Subgroups — C₁₃×#24031 #15710370

Order 3328.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3488	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3093	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2500	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×#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×#1792	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1792	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1789	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#550	—	2	1	no	—
20	C₁₃×#548	—	2	1	no	—
21	C₁₃×#546	—	2	1	no	—
22	C₁₃×#546	—	2	2	no	—
23	D₄²×C₁₃	—	2	2	no	—
24	D₄²×C₁₃	—	2	1	no	—
25	C₁₃×#537	—	2	1	no	—
26	C₁₃×#537	C₂²	1	1	yes	characteristic
27	C₁₃×#535	—	2	1	no	—
28	C₁₃×#535	C₂²	1	1	yes	characteristic
29	C₁₃×#525	—	2	1	no	—
30	C₁₃×#525	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#121	—	2	1	no	—
32	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
33	C₁₃×#520	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#419	—	2	1	no	—
48	C₁₃×#418	—	2	1	no	—
49	C₁₃×#417	C₂²	1	1	yes	characteristic
50	C₁₃×#417	C₂²	1	1	yes	characteristic
51	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#416	—	2	1	no	—
56	C₁₃×#416	—	2	1	no	—
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#394	—	2	2	no	—
61	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
62	C₁₃×#390	C₂²	1	1	yes	characteristic, complemented
63	C₁₃×#388	—	2	2	no	—
64	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#382	C₂²	1	1	yes	characteristic, complemented
66	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
68	C₁₃×#343	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#339	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×H(5,𝔽₂)	—	2	2	no	—
72	C₁₃×H(5,𝔽₂)	—	2	2	no	—
73	C₁₃×H(5,𝔽₂)	—	4	1	no	—
74	C₁₃×H(5,𝔽₂)	—	4	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	—	2	1	no	—
79	C₂×C₁₃×#41	—	2	2	no	—
80	C₂×C₁₃×#41	—	2	2	no	—
81	C₂×C₁₃×#41	—	4	1	no	—
82	C₂×C₁₃×#41	—	4	1	no	—
83	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
84	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
85	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
88	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₁₃	—	2	1	no	—
90	C₂²×D₄×C₁₃	—	2	2	no	—
91	C₂²×D₄×C₁₃	—	2	2	no	—
92	C₂²×D₄×C₁₃	—	2	1	no	—
93	C₂²×D₄×C₁₃	—	2	1	no	—
94	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
95	C₂²×D₄×C₁₃	D₄	1	2	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₁₃	—	2	1	no	—
98	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×M₁₆	—	2	1	no	—
100	C₂×C₁₃×M₁₆	—	4	1	no	—
101	C₂×C₁₃×M₁₆	—	4	1	no	—
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₁₃	—	2	1	no	—
107	C₁₃×#127	—	2	2	no	—
108	C₁₃×#127	—	2	1	no	—
109	C₁₃×#124	—	2	2	no	—
110	C₁₃×#124	—	2	1	no	—
111	C₁₃×#123	—	2	2	no	—
112	C₁₃×#123	—	2	1	no	—
113	C₁₃×C₂²⋊Q₈	—	2	2	no	—
114	C₁₃×C₂²⋊Q₈	—	2	1	no	—
115	C₁₃×C₂²⋊Q₈	—	2	1	no	—
116	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
117	C₁₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₁₃×#121	—	2	2	no	—
119	C₁₃×#121	—	2	2	no	—
120	C₁₃×#121	—	2	2	no	—
121	C₁₃×#121	—	2	2	no	—
122	C₁₃×#121	—	2	2	no	—
123	C₁₃×#121	—	2	1	no	—
124	C₁₃×#121	—	2	1	no	—
125	C₁₃×#121	—	2	1	no	—
126	C₁₃×#121	—	2	1	no	—
