Subgroups — C₁₃×#61063 #15747402

Order 3328.

2818 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×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3488	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3275	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3274	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3271	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
18	C₁₃×#576	—	2	8	no	—
19	C₁₃×#575	—	2	8	no	—
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
26	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
29	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
32	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#550	C₂²	1	4	yes	complemented
36	C₁₃×#548	C₂²	1	4	yes	complemented
37	C₁₃×#546	—	2	4	no	—
38	C₁₃×#546	C₂²	1	4	yes	complemented
39	D₄²×C₁₃	—	2	4	no	—
40	D₄²×C₁₃	C₂²	1	4	yes	complemented
41	C₁₃×#537	—	2	2	no	—
42	C₁₃×#537	C₂²	1	2	yes	complemented
43	C₁₃×#535	—	2	2	no	—
44	C₁₃×#535	C₂²	1	2	yes	complemented
45	C₁₃×#525	—	2	2	no	—
46	C₁₃×#525	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#121	—	2	2	no	—
48	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
49	C₁₃×#520	C₂²	1	2	yes	complemented
50	C₁₃×#496	C₂²	1	4	yes	complemented
51	C₁₃×#495	C₂²	1	2	yes	complemented
52	C₁₃×#493	C₂²	1	2	yes	complemented
53	C₁₃×#470	C₂²	1	2	yes	complemented
54	C₁₃×#469	C₂²	1	4	yes	complemented
55	C₁₃×#469	C₂²	1	2	yes	complemented
56	C₁₃×#469	C₂²	1	4	yes	complemented
57	C₁₃×#465	C₂²	1	4	yes	complemented
58	C₁₃×#464	C₂²	1	4	yes	complemented
59	C₁₃×#463	C₂²	1	4	yes	complemented
60	C₁₃×#460	C₂²	1	4	yes	complemented
61	C₁₃×#459	C₂²	1	4	yes	complemented
62	C₁₃×#452	C₂²	1	4	yes	complemented
63	C₁₃×#450	C₂²	1	4	yes	complemented
64	C₁₃×#449	C₂²	1	4	yes	complemented
65	C₁₃×#449	C₂²	1	4	yes	complemented
66	C₁₃×#449	C₂²	1	4	yes	complemented
67	C₁₃×#448	C₂²	1	4	yes	complemented
68	C₁₃×#447	C₂²	1	4	yes	complemented
69	C₁₃×#447	C₂²	1	4	yes	complemented
70	C₁₃×#442	C₂²	1	2	yes	complemented
71	C₁₃×#441	C₂²	1	2	yes	complemented
72	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
73	C₁₃×#436	C₂²	1	4	yes	complemented
74	C₁₃×#435	C₂²	1	4	yes	complemented
75	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#424	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#417	C₂²	1	2	yes	complemented
78	C₁₃×#417	C₂²	1	2	yes	complemented
79	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
80	C₁₃×#408	C₂²	1	1	yes	characteristic, complemented
81	C₁₃×#407	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×H(5,𝔽₂)	—	2	8	no	—
84	C₁₃×H(5,𝔽₂)	—	4	4	no	—
85	C₂×C₁₃×#41	—	2	2	no	—
86	C₂×C₁₃×#41	—	2	2	no	—
87	C₂×C₁₃×#41	—	2	2	no	—
88	C₂×C₁₃×#41	—	2	8	no	—
89	C₂×C₁₃×#41	—	4	4	no	—
90	C₂×C₁₃×#41	C₂³	1	2	yes	—
91	C₂×C₁₃×#41	C₂³	1	2	yes	—
92	C₂×C₁₃×#41	C₂³	1	2	yes	—
93	C₂×C₁₃×#41	C₂³	1	4	yes	—
94	C₂×C₁₃×#41	C₂³	1	2	yes	—
95	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	—	2	2	no	—
98	C₂²×D₄×C₁₃	—	2	2	no	—
99	C₂²×D₄×C₁₃	—	2	2	no	—
100	C₂²×D₄×C₁₃	—	2	4	no	—
101	C₂²×D₄×C₁₃	—	2	4	no	—
102	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
104	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
105	C₂³×C₄×C₁₃	—	2	2	no	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#137	—	2	8	no	—
108	C₁₃×#137	—	2	8	no	—
109	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
110	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
112	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
113	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
114	C₁₃×#135	—	2	8	no	—
115	C₁₃×#135	—	2	8	no	—
116	C₁₃×#135	—	2	4	no	—
117	C₁₃×#135	D₄	1	8	yes	complemented
118	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×D₈	—	2	8	no	—
