	2	2	no	—
246	C₁₃×C₄⋊C₄	—	2	1	no	—
247	C₁₃×C₄⋊C₄	—	2	1	no	—
248	C₁₃×C₄⋊C₄	—	2	1	no	—
249	C₁₃×C₄⋊C₄	—	2	1	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	—	8	2	no	—
257	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
262	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	2	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	2	2	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	1	no	—
269	C₁₃×C₂²⋊C₄	—	2	1	no	—
270	C₁₃×C₂²⋊C₄	—	2	1	no	—
271	C₁₃×C₂²⋊C₄	—	2	1	no	—
272	C₁₃×C₂²⋊C₄	—	2	1	no	—
273	C₁₃×C₂²⋊C₄	—	2	1	no	—
274	C₁₃×C₂²⋊C₄	—	2	1	no	—
275	C₁₃×C₂²⋊C₄	—	2	2	no	—
276	C₁₃×C₂²⋊C₄	—	2	2	no	—
277	C₁₃×C₂²⋊C₄	—	2	1	no	—
278	C₁₃×C₂²⋊C₄	—	2	1	no	—
279	C₁₃×C₂²⋊C₄	—	4	2	no	—
280	C₁₃×C₂²⋊C₄	—	4	4	no	—
281	C₁₃×C₂²⋊C₄	—	4	1	no	—
282	C₁₃×C₂²⋊C₄	—	4	1	no	—
283	C₁₃×C₂²⋊C₄	—	8	2	no	—
284	C₄²×C₁₃	—	2	2	no	—
285	C₄²×C₁₃	—	2	1	no	—
286	C₄²×C₁₃	—	2	1	no	—
287	C₄²×C₁₃	—	2	1	no	—
288	C₄²×C₁₃	—	2	1	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	—	4	1	no	—
295	C₄²×C₁₃	—	4	1	no	—
296	#3494	C₂×C₁₃	1	1	yes	characteristic
297	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#2911	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#2500	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#2061	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
308	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#1856	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#1826	C₂×C₁₃	1	1	yes	characteristic, complemented
311	C₂³×C₁₃	—	2	1	no	—
312	C₂³×C₁₃	—	2	1	no	—
313	C₂³×C₁₃	—	2	2	no	—
314	C₂³×C₁₃	—	2	1	no	—
315	C₂³×C₁₃	—	2	2	no	—
316	C₂³×C₁₃	—	2	2	no	—
317	C₂³×C₁₃	—	4	1	no	—
318	C₂³×C₁₃	—	4	1	no	—
319	C₂³×C₁₃	—	4	2	no	—
320	C₂³×C₁₃	—	4	2	no	—
321	C₂³×C₁₃	#120	1	1	yes	characteristic
322	C₂³×C₁₃	#120	1	1	yes	characteristic
323	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₃	—	2	1	no	—
325	Q₈×C₁₃	—	2	1	no	—
326	Q₈×C₁₃	—	8	2	no	—
327	D₄×C₁₃	—	2	1	no	—
328	D₄×C₁₃	—	2	1	no	—
329	D₄×C₁₃	—	4	4	no	—
330	D₄×C₁₃	—	4	2	no	—
331	D₄×C₁₃	—	4	1	no	—
332	D₄×C₁₃	—	4	1	no	—
333	D₄×C₁₃	—	4	1	no	—
334	D₄×C₁₃	—	4	1	no	—
335	D₄×C₁₃	—	4	1	no	—
336	D₄×C₁₃	—	4	1	no	—
337	D₄×C₁₃	—	8	1	no	—
338	D₄×C₁₃	—	8	2	no	—
339	D₄×C₁₃	—	8	2	no	—
340	D₄×C₁₃	—	8	2	no	—
341	C₂×C₄×C₁₃	—	2	1	no	—
342	C₂×C₄×C₁₃	—	2	1	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	1	no	—
345	C₂×C₄×C₁₃	—	2	1	no	—
346	C₂×C₄×C₁₃	—	2	1	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	1	no	—
350	C₂×C₄×C₁₃	—	2	1	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	1	no	—
358	C₂×C₄×C₁₃	—	2	1	no	—
359	C₂×C₄×C₁₃	—	2	2	no	—
360	C₂×C₄×C₁₃	—	4	1	no	—
361	C₂×C₄×C₁₃	—	4	2	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	2	no	—
366	C₂×C₄×C₁₃	—	4	1	no	—
367	C₂×C₄×C₁₃	—	4	2	no	—
368	C₂×C₄×C₁₃	—	4	1	no	—
369	C₂×C₄×C₁₃	—	4	2	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	2	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	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
383	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
384	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
385	C₈×C₁₃	—	2	2	no	—
386	C₈×C₁₃	—	2	2	no	—
387	C₈×C₁₃	—	4	1	no	—
388	C₈×C₁₃	—	4	1	no	—
389	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
390	#555	—	2	1	no	—
391	#553	—	2	1	no	—
392	#553	—	2	1	no	—
393	#551	—	2	2	no	—
394	#547	—	2	1	no	—
395	#546	—	2	2	no	—
396	#544	C₂²×C₁₃	1	1	yes	characteristic
397	#542	—	2	1	no	—
398	#540	—	2	1	no	—
399	#535	C₂²×C₁₃	1	1	yes	characteristic
400	#532	—	2	1	no	—
401	#529	—	2	1	no	—
