Subgroups — C₁₃×#23956 #15710295

Order 3328.

1284 conjugacy classes of subgroups.

The subgroup lattice has 964 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, complemented
2	C₁₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2431	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2028	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2027	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2004	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2002	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1887	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1871	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1826	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₁₃×#555	—	2	1	no	—
21	C₁₃×#553	—	2	1	no	—
22	C₁₃×#553	—	2	1	no	—
23	C₁₃×#551	—	2	2	no	—
24	C₁₃×#547	—	2	1	no	—
25	C₁₃×#546	—	2	2	no	—
26	C₁₃×#544	C₂²	1	1	yes	characteristic
27	C₁₃×#542	—	2	1	no	—
28	C₁₃×#540	—	2	1	no	—
29	C₁₃×#535	C₂²	1	1	yes	characteristic
30	C₁₃×#532	—	2	1	no	—
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#529	—	2	1	no	—
33	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
34	C₁₃×#525	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
36	C₁₃×#520	C₂²	1	1	yes	characteristic
37	C₁₃×#518	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
39	C₁₃×#452	—	2	1	no	—
40	C₁₃×#452	—	2	1	no	—
41	C₁₃×#449	—	2	1	no	—
42	C₁₃×#449	—	2	1	no	—
43	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₁₃×#419	C₂²	1	1	yes	characteristic
46	C₁₃×#419	C₂²	1	1	yes	characteristic
47	C₁₃×#419	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₁₃×#418	C₂²	1	1	yes	characteristic
51	C₁₃×#417	—	2	1	no	—
52	C₁₃×#417	—	2	1	no	—
53	C₁₃×#416	—	2	1	no	—
54	C₁₃×#416	—	2	1	no	—
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₁₃×#407	C₂²	1	1	yes	characteristic
58	C₁₃×#392	—	2	2	no	—
59	C₁₃×#391	C₂²	1	1	yes	characteristic
60	C₁₃×#390	C₂²	1	1	yes	characteristic
61	C₁₃×#386	—	2	2	no	—
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	—	2	2	no	—
73	C₂×C₁₃×#41	—	2	2	no	—
74	C₂×C₁₃×#41	—	2	1	no	—
75	C₂×C₁₃×#41	—	2	1	no	—
76	C₂×C₁₃×#41	—	2	1	no	—
77	C₂×C₁₃×#41	—	2	1	no	—
78	C₂×C₁₃×#41	—	4	1	no	—
79	C₂×C₁₃×#41	—	4	1	no	—
80	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	2	no	—
84	C₂²×D₄×C₁₃	D₄	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	—	2	1	no	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#137	—	2	2	no	—
90	C₁₃×#137	—	4	1	no	—
91	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
92	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
93	C₂×C₁₃×Q₁₆	—	2	1	no	—
94	C₂×C₁₃×SD₁₆	—	2	1	no	—
95	C₂×C₁₃×SD₁₆	—	2	1	no	—
96	C₂×C₁₃×D₈	—	2	1	no	—
97	C₂×C₁₃×M₁₆	—	2	1	no	—
98	C₂×C₁₃×M₁₆	—	4	1	no	—
99	C₂×C₁₃×M₁₆	—	4	1	no	—
100	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	—	2	1	no	—
105	C₁₃×C₄⋊Q₈	—	2	1	no	—
106	C₁₃×C₄⋊Q₈	—	2	1	no	—
107	C₁₃×#127	—	2	1	no	—
108	C₁₃×#127	—	2	2	no	—
109	C₁₃×#127	—	4	1	no	—
110	C₁₃×#126	—	2	2	no	—
111	C₁₃×#126	—	2	2	no	—
112	C₁₃×#125	—	2	1	no	—
113	C₁₃×#125	—	2	1	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	—	2	1	no	—
117	C₁₃×#124	—	2	2	no	—
118	C₁₃×#124	—	4	1	no	—