128	C₂×C₁₃×D₈	—	2	4	no	—
129	C₂×C₁₃×D₈	C₂³	1	2	yes	—
130	C₂×C₁₃×D₈	C₂³	1	4	yes	—
131	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×D₈	C₂³	1	2	yes	—
133	C₂×C₁₃×D₈	C₂³	1	2	yes	—
134	C₂×C₁₃×D₈	C₂³	1	4	yes	—
135	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
136	C₁₃×#131	—	2	4	no	—
137	C₂×C₁₃×M₁₆	—	2	4	no	—
138	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
139	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
141	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
142	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
143	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#127	—	2	4	no	—
147	C₁₃×#127	C₂³	1	4	yes	—
148	C₁₃×#124	—	2	4	no	—
149	C₁₃×#124	C₂³	1	4	yes	—
150	C₁₃×#123	—	2	4	no	—
151	C₁₃×#123	D₄	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	—	2	2	no	—
153	C₁₃×C₂²⋊Q₈	—	2	4	no	—
154	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
155	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	4	no	—
158	C₁₃×#121	—	2	4	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	2	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	—	2	4	no	—
164	C₁₃×#121	—	2	4	no	—
165	C₁₃×#121	—	2	4	no	—
166	C₁₃×#121	—	2	4	no	—
167	C₁₃×#121	D₄	1	2	yes	—
168	C₁₃×#121	C₂³	1	4	yes	—
169	C₁₃×#121	C₂³	1	4	yes	—
170	C₁₃×#121	C₂³	1	4	yes	—
171	C₁₃×#120	—	2	4	no	—
172	C₁₃×#120	—	2	4	no	—
173	C₁₃×#120	—	2	4	no	—
174	C₁₃×#120	—	2	4	no	—
175	C₁₃×#120	D₄	1	2	yes	—
176	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
177	C₄×D₄×C₁₃	—	2	4	no	—
178	C₄×D₄×C₁₃	—	2	4	no	—
179	C₄×D₄×C₁₃	—	2	4	no	—
180	C₄×D₄×C₁₃	C₂³	1	4	yes	—
181	C₄×D₄×C₁₃	C₂³	1	4	yes	—
182	C₁₃×#117	—	2	2	no	—
183	C₁₃×#117	C₂³	1	1	yes	characteristic
184	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×#106	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	4	yes	—
192	C₁₃×#103	C₂³	1	4	yes	—
193	C₁₃×#102	C₂³	1	4	yes	—
194	C₁₃×#102	C₂³	1	4	yes	—
195	C₁₃×#102	C₂³	1	4	yes	—
196	C₁₃×#102	C₂³	1	4	yes	—
197	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
198	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
199	C₁₃×#97	C₂³	1	2	yes	—
200	C₄×C₈×C₁₃	C₂³	1	2	yes	—
201	#61063	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂⁴×C₁₃	—	2	2	no	—
203	C₂⁴×C₁₃	—	2	4	no	—
204	C₂⁴×C₁₃	—	2	2	no	—
205	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
206	C₁₃×#41	—	2	2	no	—
207	C₁₃×#41	—	2	4	no	—
208	C₁₃×#41	—	2	2	no	—
209	C₁₃×#41	—	2	8	no	—
210	C₁₃×#41	—	2	4	no	—
211	C₁₃×#41	—	2	4	no	—
212	C₁₃×#41	—	2	4	no	—
213	C₁₃×#41	—	2	4	no	—
214	C₁₃×#41	—	4	8	no	—
215	C₁₃×#41	—	4	2	no	—
216	C₁₃×#41	—	4	2	no	—
217	C₁₃×#41	—	4	4	no	—
218	C₁₃×#41	—	4	8	no	—
219	C₁₃×#41	—	4	8	no	—
220	C₁₃×#41	C₂×D₄	1	8	yes	complemented
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	4	2	no	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
226	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	—	2	2	no	—
228	C₂×D₄×C₁₃	—	2	8	no	—
229	C₂×D₄×C₁₃	—	2	4	no	—
230	C₂×D₄×C₁₃	—	2	4	no	—
231	C₂×D₄×C₁₃	—	2	2	no	—
232	C₂×D₄×C₁₃	—	2	2	no	—
233	C₂×D₄×C₁₃	—	2	4	no	—
234	C₂×D₄×C₁₃	—	2	2	no	—
235	C₂×D₄×C₁₃	—	2	4	no	—
236	C₂×D₄×C₁₃	—	2	4	no	—
237	C₂×D₄×C₁₃	—	2	4	no	—
238	C₂×D₄×C₁₃	—	2	2	no	—
239	C₂×D₄×C₁₃	—	2	4	no	—
240	C₂×D₄×C₁₃	—	2	2	no	—
241	C₂×D₄×C₁₃	—	2	4	no	—
242	C₂×D₄×C₁₃	—	2	4	no	—
243	C₂×D₄×C₁₃	—	2	4	no	—
244	C₂×D₄×C₁₃	—	4	2	no	—
245	C₂×D₄×C₁₃	—	4	4	no	—
246	C₂×D₄×C₁₃	—	4	8	no	—
247	C₂×D₄×C₁₃	—	4	16	no	—
248	C₂×D₄×C₁₃	—	4	8	no	—
249	C₂×D₄×C₁₃	—	8	8	no	—
250	C₂×D₄×C₁₃	—	8	4	no	—
251	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
253	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
254	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