127	C₁₃×#121	—	2	1	no	—
128	C₁₃×#121	—	2	1	no	—
129	C₁₃×#121	—	2	2	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	1	no	—
132	C₁₃×#121	D₄	1	1	yes	characteristic
133	C₁₃×#121	D₄	1	1	yes	characteristic
134	C₁₃×#120	—	2	2	no	—
135	C₁₃×#120	—	2	2	no	—
136	C₁₃×#120	—	2	2	no	—
137	C₁₃×#120	—	2	1	no	—
138	C₁₃×#120	—	2	2	no	—
139	C₄×Q₈×C₁₃	—	2	1	no	—
140	C₄×D₄×C₁₃	—	2	2	no	—
141	C₄×D₄×C₁₃	—	2	2	no	—
142	C₄×D₄×C₁₃	—	2	1	no	—
143	C₄×D₄×C₁₃	—	2	2	no	—
144	C₄×D₄×C₁₃	—	2	1	no	—
145	C₄×D₄×C₁₃	—	2	1	no	—
146	C₁₃×#117	—	2	1	no	—
147	C₁₃×#117	—	2	1	no	—
148	C₁₃×#117	—	2	1	no	—
149	C₁₃×#117	—	2	1	no	—
150	C₁₃×#117	—	2	1	no	—
151	C₁₃×#117	C₂³	1	1	yes	characteristic
152	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
162	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
163	C₂×C₄²×C₁₃	—	2	1	no	—
164	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
166	C₁₃×#107	—	2	1	no	—
167	C₁₃×#107	—	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×#104	—	4	1	no	—
173	C₁₃×#104	—	4	1	no	—
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	#24031	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂⁴×C₁₃	—	2	2	no	—
196	C₂⁴×C₁₃	—	2	1	no	—
197	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
198	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₁₃×#41	—	2	1	no	—
200	C₁₃×#41	—	2	1	no	—
201	C₁₃×#41	—	2	2	no	—
202	C₁₃×#41	—	2	2	no	—
203	C₁₃×#41	—	2	1	no	—
204	C₁₃×#41	—	2	1	no	—
205	C₁₃×#41	—	2	1	no	—
206	C₁₃×#41	—	2	1	no	—
207	C₁₃×#41	—	2	1	no	—
208	C₁₃×#41	—	2	1	no	—
209	C₁₃×#41	—	2	1	no	—
210	C₁₃×#41	—	2	1	no	—
211	C₁₃×#41	—	4	2	no	—
212	C₁₃×#41	—	4	2	no	—
213	C₁₃×#41	—	4	1	no	—
214	C₁₃×#41	—	4	1	no	—
215	C₁₃×#41	—	4	2	no	—
216	C₁₃×#41	—	4	2	no	—
217	C₁₃×#41	—	4	2	no	—
218	C₁₃×#41	—	4	2	no	—
219	C₁₃×#41	—	4	2	no	—
220	C₁₃×#41	—	4	2	no	—
221	C₁₃×#41	#41	1	2	yes	—
222	C₁₃×#41	#41	1	2	yes	—
223	C₂×Q₈×C₁₃	—	2	1	no	—
224	C₂×Q₈×C₁₃	—	2	2	no	—
225	C₂×Q₈×C₁₃	—	4	1	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
229	C₂×D₄×C₁₃	—	2	1	no	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	2	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	—	2	1	no	—
238	C₂×D₄×C₁₃	—	2	1	no	—
239	C₂×D₄×C₁₃	—	2	2	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	2	no	—
242	C₂×D₄×C₁₃	—	2	1	no	—
243	C₂×D₄×C₁₃	—	2	2	no	—
244	C₂×D₄×C₁₃	—	2	1	no	—
245	C₂×D₄×C₁₃	—	2	1	no	—
246	C₂×D₄×C₁₃	—	2	1	no	—
247	C₂×D₄×C₁₃	—	2	1	no	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	1	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	1	no	—
252	C₂×D₄×C₁₃	—	4	2	no	—
253	C₂×D₄×C₁₃	—	4	2	no	—
254	C₂×D₄×C₁₃	—	4	2	no	—
255	C₂×D₄×C₁₃	—	4	2	no	—
256	C₂×D₄×C₁₃	—	4	4	no	—
257	C₂×D₄×C₁₃	—	4	4	no	—
258	C₂×D₄×C₁₃	—	4	2	no	—
259	C₂×D₄×C₁₃	—	4	2	no	—
260	C₂×D₄×C₁₃	—	8	2	no	—
261	C₂×D₄×C₁₃	—	8	4	no	—
262	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
264	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₁₃	—	2	1	no	—
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	1	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	1	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	2	no	—
274	C₂²×C₄×C₁₃	—	2	1	no	—
275	C₂²×C₄×C₁₃	—	2	1	no	—
276	C₂²×C₄×C₁₃	—	2	1	no	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	1	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	—	4	2	no	—