119	C₁₃×#123	—	2	2	no	—
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	2	no	—
122	C₁₃×#123	—	2	2	no	—
123	C₁₃×#123	—	2	1	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
127	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic, complemented
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	2	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	1	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	1	no	—
137	C₁₃×#121	D₄	1	1	yes	characteristic, complemented
138	C₁₃×#121	D₄	1	1	yes	characteristic, complemented
139	C₁₃×#120	—	2	1	no	—
140	C₁₃×#120	—	2	2	no	—
141	C₄×Q₈×C₁₃	—	2	1	no	—
142	C₄×D₄×C₁₃	—	2	2	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	1	no	—
145	C₄×D₄×C₁₃	—	2	2	no	—
146	C₄×D₄×C₁₃	—	2	1	no	—
147	C₄×D₄×C₁₃	—	2	1	no	—
148	C₄×D₄×C₁₃	—	2	1	no	—
149	C₄×D₄×C₁₃	—	2	1	no	—
150	C₄×D₄×C₁₃	—	2	1	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₁₃×#117	—	2	2	no	—
153	C₁₃×#117	—	2	1	no	—
154	C₁₃×#117	—	2	1	no	—
155	C₁₃×#117	—	2	1	no	—
156	C₁₃×#117	D₄	1	1	yes	characteristic, complemented
157	C₁₃×#117	D₄	1	1	yes	characteristic, complemented
158	C₁₃×#117	C₂³	1	1	yes	characteristic
159	C₁₃×#117	C₂³	1	1	yes	characteristic
160	C₁₃×#117	C₂³	1	1	yes	characteristic
161	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic, complemented
163	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic, complemented
164	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
166	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
169	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
171	C₂×C₄²×C₁₃	—	2	1	no	—
172	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₁₃×#104	—	4	1	no	—
175	C₁₃×#104	—	4	1	no	—
176	C₁₃×#103	—	2	1	no	—
177	C₁₃×#103	—	2	1	no	—
178	C₁₃×#103	—	2	1	no	—
179	C₁₃×#103	—	2	1	no	—
180	C₁₃×#103	—	2	1	no	—
181	C₁₃×#103	—	2	1	no	—
182	C₁₃×#102	—	2	1	no	—
183	C₁₃×#102	—	2	1	no	—
184	C₁₃×#102	—	2	1	no	—
185	C₁₃×#102	—	2	1	no	—
186	C₁₃×#102	—	2	1	no	—
187	C₁₃×#102	—	2	1	no	—
188	C₁₃×#100	—	4	1	no	—
189	C₁₃×#100	—	4	1	no	—
190	C₁₃×C₂²⋊C₈	—	2	1	no	—
191	C₁₃×C₂²⋊C₈	—	2	1	no	—
192	C₁₃×#95	—	2	1	no	—
193	C₁₃×#95	—	2	2	no	—
194	#23956	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂⁴×C₁₃	—	2	1	no	—
196	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
197	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₁₃×#41	—	2	4	no	—
199	C₁₃×#41	—	2	4	no	—
200	C₁₃×#41	—	2	1	no	—
201	C₁₃×#41	—	2	1	no	—
202	C₁₃×#41	—	2	1	no	—
203	C₁₃×#41	—	2	1	no	—
204	C₁₃×#41	—	4	2	no	—
205	C₁₃×#41	—	4	2	no	—
206	C₁₃×#41	—	4	2	no	—
207	C₁₃×#41	—	4	2	no	—
208	C₁₃×#41	—	4	2	no	—
209	C₁₃×#41	—	4	2	no	—
210	C₁₃×#41	—	8	4	no	—
211	C₂×Q₈×C₁₃	—	2	2	no	—
212	C₂×Q₈×C₁₃	—	2	1	no	—
213	C₂×Q₈×C₁₃	—	2	1	no	—
214	C₂×Q₈×C₁₃	—	2	1	no	—
215	C₂×Q₈×C₁₃	—	2	1	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
218	C₂×Q₈×C₁₃	#41	1	2	yes	complemented
219	C₂×D₄×C₁₃	—	2	1	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	1	no	—
222	C₂×D₄×C₁₃	—	2	2	no	—
223	C₂×D₄×C₁₃	—	2	2	no	—
224	C₂×D₄×C₁₃	—	2	1	no	—
225	C₂×D₄×C₁₃	—	2	2	no	—
226	C₂×D₄×C₁₃	—	2	1	no	—
227	C₂×D₄×C₁₃	—	2	1	no	—
228	C₂×D₄×C₁₃	—	2	1	no	—