255	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₁₃	—	2	2	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	2	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	2	no	—
262	C₂²×C₄×C₁₃	—	2	2	no	—
263	C₂²×C₄×C₁₃	—	2	2	no	—
264	C₂²×C₄×C₁₃	—	2	4	no	—
265	C₂²×C₄×C₁₃	—	2	2	no	—
266	C₂²×C₄×C₁₃	—	2	4	no	—
267	C₂²×C₄×C₁₃	—	4	8	no	—
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	2	yes	—
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₁₃×Q₁₆	—	2	4	no	—
274	C₁₃×Q₁₆	—	2	2	no	—
275	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
276	C₁₃×SD₁₆	—	2	8	no	—
277	C₁₃×SD₁₆	—	2	4	no	—
278	C₁₃×SD₁₆	—	2	4	no	—
279	C₁₃×SD₁₆	—	2	4	no	—
280	C₁₃×SD₁₆	—	4	4	no	—
281	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
282	C₁₃×D₈	—	2	8	no	—
283	C₁₃×D₈	—	2	4	no	—
284	C₁₃×D₈	—	2	4	no	—
285	C₁₃×D₈	—	2	4	no	—
286	C₁₃×D₈	—	2	2	no	—
287	C₁₃×D₈	—	4	4	no	—
288	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
289	C₁₃×M₁₆	—	2	2	no	—
290	C₁₃×M₁₆	—	2	2	no	—
291	C₁₃×M₁₆	—	2	4	no	—
292	C₁₃×M₁₆	—	2	4	no	—
293	C₁₃×M₁₆	—	2	4	no	—
294	C₂×C₈×C₁₃	—	2	2	no	—
295	C₂×C₈×C₁₃	—	2	4	no	—
296	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
297	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
298	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
299	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
300	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₁₃×C₄⋊C₄	—	2	2	no	—
303	C₁₃×C₄⋊C₄	—	2	4	no	—
304	C₁₃×C₄⋊C₄	—	2	4	no	—
305	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
306	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
307	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₁₃×C₂²⋊C₄	—	2	4	no	—
309	C₁₃×C₂²⋊C₄	—	2	4	no	—
310	C₁₃×C₂²⋊C₄	—	2	4	no	—
311	C₁₃×C₂²⋊C₄	—	2	4	no	—
312	C₁₃×C₂²⋊C₄	—	2	4	no	—
313	C₁₃×C₂²⋊C₄	—	2	4	no	—
314	C₁₃×C₂²⋊C₄	—	2	4	no	—
315	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
316	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
317	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
318	C₄²×C₁₃	—	2	4	no	—
319	C₄²×C₁₃	C₂⁴	1	2	yes	—
320	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
321	C₂×#575	C₂×C₁₃	1	1	yes	characteristic, complemented
322	#3488	C₂×C₁₃	1	2	yes	complemented
323	#3275	C₂×C₁₃	1	4	yes	complemented
324	#3274	C₂×C₁₃	1	4	yes	complemented
325	#3271	C₂×C₁₃	1	4	yes	complemented
326	#3264	C₂×C₁₃	1	4	yes	complemented
327	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
328	#3060	C₂×C₁₃	1	1	yes	characteristic, complemented
329	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
330	#3045	C₂×C₁₃	1	2	yes	complemented
331	#3012	C₂×C₁₃	1	2	yes	complemented
332	#3006	C₂×C₁₃	1	2	yes	complemented
333	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
334	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
335	C₂³×C₁₃	—	2	2	no	—
336	C₂³×C₁₃	—	2	2	no	—
337	C₂³×C₁₃	—	2	4	no	—
338	C₂³×C₁₃	—	2	2	no	—
339	C₂³×C₁₃	—	4	2	no	—
340	C₂³×C₁₃	—	4	4	no	—
341	C₂³×C₁₃	—	4	8	no	—
342	C₂³×C₁₃	—	4	4	no	—
343	C₂³×C₁₃	—	4	4	no	—
344	C₂³×C₁₃	—	8	2	no	—
345	C₂³×C₁₃	—	8	2	no	—
346	C₂³×C₁₃	—	8	4	no	—
347	C₂³×C₁₃	—	8	2	no	—
348	C₂³×C₁₃	—	8	4	no	—
349	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
351	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	Q₈×C₁₃	—	2	2	no	—
353	Q₈×C₁₃	—	2	2	no	—
354	Q₈×C₁₃	—	2	2	no	—
355	Q₈×C₁₃	—	2	2	no	—
356	Q₈×C₁₃	—	4	4	no	—
357	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
358	D₄×C₁₃	—	2	8	no	—
359	D₄×C₁₃	—	2	4	no	—
360	D₄×C₁₃	—	2	2	no	—
361	D₄×C₁₃	—	2	4	no	—
362	D₄×C₁₃	—	2	2	no	—
363	D₄×C₁₃	—	2	2	no	—
364	D₄×C₁₃	—	2	2	no	—
365	D₄×C₁₃	—	2	4	no	—
366	D₄×C₁₃	—	4	4	no	—
367	D₄×C₁₃	—	4	8	no	—
368	D₄×C₁₃	—	4	4	no	—