283	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₁₃×M₁₆	—	2	1	no	—
291	C₁₃×M₁₆	—	2	1	no	—
292	C₁₃×M₁₆	—	2	1	no	—
293	C₁₃×M₁₆	—	2	1	no	—
294	C₁₃×M₁₆	—	2	1	no	—
295	C₁₃×M₁₆	—	2	1	no	—
296	C₁₃×M₁₆	—	2	1	no	—
297	C₁₃×M₁₆	—	2	1	no	—
298	C₁₃×M₁₆	—	4	2	no	—
299	C₂×C₈×C₁₃	—	2	1	no	—
300	C₂×C₈×C₁₃	—	2	1	no	—
301	C₂×C₈×C₁₃	—	2	1	no	—
302	C₂×C₈×C₁₃	—	2	1	no	—
303	C₂×C₈×C₁₃	—	4	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	2	no	—
306	C₁₃×C₄⋊C₄	—	2	1	no	—
307	C₁₃×C₄⋊C₄	—	2	1	no	—
308	C₁₃×C₄⋊C₄	—	2	1	no	—
309	C₁₃×C₄⋊C₄	—	2	1	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	1	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	8	2	no	—
315	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	1	no	—
329	C₁₃×C₂²⋊C₄	—	4	2	no	—
330	C₁₃×C₂²⋊C₄	—	4	4	no	—
331	C₁₃×C₂²⋊C₄	—	4	1	no	—
332	C₁₃×C₂²⋊C₄	—	4	1	no	—
333	C₁₃×C₂²⋊C₄	—	8	2	no	—
334	C₄²×C₁₃	—	2	2	no	—
335	C₄²×C₁₃	—	2	1	no	—
336	C₄²×C₁₃	—	2	1	no	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	1	no	—
340	C₄²×C₁₃	—	4	1	no	—
341	C₄²×C₁₃	—	4	1	no	—
342	#3488	C₂×C₁₃	1	1	yes	characteristic
343	#3093	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#2896	C₂×C₁₃	1	1	yes	characteristic, complemented
345	#2500	C₂×C₁₃	1	1	yes	characteristic, complemented
346	#2040	C₂×C₁₃	1	1	yes	characteristic, complemented
347	#2039	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#2037	C₂×C₁₃	1	1	yes	characteristic, complemented
350	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
351	#1871	C₂×C₁₃	1	1	yes	characteristic, complemented
352	#1860	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
354	#1792	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#1792	C₂×C₁₃	1	1	yes	characteristic, complemented
356	#1789	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂³×C₁₃	—	2	1	no	—
358	C₂³×C₁₃	—	2	1	no	—
359	C₂³×C₁₃	—	2	1	no	—
360	C₂³×C₁₃	—	2	2	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	2	1	no	—
363	C₂³×C₁₃	—	2	2	no	—
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	4	1	no	—
366	C₂³×C₁₃	—	4	1	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	4	2	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	4	2	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	8	1	no	—
373	C₂³×C₁₃	—	8	2	no	—
374	C₂³×C₁₃	—	8	2	no	—
375	C₂³×C₁₃	#120	1	1	yes	characteristic
376	C₂³×C₁₃	#120	1	1	yes	characteristic
377	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
378	Q₈×C₁₃	—	2	1	no	—
379	Q₈×C₁₃	—	2	1	no	—
380	Q₈×C₁₃	—	2	1	no	—
381	Q₈×C₁₃	—	2	1	no	—
382	Q₈×C₁₃	—	2	1	no	—
383	Q₈×C₁₃	—	4	2	no	—
384	Q₈×C₁₃	#123	1	2	yes	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	1	no	—
388	D₄×C₁₃	—	2	1	no	—
389	D₄×C₁₃	—	2	1	no	—
390	D₄×C₁₃	—	2	1	no	—
391	D₄×C₁₃	—	2	1	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	4	2	no	—
394	D₄×C₁₃	—	4	4	no	—
395	D₄×C₁₃	—	4	2	no	—
396	D₄×C₁₃	—	4	4	no	—
397	D₄×C₁₃	—	4	4	no	—
398	D₄×C₁₃	—	4	2	no	—
399	D₄×C₁₃	—	4	1	no	—
400	D₄×C₁₃	—	4	1	no	—
401	D₄×C₁₃	—	4	1	no	—
402	D₄×C₁₃	—	4	1	no	—
403	D₄×C₁₃	—	4	1	no	—
404	D₄×C₁₃	—	4	1	no	—
405	D₄×C₁₃	—	4	1	no	—
406	D₄×C₁₃	—	4	1	no	—
407	D₄×C₁₃	—	8	1	no	—
408	D₄×C₁₃	—	8	2	no	—
409	D₄×C₁₃	—	8	2	no	—
