Subgroups — C₁₃×#60771 #15747110

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 810 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	2	yes	maximal, complemented
2	C₁₃×#3204	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3199	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3198	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3197	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3194	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3192	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3096	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#550	—	2	2	no	—
24	C₁₃×#548	—	2	2	no	—
25	C₁₃×#546	—	2	4	no	—
26	C₁₃×#546	—	2	2	no	—
27	D₄²×C₁₃	—	2	4	no	—
28	D₄²×C₁₃	—	2	2	no	—
29	C₁₃×#537	C₂²	1	2	yes	—
30	C₁₃×#537	C₂²	1	4	yes	complemented
31	C₁₃×#535	C₂²	1	2	yes	—
32	C₁₃×#535	C₂²	1	4	yes	complemented
33	C₁₃×#525	C₂²	1	2	yes	complemented
34	C₁₃×#525	C₂²	1	4	yes	complemented
35	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
37	C₁₃×#520	C₂²	1	2	yes	complemented
38	C₁₃×#485	C₂²	1	4	yes	complemented
39	C₁₃×#483	C₂²	1	4	yes	complemented
40	C₁₃×#482	C₂²	1	4	yes	complemented
41	C₁₃×#482	C₂²	1	4	yes	complemented
42	C₁₃×#482	C₂²	1	4	yes	complemented
43	C₁₃×#481	C₂²	1	4	yes	complemented
44	C₁₃×#481	C₂²	1	4	yes	complemented
45	C₁₃×#480	C₂²	1	4	yes	complemented
46	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#470	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#469	C₂²	1	2	yes	complemented
49	C₁₃×#469	C₂²	1	2	yes	complemented
50	C₁₃×#469	C₂²	1	2	yes	complemented
51	C₁₃×#469	C₂²	1	2	yes	complemented
52	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#469	C₂²	1	1	yes	characteristic, complemented
54	C₁₃×#469	C₂²	1	4	yes	complemented
55	C₁₃×#468	C₂²	1	2	yes	complemented
56	C₁₃×#468	C₂²	1	2	yes	complemented
57	C₁₃×#468	C₂²	1	4	yes	complemented
58	C₁₃×#466	C₂²	1	4	yes	complemented
59	C₁₃×#465	C₂²	1	4	yes	complemented
60	C₁₃×#452	C₂²	1	4	yes	complemented
61	C₁₃×#450	C₂²	1	4	yes	complemented
62	C₁₃×#449	C₂²	1	4	yes	complemented
63	C₁₃×#449	C₂²	1	4	yes	complemented
64	C₁₃×#449	C₂²	1	4	yes	complemented
65	C₁₃×#447	C₂²	1	4	yes	complemented
66	C₁₃×#447	C₂²	1	4	yes	complemented
67	C₁₃×#447	C₂²	1	4	yes	complemented
68	C₁₃×#428	C₂²	1	2	yes	complemented
69	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#418	C₂²	1	2	yes	complemented
72	C₁₃×#417	C₂²	1	2	yes	complemented
73	C₁₃×#416	C₂²	1	2	yes	complemented
74	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
75	C₁₃×#408	C₂²	1	2	yes	complemented
76	C₁₃×#408	C₂²	1	2	yes	complemented
77	C₁₃×#408	C₂²	1	2	yes	complemented
78	C₁₃×#408	C₂²	1	2	yes	complemented
79	C₁₃×#407	C₂²	1	2	yes	complemented
80	C₁₃×#407	C₂²	1	2	yes	complemented
81	C₁₃×H(5,𝔽₂)	—	4	4	no	—
82	C₁₃×H(5,𝔽₂)	—	4	4	no	—
83	C₂×C₁₃×#41	—	2	2	no	—
84	C₂×C₁₃×#41	—	4	2	no	—
85	C₂×C₁₃×#41	—	4	2	no	—
86	C₂×C₁₃×#41	D₄	1	2	yes	—
87	C₂×C₁₃×#41	D₄	1	2	yes	—
88	C₂×C₁₃×#41	C₂³	1	2	yes	—
89	C₂×C₁₃×#41	C₂³	1	4	yes	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₁₃	—	2	2	no	—
94	C₂²×D₄×C₁₃	—	2	4	no	—
95	C₂²×D₄×C₁₃	—	2	4	no	—
96	C₂²×D₄×C₁₃	—	2	2	no	—
97	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
98	C₂²×D₄×C₁₃	D₄	1	2	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
