Subgroups — C₁₃×#24034 #15710373

Order 3328.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#550	—	2	4	no	—
20	C₁₃×#550	—	2	4	no	—
21	C₂×C₁₃×#127	—	2	1	no	—
22	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#121	—	2	1	no	—
24	C₂×C₁₃×#121	—	2	1	no	—
25	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	—	2	1	no	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₁₃×#482	—	2	4	no	—
32	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₁₃×#416	—	2	4	no	—
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₁₃×#397	—	2	1	no	—
51	C₁₃×#394	—	2	1	no	—
52	C₁₃×#389	C₂²	1	1	yes	characteristic
53	C₁₃×#389	C₂²	1	1	yes	characteristic
54	C₁₃×#388	—	2	1	no	—
55	C₁₃×#387	—	2	1	no	—
56	C₁₃×#380	C₂²	1	1	yes	characteristic
57	C₁₃×#380	C₂²	1	1	yes	characteristic
58	C₁₃×#380	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₁₃×#340	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	2	no	—
70	C₂×C₁₃×#41	—	4	1	no	—
71	C₂×C₁₃×#41	—	4	1	no	—
72	C₂×C₁₃×#41	—	4	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	D₄	1	4	yes	—
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	—	2	1	no	—
79	C₂²×D₄×C₁₃	—	2	1	no	—
80	C₂²×D₄×C₁₃	—	2	1	no	—
81	C₂²×D₄×C₁₃	—	2	1	no	—
82	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	—	2	1	no	—
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₁₃	—	2	2	no	—
90	C₂²×C₈×C₁₃	—	4	1	no	—
91	C₂²×C₈×C₁₃	—	4	1	no	—
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#127	—	2	8	no	—
97	C₁₃×#127	—	2	2	no	—
98	C₁₃×#127	—	2	2	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#121	—	2	8	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	2	2	no	—
104	C₁₃×#121	D₄	1	4	yes	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₁₃×#117	—	2	2	no	—
111	C₁₃×#117	—	2	2	no	—
112	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
125	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	—	2	1	no	—
130	C₂×C₄²×C₁₃	—	2	1	no	—
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₁₃×#107	—	2	2	no	—
133	C₁₃×#106	—	2	2	no	—
134	C₁₃×#103	—	2	2	no	—
135	C₁₃×#103	—	2	2	no	—
136	C₁₃×#103	—	2	2	no	—
137	C₁₃×#103	—	2	2	no	—
138	C₁₃×#102	—	2	2	no	—
139	C₁₃×#102	—	2	2	no	—
140	C₁₃×#102	—	2	2	no	—
141	C₁₃×#102	—	2	2	no	—
142	C₁₃×#102	—	4	1	no	—
143	C₁₃×#102	—	4	1	no	—
144	C₁₃×#102	—	4	1	no	—
145	C₁₃×#102	—	4	1	no	—
146	C₁₃×C₂²⋊C₈	—	2	2	no	—
147	C₁₃×C₂²⋊C₈	—	4	1	no	—
148	C₁₃×C₂²⋊C₈	—	4	1	no	—
149	C₁₃×#95	—	2	1	no	—
150	C₁₃×#95	—	2	1	no	—
151	C₁₃×#95	—	2	1	no	—
152	C₁₃×#95	—	2	1	no	—
153	C₁₃×#95	—	2	1	no	—
154	#24034	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₂⁴×C₁₃	—	2	1	no	—
157	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₁₃×#41	—	2	8	no	—
160	C₁₃×#41	—	4	4	no	—
161	C₁₃×#41	—	4	4	no	—
162	C₁₃×#41	—	4	4	no	—
163	C₁₃×#41	—	4	4	no	—
164	C₁₃×#41	—	4	4	no	—
165	C₁₃×#41	—	4	4	no	—
166	C₁₃×#41	—	4	4	no	—
167	C₂×Q₈×C₁₃	—	2	1	no	—
168	C₂×Q₈×C₁₃	—	2	1	no	—
169	C₂×Q₈×C₁₃	—	2	1	no	—
170	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
171	C₂×Q₈×C₁₃	#41	1	2	yes	—
172	C₂×Q₈×C₁₃	#41	1	2	yes	—
173	C₂×D₄×C₁₃	—	2	4	no	—
174	C₂×D₄×C₁₃	—	2	4	no	—
175	C₂×D₄×C₁₃	—	2	2	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	2	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	4	1	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	2	no	—