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	1	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	—	2	1	no	—
234	C₂×D₄×C₁₃	—	2	1	no	—
235	C₂×D₄×C₁₃	—	2	1	no	—
236	C₂×D₄×C₁₃	—	2	1	no	—
237	C₂×D₄×C₁₃	—	4	2	no	—
238	C₂×D₄×C₁₃	—	4	4	no	—
239	C₂×D₄×C₁₃	—	4	2	no	—
240	C₂×D₄×C₁₃	—	4	1	no	—
241	C₂×D₄×C₁₃	—	4	1	no	—
242	C₂×D₄×C₁₃	—	4	4	no	—
243	C₂×D₄×C₁₃	—	8	2	no	—
244	C₂×D₄×C₁₃	—	8	2	no	—
245	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×D₄×C₁₃	#41	1	2	yes	complemented
247	C₂²×C₄×C₁₃	—	2	1	no	—
248	C₂²×C₄×C₁₃	—	2	1	no	—
249	C₂²×C₄×C₁₃	—	2	1	no	—
250	C₂²×C₄×C₁₃	—	2	1	no	—
251	C₂²×C₄×C₁₃	—	2	1	no	—
252	C₂²×C₄×C₁₃	—	2	1	no	—
253	C₂²×C₄×C₁₃	—	2	1	no	—
254	C₂²×C₄×C₁₃	—	2	2	no	—
255	C₂²×C₄×C₁₃	—	2	2	no	—
256	C₂²×C₄×C₁₃	—	2	2	no	—
257	C₂²×C₄×C₁₃	—	2	1	no	—
258	C₂²×C₄×C₁₃	—	2	1	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	4	2	no	—
261	C₂²×C₄×C₁₃	—	4	2	no	—
262	C₂²×C₄×C₁₃	—	4	1	no	—
263	C₂²×C₄×C₁₃	—	4	1	no	—
264	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₁₃×Q₁₆	—	4	2	no	—
272	C₁₃×SD₁₆	—	4	2	no	—
273	C₁₃×SD₁₆	—	4	2	no	—
274	C₁₃×D₈	—	4	2	no	—
275	C₁₃×M₁₆	—	2	1	no	—
276	C₁₃×M₁₆	—	2	1	no	—
277	C₁₃×M₁₆	—	2	1	no	—
278	C₁₃×M₁₆	—	2	1	no	—
279	C₁₃×M₁₆	—	2	1	no	—
280	C₁₃×M₁₆	—	2	1	no	—
281	C₁₃×M₁₆	—	2	1	no	—
282	C₁₃×M₁₆	—	2	1	no	—
283	C₁₃×M₁₆	—	4	2	no	—
284	C₂×C₈×C₁₃	—	2	1	no	—
285	C₂×C₈×C₁₃	—	2	1	no	—
286	C₂×C₈×C₁₃	—	2	1	no	—
287	C₂×C₈×C₁₃	—	2	1	no	—
288	C₂×C₈×C₁₃	—	4	2	no	—
289	C₁₃×C₄⋊C₄	—	2	2	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	2	no	—
293	C₁₃×C₄⋊C₄	—	2	1	no	—
294	C₁₃×C₄⋊C₄	—	2	1	no	—
295	C₁₃×C₄⋊C₄	—	2	1	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	1	no	—
299	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
304	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
305	C₁₃×C₂²⋊C₄	—	2	2	no	—
306	C₁₃×C₂²⋊C₄	—	2	2	no	—
307	C₁₃×C₂²⋊C₄	—	2	2	no	—
308	C₁₃×C₂²⋊C₄	—	2	2	no	—
309	C₁₃×C₂²⋊C₄	—	2	2	no	—
310	C₁₃×C₂²⋊C₄	—	2	1	no	—
311	C₁₃×C₂²⋊C₄	—	2	1	no	—
312	C₁₃×C₂²⋊C₄	—	2	1	no	—
313	C₁₃×C₂²⋊C₄	—	2	1	no	—
314	C₁₃×C₂²⋊C₄	—	2	1	no	—
315	C₁₃×C₂²⋊C₄	—	2	1	no	—
316	C₁₃×C₂²⋊C₄	—	2	1	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	1	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	4	4	no	—
322	C₁₃×C₂²⋊C₄	—	4	2	no	—
323	C₁₃×C₂²⋊C₄	—	8	2	no	—
324	C₄²×C₁₃	—	2	2	no	—
325	C₄²×C₁₃	—	2	1	no	—
326	C₄²×C₁₃	—	2	1	no	—
327	C₄²×C₁₃	—	2	1	no	—
328	C₄²×C₁₃	—	2	1	no	—
329	C₄²×C₁₃	—	2	1	no	—
330	C₄²×C₁₃	—	2	1	no	—
331	C₄²×C₁₃	—	2	1	no	—
332	C₄²×C₁₃	—	2	1	no	—
333	C₄²×C₁₃	—	2	1	no	—
334	#3494	C₂×C₁₃	1	1	yes	characteristic, complemented
335	#3005	C₂×C₁₃	1	1	yes	characteristic, complemented
336	#2896	C₂×C₁₃	1	1	yes	characteristic, complemented
337	#2431	C₂×C₁₃	1	1	yes	characteristic, complemented
338	#2028	C₂×C₁₃	1	1	yes	characteristic, complemented
339	#2027	C₂×C₁₃	1	1	yes	characteristic, complemented
340	#2004	C₂×C₁₃	1	1	yes	characteristic, complemented
341	#2002	C₂×C₁₃	1	1	yes	characteristic, complemented
342	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