101	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
103	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
104	C₁₃×#135	—	4	2	no	—
105	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×D₈	—	4	2	no	—
109	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₂×C₁₃×D₈	C₂³	1	2	yes	—
112	C₂×C₁₃×D₈	C₂³	1	2	yes	—
113	C₂×C₁₃×M₁₆	—	4	2	no	—
114	C₂×C₁₃×M₁₆	—	4	2	no	—
115	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
124	C₁₃×#127	—	2	2	no	—
125	C₁₃×#127	—	2	4	no	—
126	C₁₃×#124	—	2	2	no	—
127	C₁₃×#124	—	2	4	no	—
128	C₁₃×#123	—	2	2	no	—
129	C₁₃×#123	—	2	4	no	—
130	C₁₃×C₂²⋊Q₈	—	2	2	no	—
131	C₁₃×C₂²⋊Q₈	—	2	4	no	—
132	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#121	—	2	4	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	4	no	—
138	C₁₃×#121	—	2	4	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	2	no	—
141	C₁₃×#121	—	2	4	no	—
142	C₁₃×#121	—	2	2	no	—
143	C₁₃×#121	—	2	4	no	—
144	C₁₃×#121	C₂³	1	4	yes	—
145	C₁₃×#121	C₂³	1	4	yes	—
146	C₁₃×#121	C₂³	1	4	yes	—
147	C₁₃×#121	C₂³	1	4	yes	—
148	C₁₃×#121	C₂³	1	2	yes	—
149	C₁₃×#121	C₂³	1	2	yes	—
150	C₁₃×#121	C₂³	1	4	yes	—
151	C₁₃×#120	—	2	2	no	—
152	C₁₃×#120	—	2	4	no	—
153	C₁₃×#120	—	2	4	no	—
154	C₁₃×#120	—	2	4	no	—
155	C₁₃×#120	—	2	4	no	—
156	C₄×Q₈×C₁₃	—	2	2	no	—
157	C₄×D₄×C₁₃	—	2	4	no	—
158	C₄×D₄×C₁₃	—	2	2	no	—
159	C₄×D₄×C₁₃	—	2	2	no	—
160	C₄×D₄×C₁₃	—	2	4	no	—
161	C₄×D₄×C₁₃	—	2	2	no	—
162	C₄×D₄×C₁₃	—	2	4	no	—
163	C₁₃×#117	C₂³	1	2	yes	—
164	C₁₃×#117	C₂³	1	4	yes	—
165	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
167	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
169	C₁₃×#107	C₂³	1	2	yes	—
170	C₁₃×#107	C₂³	1	4	yes	—
171	C₁₃×#106	C₂³	1	2	yes	—
172	C₁₃×#106	C₂³	1	2	yes	—
173	C₁₃×#106	C₂³	1	1	yes	characteristic
174	C₁₃×#106	C₂³	1	1	yes	characteristic
175	C₁₃×#106	C₂³	1	4	yes	—
176	C₁₃×#103	C₂³	1	2	yes	—
177	C₁₃×#103	C₂³	1	2	yes	—
178	C₁₃×#103	C₂³	1	4	yes	—
179	C₁₃×#102	C₂³	1	4	yes	—
180	C₁₃×#102	C₂³	1	4	yes	—
181	C₁₃×#102	C₂³	1	2	yes	—
182	C₁₃×#102	C₂³	1	2	yes	—
183	C₁₃×#102	C₂³	1	4	yes	—
184	C₁₃×#102	C₂³	1	4	yes	—
185	C₁₃×#102	C₂³	1	4	yes	—
186	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
187	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
188	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
189	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
190	#60771	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂⁴×C₁₃	—	2	4	no	—
192	C₂⁴×C₁₃	—	2	2	no	—
193	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
195	C₁₃×#41	—	2	4	no	—
196	C₁₃×#41	—	2	4	no	—
197	C₁₃×#41	—	2	4	no	—
198	C₁₃×#41	—	2	4	no	—
199	C₁₃×#41	—	4	2	no	—
200	C₁₃×#41	—	4	2	no	—
201	C₁₃×#41	—	4	4	no	—
202	C₁₃×#41	—	4	4	no	—
203	C₁₃×#41	—	4	4	no	—
204	C₁₃×#41	—	4	4	no	—
205	C₁₃×#41	—	4	8	no	—
206	C₂×Q₈×C₁₃	—	4	2	no	—
207	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	4	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	2	no	—
216	C₂×D₄×C₁₃	—	2	4	no	—
217	C₂×D₄×C₁₃	—	2	4	no	—
218	C₂×D₄×C₁₃	—	2	4	no	—
219	C₂×D₄×C₁₃	—	2	4	no	—
220	C₂×D₄×C₁₃	—	2	2	no	—
221	C₂×D₄×C₁₃	—	2	4	no	—
222	C₂×D₄×C₁₃	—	2	4	no	—
223	C₂×D₄×C₁₃	—	4	2	no	—
224	C₂×D₄×C₁₃	—	4	4	no	—
225	C₂×D₄×C₁₃	—	4	4	no	—
226	C₂×D₄×C₁₃	—	4	4	no	—
227	C₂×D₄×C₁₃	—	4	16	no	—
228	C₂×D₄×C₁₃	—	4	8	no	—