410	D₄×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	8	2	no	—
412	D₄×C₁₃	#123	1	2	yes	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	1	no	—
415	C₂×C₄×C₁₃	—	2	1	no	—
416	C₂×C₄×C₁₃	—	2	1	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	1	no	—
421	C₂×C₄×C₁₃	—	2	1	no	—
422	C₂×C₄×C₁₃	—	2	1	no	—
423	C₂×C₄×C₁₃	—	2	1	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	2	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	1	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	2	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	4	1	no	—
437	C₂×C₄×C₁₃	—	4	1	no	—
438	C₂×C₄×C₁₃	—	4	1	no	—
439	C₂×C₄×C₁₃	—	4	1	no	—
440	C₂×C₄×C₁₃	—	4	1	no	—
441	C₂×C₄×C₁₃	—	4	1	no	—
442	C₂×C₄×C₁₃	—	4	2	no	—
443	C₂×C₄×C₁₃	—	4	1	no	—
444	C₂×C₄×C₁₃	—	4	2	no	—
445	C₂×C₄×C₁₃	—	4	1	no	—
446	C₂×C₄×C₁₃	—	4	2	no	—
447	C₂×C₄×C₁₃	—	4	1	no	—
448	C₂×C₄×C₁₃	—	4	1	no	—
449	C₂×C₄×C₁₃	—	4	1	no	—
450	C₂×C₄×C₁₃	—	8	2	no	—
451	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
452	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
457	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
459	C₈×C₁₃	—	4	1	no	—
460	C₈×C₁₃	—	4	1	no	—
461	C₈×C₁₃	—	4	1	no	—
462	C₈×C₁₃	—	4	1	no	—
463	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	1	yes	characteristic
464	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
465	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
466	#550	—	2	1	no	—
467	#548	—	2	1	no	—
468	#546	—	2	1	no	—
469	#546	—	2	2	no	—
470	D₄²	—	2	2	no	—
471	D₄²	—	2	1	no	—
472	#537	—	2	1	no	—
473	#537	C₂²×C₁₃	1	1	yes	characteristic
474	#535	—	2	1	no	—
475	#535	C₂²×C₁₃	1	1	yes	characteristic
476	#525	—	2	1	no	—
477	#525	C₂²×C₁₃	1	1	yes	characteristic
478	C₂×#121	—	2	1	no	—
479	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
480	#520	C₂²×C₁₃	1	1	yes	characteristic
481	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
482	#485	—	2	1	no	—
483	#485	—	2	1	no	—
484	#482	—	2	1	no	—
485	#482	—	2	1	no	—
486	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
489	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
491	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#419	—	2	1	no	—
495	#418	—	2	1	no	—
496	#417	C₂²×C₁₃	1	1	yes	characteristic
497	#417	C₂²×C₁₃	1	1	yes	characteristic
498	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#416	—	2	1	no	—
503	#416	—	2	1	no	—
504	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic, complemented
506	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
507	#394	—	2	2	no	—
508	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#390	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#388	—	2	2	no	—
511	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
512	#382	C₂²×C₁₃	1	1	yes	characteristic, complemented
513	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
514	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#343	C₂²×C₁₃	1	1	yes	characteristic, complemented
516	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#339	C₂²×C₁₃	1	1	yes	characteristic, complemented
518	C₂²×C₁₃	—	2	1	no	—
519	C₂²×C₁₃	—	2	1	no	—
520	C₂²×C₁₃	—	2	1	no	—
521	C₂²×C₁₃	—	2	1	no	—
522	C₂²×C₁₃	—	2	2	no	—
523	C₂²×C₁₃	—	2	1	no	—
524	C₂²×C₁₃	—	2	1	no	—
525	C₂²×C₁₃	—	2	1	no	—
526	C₂²×C₁₃	—	2	1	no	—