369	D₄×C₁₃	—	4	8	no	—
370	D₄×C₁₃	—	4	4	no	—
371	D₄×C₁₃	—	4	4	no	—
372	D₄×C₁₃	—	4	8	no	—
373	D₄×C₁₃	—	4	4	no	—
374	D₄×C₁₃	—	4	4	no	—
375	D₄×C₁₃	—	8	4	no	—
376	D₄×C₁₃	—	8	4	no	—
377	D₄×C₁₃	—	8	4	no	—
378	D₄×C₁₃	—	8	4	no	—
379	D₄×C₁₃	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₁₃	—	2	2	no	—
381	C₂×C₄×C₁₃	—	2	2	no	—
382	C₂×C₄×C₁₃	—	2	4	no	—
383	C₂×C₄×C₁₃	—	2	8	no	—
384	C₂×C₄×C₁₃	—	2	2	no	—
385	C₂×C₄×C₁₃	—	2	2	no	—
386	C₂×C₄×C₁₃	—	2	2	no	—
387	C₂×C₄×C₁₃	—	2	2	no	—
388	C₂×C₄×C₁₃	—	2	4	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	4	4	no	—
391	C₂×C₄×C₁₃	—	4	8	no	—
392	C₂×C₄×C₁₃	—	4	4	no	—
393	C₂×C₄×C₁₃	—	4	4	no	—
394	C₂×C₄×C₁₃	—	4	4	no	—
395	C₂×C₄×C₁₃	—	8	4	no	—
396	C₂×C₄×C₁₃	—	8	2	no	—
397	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
398	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
403	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
404	C₈×C₁₃	—	2	2	no	—
405	C₈×C₁₃	—	2	2	no	—
406	C₈×C₁₃	—	2	2	no	—
407	C₈×C₁₃	C₂²×D₄	1	2	yes	—
408	C₈×C₁₃	C₂²×D₄	1	2	yes	—
409	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
410	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
411	#576	—	2	8	no	—
412	#575	—	2	8	no	—
413	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
414	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
415	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
416	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
417	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
418	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
419	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
420	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
421	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
423	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
424	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
426	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	#550	C₂²×C₁₃	1	4	yes	complemented
429	#548	C₂²×C₁₃	1	4	yes	complemented
430	#546	—	2	4	no	—
431	#546	C₂²×C₁₃	1	4	yes	complemented
432	D₄²	—	2	4	no	—
433	D₄²	C₂²×C₁₃	1	4	yes	complemented
434	#537	—	2	2	no	—
435	#537	C₂²×C₁₃	1	2	yes	complemented
436	#535	—	2	2	no	—
437	#535	C₂²×C₁₃	1	2	yes	complemented
438	#525	—	2	2	no	—
439	#525	C₂²×C₁₃	1	1	yes	characteristic
440	C₂×#121	—	2	2	no	—
441	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
442	#520	C₂²×C₁₃	1	2	yes	complemented
443	#496	C₂²×C₁₃	1	4	yes	complemented
444	#495	C₂²×C₁₃	1	2	yes	complemented
445	#493	C₂²×C₁₃	1	2	yes	complemented
446	#470	C₂²×C₁₃	1	2	yes	complemented
447	#469	C₂²×C₁₃	1	4	yes	complemented
448	#469	C₂²×C₁₃	1	2	yes	complemented
449	#469	C₂²×C₁₃	1	4	yes	complemented
450	#465	C₂²×C₁₃	1	4	yes	complemented
451	#464	C₂²×C₁₃	1	4	yes	complemented
452	#463	C₂²×C₁₃	1	4	yes	complemented
453	#460	C₂²×C₁₃	1	4	yes	complemented
454	#459	C₂²×C₁₃	1	4	yes	complemented
455	#452	C₂²×C₁₃	1	4	yes	complemented
456	#450	C₂²×C₁₃	1	4	yes	complemented
457	#449	C₂²×C₁₃	1	4	yes	complemented
458	#449	C₂²×C₁₃	1	4	yes	complemented
459	#449	C₂²×C₁₃	1	4	yes	complemented
460	#448	C₂²×C₁₃	1	4	yes	complemented
461	#447	C₂²×C₁₃	1	4	yes	complemented
462	#447	C₂²×C₁₃	1	4	yes	complemented
463	#442	C₂²×C₁₃	1	2	yes	complemented
464	#441	C₂²×C₁₃	1	2	yes	complemented
465	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
466	#436	C₂²×C₁₃	1	4	yes	complemented
467	#435	C₂²×C₁₃	1	4	yes	complemented
468	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#424	C₂²×C₁₃	1	1	yes	characteristic, complemented
470	#417	C₂²×C₁₃	1	2	yes	complemented
471	#417	C₂²×C₁₃	1	2	yes	complemented
472	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