194	C₂×D₄×C₁₃	—	4	2	no	—
195	C₂×D₄×C₁₃	—	4	2	no	—
196	C₂×D₄×C₁₃	—	4	2	no	—
197	C₂×D₄×C₁₃	—	4	2	no	—
198	C₂×D₄×C₁₃	—	8	1	no	—
199	C₂×D₄×C₁₃	—	8	1	no	—
200	C₂×D₄×C₁₃	—	8	1	no	—
201	C₂×D₄×C₁₃	—	8	1	no	—
202	C₂×D₄×C₁₃	—	8	1	no	—
203	C₂×D₄×C₁₃	—	8	1	no	—
204	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
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	4	no	—
212	C₂²×C₄×C₁₃	—	2	1	no	—
213	C₂²×C₄×C₁₃	—	2	4	no	—
214	C₂²×C₄×C₁₃	—	2	1	no	—
215	C₂²×C₄×C₁₃	—	2	1	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	—	2	1	no	—
222	C₂²×C₄×C₁₃	—	2	1	no	—
223	C₂²×C₄×C₁₃	—	2	1	no	—
224	C₂²×C₄×C₁₃	—	4	2	no	—
225	C₂²×C₄×C₁₃	—	4	2	no	—
226	C₂²×C₄×C₁₃	—	4	2	no	—
227	C₂²×C₄×C₁₃	—	4	2	no	—
228	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	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	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	C₂×C₈×C₁₃	—	2	1	no	—
247	C₂×C₈×C₁₃	—	4	4	no	—
248	C₁₃×C₄⋊C₄	—	2	4	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	—	4	2	no	—
260	C₁₃×C₄⋊C₄	—	8	1	no	—
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₂²⋊C₄	—	2	4	no	—
263	C₁₃×C₂²⋊C₄	—	2	2	no	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	2	no	—
266	C₁₃×C₂²⋊C₄	—	4	2	no	—
267	C₁₃×C₂²⋊C₄	—	4	2	no	—
268	C₁₃×C₂²⋊C₄	—	8	1	no	—
269	C₁₃×C₂²⋊C₄	—	8	1	no	—
270	C₄²×C₁₃	—	2	4	no	—
271	C₄²×C₁₃	—	2	1	no	—
272	C₄²×C₁₃	—	2	1	no	—
273	C₄²×C₁₃	—	4	2	no	—
274	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
275	C₂×#482	C₂×C₁₃	1	1	yes	characteristic, complemented
276	C₂×#416	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#2485	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#2041	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#2033	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#1893	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#1869	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
287	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
288	#1788	C₂×C₁₃	1	1	yes	characteristic, complemented
289	C₂³×C₁₃	—	2	1	no	—
290	C₂³×C₁₃	—	2	1	no	—
291	C₂³×C₁₃	—	2	1	no	—
292	C₂³×C₁₃	—	2	1	no	—
293	C₂³×C₁₃	—	2	1	no	—
294	C₂³×C₁₃	—	2	1	no	—
295	C₂³×C₁₃	—	2	1	no	—
296	C₂³×C₁₃	—	2	2	no	—
297	C₂³×C₁₃	—	2	2	no	—
298	C₂³×C₁₃	—	2	1	no	—
299	C₂³×C₁₃	—	2	1	no	—
300	C₂³×C₁₃	—	2	1	no	—
301	C₂³×C₁₃	—	2	1	no	—
302	C₂³×C₁₃	—	2	1	no	—
303	C₂³×C₁₃	—	2	1	no	—
304	C₂³×C₁₃	—	4	1	no	—
305	C₂³×C₁₃	—	4	1	no	—
306	C₂³×C₁₃	—	4	1	no	—
307	C₂³×C₁₃	—	4	1	no	—
308	C₂³×C₁₃	—	4	1	no	—
309	C₂³×C₁₃	—	4	1	no	—
310	C₂³×C₁₃	—	4	1	no	—
311	C₂³×C₁₃	—	4	1	no	—
312	C₂³×C₁₃	—	4	1	no	—
313	C₂³×C₁₃	—	4	1	no	—
314	C₂³×C₁₃	—	4	1	no	—
315	C₂³×C₁₃	—	4	1	no	—
316	C₂³×C₁₃	#120	1	2	yes	—
317	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
318	Q₈×C₁₃	—	2	2	no	—
319	Q₈×C₁₃	—	2	2	no	—
320	Q₈×C₁₃	—	2	2	no	—
321	Q₈×C₁₃	#123	1	4	yes	—
322	D₄×C₁₃	—	2	2	no	—
323	D₄×C₁₃	—	2	2	no	—
324	D₄×C₁₃	—	2	2	no	—
325	D₄×C₁₃	—	2	2	no	—
326	D₄×C₁₃	—	4	4	no	—
327	D₄×C₁₃	—	4	8	no	—
328	D₄×C₁₃	—	4	8	no	—
329	D₄×C₁₃	—	4	8	no	—
330	D₄×C₁₃	—	4	1	no	—
331	D₄×C₁₃	—	4	1	no	—
332	D₄×C₁₃	—	4	1	no	—
333	D₄×C₁₃	—	4	1	no	—
334	D₄×C₁₃	—	8	4	no	—