527	C₂²×C₁₃	—	4	1	no	—
528	C₂²×C₁₃	—	4	1	no	—
529	C₂²×C₁₃	—	4	1	no	—
530	C₂²×C₁₃	—	4	1	no	—
531	C₂²×C₁₃	—	4	2	no	—
532	C₂²×C₁₃	—	4	1	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	1	no	—
535	C₂²×C₁₃	—	4	2	no	—
536	C₂²×C₁₃	—	4	1	no	—
537	C₂²×C₁₃	—	4	1	no	—
538	C₂²×C₁₃	—	8	1	no	—
539	C₂²×C₁₃	—	8	1	no	—
540	C₂²×C₁₃	—	8	2	no	—
541	C₂²×C₁₃	—	8	2	no	—
542	C₂²×C₁₃	—	8	4	no	—
543	C₂²×C₁₃	—	16	4	no	—
544	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
545	C₂²×C₁₃	#546	1	1	yes	characteristic
546	C₂²×C₁₃	#546	1	1	yes	characteristic
547	C₄×C₁₃	—	2	1	no	—
548	C₄×C₁₃	—	2	1	no	—
549	C₄×C₁₃	—	2	2	no	—
550	C₄×C₁₃	—	4	2	no	—
551	C₄×C₁₃	—	4	1	no	—
552	C₄×C₁₃	—	4	1	no	—
553	C₄×C₁₃	—	4	1	no	—
554	C₄×C₁₃	—	4	2	no	—
555	C₄×C₁₃	—	4	1	no	—
556	C₄×C₁₃	—	8	1	no	—
557	C₄×C₁₃	—	8	1	no	—
558	C₄×C₁₃	—	8	1	no	—
559	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
560	C₄×C₁₃	#534	1	1	yes	characteristic
561	C₄×C₁₃	#546	1	1	yes	characteristic
562	C₄×C₁₃	#546	1	1	yes	characteristic
563	H(5,𝔽₂)	—	2	2	no	—
564	H(5,𝔽₂)	—	2	2	no	—
565	H(5,𝔽₂)	—	4	1	no	—
566	H(5,𝔽₂)	—	4	1	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	—	2	1	no	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	1	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	4	1	no	—
574	C₂×#41	—	4	1	no	—
575	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
576	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
577	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
579	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
580	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
587	C₂²×D₄	D₄×C₁₃	1	2	yes	—
588	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
589	C₂³×C₄	—	2	1	no	—
590	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
591	C₂×M₁₆	—	2	1	no	—
592	C₂×M₁₆	—	4	1	no	—
593	C₂×M₁₆	—	4	1	no	—
594	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
596	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
597	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
598	C₂²×C₈	—	2	1	no	—
599	#127	—	2	2	no	—
600	#127	—	2	1	no	—
601	#124	—	2	2	no	—
602	#124	—	2	1	no	—
603	#123	—	2	2	no	—
604	#123	—	2	1	no	—
605	C₂²⋊Q₈	—	2	2	no	—
606	C₂²⋊Q₈	—	2	1	no	—
607	C₂²⋊Q₈	—	2	1	no	—
608	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
609	C₂²⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
610	#121	—	2	2	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	—	2	1	no	—
616	#121	—	2	1	no	—
617	#121	—	2	1	no	—
618	#121	—	2	1	no	—
619	#121	—	2	1	no	—
620	#121	—	2	1	no	—
621	#121	—	2	2	no	—
622	#121	—	2	1	no	—
623	#121	—	2	1	no	—
624	#121	D₄×C₁₃	1	1	yes	characteristic
625	#121	D₄×C₁₃	1	1	yes	characteristic
626	#120	—	2	2	no	—
627	#120	—	2	2	no	—
628	#120	—	2	2	no	—
629	#120	—	2	1	no	—
630	#120	—	2	2	no	—
631	C₄×Q₈	—	2	1	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	1	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	1	no	—
637	C₄×D₄	—	2	1	no	—
638	#117	—	2	1	no	—
639	#117	—	2	1	no	—
640	#117	—	2	1	no	—
641	#117	—	2	1	no	—
642	#117	—	2	1	no	—
643	#117	C₂³×C₁₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	2	no	—
646	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	—	2	2	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	2	no	—