229	C₂×D₄×C₁₃	—	8	4	no	—
230	C₂×D₄×C₁₃	—	8	8	no	—
231	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
232	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
233	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
235	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
236	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₁₃	—	2	2	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	2	4	no	—
240	C₂²×C₄×C₁₃	—	2	2	no	—
241	C₂²×C₄×C₁₃	—	2	4	no	—
242	C₂²×C₄×C₁₃	—	2	2	no	—
243	C₂²×C₄×C₁₃	—	4	2	no	—
244	C₂²×C₄×C₁₃	—	4	2	no	—
245	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
249	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₁₃×Q₁₆	—	4	1	no	—
255	C₁₃×SD₁₆	—	4	2	no	—
256	C₁₃×SD₁₆	—	4	4	no	—
257	C₁₃×D₈	—	4	2	no	—
258	C₁₃×D₈	—	4	2	no	—
259	C₁₃×D₈	—	4	1	no	—
260	C₁₃×D₈	—	4	4	no	—
261	C₁₃×M₁₆	—	2	4	no	—
262	C₁₃×M₁₆	—	4	1	no	—
263	C₁₃×M₁₆	—	4	1	no	—
264	C₁₃×M₁₆	—	4	1	no	—
265	C₁₃×M₁₆	—	4	1	no	—
266	C₁₃×M₁₆	—	4	2	no	—
267	C₂×C₈×C₁₃	—	2	2	no	—
268	C₂×C₈×C₁₃	—	2	2	no	—
269	C₂×C₈×C₁₃	—	4	2	no	—
270	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
273	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	—	2	2	no	—
277	C₁₃×C₄⋊C₄	—	2	2	no	—
278	C₁₃×C₄⋊C₄	—	2	4	no	—
279	C₁₃×C₄⋊C₄	—	2	2	no	—
280	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₂²⋊C₄	—	2	4	no	—
284	C₁₃×C₂²⋊C₄	—	2	2	no	—
285	C₁₃×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	4	no	—
287	C₁₃×C₂²⋊C₄	—	2	2	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	—	2	4	no	—
294	C₁₃×C₂²⋊C₄	—	2	2	no	—
295	C₄²×C₁₃	—	2	4	no	—
296	C₄²×C₁₃	—	2	2	no	—
297	#3488	C₂×C₁₃	1	2	yes	complemented
298	#3204	C₂×C₁₃	1	2	yes	complemented
299	#3199	C₂×C₁₃	1	2	yes	complemented
300	#3198	C₂×C₁₃	1	4	yes	complemented
301	#3197	C₂×C₁₃	1	2	yes	complemented
302	#3194	C₂×C₁₃	1	4	yes	complemented
303	#3192	C₂×C₁₃	1	2	yes	complemented
304	#3099	C₂×C₁₃	1	2	yes	complemented
305	#3096	C₂×C₁₃	1	2	yes	complemented
306	#3055	C₂×C₁₃	1	2	yes	complemented
307	#3054	C₂×C₁₃	1	1	yes	characteristic, complemented
308	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#3012	C₂×C₁₃	1	2	yes	complemented
310	#3008	C₂×C₁₃	1	2	yes	complemented
311	#2879	C₂×C₁₃	1	1	yes	characteristic, complemented
312	C₂³×C₁₃	—	2	2	no	—
313	C₂³×C₁₃	—	2	4	no	—
314	C₂³×C₁₃	—	2	2	no	—
315	C₂³×C₁₃	—	4	2	no	—
316	C₂³×C₁₃	—	4	2	no	—
317	C₂³×C₁₃	—	4	4	no	—
318	C₂³×C₁₃	—	4	8	no	—
319	C₂³×C₁₃	—	4	4	no	—
320	C₂³×C₁₃	—	8	2	no	—
321	C₂³×C₁₃	—	8	4	no	—
322	C₂³×C₁₃	—	8	2	no	—
323	C₂³×C₁₃	—	8	4	no	—
324	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
325	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
326	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
327	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₁₃	—	2	4	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	4	2	no	—
332	D₄×C₁₃	—	2	8	no	—
333	D₄×C₁₃	—	2	4	no	—
334	D₄×C₁₃	—	2	4	no	—
335	D₄×C₁₃	—	2	2	no	—
336	D₄×C₁₃	—	2	4	no	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	4	2	no	—
339	D₄×C₁₃	—	4	4	no	—
340	D₄×C₁₃	—	4	8	no	—
341	D₄×C₁₃	—	4	8	no	—
342	D₄×C₁₃	—	4	8	no	—
343	D₄×C₁₃	—	4	4	no	—
344	D₄×C₁₃	—	4	4	no	—
345	D₄×C₁₃	—	4	4	no	—
346	D₄×C₁₃	—	8	4	no	—
347	D₄×C₁₃	—	8	2	no	—
348	D₄×C₁₃	—	8	4	no	—
349	D₄×C₁₃	—	8	4	no	—