335	D₄×C₁₃	—	8	4	no	—
336	D₄×C₁₃	—	8	4	no	—
337	C₂×C₄×C₁₃	—	2	1	no	—
338	C₂×C₄×C₁₃	—	2	2	no	—
339	C₂×C₄×C₁₃	—	2	1	no	—
340	C₂×C₄×C₁₃	—	2	1	no	—
341	C₂×C₄×C₁₃	—	2	2	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	2	1	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	2	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	1	no	—
354	C₂×C₄×C₁₃	—	2	1	no	—
355	C₂×C₄×C₁₃	—	4	8	no	—
356	C₂×C₄×C₁₃	—	4	8	no	—
357	C₂×C₄×C₁₃	—	4	1	no	—
358	C₂×C₄×C₁₃	—	4	1	no	—
359	C₂×C₄×C₁₃	—	4	1	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	1	no	—
373	C₂×C₄×C₁₃	—	4	1	no	—
374	C₂×C₄×C₁₃	—	4	1	no	—
375	C₂×C₄×C₁₃	#120	1	2	yes	—
376	C₂×C₄×C₁₃	#135	1	2	yes	—
377	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
380	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
381	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
382	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
383	C₈×C₁₃	—	4	1	no	—
384	C₈×C₁₃	—	4	1	no	—
385	C₈×C₁₃	—	4	1	no	—
386	C₈×C₁₃	—	4	1	no	—
387	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
388	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
389	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
390	#550	—	2	4	no	—
391	#550	—	2	4	no	—
392	C₂×#127	—	2	1	no	—
393	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#121	—	2	1	no	—
395	C₂×#121	—	2	1	no	—
396	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	C₂×C₄×D₄	—	2	1	no	—
400	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
402	#482	—	2	4	no	—
403	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
404	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
405	#416	—	2	4	no	—
406	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
407	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
408	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
409	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
410	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
411	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
412	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
418	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
419	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
421	#397	—	2	1	no	—
422	#394	—	2	1	no	—
423	#389	C₂²×C₁₃	1	1	yes	characteristic
424	#389	C₂²×C₁₃	1	1	yes	characteristic
425	#388	—	2	1	no	—
426	#387	—	2	1	no	—
427	#380	C₂²×C₁₃	1	1	yes	characteristic
428	#380	C₂²×C₁₃	1	1	yes	characteristic
429	#380	C₂²×C₁₃	1	1	yes	characteristic
430	#340	C₂²×C₁₃	1	1	yes	characteristic
431	#340	C₂²×C₁₃	1	1	yes	characteristic
432	#336	C₂²×C₁₃	1	1	yes	characteristic
433	#336	C₂²×C₁₃	1	1	yes	characteristic
434	C₂²×C₁₃	—	2	2	no	—
435	C₂²×C₁₃	—	2	2	no	—
436	C₂²×C₁₃	—	2	2	no	—
437	C₂²×C₁₃	—	4	1	no	—
438	C₂²×C₁₃	—	4	1	no	—
439	C₂²×C₁₃	—	4	1	no	—
440	C₂²×C₁₃	—	4	1	no	—
441	C₂²×C₁₃	—	4	2	no	—
442	C₂²×C₁₃	—	4	2	no	—
443	C₂²×C₁₃	—	4	1	no	—
444	C₂²×C₁₃	—	4	1	no	—
445	C₂²×C₁₃	—	4	2	no	—
446	C₂²×C₁₃	—	4	2	no	—
447	C₂²×C₁₃	—	4	1	no	—
448	C₂²×C₁₃	—	4	2	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	1	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	—	8	1	no	—
455	C₂²×C₁₃	—	8	1	no	—
456	C₂²×C₁₃	—	8	1	no	—
457	C₂²×C₁₃	—	8	1	no	—
458	C₂²×C₁₃	—	8	1	no	—