343	#1887	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#1885	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#1883	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#1882	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#1826	C₂×C₁₃	1	1	yes	characteristic, complemented
349	C₂³×C₁₃	—	2	1	no	—
350	C₂³×C₁₃	—	2	1	no	—
351	C₂³×C₁₃	—	2	2	no	—
352	C₂³×C₁₃	—	2	1	no	—
353	C₂³×C₁₃	—	2	2	no	—
354	C₂³×C₁₃	—	2	2	no	—
355	C₂³×C₁₃	—	2	2	no	—
356	C₂³×C₁₃	—	4	1	no	—
357	C₂³×C₁₃	—	4	1	no	—
358	C₂³×C₁₃	—	4	2	no	—
359	C₂³×C₁₃	—	4	2	no	—
360	C₂³×C₁₃	—	4	2	no	—
361	C₂³×C₁₃	—	4	2	no	—
362	C₂³×C₁₃	—	4	1	no	—
363	C₂³×C₁₃	—	4	1	no	—
364	C₂³×C₁₃	#120	1	1	yes	characteristic
365	C₂³×C₁₃	#120	1	1	yes	characteristic
366	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	1	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	1	no	—
371	Q₈×C₁₃	—	4	1	no	—
372	Q₈×C₁₃	—	4	1	no	—
373	Q₈×C₁₃	—	8	2	no	—
374	D₄×C₁₃	—	2	2	no	—
375	D₄×C₁₃	—	2	1	no	—
376	D₄×C₁₃	—	2	2	no	—
377	D₄×C₁₃	—	2	1	no	—
378	D₄×C₁₃	—	4	4	no	—
379	D₄×C₁₃	—	4	2	no	—
380	D₄×C₁₃	—	4	4	no	—
381	D₄×C₁₃	—	4	4	no	—
382	D₄×C₁₃	—	4	1	no	—
383	D₄×C₁₃	—	4	1	no	—
384	D₄×C₁₃	—	4	1	no	—
385	D₄×C₁₃	—	4	1	no	—
386	D₄×C₁₃	—	4	1	no	—
387	D₄×C₁₃	—	4	1	no	—
388	D₄×C₁₃	—	4	1	no	—
389	D₄×C₁₃	—	4	1	no	—
390	D₄×C₁₃	—	8	1	no	—
391	D₄×C₁₃	—	8	2	no	—
392	D₄×C₁₃	—	8	2	no	—
393	D₄×C₁₃	—	8	2	no	—
394	D₄×C₁₃	—	8	8	no	—
395	C₂×C₄×C₁₃	—	2	1	no	—
396	C₂×C₄×C₁₃	—	2	1	no	—
397	C₂×C₄×C₁₃	—	2	1	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	2	1	no	—
400	C₂×C₄×C₁₃	—	2	1	no	—
401	C₂×C₄×C₁₃	—	2	1	no	—
402	C₂×C₄×C₁₃	—	2	1	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	1	no	—
405	C₂×C₄×C₁₃	—	2	2	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	1	no	—
408	C₂×C₄×C₁₃	—	2	1	no	—
409	C₂×C₄×C₁₃	—	2	1	no	—
410	C₂×C₄×C₁₃	—	2	1	no	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	1	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	4	4	no	—
416	C₂×C₄×C₁₃	—	4	4	no	—
417	C₂×C₄×C₁₃	—	4	1	no	—
418	C₂×C₄×C₁₃	—	4	2	no	—
419	C₂×C₄×C₁₃	—	4	1	no	—
420	C₂×C₄×C₁₃	—	4	1	no	—
421	C₂×C₄×C₁₃	—	4	1	no	—
422	C₂×C₄×C₁₃	—	4	1	no	—
423	C₂×C₄×C₁₃	—	4	1	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	—	4	1	no	—
426	C₂×C₄×C₁₃	—	4	1	no	—
427	C₂×C₄×C₁₃	—	4	1	no	—
428	C₂×C₄×C₁₃	—	8	1	no	—
429	C₂×C₄×C₁₃	—	8	2	no	—
430	C₂×C₄×C₁₃	—	8	2	no	—
431	C₂×C₄×C₁₃	—	8	2	no	—
432	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
433	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
434	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
438	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
440	C₈×C₁₃	—	4	1	no	—
441	C₈×C₁₃	—	4	1	no	—
442	C₈×C₁₃	—	4	1	no	—
443	C₈×C₁₃	—	4	1	no	—
444	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
445	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
447	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
448	#555	—	2	1	no	—
449	#553	—	2	1	no	—
450	#553	—	2	1	no	—
451	#551	—	2	2	no	—
452	#547	—	2	1	no	—
453	#546	—	2	2	no	—
454	#544	C₂²×C₁₃	1	1	yes	characteristic
455	#542	—	2	1	no	—
456	#540	—	2	1	no	—
457	#535	C₂²×C₁₃	1	1	yes	characteristic
458	#532	—	2	1	no	—
459	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
460	#529	—	2	1	no	—
461	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