473	#408	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#407	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	C₂²×C₁₃	—	2	2	no	—
477	C₂²×C₁₃	—	2	2	no	—
478	C₂²×C₁₃	—	2	4	no	—
479	C₂²×C₁₃	—	2	2	no	—
480	C₂²×C₁₃	—	2	2	no	—
481	C₂²×C₁₃	—	2	4	no	—
482	C₂²×C₁₃	—	2	2	no	—
483	C₂²×C₁₃	—	4	2	no	—
484	C₂²×C₁₃	—	4	2	no	—
485	C₂²×C₁₃	—	4	4	no	—
486	C₂²×C₁₃	—	4	2	no	—
487	C₂²×C₁₃	—	4	2	no	—
488	C₂²×C₁₃	—	4	4	no	—
489	C₂²×C₁₃	—	4	2	no	—
490	C₂²×C₁₃	—	4	4	no	—
491	C₂²×C₁₃	—	8	2	no	—
492	C₂²×C₁₃	—	8	8	no	—
493	C₂²×C₁₃	—	16	4	no	—
494	C₂²×C₁₃	—	16	8	no	—
495	C₂²×C₁₃	D₄²	1	2	yes	—
496	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₁₃	—	2	4	no	—
498	C₄×C₁₃	—	2	2	no	—
499	C₄×C₁₃	—	2	4	no	—
500	C₄×C₁₃	—	2	2	no	—
501	C₄×C₁₃	—	4	4	no	—
502	C₄×C₁₃	—	4	2	no	—
503	C₄×C₁₃	D₄²	1	2	yes	—
504	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
505	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	H(5,𝔽₂)	—	2	8	no	—
507	H(5,𝔽₂)	—	4	4	no	—
508	C₂×#41	—	2	2	no	—
509	C₂×#41	—	2	2	no	—
510	C₂×#41	—	2	2	no	—
511	C₂×#41	—	2	8	no	—
512	C₂×#41	—	4	4	no	—
513	C₂×#41	C₂³×C₁₃	1	2	yes	—
514	C₂×#41	C₂³×C₁₃	1	2	yes	—
515	C₂×#41	C₂³×C₁₃	1	4	yes	—
516	C₂×#41	C₂³×C₁₃	1	2	yes	—
517	C₂×#41	C₂³×C₁₃	1	2	yes	—
518	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
519	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
520	C₂²×D₄	—	2	2	no	—
521	C₂²×D₄	—	2	2	no	—
522	C₂²×D₄	—	2	2	no	—
523	C₂²×D₄	—	2	4	no	—
524	C₂²×D₄	—	2	4	no	—
525	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
526	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
527	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
528	C₂³×C₄	—	2	2	no	—
529	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
530	#137	—	2	8	no	—
531	#137	—	2	8	no	—
532	AGL(1,ℤ/8)	—	2	8	no	—
533	AGL(1,ℤ/8)	—	2	8	no	—
534	AGL(1,ℤ/8)	—	2	16	no	—
535	AGL(1,ℤ/8)	—	2	8	no	—
536	AGL(1,ℤ/8)	—	4	4	no	—
537	#135	—	2	8	no	—
538	#135	—	2	8	no	—
539	#135	—	2	4	no	—
540	#135	D₄×C₁₃	1	8	yes	complemented
541	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
542	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
543	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
544	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
547	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
549	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
550	C₂×D₈	—	2	8	no	—
551	C₂×D₈	—	2	4	no	—
552	C₂×D₈	C₂³×C₁₃	1	2	yes	—
553	C₂×D₈	C₂³×C₁₃	1	4	yes	—
554	C₂×D₈	C₂³×C₁₃	1	2	yes	—
555	C₂×D₈	C₂³×C₁₃	1	2	yes	—
556	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×D₈	C₂³×C₁₃	1	4	yes	—
558	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
559	#131	—	2	4	no	—
560	C₂×M₁₆	—	2	4	no	—
561	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
562	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
563	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
564	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
565	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
566	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
567	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
568	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
569	#127	—	2	4	no	—
570	#127	C₂³×C₁₃	1	4	yes	—
571	#124	—	2	4	no	—
572	#124	C₂³×C₁₃	1	4	yes	—
573	#123	—	2	4	no	—
574	#123	D₄×C₁₃	1	2	yes	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
579	#121	—	2	2	no	—
580	#121	—	2	4	no	—
581	#121	—	2	4	no	—
582	#121	—	2	2	no	—
583	#121	—	2	2	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	4	no	—
587	#121	—	2	4	no	—
588	#121	—	2	4	no	—
589	#121	—	2	4	no	—
590	#121	D₄×C₁₃	1	2	yes	—
591	#121	C₂³×C₁₃	1	4	yes	—
592	#121	C₂³×C₁₃	1	4	yes	—