459	C₂²×C₁₃	—	8	1	no	—
460	C₂²×C₁₃	—	8	1	no	—
461	C₂²×C₁₃	—	8	1	no	—
462	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
463	C₂²×C₁₃	#546	1	1	yes	characteristic
464	C₂²×C₁₃	#546	1	1	yes	characteristic
465	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
466	C₂²×C₁₃	#575	1	1	yes	characteristic
467	C₂²×C₁₃	#576	1	1	yes	characteristic
468	C₂²×C₁₃	#577	1	1	yes	characteristic
469	C₄×C₁₃	—	2	2	no	—
470	C₄×C₁₃	—	2	4	no	—
471	C₄×C₁₃	—	2	2	no	—
472	C₄×C₁₃	—	4	1	no	—
473	C₄×C₁₃	—	4	1	no	—
474	C₄×C₁₃	—	4	2	no	—
475	C₄×C₁₃	—	8	1	no	—
476	C₄×C₁₃	—	8	1	no	—
477	C₄×C₁₃	—	8	1	no	—
478	C₄×C₁₃	—	8	1	no	—
479	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
480	C₄×C₁₃	#534	1	1	yes	characteristic
481	C₄×C₁₃	#546	1	1	yes	characteristic
482	C₄×C₁₃	#546	1	1	yes	characteristic
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	2	no	—
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	2	2	no	—
490	C₂×#41	—	4	1	no	—
491	C₂×#41	—	4	1	no	—
492	C₂×#41	—	4	1	no	—
493	C₂×#41	—	4	1	no	—
494	C₂×#41	D₄×C₁₃	1	4	yes	—
495	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	—	2	1	no	—
499	C₂²×D₄	—	2	1	no	—
500	C₂²×D₄	—	2	1	no	—
501	C₂²×D₄	—	2	1	no	—
502	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
503	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
505	C₂³×C₄	—	2	1	no	—
506	C₂³×C₄	—	2	1	no	—
507	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	4	1	no	—
511	C₂²×C₈	—	4	1	no	—
512	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
513	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
514	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
515	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
516	#127	—	2	8	no	—
517	#127	—	2	2	no	—
518	#127	—	2	2	no	—
519	#121	—	2	8	no	—
520	#121	—	2	8	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	2	2	no	—
524	#121	D₄×C₁₃	1	4	yes	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×D₄	—	2	8	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	#117	—	2	2	no	—
531	#117	—	2	2	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
548	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₄²	—	2	1	no	—
550	C₂×C₄²	—	2	1	no	—
551	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
552	#107	—	2	2	no	—
553	#106	—	2	2	no	—
554	#103	—	2	2	no	—
555	#103	—	2	2	no	—
556	#103	—	2	2	no	—
557	#103	—	2	2	no	—
558	#102	—	2	2	no	—
559	#102	—	2	2	no	—
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	4	1	no	—
563	#102	—	4	1	no	—
564	#102	—	4	1	no	—
565	#102	—	4	1	no	—
566	C₂²⋊C₈	—	2	2	no	—
567	C₂²⋊C₈	—	4	1	no	—
568	C₂²⋊C₈	—	4	1	no	—
569	#95	—	2	1	no	—
570	#95	—	2	1	no	—
571	#95	—	2	1	no	—
572	#95	—	2	1	no	—
573	#95	—	2	1	no	—
574	C₂×C₁₃	—	4	2	no	—
575	C₂×C₁₃	—	8	1	no	—
576	C₂×C₁₃	—	8	2	no	—
577	C₂×C₁₃	—	8	2	no	—
578	C₂×C₁₃	#2405	1	1	yes	characteristic
579	C₂×C₁₃	#3002	1	1	yes	characteristic
580	C₂×C₁₃	#3012	1	1	yes	characteristic
581	C₂×C₁₃	#3304	1	1	yes	characteristic
582	C₂×C₁₃	#3305	1	1	yes	characteristic
583	C₂×C₁₃	#3309	1	1	yes	characteristic
584	C₂×C₁₃	#3317	1	1	yes	characteristic
585	C₂⁴	—	2	1	no	—
586	C₂⁴	—	2	1	no	—
587	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
588	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