462	#525	C₂²×C₁₃	1	1	yes	characteristic
463	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
464	#520	C₂²×C₁₃	1	1	yes	characteristic
465	#518	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
467	#452	—	2	1	no	—
468	#452	—	2	1	no	—
469	#449	—	2	1	no	—
470	#449	—	2	1	no	—
471	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
472	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
473	#419	C₂²×C₁₃	1	1	yes	characteristic
474	#419	C₂²×C₁₃	1	1	yes	characteristic
475	#419	C₂²×C₁₃	1	1	yes	characteristic
476	#418	C₂²×C₁₃	1	1	yes	characteristic
477	#418	C₂²×C₁₃	1	1	yes	characteristic
478	#418	C₂²×C₁₃	1	1	yes	characteristic
479	#417	—	2	1	no	—
480	#417	—	2	1	no	—
481	#416	—	2	1	no	—
482	#416	—	2	1	no	—
483	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
484	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
485	#407	C₂²×C₁₃	1	1	yes	characteristic
486	#392	—	2	2	no	—
487	#391	C₂²×C₁₃	1	1	yes	characteristic
488	#390	C₂²×C₁₃	1	1	yes	characteristic
489	#386	—	2	2	no	—
490	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
491	#343	C₂²×C₁₃	1	1	yes	characteristic
492	#343	C₂²×C₁₃	1	1	yes	characteristic
493	#339	C₂²×C₁₃	1	1	yes	characteristic
494	#339	C₂²×C₁₃	1	1	yes	characteristic
495	#339	C₂²×C₁₃	1	1	yes	characteristic
496	#339	C₂²×C₁₃	1	1	yes	characteristic
497	#339	C₂²×C₁₃	1	1	yes	characteristic
498	#339	C₂²×C₁₃	1	1	yes	characteristic
499	C₂²×C₁₃	—	2	1	no	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	1	no	—
503	C₂²×C₁₃	—	2	1	no	—
504	C₂²×C₁₃	—	2	1	no	—
505	C₂²×C₁₃	—	2	1	no	—
506	C₂²×C₁₃	—	2	1	no	—
507	C₂²×C₁₃	—	4	4	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	2	no	—
511	C₂²×C₁₃	—	4	2	no	—
512	C₂²×C₁₃	—	4	1	no	—
513	C₂²×C₁₃	—	4	1	no	—
514	C₂²×C₁₃	—	4	2	no	—
515	C₂²×C₁₃	—	8	1	no	—
516	C₂²×C₁₃	—	8	1	no	—
517	C₂²×C₁₃	—	8	2	no	—
518	C₂²×C₁₃	—	8	2	no	—
519	C₂²×C₁₃	—	8	2	no	—
520	C₂²×C₁₃	—	8	1	no	—
521	C₂²×C₁₃	—	8	1	no	—
522	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
523	C₂²×C₁₃	#546	1	1	yes	characteristic
524	C₂²×C₁₃	#546	1	1	yes	characteristic
525	C₄×C₁₃	—	2	1	no	—
526	C₄×C₁₃	—	2	1	no	—
527	C₄×C₁₃	—	4	2	no	—
528	C₄×C₁₃	—	4	2	no	—
529	C₄×C₁₃	—	4	1	no	—
530	C₄×C₁₃	—	4	1	no	—
531	C₄×C₁₃	—	4	1	no	—
532	C₄×C₁₃	—	4	1	no	—
533	C₄×C₁₃	—	4	1	no	—
534	C₄×C₁₃	—	4	1	no	—
535	C₄×C₁₃	—	4	2	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	8	1	no	—
538	C₄×C₁₃	#525	1	1	yes	characteristic
539	C₄×C₁₃	#535	1	1	yes	characteristic
540	C₄×C₁₃	#546	1	1	yes	characteristic
541	C₄×C₁₃	#546	1	1	yes	characteristic
542	C₂×#41	—	2	2	no	—
543	C₂×#41	—	2	2	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	1	no	—
546	C₂×#41	—	2	1	no	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	2	1	no	—
549	C₂×#41	—	4	1	no	—
550	C₂×#41	—	4	1	no	—
551	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	2	no	—
555	C₂²×D₄	D₄×C₁₃	1	2	yes	—
556	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
558	C₂³×C₄	—	2	1	no	—
559	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
560	#137	—	2	2	no	—
561	#137	—	4	1	no	—
562	AGL(1,ℤ/8)	—	2	2	no	—
563	AGL(1,ℤ/8)	—	4	1	no	—
564	C₂×Q₁₆	—	2	1	no	—