402	#525	C₂²×C₁₃	1	1	yes	characteristic
403	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
404	#520	C₂²×C₁₃	1	1	yes	characteristic
405	#518	C₂²×C₁₃	1	1	yes	characteristic
406	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
408	#485	—	2	1	no	—
409	#485	—	2	1	no	—
410	#482	—	2	1	no	—
411	#482	—	2	1	no	—
412	#428	—	2	1	no	—
413	#428	—	2	1	no	—
414	#428	C₂²×C₁₃	1	1	yes	characteristic
415	#428	C₂²×C₁₃	1	1	yes	characteristic
416	#428	C₂²×C₁₃	1	1	yes	characteristic
417	#428	C₂²×C₁₃	1	1	yes	characteristic
418	#428	C₂²×C₁₃	1	1	yes	characteristic
419	#428	C₂²×C₁₃	1	1	yes	characteristic
420	#427	—	2	1	no	—
421	#427	—	2	1	no	—
422	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
423	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
424	#417	C₂²×C₁₃	1	1	yes	characteristic
425	#417	C₂²×C₁₃	1	1	yes	characteristic
426	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
427	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
428	#407	C₂²×C₁₃	1	1	yes	characteristic
429	#394	—	2	2	no	—
430	#390	C₂²×C₁₃	1	1	yes	characteristic
431	#390	C₂²×C₁₃	1	1	yes	characteristic
432	#388	—	2	2	no	—
433	#384	C₂²×C₁₃	1	1	yes	characteristic
434	#382	C₂²×C₁₃	1	1	yes	characteristic
435	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
436	#343	C₂²×C₁₃	1	1	yes	characteristic
437	#343	C₂²×C₁₃	1	1	yes	characteristic
438	#339	C₂²×C₁₃	1	1	yes	characteristic
439	#339	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	C₂²×C₁₃	—	2	1	no	—
445	C₂²×C₁₃	—	2	1	no	—
446	C₂²×C₁₃	—	2	1	no	—
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	2	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	2	no	—
454	C₂²×C₁₃	—	4	2	no	—
455	C₂²×C₁₃	—	4	1	no	—
456	C₂²×C₁₃	—	4	1	no	—
457	C₂²×C₁₃	—	4	2	no	—
458	C₂²×C₁₃	—	8	1	no	—
459	C₂²×C₁₃	—	8	1	no	—
460	C₂²×C₁₃	—	8	2	no	—
461	C₂²×C₁₃	—	8	2	no	—
462	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
463	C₂²×C₁₃	#547	1	1	yes	characteristic
464	C₂²×C₁₃	#547	1	1	yes	characteristic
465	C₄×C₁₃	—	2	1	no	—
466	C₄×C₁₃	—	2	1	no	—
467	C₄×C₁₃	—	4	2	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	—	4	1	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	4	1	no	—
476	C₄×C₁₃	—	8	1	no	—
477	C₄×C₁₃	—	8	1	no	—
478	C₄×C₁₃	—	8	1	no	—
479	C₄×C₁₃	#525	1	1	yes	characteristic
480	C₄×C₁₃	#536	1	1	yes	characteristic
481	C₄×C₁₃	#547	1	1	yes	characteristic
482	C₄×C₁₃	#547	1	1	yes	characteristic
483	C₂×#41	—	2	2	no	—
484	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
485	C₂²×D₄	D₄×C₁₃	1	2	yes	—
486	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	2	no	—
490	C₂×M₁₆	—	2	2	no	—
491	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
492	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
493	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
495	C₂²×C₈	—	2	1	no	—
496	C₄⋊Q₈	—	2	1	no	—
497	C₄⋊Q₈	—	2	1	no	—
498	#127	—	2	1	no	—
499	#126	—	2	2	no	—
500	#126	—	2	2	no	—
501	#125	—	2	1	no	—
502	#125	—	2	1	no	—
503	#124	—	2	2	no	—
504	#124	—	2	2	no	—
505	#124	—	2	1	no	—
506	#123	—	2	2	no	—
507	#123	—	2	2	no	—
508	#123	—	2	2	no	—
509	#123	—	2	2	no	—
510	#123	—	2	1	no	—
511	C₂²⋊Q₈	—	2	2	no	—
512	C₂²⋊Q₈	—	2	2	no	—
513	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
514	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
515	#121	—	2	2	no	—
516	#121	—	2	2	no	—
517	#121	—	2	2	no	—
518	#121	—	2	1	no	—
519	#121	—	2	1	no	—
520	#121	—	2	1	no	—
521	#121	—	2	1	no	—
522	#121	—	2	1	no	—
523	#121	—	2	1	no	—
524	#121	D₄×C₁₃	1	1	yes	characteristic