593	#121	C₂³×C₁₃	1	4	yes	—
594	#120	—	2	4	no	—
595	#120	—	2	4	no	—
596	#120	—	2	4	no	—
597	#120	—	2	4	no	—
598	#120	D₄×C₁₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
600	C₄×D₄	—	2	4	no	—
601	C₄×D₄	—	2	4	no	—
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	C₂³×C₁₃	1	4	yes	—
604	C₄×D₄	C₂³×C₁₃	1	4	yes	—
605	#117	—	2	2	no	—
606	#117	C₂³×C₁₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
609	C₂×C₂²⋊C₄	—	2	2	no	—
610	C₂×C₂²⋊C₄	—	2	4	no	—
611	#106	C₂³×C₁₃	1	2	yes	—
612	#106	C₂³×C₁₃	1	2	yes	—
613	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
614	#103	C₂³×C₁₃	1	4	yes	—
615	#103	C₂³×C₁₃	1	4	yes	—
616	#102	C₂³×C₁₃	1	4	yes	—
617	#102	C₂³×C₁₃	1	4	yes	—
618	#102	C₂³×C₁₃	1	4	yes	—
619	#102	C₂³×C₁₃	1	4	yes	—
620	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
621	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
622	#97	C₂³×C₁₃	1	2	yes	—
623	C₄×C₈	C₂³×C₁₃	1	2	yes	—
624	C₂×C₁₃	—	2	2	no	—
625	C₂×C₁₃	—	4	2	no	—
626	C₂×C₁₃	—	4	2	no	—
627	C₂×C₁₃	—	4	4	no	—
628	C₂×C₁₃	—	8	2	no	—
629	C₂×C₁₃	—	8	4	no	—
630	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
631	C₂×C₁₃	#3585	1	2	yes	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	4	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
636	#41	—	2	2	no	—
637	#41	—	2	4	no	—
638	#41	—	2	2	no	—
639	#41	—	2	8	no	—
640	#41	—	2	4	no	—
641	#41	—	2	4	no	—
642	#41	—	2	4	no	—
643	#41	—	2	4	no	—
644	#41	—	4	8	no	—
645	#41	—	4	2	no	—
646	#41	—	4	2	no	—
647	#41	—	4	4	no	—
648	#41	—	4	8	no	—
649	#41	—	4	8	no	—
650	#41	C₂×D₄×C₁₃	1	8	yes	complemented
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	2	4	no	—
653	C₂×Q₈	—	4	2	no	—
654	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
655	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
657	C₂×D₄	—	2	2	no	—
658	C₂×D₄	—	2	8	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	4	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	4	8	no	—
677	C₂×D₄	—	4	16	no	—
678	C₂×D₄	—	4	8	no	—
679	C₂×D₄	—	8	8	no	—
680	C₂×D₄	—	8	4	no	—
681	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
682	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
684	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
685	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
686	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	4	8	no	—
698	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
703	Q₁₆	—	2	4	no	—
704	Q₁₆	—	2	2	no	—
705	Q₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
706	SD₁₆	—	2	8	no	—
707	SD₁₆	—	2	4	no	—
708	SD₁₆	—	2	4	no	—
709	SD₁₆	—	2	4	no	—
710	SD₁₆	—	4	4	no	—
711	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
712	D₈	—	2	8	no	—
713	D₈	—	2	4	no	—
714	D₈	—	2	4	no	—
715	D₈	—	2	4	no	—
716	D₈	—	2	2	no	—
717	D₈	—	4	4	no	—
718	D₈	C₂×D₄×C₁₃	1	4	yes	complemented
719	M₁₆	—	2	2	no	—
720	M₁₆	—	2	2	no	—
721	M₁₆	—	2	4	no	—
722	M₁₆	—	2	4	no	—
723	M₁₆	—	2	4	no	—
724	C₂×C₈	—	2	2	no	—
725	C₂×C₈	—	2	4	no	—
726	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
727	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
728	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
730	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
731	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
737	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
746	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
747	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
748	C₄²	—	2	4	no	—
749	C₄²	C₂⁴×C₁₃	1	2	yes	—
750	C₁₃	#61063	1	1	yes	characteristic, direct product factor, Sylow
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	8	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	4	4	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	4	no	—