565	C₂×SD₁₆	—	2	1	no	—
566	C₂×SD₁₆	—	2	1	no	—
567	C₂×D₈	—	2	1	no	—
568	C₂×M₁₆	—	2	1	no	—
569	C₂×M₁₆	—	4	1	no	—
570	C₂×M₁₆	—	4	1	no	—
571	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
572	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
573	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
575	C₂²×C₈	—	2	1	no	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	—	2	1	no	—
578	#127	—	2	1	no	—
579	#127	—	2	2	no	—
580	#127	—	4	1	no	—
581	#126	—	2	2	no	—
582	#126	—	2	2	no	—
583	#125	—	2	1	no	—
584	#125	—	2	1	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#124	—	2	1	no	—
588	#124	—	2	2	no	—
589	#124	—	4	1	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	#123	—	2	2	no	—
594	#123	—	2	1	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
598	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic, complemented
599	#121	—	2	2	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	—	2	1	no	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	1	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	D₄×C₁₃	1	1	yes	characteristic, complemented
609	#121	D₄×C₁₃	1	1	yes	characteristic, complemented
610	#120	—	2	1	no	—
611	#120	—	2	2	no	—
612	C₄×Q₈	—	2	1	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	1	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	—	2	1	no	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	1	no	—
627	#117	D₄×C₁₃	1	1	yes	characteristic, complemented
628	#117	D₄×C₁₃	1	1	yes	characteristic, complemented
629	#117	C₂³×C₁₃	1	1	yes	characteristic
630	#117	C₂³×C₁₃	1	1	yes	characteristic
631	#117	C₂³×C₁₃	1	1	yes	characteristic
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic, complemented
634	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic, complemented
635	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	—	2	1	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
642	C₂×C₄²	—	2	1	no	—
643	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
645	#104	—	4	1	no	—
646	#104	—	4	1	no	—
647	#103	—	2	1	no	—
648	#103	—	2	1	no	—
649	#103	—	2	1	no	—
650	#103	—	2	1	no	—
651	#103	—	2	1	no	—
652	#103	—	2	1	no	—
653	#102	—	2	1	no	—
654	#102	—	2	1	no	—
655	#102	—	2	1	no	—
656	#102	—	2	1	no	—
657	#102	—	2	1	no	—
658	#102	—	2	1	no	—
659	#100	—	4	1	no	—
660	#100	—	4	1	no	—
661	C₂²⋊C₈	—	2	1	no	—
662	C₂²⋊C₈	—	2	1	no	—
663	#95	—	2	1	no	—
664	#95	—	2	2	no	—
665	C₂×C₁₃	—	2	1	no	—
666	C₂×C₁₃	—	2	1	no	—
667	C₂×C₁₃	—	4	1	no	—
668	C₂×C₁₃	—	4	1	no	—
669	C₂×C₁₃	—	8	1	no	—
670	C₂×C₁₃	—	8	2	no	—
671	C₂×C₁₃	—	8	2	no	—
672	C₂×C₁₃	#2404	1	1	yes	characteristic
673	C₂×C₁₃	#3018	1	1	yes	characteristic
674	C₂×C₁₃	#3019	1	1	yes	characteristic
675	C₂⁴	—	2	1	no	—
676	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
677	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
678	#41	—	2	4	no	—
679	#41	—	2	4	no	—
680	#41	—	2	1	no	—
681	#41	—	2	1	no	—
682	#41	—	2	1	no	—
683	#41	—	2	1	no	—
684	#41	—	4	2	no	—
685	#41	—	4	2	no	—
686	#41	—	4	2	no	—
687	#41	—	4	2	no	—
688	#41	—	4	2	no	—
689	#41	—	4	2	no	—
690	#41	—	8	4	no	—
691	C₂×Q₈	—	2	2	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	2	1	no	—