525	#121	D₄×C₁₃	1	1	yes	characteristic
526	#120	—	2	1	no	—
527	#120	—	2	2	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	2	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	—	2	1	no	—
535	C₄×D₄	—	2	1	no	—
536	C₄×D₄	—	2	1	no	—
537	C₄×D₄	—	2	1	no	—
538	C₄×D₄	—	2	1	no	—
539	#117	—	2	2	no	—
540	#117	—	2	1	no	—
541	#117	—	2	1	no	—
542	#117	—	2	1	no	—
543	#117	—	2	1	no	—
544	#117	—	2	1	no	—
545	#117	—	2	1	no	—
546	#117	—	2	1	no	—
547	#117	D₄×C₁₃	1	1	yes	characteristic
548	#117	D₄×C₁₃	1	1	yes	characteristic
549	#117	C₂³×C₁₃	1	1	yes	characteristic
550	#117	C₂³×C₁₃	1	1	yes	characteristic
551	#117	C₂³×C₁₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	2	no	—
554	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	—	2	1	no	—
560	C₂×C₂²⋊C₄	—	2	2	no	—
561	C₂×C₂²⋊C₄	—	2	1	no	—
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	2	no	—
564	C₂×C₂²⋊C₄	—	2	2	no	—
565	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
566	C₂×C₄²	—	2	1	no	—
567	C₂×C₄²	—	2	1	no	—
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	#107	—	2	1	no	—
574	#107	—	2	1	no	—
575	#107	—	2	1	no	—
576	#106	—	2	1	no	—
577	#106	—	2	1	no	—
578	#106	—	2	1	no	—
579	#106	—	2	1	no	—
580	#106	—	2	1	no	—
581	#106	—	2	1	no	—
582	#104	—	2	2	no	—
583	#104	—	2	2	no	—
584	#103	—	2	1	no	—
585	#103	—	2	1	no	—
586	#102	—	2	1	no	—
587	#102	—	2	1	no	—
588	#100	—	2	2	no	—
589	#100	—	2	2	no	—
590	C₂²⋊C₈	—	2	1	no	—
591	C₂²⋊C₈	—	2	1	no	—
592	#95	—	2	1	no	—
593	#95	—	2	2	no	—
594	C₂×C₁₃	—	2	1	no	—
595	C₂×C₁₃	—	2	1	no	—
596	C₂×C₁₃	—	4	1	no	—
597	C₂×C₁₃	—	4	1	no	—
598	C₂×C₁₃	—	8	1	no	—
599	C₂×C₁₃	—	8	2	no	—
600	C₂×C₁₃	#2406	1	1	yes	characteristic
601	C₂×C₁₃	#3018	1	1	yes	characteristic
602	C₂×C₁₃	#3019	1	1	yes	characteristic
603	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
604	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
605	#41	—	2	1	no	—
606	#41	—	2	1	no	—
607	#41	—	2	1	no	—
608	#41	—	2	1	no	—
609	#41	—	8	4	no	—
610	C₂×Q₈	—	2	2	no	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	8	2	no	—
626	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	1	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	C₂×D₄×C₁₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
645	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
648	M₁₆	—	2	4	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	complemented
656	M₁₆	C₁₃×#41	1	2	yes	complemented
657	C₂×C₈	—	2	4	no	—
658	C₂×C₈	—	2	1	no	—
659	C₂×C₈	—	2	1	no	—
660	C₂×C₈	—	2	1	no	—
661	C₂×C₈	—	2	1	no	—
662	C₄⋊C₄	—	2	2	no	—
663	C₄⋊C₄	—	2	2	no	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	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	—	2	1	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	8	2	no	—
677	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	2	2	no	—
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	1	no	—
689	C₂²⋊C₄	—	2	1	no	—
690	C₂²⋊C₄	—	2	1	no	—
691	C₂²⋊C₄	—	2	1	no	—
692	C₂²⋊C₄	—	2	1	no	—
693	C₂²⋊C₄	—	2	1	no	—
694	C₂²⋊C₄	—	2	1	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	2	no	—
700	C₂²⋊C₄	—	4	4	no	—
701	C₂²⋊C₄	—	4	1	no	—
702	C₂²⋊C₄	—	4	1	no	—
703	C₂²⋊C₄	—	8	2	no	—
704	C₄²	—	2	2	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	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	4	1	no	—
715	C₄²	—	4	1	no	—
716	C₁₃	#24084	1	1	yes	characteristic, direct product factor, Sylow
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	2	no	—
726	C₂³	—	4	2	no	—
727	C₂³	C₁₃×#120	1	1	yes	characteristic