653	C₂×C₂²⋊C₄	—	2	2	no	—
654	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
655	C₂×C₄²	—	2	1	no	—
656	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	#107	—	2	1	no	—
659	#107	—	2	1	no	—
660	#106	—	2	1	no	—
661	#106	—	2	1	no	—
662	#104	—	2	2	no	—
663	#104	—	2	2	no	—
664	#104	—	4	1	no	—
665	#104	—	4	1	no	—
666	#104	—	4	1	no	—
667	#104	—	4	1	no	—
668	#103	—	2	1	no	—
669	#103	—	2	1	no	—
670	#103	—	2	1	no	—
671	#103	—	2	1	no	—
672	#103	—	2	1	no	—
673	#103	—	2	1	no	—
674	#102	—	2	1	no	—
675	#102	—	2	1	no	—
676	#102	—	2	1	no	—
677	#102	—	2	1	no	—
678	#102	—	2	1	no	—
679	#102	—	2	1	no	—
680	#100	—	4	1	no	—
681	#100	—	4	1	no	—
682	C₂²⋊C₈	—	2	1	no	—
683	C₂²⋊C₈	—	2	1	no	—
684	#95	—	2	1	no	—
685	#95	—	2	2	no	—
686	C₂×C₁₃	—	2	1	no	—
687	C₂×C₁₃	—	2	1	no	—
688	C₂×C₁₃	—	4	1	no	—
689	C₂×C₁₃	—	4	1	no	—
690	C₂×C₁₃	—	4	2	no	—
691	C₂×C₁₃	—	8	1	no	—
692	C₂×C₁₃	—	8	2	no	—
693	C₂×C₁₃	—	8	1	no	—
694	C₂×C₁₃	#2405	1	1	yes	characteristic
695	C₂×C₁₃	#3018	1	1	yes	characteristic
696	C₂×C₁₃	#3019	1	1	yes	characteristic
697	C₂⁴	—	2	2	no	—
698	C₂⁴	—	2	1	no	—
699	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
700	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
701	#41	—	2	1	no	—
702	#41	—	2	1	no	—
703	#41	—	2	2	no	—
704	#41	—	2	2	no	—
705	#41	—	2	1	no	—
706	#41	—	2	1	no	—
707	#41	—	2	1	no	—
708	#41	—	2	1	no	—
709	#41	—	2	1	no	—
710	#41	—	2	1	no	—
711	#41	—	2	1	no	—
712	#41	—	2	1	no	—
713	#41	—	4	2	no	—
714	#41	—	4	2	no	—
715	#41	—	4	1	no	—
716	#41	—	4	1	no	—
717	#41	—	4	2	no	—
718	#41	—	4	2	no	—
719	#41	—	4	2	no	—
720	#41	—	4	2	no	—
721	#41	—	4	2	no	—
722	#41	—	4	2	no	—
723	#41	C₁₃×#41	1	2	yes	—
724	#41	C₁₃×#41	1	2	yes	—
725	C₂×Q₈	—	2	1	no	—
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	4	1	no	—
728	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
729	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
730	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
731	C₂×D₄	—	2	1	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	1	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	1	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	1	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	4	1	no	—
754	C₂×D₄	—	4	2	no	—
755	C₂×D₄	—	4	2	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	2	no	—
758	C₂×D₄	—	4	4	no	—
759	C₂×D₄	—	4	4	no	—
760	C₂×D₄	—	4	2	no	—
761	C₂×D₄	—	4	2	no	—
762	C₂×D₄	—	8	2	no	—
763	C₂×D₄	—	8	4	no	—
764	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
765	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	1	no	—
770	C₂²×C₄	—	2	1	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	1	no	—
777	C₂²×C₄	—	2	1	no	—
778	C₂²×C₄	—	2	1	no	—
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	1	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
792	M₁₆	—	2	1	no	—
793	M₁₆	—	2	1	no	—
794	M₁₆	—	2	1	no	—
795	M₁₆	—	2	1	no	—
796	M₁₆	—	2	1	no	—
797	M₁₆	—	2	1	no	—
798	M₁₆	—	2	1	no	—
799	M₁₆	—	2	1	no	—
800	M₁₆	—	4	2	no	—
801	C₂×C₈	—	2	1	no	—
802	C₂×C₈	—	2	1	no	—
803	C₂×C₈	—	2	1	no	—
804	C₂×C₈	—	2	1	no	—
805	C₂×C₈	—	4	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	1	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	1	no	—