694	C₂×Q₈	—	2	1	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
698	C₂×Q₈	C₁₃×#41	1	2	yes	complemented
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	2	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	4	no	—
723	C₂×D₄	—	8	2	no	—
724	C₂×D₄	—	8	2	no	—
725	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
726	C₂×D₄	C₁₃×#41	1	2	yes	complemented
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	1	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	1	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	2	1	no	—
738	C₂²×C₄	—	2	1	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	1	no	—
743	C₂²×C₄	—	4	1	no	—
744	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
749	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
751	Q₁₆	—	4	2	no	—
752	SD₁₆	—	4	2	no	—
753	SD₁₆	—	4	2	no	—
754	D₈	—	4	2	no	—
755	M₁₆	—	2	1	no	—
756	M₁₆	—	2	1	no	—
757	M₁₆	—	2	1	no	—
758	M₁₆	—	2	1	no	—
759	M₁₆	—	2	1	no	—
760	M₁₆	—	2	1	no	—
761	M₁₆	—	2	1	no	—
762	M₁₆	—	2	1	no	—
763	M₁₆	—	4	2	no	—
764	C₂×C₈	—	2	1	no	—
765	C₂×C₈	—	2	1	no	—
766	C₂×C₈	—	2	1	no	—
767	C₂×C₈	—	2	1	no	—
768	C₂×C₈	—	4	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	1	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
784	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	1	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	—	4	4	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	8	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	1	no	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	1	no	—
811	C₄²	—	2	1	no	—
812	C₄²	—	2	1	no	—
813	C₄²	—	2	1	no	—
814	C₁₃	#23956	1	1	yes	characteristic, direct product factor, Sylow
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	1	no	—
824	C₂³	—	4	2	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	4	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	1	no	—
829	C₂³	—	4	1	no	—
830	C₂³	C₁₃×#120	1	1	yes	characteristic
831	C₂³	C₁₃×#120	1	1	yes	characteristic
832	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
833	Q₈	—	2	2	no	—
834	Q₈	—	2	1	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	1	no	—
837	Q₈	—	4	1	no	—
838	Q₈	—	4	1	no	—
839	Q₈	—	8	2	no	—
840	D₄	—	2	2	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	1	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	2	no	—
846	D₄	—	4	4	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	1	no	—
849	D₄	—	4	1	no	—
850	D₄	—	4	1	no	—
851	D₄	—	4	1	no	—
852	D₄	—	4	1	no	—
853	D₄	—	4	1	no	—
854	D₄	—	4	1	no	—
855	D₄	—	4	1	no	—
856	D₄	—	8	2	no	—
857	D₄	—	8	1	no	—
858	D₄	—	8	2	no	—
859	D₄	—	8	2	no	—
860	D₄	—	8	8	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	1	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	1	no	—
886	C₂×C₄	—	4	1	no	—
887	C₂×C₄	—	4	1	no	—
888	C₂×C₄	—	4	1	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	1	no	—
893	C₂×C₄	—	4	1	no	—
894	C₂×C₄	—	8	1	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
899	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
903	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
904	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