350	D₄×C₁₃	—	8	4	no	—
351	C₂×C₄×C₁₃	—	2	2	no	—
352	C₂×C₄×C₁₃	—	2	2	no	—
353	C₂×C₄×C₁₃	—	2	2	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	4	no	—
359	C₂×C₄×C₁₃	—	2	4	no	—
360	C₂×C₄×C₁₃	—	2	2	no	—
361	C₂×C₄×C₁₃	—	2	4	no	—
362	C₂×C₄×C₁₃	—	2	2	no	—
363	C₂×C₄×C₁₃	—	2	2	no	—
364	C₂×C₄×C₁₃	—	4	2	no	—
365	C₂×C₄×C₁₃	—	4	4	no	—
366	C₂×C₄×C₁₃	—	4	8	no	—
367	C₂×C₄×C₁₃	—	4	4	no	—
368	C₂×C₄×C₁₃	—	8	2	no	—
369	C₂×C₄×C₁₃	—	8	4	no	—
370	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
373	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
374	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
376	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
377	C₈×C₁₃	—	2	1	no	—
378	C₈×C₁₃	—	2	1	no	—
379	C₈×C₁₃	—	2	1	no	—
380	C₈×C₁₃	—	2	1	no	—
381	C₈×C₁₃	—	2	4	no	—
382	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
383	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
385	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
387	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
388	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
389	#550	—	2	2	no	—
390	#548	—	2	2	no	—
391	#546	—	2	4	no	—
392	#546	—	2	2	no	—
393	D₄²	—	2	4	no	—
394	D₄²	—	2	2	no	—
395	#537	C₂²×C₁₃	1	2	yes	—
396	#537	C₂²×C₁₃	1	4	yes	complemented
397	#535	C₂²×C₁₃	1	2	yes	—
398	#535	C₂²×C₁₃	1	4	yes	complemented
399	#525	C₂²×C₁₃	1	4	yes	complemented
400	#525	C₂²×C₁₃	1	2	yes	complemented
401	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
402	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
403	#520	C₂²×C₁₃	1	2	yes	complemented
404	#485	C₂²×C₁₃	1	4	yes	complemented
405	#483	C₂²×C₁₃	1	4	yes	complemented
406	#482	C₂²×C₁₃	1	4	yes	complemented
407	#482	C₂²×C₁₃	1	4	yes	complemented
408	#482	C₂²×C₁₃	1	4	yes	complemented
409	#481	C₂²×C₁₃	1	4	yes	complemented
410	#481	C₂²×C₁₃	1	4	yes	complemented
411	#480	C₂²×C₁₃	1	4	yes	complemented
412	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
413	#470	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	#469	C₂²×C₁₃	1	4	yes	complemented
416	#469	C₂²×C₁₃	1	2	yes	complemented
417	#469	C₂²×C₁₃	1	2	yes	complemented
418	#469	C₂²×C₁₃	1	2	yes	complemented
419	#469	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	#469	C₂²×C₁₃	1	2	yes	complemented
421	#468	C₂²×C₁₃	1	2	yes	complemented
422	#468	C₂²×C₁₃	1	4	yes	complemented
423	#468	C₂²×C₁₃	1	2	yes	complemented
424	#466	C₂²×C₁₃	1	4	yes	complemented
425	#465	C₂²×C₁₃	1	4	yes	complemented
426	#452	C₂²×C₁₃	1	4	yes	complemented
427	#450	C₂²×C₁₃	1	4	yes	complemented
428	#449	C₂²×C₁₃	1	4	yes	complemented
429	#449	C₂²×C₁₃	1	4	yes	complemented
430	#449	C₂²×C₁₃	1	4	yes	complemented
431	#447	C₂²×C₁₃	1	4	yes	complemented
432	#447	C₂²×C₁₃	1	4	yes	complemented
433	#447	C₂²×C₁₃	1	4	yes	complemented
434	#428	C₂²×C₁₃	1	2	yes	complemented
435	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#418	C₂²×C₁₃	1	2	yes	complemented
438	#417	C₂²×C₁₃	1	2	yes	complemented
439	#416	C₂²×C₁₃	1	2	yes	complemented
440	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
441	#408	C₂²×C₁₃	1	2	yes	complemented
442	#408	C₂²×C₁₃	1	2	yes	complemented
443	#408	C₂²×C₁₃	1	2	yes	complemented
444	#408	C₂²×C₁₃	1	2	yes	complemented
445	#407	C₂²×C₁₃	1	2	yes	complemented