589	#41	—	2	8	no	—
590	#41	—	4	4	no	—
591	#41	—	4	4	no	—
592	#41	—	4	4	no	—
593	#41	—	4	4	no	—
594	#41	—	4	4	no	—
595	#41	—	4	4	no	—
596	#41	—	4	4	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
601	C₂×Q₈	C₁₃×#41	1	2	yes	—
602	C₂×Q₈	C₁₃×#41	1	2	yes	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	4	no	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	4	1	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂×D₄	—	4	2	no	—
624	C₂×D₄	—	4	2	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	2	no	—
628	C₂×D₄	—	8	1	no	—
629	C₂×D₄	—	8	1	no	—
630	C₂×D₄	—	8	1	no	—
631	C₂×D₄	—	8	1	no	—
632	C₂×D₄	—	8	1	no	—
633	C₂×D₄	—	8	1	no	—
634	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
635	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
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	—	2	4	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	2	1	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	—	2	1	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	4	2	no	—
655	C₂²×C₄	—	4	2	no	—
656	C₂²×C₄	—	4	2	no	—
657	C₂²×C₄	—	4	2	no	—
658	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
663	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₂×C₈	—	2	1	no	—
666	C₂×C₈	—	2	1	no	—
667	C₂×C₈	—	2	1	no	—
668	C₂×C₈	—	2	1	no	—
669	C₂×C₈	—	2	1	no	—
670	C₂×C₈	—	2	1	no	—
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	C₂×C₈	—	2	1	no	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	4	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	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	—	4	2	no	—
690	C₄⋊C₄	—	8	1	no	—
691	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	4	2	no	—
697	C₂²⋊C₄	—	4	2	no	—
698	C₂²⋊C₄	—	8	1	no	—
699	C₂²⋊C₄	—	8	1	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	1	no	—
702	C₄²	—	2	1	no	—
703	C₄²	—	4	2	no	—
704	C₁₃	#24034	1	1	yes	characteristic, direct product factor, Sylow
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	1	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	1	no	—
715	C₂³	—	2	1	no	—
716	C₂³	—	2	1	no	—
717	C₂³	—	2	1	no	—
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	4	1	no	—
721	C₂³	—	4	1	no	—
722	C₂³	—	4	1	no	—
723	C₂³	—	4	1	no	—
724	C₂³	—	4	1	no	—
725	C₂³	—	4	1	no	—
726	C₂³	—	4	1	no	—
727	C₂³	—	4	1	no	—
728	C₂³	—	4	1	no	—
729	C₂³	—	4	1	no	—
730	C₂³	—	4	1	no	—
731	C₂³	—	4	1	no	—
732	C₂³	C₁₃×#120	1	2	yes	—
733	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
734	Q₈	—	2	2	no	—
735	Q₈	—	2	2	no	—
736	Q₈	—	2	2	no	—
737	Q₈	C₁₃×#123	1	4	yes	—
738	D₄	—	2	2	no	—
739	D₄	—	2	2	no	—
740	D₄	—	2	2	no	—
741	D₄	—	2	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	8	no	—
744	D₄	—	4	8	no	—
745	D₄	—	4	8	no	—
746	D₄	—	4	1	no	—
747	D₄	—	4	1	no	—
748	D₄	—	4	1	no	—
749	D₄	—	4	1	no	—
750	D₄	—	8	4	no	—
751	D₄	—	8	4	no	—
752	D₄	—	8	4	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	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	1	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	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	1	no	—
780	C₂×C₄	—	4	1	no	—
781	C₂×C₄	—	4	1	no	—
782	C₂×C₄	—	4	1	no	—
783	C₂×C₄	—	4	1	no	—