905	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₈	—	4	1	no	—
907	C₈	—	4	1	no	—
908	C₈	—	4	1	no	—
909	C₈	—	4	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	4	4	no	—
919	C₂²	—	4	2	no	—
920	C₂²	—	4	1	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	2	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	8	1	no	—
927	C₂²	—	8	1	no	—
928	C₂²	—	8	2	no	—
929	C₂²	—	8	2	no	—
930	C₂²	—	8	2	no	—
931	C₂²	—	8	1	no	—
932	C₂²	—	8	1	no	—
933	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
934	C₂²	C₁₃×#546	1	1	yes	characteristic
935	C₂²	C₁₃×#546	1	1	yes	characteristic
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	2	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	1	no	—
948	C₄	—	8	1	no	—
949	C₄	C₁₃×#525	1	1	yes	characteristic
950	C₄	C₁₃×#535	1	1	yes	characteristic
951	C₄	C₁₃×#546	1	1	yes	characteristic
952	C₄	C₁₃×#546	1	1	yes	characteristic
953	C₂	—	2	1	no	—
954	C₂	—	2	1	no	—
955	C₂	—	4	1	no	—
956	C₂	—	4	1	no	—
957	C₂	—	8	2	no	—
958	C₂	—	8	2	no	—
959	C₂	—	8	1	no	—
960	C₂	C₁₃×#2404	1	1	yes	characteristic
961	C₂	C₁₃×#3018	1	1	yes	characteristic
962	C₂	C₁₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
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
1. C₁₃×#3494	C₂	semidirect
2. C₁₃×#3005	C₂	semidirect
3. C₁₃×#2896	C₂	semidirect
4. C₁₃×#2431	C₂	semidirect
5. C₁₃×#2028	C₂	semidirect
6. C₁₃×#2027	C₂	semidirect
7. C₁₃×#2004	C₂	semidirect
8. C₁₃×#2002	C₂	semidirect
9. C₁₃×#1900	C₂	semidirect
10. C₁₃×#1887	C₂	semidirect
11. C₁₃×#1885	C₂	semidirect
12. C₁₃×#1883	C₂	semidirect
13. C₁₃×#1882	C₂	semidirect
14. C₁₃×#1871	C₂	semidirect
15. C₁₃×#1826	C₂	semidirect
126. C₁₃×C₂²⋊Q₈	D₄	semidirect
127. C₁₃×C₂²⋊Q₈	D₄	semidirect
137. C₁₃×#121	D₄	semidirect
138. C₁₃×#121	D₄	semidirect
156. C₁₃×#117	D₄	semidirect
157. C₁₃×#117	D₄	semidirect
162. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
163. C₂×C₁₃×C₄⋊C₄	D₄	semidirect
194. #23956	C₁₃	direct (N × H)
218. C₂×Q₈×C₁₃	#41	semidirect
246. C₂×D₄×C₁₃	#41	semidirect
334. #3494	C₂×C₁₃	semidirect
335. #3005	C₂×C₁₃	semidirect
336. #2896	C₂×C₁₃	semidirect
337. #2431	C₂×C₁₃	semidirect
338. #2028	C₂×C₁₃	semidirect
339. #2027	C₂×C₁₃	semidirect
340. #2004	C₂×C₁₃	semidirect
341. #2002	C₂×C₁₃	semidirect
342. #1900	C₂×C₁₃	semidirect
343. #1887	C₂×C₁₃	semidirect
344. #1885	C₂×C₁₃	semidirect
345. #1883	C₂×C₁₃	semidirect
346. #1882	C₂×C₁₃	semidirect
347. #1871	C₂×C₁₃	semidirect
348. #1826	C₂×C₁₃	semidirect
597. C₂²⋊Q₈	D₄×C₁₃	semidirect
598. C₂²⋊Q₈	D₄×C₁₃	semidirect
608. #121	D₄×C₁₃	semidirect
609. #121	D₄×C₁₃	semidirect
627. #117	D₄×C₁₃	semidirect
628. #117	D₄×C₁₃	semidirect
633. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
634. C₂×C₄⋊C₄	D₄×C₁₃	semidirect
698. C₂×Q₈	C₁₃×#41	semidirect
726. C₂×D₄	C₁₃×#41	semidirect
814. C₁₃	#23956	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×#3005	2
C₁₃×#2896	2
C₁₃×#2431	2
C₁₃×#2028	2
C₁₃×#2027	2
C₁₃×#2004	2
C₁₃×#2002	2
C₁₃×#1900	2
C₁₃×#1887	2
C₁₃×#1885	2
C₁₃×#1883	2
C₁₃×#1882	2
C₁₃×#1871	2
C₁₃×#1826	2
#23956	13

Subgroups — C13×#23956 #15710295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23956 #15710295