446	#407	C₂²×C₁₃	1	2	yes	complemented
447	C₂²×C₁₃	—	2	2	no	—
448	C₂²×C₁₃	—	2	4	no	—
449	C₂²×C₁₃	—	2	2	no	—
450	C₂²×C₁₃	—	2	2	no	—
451	C₂²×C₁₃	—	2	4	no	—
452	C₂²×C₁₃	—	2	1	no	—
453	C₂²×C₁₃	—	2	1	no	—
454	C₂²×C₁₃	—	2	4	no	—
455	C₂²×C₁₃	—	4	4	no	—
456	C₂²×C₁₃	—	4	2	no	—
457	C₂²×C₁₃	—	4	4	no	—
458	C₂²×C₁₃	—	4	2	no	—
459	C₂²×C₁₃	—	4	4	no	—
460	C₂²×C₁₃	—	4	2	no	—
461	C₂²×C₁₃	—	8	2	no	—
462	C₂²×C₁₃	—	8	4	no	—
463	C₂²×C₁₃	—	16	4	no	—
464	C₂²×C₁₃	—	16	8	no	—
465	C₂²×C₁₃	#534	1	2	yes	—
466	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
467	C₄×C₁₃	—	2	1	no	—
468	C₄×C₁₃	—	2	1	no	—
469	C₄×C₁₃	—	2	4	no	—
470	C₄×C₁₃	—	4	4	no	—
471	C₄×C₁₃	—	4	2	no	—
472	C₄×C₁₃	—	4	2	no	—
473	C₄×C₁₃	—	4	2	no	—
474	C₄×C₁₃	#534	1	2	yes	—
475	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
476	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
477	H(5,𝔽₂)	—	4	4	no	—
478	H(5,𝔽₂)	—	4	4	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	4	2	no	—
481	C₂×#41	—	4	2	no	—
482	C₂×#41	D₄×C₁₃	1	2	yes	—
483	C₂×#41	D₄×C₁₃	1	2	yes	—
484	C₂×#41	C₂³×C₁₃	1	2	yes	—
485	C₂×#41	C₂³×C₁₃	1	4	yes	—
486	C₂×#41	C₂³×C₁₃	1	2	yes	—
487	C₂×#41	C₂³×C₁₃	1	2	yes	—
488	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
489	C₂²×D₄	—	2	2	no	—
490	C₂²×D₄	—	2	4	no	—
491	C₂²×D₄	—	2	4	no	—
492	C₂²×D₄	—	2	2	no	—
493	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
494	C₂²×D₄	D₄×C₁₃	1	2	yes	—
495	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
496	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
497	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
499	AGL(1,ℤ/8)	—	4	4	no	—
500	#135	—	4	2	no	—
501	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
502	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
503	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
504	C₂×D₈	—	4	2	no	—
505	C₂×D₈	C₂³×C₁₃	1	2	yes	—
506	C₂×D₈	C₂³×C₁₃	1	2	yes	—
507	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
508	C₂×D₈	C₂³×C₁₃	1	4	yes	—
509	C₂×M₁₆	—	4	2	no	—
510	C₂×M₁₆	—	4	2	no	—
511	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
512	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
513	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
514	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
515	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
516	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
520	#127	—	2	2	no	—
521	#127	—	2	4	no	—
522	#124	—	2	2	no	—
523	#124	—	2	4	no	—
524	#123	—	2	2	no	—
525	#123	—	2	4	no	—
526	C₂²⋊Q₈	—	2	2	no	—
527	C₂²⋊Q₈	—	2	4	no	—
528	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
529	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
530	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
531	#121	—	2	4	no	—
532	#121	—	2	2	no	—
533	#121	—	2	4	no	—
534	#121	—	2	4	no	—
535	#121	—	2	4	no	—
536	#121	—	2	2	no	—
537	#121	—	2	4	no	—
538	#121	—	2	2	no	—
539	#121	—	2	4	no	—
540	#121	C₂³×C₁₃	1	2	yes	—
541	#121	C₂³×C₁₃	1	4	yes	—
542	#121	C₂³×C₁₃	1	4	yes	—
543	#121	C₂³×C₁₃	1	4	yes	—
544	#121	C₂³×C₁₃	1	4	yes	—
545	#121	C₂³×C₁₃	1	4	yes	—
546	#121	C₂³×C₁₃	1	2	yes	—
547	#120	—	2	2	no	—
548	#120	—	2	4	no	—
549	#120	—	2	4	no	—
550	#120	—	2	4	no	—