784	C₂×C₄	—	4	1	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	C₁₃×#120	1	2	yes	—
792	C₂×C₄	C₁₃×#135	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
794	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
795	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
796	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
797	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
798	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
799	C₈	—	4	1	no	—
800	C₈	—	4	1	no	—
801	C₈	—	4	1	no	—
802	C₈	—	4	1	no	—
803	C₂²	—	2	2	no	—
804	C₂²	—	2	2	no	—
805	C₂²	—	2	2	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	2	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	1	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	1	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	8	1	no	—
824	C₂²	—	8	1	no	—
825	C₂²	—	8	1	no	—
826	C₂²	—	8	1	no	—
827	C₂²	—	8	1	no	—
828	C₂²	—	8	1	no	—
829	C₂²	—	8	1	no	—
830	C₂²	—	8	1	no	—
831	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
832	C₂²	C₁₃×#546	1	1	yes	characteristic
833	C₂²	C₁₃×#546	1	1	yes	characteristic
834	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
835	C₂²	C₁₃×#575	1	1	yes	characteristic
836	C₂²	C₁₃×#576	1	1	yes	characteristic
837	C₂²	C₁₃×#577	1	1	yes	characteristic
838	C₄	—	2	2	no	—
839	C₄	—	2	4	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	4	1	no	—
844	C₄	—	8	1	no	—
845	C₄	—	8	1	no	—
846	C₄	—	8	1	no	—
847	C₄	—	8	1	no	—
848	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
849	C₄	C₁₃×#534	1	1	yes	characteristic
850	C₄	C₁₃×#546	1	1	yes	characteristic
851	C₄	C₁₃×#546	1	1	yes	characteristic
852	C₂	—	4	2	no	—
853	C₂	—	8	1	no	—
854	C₂	—	8	2	no	—
855	C₂	—	8	2	no	—
856	C₂	C₁₃×#2405	1	1	yes	characteristic
857	C₂	C₁₃×#3002	1	1	yes	characteristic
858	C₂	C₁₃×#3012	1	1	yes	characteristic
859	C₂	C₁₃×#3304	1	1	yes	characteristic
860	C₂	C₁₃×#3305	1	1	yes	characteristic
861	C₂	C₁₃×#3309	1	1	yes	characteristic
862	C₂	C₁₃×#3317	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#482	C₂	semidirect
3. C₂×C₁₃×#416	C₂	semidirect
4. C₁₃×#2485	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#2041	C₂	semidirect
7. C₁₃×#2034	C₂	semidirect
8. C₁₃×#2033	C₂	semidirect
9. C₁₃×#1893	C₂	semidirect
10. C₁₃×#1869	C₂	semidirect
11. C₁₃×#1865	C₂	semidirect
12. C₁₃×#1863	C₂	semidirect
13. C₁₃×#1788	C₂	semidirect
14. C₁₃×#1788	C₂	semidirect
15. C₁₃×#1788	C₂	semidirect
154. #24034	C₁₃	direct (N × H)
275. C₂×#482	C₂×C₁₃	semidirect
276. C₂×#416	C₂×C₁₃	semidirect
277. #2485	C₂×C₁₃	semidirect
278. #2041	C₂×C₁₃	semidirect
279. #2041	C₂×C₁₃	semidirect
280. #2034	C₂×C₁₃	semidirect
281. #2033	C₂×C₁₃	semidirect
282. #1893	C₂×C₁₃	semidirect
283. #1869	C₂×C₁₃	semidirect
284. #1865	C₂×C₁₃	semidirect
285. #1863	C₂×C₁₃	semidirect
286. #1788	C₂×C₁₃	semidirect
287. #1788	C₂×C₁₃	semidirect
288. #1788	C₂×C₁₃	semidirect
704. C₁₃	#24034	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#550	2
C₂×C₁₃×#482	2
C₂×C₁₃×#416	2
C₁₃×#2485	2
C₁₃×#2041	2
C₁₃×#2034	2
C₁₃×#2033	2
C₁₃×#1893	2
C₁₃×#1869	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1788	2
#24034	13

Subgroups — C13×#24034 #15710373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24034 #15710373