813	C₄⋊C₄	—	2	1	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	8	2	no	—
817	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
818	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	1	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	1	no	—
827	C₂²⋊C₄	—	2	1	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	4	no	—
833	C₂²⋊C₄	—	4	1	no	—
834	C₂²⋊C₄	—	4	1	no	—
835	C₂²⋊C₄	—	8	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	1	no	—
838	C₄²	—	2	1	no	—
839	C₄²	—	2	1	no	—
840	C₄²	—	2	1	no	—
841	C₄²	—	2	1	no	—
842	C₄²	—	4	1	no	—
843	C₄²	—	4	1	no	—
844	C₁₃	#24031	1	1	yes	characteristic, direct product factor, Sylow
845	C₂³	—	2	1	no	—
846	C₂³	—	2	1	no	—
847	C₂³	—	2	1	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	1	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	4	2	no	—
857	C₂³	—	4	4	no	—
858	C₂³	—	4	2	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	8	1	no	—
861	C₂³	—	8	2	no	—
862	C₂³	—	8	2	no	—
863	C₂³	C₁₃×#120	1	1	yes	characteristic
864	C₂³	C₁₃×#120	1	1	yes	characteristic
865	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
866	Q₈	—	2	1	no	—
867	Q₈	—	2	1	no	—
868	Q₈	—	2	1	no	—
869	Q₈	—	2	1	no	—
870	Q₈	—	2	1	no	—
871	Q₈	—	4	2	no	—
872	Q₈	C₁₃×#123	1	2	yes	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	1	no	—
876	D₄	—	2	1	no	—
877	D₄	—	2	1	no	—
878	D₄	—	2	1	no	—
879	D₄	—	2	1	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	4	no	—
883	D₄	—	4	2	no	—
884	D₄	—	4	4	no	—
885	D₄	—	4	4	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	4	1	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	1	no	—
892	D₄	—	4	1	no	—
893	D₄	—	4	1	no	—
894	D₄	—	4	1	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	1	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	C₁₃×#123	1	2	yes	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	4	2	no	—
921	C₂×C₄	—	4	2	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	1	no	—
925	C₂×C₄	—	4	1	no	—
926	C₂×C₄	—	4	1	no	—
927	C₂×C₄	—	4	1	no	—
928	C₂×C₄	—	4	1	no	—
929	C₂×C₄	—	4	1	no	—
930	C₂×C₄	—	4	2	no	—
931	C₂×C₄	—	4	1	no	—
932	C₂×C₄	—	4	2	no	—
933	C₂×C₄	—	4	1	no	—
934	C₂×C₄	—	4	2	no	—
935	C₂×C₄	—	4	1	no	—
936	C₂×C₄	—	4	1	no	—
937	C₂×C₄	—	4	1	no	—
938	C₂×C₄	—	8	2	no	—
939	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
940	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
941	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
942	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
943	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
944	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
945	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
946	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
947	C₈	—	4	1	no	—
948	C₈	—	4	1	no	—
949	C₈	—	4	1	no	—
950	C₈	—	4	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	1	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	1	no	—
968	C₂²	—	4	1	no	—
969	C₂²	—	4	1	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	8	1	no	—
972	C₂²	—	8	1	no	—
973	C₂²	—	8	2	no	—
974	C₂²	—	8	2	no	—
975	C₂²	—	8	4	no	—
976	C₂²	—	16	4	no	—
977	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
978	C₂²	C₁₃×#546	1	1	yes	characteristic
979	C₂²	C₁₃×#546	1	1	yes	characteristic