551	#120	—	2	4	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×D₄	—	2	4	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	4	no	—
559	#117	C₂³×C₁₃	1	2	yes	—
560	#117	C₂³×C₁₃	1	4	yes	—
561	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
563	C₂×C₂²⋊C₄	—	2	2	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	#107	C₂³×C₁₃	1	2	yes	—
566	#107	C₂³×C₁₃	1	4	yes	—
567	#106	C₂³×C₁₃	1	2	yes	—
568	#106	C₂³×C₁₃	1	2	yes	—
569	#106	C₂³×C₁₃	1	1	yes	characteristic
570	#106	C₂³×C₁₃	1	1	yes	characteristic
571	#106	C₂³×C₁₃	1	4	yes	—
572	#103	C₂³×C₁₃	1	2	yes	—
573	#103	C₂³×C₁₃	1	2	yes	—
574	#103	C₂³×C₁₃	1	4	yes	—
575	#102	C₂³×C₁₃	1	4	yes	—
576	#102	C₂³×C₁₃	1	4	yes	—
577	#102	C₂³×C₁₃	1	2	yes	—
578	#102	C₂³×C₁₃	1	2	yes	—
579	#102	C₂³×C₁₃	1	4	yes	—
580	#102	C₂³×C₁₃	1	4	yes	—
581	#102	C₂³×C₁₃	1	4	yes	—
582	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
583	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
584	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
585	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
586	C₂×C₁₃	—	2	2	no	—
587	C₂×C₁₃	—	4	1	no	—
588	C₂×C₁₃	—	4	1	no	—
589	C₂×C₁₃	—	4	4	no	—
590	C₂×C₁₃	—	8	4	no	—
591	C₂×C₁₃	—	8	2	no	—
592	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
593	C₂×C₁₃	#3585	1	2	yes	—
594	C₂⁴	—	2	4	no	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
598	#41	—	2	4	no	—
599	#41	—	2	4	no	—
600	#41	—	2	4	no	—
601	#41	—	2	4	no	—
602	#41	—	4	2	no	—
603	#41	—	4	2	no	—
604	#41	—	4	4	no	—
605	#41	—	4	4	no	—
606	#41	—	4	4	no	—
607	#41	—	4	4	no	—
608	#41	—	4	8	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
613	C₂×D₄	—	2	2	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	2	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	4	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	4	2	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	16	no	—
631	C₂×D₄	—	4	8	no	—
632	C₂×D₄	—	8	4	no	—
633	C₂×D₄	—	8	8	no	—
634	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
635	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
636	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
638	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
639	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
652	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
657	Q₁₆	—	4	1	no	—
658	SD₁₆	—	4	2	no	—
659	SD₁₆	—	4	4	no	—
660	D₈	—	4	2	no	—
661	D₈	—	4	2	no	—
662	D₈	—	4	1	no	—
663	D₈	—	4	4	no	—
664	M₁₆	—	2	4	no	—
665	M₁₆	—	4	1	no	—
666	M₁₆	—	4	1	no	—
667	M₁₆	—	4	1	no	—
668	M₁₆	—	4	1	no	—
669	M₁₆	—	4	2	no	—
670	C₂×C₈	—	2	2	no	—
671	C₂×C₈	—	2	2	no	—
672	C₂×C₈	—	4	2	no	—
673	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
674	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
675	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
676	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
677	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	4	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	2	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	2	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₄²	—	2	4	no	—
699	C₄²	—	2	2	no	—
700	C₁₃	#60771	1	1	yes	characteristic, direct product factor, Sylow
701	C₂³	—	2	2	no	—
702	C₂³	—	2	4	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	4	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	4	no	—