763	C₂³	—	8	2	no	—
764	C₂³	—	8	4	no	—
765	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
766	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
767	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
768	Q₈	—	2	2	no	—
769	Q₈	—	2	2	no	—
770	Q₈	—	2	2	no	—
771	Q₈	—	2	2	no	—
772	Q₈	—	4	4	no	—
773	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
774	D₄	—	2	8	no	—
775	D₄	—	2	4	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	4	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	2	no	—
780	D₄	—	2	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	4	4	no	—
783	D₄	—	4	8	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	8	no	—
786	D₄	—	4	4	no	—
787	D₄	—	4	4	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	4	no	—
791	D₄	—	8	4	no	—
792	D₄	—	8	4	no	—
793	D₄	—	8	4	no	—
794	D₄	—	8	4	no	—
795	D₄	C₂²×D₄×C₁₃	1	4	yes	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	8	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
814	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
818	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
819	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
820	C₈	—	2	2	no	—
821	C₈	—	2	2	no	—
822	C₈	—	2	2	no	—
823	C₈	C₂²×D₄×C₁₃	1	2	yes	—
824	C₈	C₂²×D₄×C₁₃	1	2	yes	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	4	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	4	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	8	2	no	—
841	C₂²	—	8	8	no	—
842	C₂²	—	16	4	no	—
843	C₂²	—	16	8	no	—
844	C₂²	D₄²×C₁₃	1	2	yes	—
845	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
846	C₄	—	2	4	no	—
847	C₄	—	2	2	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	2	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	2	no	—
852	C₄	D₄²×C₁₃	1	2	yes	—
853	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
854	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
855	C₂	—	2	2	no	—
856	C₂	—	4	2	no	—
857	C₂	—	4	2	no	—
858	C₂	—	4	4	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	4	no	—
861	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
862	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 ◁ C₁₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₂×C₁₃×#575	C₂	semidirect
3. C₁₃×#3488	C₂	semidirect
4. C₁₃×#3275	C₂	semidirect
5. C₁₃×#3274	C₂	semidirect
6. C₁₃×#3271	C₂	semidirect
7. C₁₃×#3264	C₂	semidirect
8. C₁₃×#3155	C₂	semidirect
9. C₁₃×#3060	C₂	semidirect
10. C₂×C₁₃×#469	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3012	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#2952	C₂	semidirect
15. C₁₃×#2930	C₂	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
21. C₂×C₁₃×#137	C₂²	semidirect
22. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₁₃×#135	C₂²	semidirect
29. C₂×C₁₃×#135	C₂²	semidirect
30. C₂×C₁₃×#135	C₂²	semidirect
31. C₂²×C₁₃×D₈	C₂²	semidirect
32. C₂²×C₁₃×D₈	C₂²	semidirect
33. C₂×C₁₃×#131	C₂²	semidirect
34. C₂²×C₁₃×M₁₆	C₂²	semidirect
35. C₁₃×#550	C₂²	semidirect
36. C₁₃×#548	C₂²	semidirect
38. C₁₃×#546	C₂²	semidirect
40. D₄²×C₁₃	C₂²	semidirect
42. C₁₃×#537	C₂²	semidirect
44. C₁₃×#535	C₂²	semidirect
48. C₂×C₁₃×#121	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#496	C₂²	semidirect
51. C₁₃×#495	C₂²	semidirect
52. C₁₃×#493	C₂²	semidirect
53. C₁₃×#470	C₂²	semidirect
54. C₁₃×#469	C₂²	semidirect
55. C₁₃×#469	C₂²	semidirect
56. C₁₃×#469	C₂²	semidirect
57. C₁₃×#465	C₂²	semidirect
58. C₁₃×#464	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#460	C₂²	semidirect
61. C₁₃×#459	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#450	C₂²	semidirect
64. C₁₃×#449	C₂²	semidirect