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	1	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	8	1	no	—
990	C₄	—	8	1	no	—
991	C₄	—	8	1	no	—
992	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
993	C₄	C₁₃×#534	1	1	yes	characteristic
994	C₄	C₁₃×#546	1	1	yes	characteristic
995	C₄	C₁₃×#546	1	1	yes	characteristic
996	C₂	—	2	1	no	—
997	C₂	—	2	1	no	—
998	C₂	—	4	1	no	—
999	C₂	—	4	1	no	—
1000	C₂	—	4	2	no	—
1001	C₂	—	8	1	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	1	no	—
1004	C₂	C₁₃×#2405	1	1	yes	characteristic
1005	C₂	C₁₃×#3018	1	1	yes	characteristic
1006	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×#3488	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×#2896	C₂	semidirect
4. C₁₃×#2500	C₂	semidirect
5. C₁₃×#2040	C₂	semidirect
6. C₁₃×#2039	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×#1792	C₂	semidirect
14. C₁₃×#1792	C₂	semidirect
15. C₁₃×#1789	C₂	semidirect
18. C₂²×C₁₃×M₁₆	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
39. C₁₃×#428	C₂²	semidirect
40. C₁₃×#428	C₂²	semidirect
43. C₂×C₁₃×#104	C₂²	semidirect
44. C₂×C₁₃×#104	C₂²	semidirect
45. C₂×C₁₃×#104	C₂²	semidirect
46. C₂×C₁₃×#104	C₂²	semidirect
51. C₁₃×#417	C₂²	semidirect
52. C₁₃×#417	C₂²	semidirect
53. C₁₃×#417	C₂²	semidirect
54. C₁₃×#417	C₂²	semidirect
57. C₂×C₁₃×#100	C₂²	semidirect
58. C₂×C₁₃×#100	C₂²	semidirect
59. C₁₃×#407	C₂²	semidirect
61. C₁₃×#390	C₂²	semidirect
62. C₁₃×#390	C₂²	semidirect
64. C₁₃×#384	C₂²	semidirect
65. C₁₃×#382	C₂²	semidirect
66. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
67. C₁₃×#343	C₂²	semidirect
68. C₁₃×#343	C₂²	semidirect
69. C₁₃×#339	C₂²	semidirect
70. C₁₃×#339	C₂²	semidirect
194. #24031	C₁₃	direct (N × H)
343. #3093	C₂×C₁₃	semidirect
344. #2896	C₂×C₁₃	semidirect
345. #2500	C₂×C₁₃	semidirect
346. #2040	C₂×C₁₃	semidirect
347. #2039	C₂×C₁₃	semidirect
348. #2037	C₂×C₁₃	semidirect
349. #2037	C₂×C₁₃	semidirect
350. #1900	C₂×C₁₃	semidirect
351. #1871	C₂×C₁₃	semidirect
352. #1860	C₂×C₁₃	semidirect
353. #1859	C₂×C₁₃	semidirect
354. #1792	C₂×C₁₃	semidirect
355. #1792	C₂×C₁₃	semidirect
356. #1789	C₂×C₁₃	semidirect
465. C₂²×M₁₆	C₂²×C₁₃	semidirect
481. C₂×#117	C₂²×C₁₃	semidirect
486. #428	C₂²×C₁₃	semidirect
487. #428	C₂²×C₁₃	semidirect
490. C₂×#104	C₂²×C₁₃	semidirect
491. C₂×#104	C₂²×C₁₃	semidirect
492. C₂×#104	C₂²×C₁₃	semidirect
493. C₂×#104	C₂²×C₁₃	semidirect
498. #417	C₂²×C₁₃	semidirect
499. #417	C₂²×C₁₃	semidirect
500. #417	C₂²×C₁₃	semidirect
501. #417	C₂²×C₁₃	semidirect
504. C₂×#100	C₂²×C₁₃	semidirect
505. C₂×#100	C₂²×C₁₃	semidirect
506. #407	C₂²×C₁₃	semidirect
508. #390	C₂²×C₁₃	semidirect
509. #390	C₂²×C₁₃	semidirect
511. #384	C₂²×C₁₃	semidirect
512. #382	C₂²×C₁₃	semidirect
513. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
514. #343	C₂²×C₁₃	semidirect
515. #343	C₂²×C₁₃	semidirect
516. #339	C₂²×C₁₃	semidirect
517. #339	C₂²×C₁₃	semidirect
844. C₁₃	#24031	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×#3488	2
C₁₃×#3093	2
C₁₃×#2896	2
C₁₃×#2500	2
C₁₃×#2040	2
C₁₃×#2039	2
C₁₃×#2037	2
C₁₃×#1900	2
C₁₃×#1871	2
C₁₃×#1860	2
C₁₃×#1859	2
C₁₃×#1792	2
C₁₃×#1789	2
#24031	13

Subgroups — C13×#24031 #15710370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24031 #15710370