707	C₂³	—	4	8	no	—
708	C₂³	—	4	4	no	—
709	C₂³	—	8	2	no	—
710	C₂³	—	8	4	no	—
711	C₂³	—	8	2	no	—
712	C₂³	—	8	4	no	—
713	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
714	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
715	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
716	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
717	Q₈	—	2	4	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	4	2	no	—
721	D₄	—	2	8	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	4	no	—
726	D₄	—	2	2	no	—
727	D₄	—	4	2	no	—
728	D₄	—	4	4	no	—
729	D₄	—	4	8	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	4	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	4	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	4	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	8	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
760	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
763	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
766	C₈	—	2	1	no	—
767	C₈	—	2	1	no	—
768	C₈	—	2	1	no	—
769	C₈	—	2	1	no	—
770	C₈	—	2	4	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	1	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	4	4	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	4	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	4	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	8	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	4	no	—
788	C₂²	—	16	8	no	—
789	C₂²	C₁₃×#534	1	2	yes	—
790	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	4	4	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	C₁₃×#534	1	2	yes	—
799	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	—	2	2	no	—
802	C₂	—	4	1	no	—
803	C₂	—	4	4	no	—
804	C₂	—	4	1	no	—
805	C₂	—	8	4	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
808	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3488	C₂	semidirect
2. C₁₃×#3204	C₂	semidirect
3. C₁₃×#3199	C₂	semidirect
4. C₁₃×#3198	C₂	semidirect
5. C₁₃×#3197	C₂	semidirect
6. C₁₃×#3194	C₂	semidirect
7. C₁₃×#3192	C₂	semidirect
8. C₁₃×#3099	C₂	semidirect
9. C₁₃×#3096	C₂	semidirect
10. C₁₃×#3055	C₂	semidirect
11. C₁₃×#3054	C₂	semidirect
12. C₂×C₁₃×#469	C₂	semidirect
13. C₁₃×#3012	C₂	semidirect
14. C₁₃×#3008	C₂	semidirect
15. C₁₃×#2879	C₂	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
20. C₂²×C₁₃×D₈	C₂²	semidirect
21. C₂²×C₁₃×M₁₆	C₂²	semidirect
22. C₂²×C₁₃×M₁₆	C₂²	semidirect
30. C₁₃×#537	C₂²	semidirect
32. C₁₃×#535	C₂²	semidirect
33. C₁₃×#525	C₂²	semidirect
34. C₁₃×#525	C₂²	semidirect
35. C₂×C₁₃×#121	C₂²	semidirect
36. C₂×C₁₃×#121	C₂²	semidirect
37. C₁₃×#520	C₂²	semidirect
38. C₁₃×#485	C₂²	semidirect
39. C₁₃×#483	C₂²	semidirect
40. C₁₃×#482	C₂²	semidirect
41. C₁₃×#482	C₂²	semidirect
42. C₁₃×#482	C₂²	semidirect
43. C₁₃×#481	C₂²	semidirect
44. C₁₃×#481	C₂²	semidirect
45. C₁₃×#480	C₂²	semidirect
46. C₁₃×#470	C₂²	semidirect
47. C₁₃×#470	C₂²	semidirect
48. C₁₃×#469	C₂²	semidirect
49. C₁₃×#469	C₂²	semidirect
50. C₁₃×#469	C₂²	semidirect
51. C₁₃×#469	C₂²	semidirect
52. C₁₃×#469	C₂²	semidirect
53. C₁₃×#469	C₂²	semidirect
54. C₁₃×#469	C₂²	semidirect
55. C₁₃×#468	C₂²	semidirect
56. C₁₃×#468	C₂²	semidirect
57. C₁₃×#468	C₂²	semidirect