728	C₂³	C₁₃×#120	1	1	yes	characteristic
729	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
730	Q₈	—	2	1	no	—
731	Q₈	—	2	1	no	—
732	Q₈	—	8	2	no	—
733	D₄	—	2	1	no	—
734	D₄	—	2	1	no	—
735	D₄	—	4	4	no	—
736	D₄	—	4	2	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	4	1	no	—
742	D₄	—	4	1	no	—
743	D₄	—	8	2	no	—
744	D₄	—	8	1	no	—
745	D₄	—	8	2	no	—
746	D₄	—	8	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	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	1	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	1	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	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	2	no	—
772	C₂×C₄	—	4	1	no	—
773	C₂×C₄	—	4	2	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	2	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	1	no	—
778	C₂×C₄	—	4	1	no	—
779	C₂×C₄	—	8	1	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	—	8	2	no	—
782	C₂×C₄	—	8	2	no	—
783	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
784	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
787	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
788	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
789	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
790	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
791	C₈	—	2	2	no	—
792	C₈	—	2	2	no	—
793	C₈	—	4	1	no	—
794	C₈	—	4	1	no	—
795	C₂²	—	2	1	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	1	no	—
798	C₂²	—	2	1	no	—
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	2	no	—
812	C₂²	—	8	2	no	—
813	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
814	C₂²	C₁₃×#547	1	1	yes	characteristic
815	C₂²	C₁₃×#547	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₄	C₁₃×#525	1	1	yes	characteristic
831	C₄	C₁₃×#536	1	1	yes	characteristic
832	C₄	C₁₃×#547	1	1	yes	characteristic
833	C₄	C₁₃×#547	1	1	yes	characteristic
834	C₂	—	2	1	no	—
835	C₂	—	2	1	no	—
836	C₂	—	4	1	no	—
837	C₂	—	4	1	no	—
838	C₂	—	8	2	no	—
839	C₂	—	8	1	no	—
840	C₂	C₁₃×#2406	1	1	yes	characteristic
841	C₂	C₁₃×#3018	1	1	yes	characteristic
842	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3494	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3093	C₂	semidirect
3. C₁₃×#2911	C₂	semidirect
4. C₁₃×#2500	C₂	semidirect
5. C₁₃×#2061	C₂	semidirect
6. C₁₃×#2060	C₂	semidirect
7. C₁₃×#2037	C₂	semidirect
8. C₁₃×#2037	C₂	semidirect
9. C₁₃×#1900	C₂	semidirect
10. C₁₃×#1871	C₂	semidirect
11. C₁₃×#1860	C₂	semidirect
12. C₁₃×#1859	C₂	semidirect
13. C₁₃×#1856	C₂	semidirect
14. C₁₃×#1856	C₂	semidirect
15. C₁₃×#1826	C₂	semidirect
182. #24084	C₁₃	direct (N × H)
235. C₁₃×M₁₆	#41	semidirect
236. C₁₃×M₁₆	#41	semidirect
297. #3093	C₂×C₁₃	semidirect
298. #2911	C₂×C₁₃	semidirect
299. #2500	C₂×C₁₃	semidirect
300. #2061	C₂×C₁₃	semidirect
301. #2060	C₂×C₁₃	semidirect
302. #2037	C₂×C₁₃	semidirect
303. #2037	C₂×C₁₃	semidirect
304. #1900	C₂×C₁₃	semidirect
305. #1871	C₂×C₁₃	semidirect
306. #1860	C₂×C₁₃	semidirect
307. #1859	C₂×C₁₃	semidirect
308. #1856	C₂×C₁₃	semidirect
309. #1856	C₂×C₁₃	semidirect
310. #1826	C₂×C₁₃	semidirect
655. M₁₆	C₁₃×#41	semidirect
656. M₁₆	C₁₃×#41	semidirect
716. C₁₃	#24084	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×#3494	2
C₁₃×#3093	2
C₁₃×#2911	2
C₁₃×#2500	2
C₁₃×#2061	2
C₁₃×#2060	2
C₁₃×#2037	2
C₁₃×#1900	2
C₁₃×#1871	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1856	2
C₁₃×#1826	2
#24084	13

Subgroups — C13×#24084 #15710423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24084 #15710423