65. C₁₃×#449	C₂²	semidirect
66. C₁₃×#449	C₂²	semidirect
67. C₁₃×#448	C₂²	semidirect
68. C₁₃×#447	C₂²	semidirect
69. C₁₃×#447	C₂²	semidirect
70. C₁₃×#442	C₂²	semidirect
71. C₁₃×#441	C₂²	semidirect
72. C₄×C₁₃×SD₁₆	C₂²	semidirect
73. C₁₃×#436	C₂²	semidirect
74. C₁₃×#435	C₂²	semidirect
75. C₂×C₁₃×#106	C₂²	semidirect
76. C₁₃×#424	C₂²	semidirect
77. C₁₃×#417	C₂²	semidirect
78. C₁₃×#417	C₂²	semidirect
79. C₂×C₁₃×#102	C₂²	semidirect
80. C₁₃×#408	C₂²	semidirect
81. C₁₃×#407	C₂²	semidirect
82. C₁₃×#405	C₂²	semidirect
117. C₁₃×#135	D₄	semidirect
201. #61063	C₁₃	direct (N × H)
220. C₁₃×#41	C₂×D₄	semidirect
275. C₁₃×Q₁₆	C₂×D₄	semidirect
281. C₁₃×SD₁₆	C₂×D₄	semidirect
288. C₁₃×D₈	C₂×D₄	semidirect
296. C₂×C₈×C₁₃	C₂×D₄	semidirect
320. C₂×#576	C₂×C₁₃	semidirect
321. C₂×#575	C₂×C₁₃	semidirect
322. #3488	C₂×C₁₃	semidirect
323. #3275	C₂×C₁₃	semidirect
324. #3274	C₂×C₁₃	semidirect
325. #3271	C₂×C₁₃	semidirect
326. #3264	C₂×C₁₃	semidirect
327. #3155	C₂×C₁₃	semidirect
328. #3060	C₂×C₁₃	semidirect
329. C₂×#469	C₂×C₁₃	semidirect
330. #3045	C₂×C₁₃	semidirect
331. #3012	C₂×C₁₃	semidirect
332. #3006	C₂×C₁₃	semidirect
333. #2952	C₂×C₁₃	semidirect
334. #2930	C₂×C₁₃	semidirect
409. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
410. C₂²×#41	C₂²×C₁₃	semidirect
413. C₂×#137	C₂²×C₁₃	semidirect
414. C₂×#137	C₂²×C₁₃	semidirect
415. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
416. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
417. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
418. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
419. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
421. C₂×#135	C₂²×C₁₃	semidirect
422. C₂×#135	C₂²×C₁₃	semidirect
423. C₂×#135	C₂²×C₁₃	semidirect
424. C₂²×D₈	C₂²×C₁₃	semidirect
425. C₂²×D₈	C₂²×C₁₃	semidirect
426. C₂×#131	C₂²×C₁₃	semidirect
427. C₂²×M₁₆	C₂²×C₁₃	semidirect
428. #550	C₂²×C₁₃	semidirect
429. #548	C₂²×C₁₃	semidirect
431. #546	C₂²×C₁₃	semidirect
433. D₄²	C₂²×C₁₃	semidirect
435. #537	C₂²×C₁₃	semidirect
437. #535	C₂²×C₁₃	semidirect
441. C₂×#121	C₂²×C₁₃	semidirect
442. #520	C₂²×C₁₃	semidirect
443. #496	C₂²×C₁₃	semidirect
444. #495	C₂²×C₁₃	semidirect
445. #493	C₂²×C₁₃	semidirect
446. #470	C₂²×C₁₃	semidirect
447. #469	C₂²×C₁₃	semidirect
448. #469	C₂²×C₁₃	semidirect
449. #469	C₂²×C₁₃	semidirect
450. #465	C₂²×C₁₃	semidirect
451. #464	C₂²×C₁₃	semidirect
452. #463	C₂²×C₁₃	semidirect
453. #460	C₂²×C₁₃	semidirect
454. #459	C₂²×C₁₃	semidirect
455. #452	C₂²×C₁₃	semidirect
456. #450	C₂²×C₁₃	semidirect
457. #449	C₂²×C₁₃	semidirect
458. #449	C₂²×C₁₃	semidirect
459. #449	C₂²×C₁₃	semidirect
460. #448	C₂²×C₁₃	semidirect
461. #447	C₂²×C₁₃	semidirect
462. #447	C₂²×C₁₃	semidirect
463. #442	C₂²×C₁₃	semidirect
464. #441	C₂²×C₁₃	semidirect
465. C₄×SD₁₆	C₂²×C₁₃	semidirect
466. #436	C₂²×C₁₃	semidirect
467. #435	C₂²×C₁₃	semidirect
468. C₂×#106	C₂²×C₁₃	semidirect
469. #424	C₂²×C₁₃	semidirect
470. #417	C₂²×C₁₃	semidirect
471. #417	C₂²×C₁₃	semidirect
472. C₂×#102	C₂²×C₁₃	semidirect
473. #408	C₂²×C₁₃	semidirect
474. #407	C₂²×C₁₃	semidirect
475. #405	C₂²×C₁₃	semidirect
540. #135	D₄×C₁₃	semidirect
650. #41	C₂×D₄×C₁₃	semidirect
705. Q₁₆	C₂×D₄×C₁₃	semidirect
711. SD₁₆	C₂×D₄×C₁₃	semidirect
718. D₈	C₂×D₄×C₁₃	semidirect
726. C₂×C₈	C₂×D₄×C₁₃	semidirect
750. C₁₃	#61063	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×#576	2
C₂×C₁₃×#575	2
C₁₃×#3488	2
C₁₃×#3275	2
C₁₃×#3274	2
C₁₃×#3271	2
C₁₃×#3264	2
C₁₃×#3155	2
C₁₃×#3060	2
C₂×C₁₃×#469	2
C₁₃×#3045	2
C₁₃×#3012	2
C₁₃×#3006	2
C₁₃×#2952	2
C₁₃×#2930	2
#61063	13

Subgroups — C13×#61063 #15747402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61063 #15747402