58. C₁₃×#466	C₂²	semidirect
59. C₁₃×#465	C₂²	semidirect
60. C₁₃×#452	C₂²	semidirect
61. C₁₃×#450	C₂²	semidirect
62. C₁₃×#449	C₂²	semidirect
63. C₁₃×#449	C₂²	semidirect
64. C₁₃×#449	C₂²	semidirect
65. C₁₃×#447	C₂²	semidirect
66. C₁₃×#447	C₂²	semidirect
67. C₁₃×#447	C₂²	semidirect
68. C₁₃×#428	C₂²	semidirect
69. C₁₃×#427	C₂²	semidirect
70. C₂×C₁₃×#106	C₂²	semidirect
71. C₁₃×#418	C₂²	semidirect
72. C₁₃×#417	C₂²	semidirect
73. C₁₃×#416	C₂²	semidirect
74. C₂×C₁₃×#102	C₂²	semidirect
75. C₁₃×#408	C₂²	semidirect
76. C₁₃×#408	C₂²	semidirect
77. C₁₃×#408	C₂²	semidirect
78. C₁₃×#408	C₂²	semidirect
79. C₁₃×#407	C₂²	semidirect
80. C₁₃×#407	C₂²	semidirect
190. #60771	C₁₃	direct (N × H)
297. #3488	C₂×C₁₃	semidirect
298. #3204	C₂×C₁₃	semidirect
299. #3199	C₂×C₁₃	semidirect
300. #3198	C₂×C₁₃	semidirect
301. #3197	C₂×C₁₃	semidirect
302. #3194	C₂×C₁₃	semidirect
303. #3192	C₂×C₁₃	semidirect
304. #3099	C₂×C₁₃	semidirect
305. #3096	C₂×C₁₃	semidirect
306. #3055	C₂×C₁₃	semidirect
307. #3054	C₂×C₁₃	semidirect
308. C₂×#469	C₂×C₁₃	semidirect
309. #3012	C₂×C₁₃	semidirect
310. #3008	C₂×C₁₃	semidirect
311. #2879	C₂×C₁₃	semidirect
382. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
384. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
385. C₂×#135	C₂²×C₁₃	semidirect
386. C₂²×D₈	C₂²×C₁₃	semidirect
387. C₂²×M₁₆	C₂²×C₁₃	semidirect
388. C₂²×M₁₆	C₂²×C₁₃	semidirect
396. #537	C₂²×C₁₃	semidirect
398. #535	C₂²×C₁₃	semidirect
399. #525	C₂²×C₁₃	semidirect
400. #525	C₂²×C₁₃	semidirect
401. C₂×#121	C₂²×C₁₃	semidirect
402. C₂×#121	C₂²×C₁₃	semidirect
403. #520	C₂²×C₁₃	semidirect
404. #485	C₂²×C₁₃	semidirect
405. #483	C₂²×C₁₃	semidirect
406. #482	C₂²×C₁₃	semidirect
407. #482	C₂²×C₁₃	semidirect
408. #482	C₂²×C₁₃	semidirect
409. #481	C₂²×C₁₃	semidirect
410. #481	C₂²×C₁₃	semidirect
411. #480	C₂²×C₁₃	semidirect
412. #470	C₂²×C₁₃	semidirect
413. #470	C₂²×C₁₃	semidirect
414. #469	C₂²×C₁₃	semidirect
415. #469	C₂²×C₁₃	semidirect
416. #469	C₂²×C₁₃	semidirect
417. #469	C₂²×C₁₃	semidirect
418. #469	C₂²×C₁₃	semidirect
419. #469	C₂²×C₁₃	semidirect
420. #469	C₂²×C₁₃	semidirect
421. #468	C₂²×C₁₃	semidirect
422. #468	C₂²×C₁₃	semidirect
423. #468	C₂²×C₁₃	semidirect
424. #466	C₂²×C₁₃	semidirect
425. #465	C₂²×C₁₃	semidirect
426. #452	C₂²×C₁₃	semidirect
427. #450	C₂²×C₁₃	semidirect
428. #449	C₂²×C₁₃	semidirect
429. #449	C₂²×C₁₃	semidirect
430. #449	C₂²×C₁₃	semidirect
431. #447	C₂²×C₁₃	semidirect
432. #447	C₂²×C₁₃	semidirect
433. #447	C₂²×C₁₃	semidirect
434. #428	C₂²×C₁₃	semidirect
435. #427	C₂²×C₁₃	semidirect
436. C₂×#106	C₂²×C₁₃	semidirect
437. #418	C₂²×C₁₃	semidirect
438. #417	C₂²×C₁₃	semidirect
439. #416	C₂²×C₁₃	semidirect
440. C₂×#102	C₂²×C₁₃	semidirect
441. #408	C₂²×C₁₃	semidirect
442. #408	C₂²×C₁₃	semidirect
443. #408	C₂²×C₁₃	semidirect
444. #408	C₂²×C₁₃	semidirect
445. #407	C₂²×C₁₃	semidirect
446. #407	C₂²×C₁₃	semidirect
700. C₁₃	#60771	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×#3204	2
C₁₃×#3199	2
C₁₃×#3198	2
C₁₃×#3197	2
C₁₃×#3194	2
C₁₃×#3192	2
C₁₃×#3099	2
C₁₃×#3096	2
C₁₃×#3055	2
C₁₃×#3054	2
C₂×C₁₃×#469	2
C₁₃×#3012	2
C₁₃×#3008	2
C₁₃×#2879	2
#60771	13

Subgroups — C13×#60771 #15747110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60771 #15747110