Subgroups — C₁₃×#61093 #15747432

Order 3328.

2874 conjugacy classes of subgroups.

The subgroup lattice has 968 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	2	yes	maximal, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3274	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3268	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3264	C₂	1	4	yes	maximal, complemented
10	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
16	C₄×C₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
19	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
20	C₁₃×#576	—	2	16	no	—
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
23	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
28	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
31	C₁₃×#550	C₂²	1	2	yes	complemented
32	C₁₃×#550	C₂²	1	2	yes	complemented
33	C₁₃×#547	—	2	1	no	—
34	C₁₃×#547	C₂²	1	2	yes	complemented
35	C₁₃×#546	—	2	2	no	—
36	C₁₃×#546	C₂²	1	4	yes	complemented
37	D₄²×C₁₃	—	2	1	no	—
38	D₄²×C₁₃	—	2	2	no	—
39	D₄²×C₁₃	—	2	2	no	—
40	D₄²×C₁₃	C₂²	1	2	yes	complemented
41	D₄²×C₁₃	C₂²	1	2	yes	complemented
42	D₄²×C₁₃	C₂²	1	2	yes	complemented
43	C₁₃×#537	C₂²	1	2	yes	complemented
44	C₁₃×#535	—	2	2	no	—
45	C₁₃×#535	C₂²	1	2	yes	complemented
46	C₁₃×#534	—	2	2	no	—
47	C₁₃×#532	—	2	1	no	—
48	C₁₃×#532	C₂²	1	1	yes	characteristic
49	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×#127	—	2	1	no	—
51	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#121	—	2	2	no	—
53	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#496	C₂²	1	4	yes	complemented
56	C₁₃×#493	C₂²	1	2	yes	complemented
57	C₁₃×#492	C₂²	1	2	yes	complemented
58	C₁₃×#469	C₂²	1	4	yes	complemented
59	C₁₃×#468	C₂²	1	4	yes	complemented
60	C₁₃×#466	C₂²	1	4	yes	complemented
61	C₁₃×#465	C₂²	1	4	yes	complemented
62	C₁₃×#464	C₂²	1	2	yes	complemented
63	C₁₃×#463	C₂²	1	2	yes	complemented
64	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#459	C₂²	1	4	yes	complemented
68	C₁₃×#459	C₂²	1	2	yes	complemented
69	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#459	C₂²	1	2	yes	complemented
71	C₁₃×#452	C₂²	1	4	yes	complemented
72	C₁₃×#450	C₂²	1	4	yes	complemented
73	C₁₃×#449	C₂²	1	4	yes	complemented
74	C₁₃×#449	C₂²	1	4	yes	complemented
75	C₁₃×#449	C₂²	1	4	yes	complemented
76	C₁₃×#447	C₂²	1	4	yes	complemented
77	C₁₃×#447	C₂²	1	4	yes	complemented
78	C₁₃×#447	C₂²	1	4	yes	complemented
79	C₁₃×#442	C₂²	1	2	yes	complemented
80	C₁₃×#440	C₂²	1	2	yes	complemented
81	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
82	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
83	C₁₃×#436	C₂²	1	2	yes	complemented
84	C₁₃×#435	C₂²	1	4	yes	complemented
85	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
86	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
88	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#417	C₂²	1	1	yes	characteristic, complemented
90	C₁₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
92	C₁₃×#408	C₂²	1	2	yes	complemented
93	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
94	C₁₃×H(5,𝔽₂)	—	2	8	no	—
95	C₁₃×H(5,𝔽₂)	—	2	8	no	—
96	C₁₃×H(5,𝔽₂)	—	4	4	no	—
97	C₁₃×H(5,𝔽₂)	—	4	4	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	C₂³	1	4	yes	—
103	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×#41	C₂³	1	2	yes	—
105	C₂²×D₄×C₁₃	—	2	4	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	4	no	—
108	C₂²×D₄×C₁₃	—	2	2	no	—
109	C₂²×D₄×C₁₃	—	2	2	no	—
110	C₂²×D₄×C₁₃	—	2	2	no	—
111	C₂²×D₄×C₁₃	—	2	2	no	—
112	C₂²×D₄×C₁₃	—	2	1	no	—
113	C₂²×D₄×C₁₃	—	2	1	no	—
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
116	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
117	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₁₃	—	2	1	no	—
119	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
120	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
121	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
122	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
123	C₁₃×AGL(1,ℤ/8)	D₄	1	8	yes	complemented
124	C₁₃×#135	—	2	8	no	—
125	C₁₃×#135	—	2	16	no	—
126	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
130	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
131	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₁₃×D₈	—	2	8	no	—
133	C₂×C₁₃×D₈	—	2	16	no	—
134	C₂×C₁₃×D₈	C₂³	1	2	yes	—
135	C₂×C₁₃×D₈	C₂³	1	4	yes	—
136	C₂×C₁₃×D₈	C₂³	1	4	yes	—
137	C₂×C₁₃×D₈	C₂³	1	4	yes	—
138	C₂×C₁₃×D₈	C₂³	1	4	yes	—
139	C₂×C₁₃×D₈	C₂³	1	2	yes	—
140	C₁₃×#131	—	2	8	no	—
141	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
143	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
146	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
147	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
148	C₁₃×#127	—	2	2	no	—
149	C₁₃×#127	—	2	2	no	—
150	C₁₃×#127	—	2	2	no	—
151	C₁₃×#127	—	2	1	no	—
152	C₁₃×#127	—	2	1	no	—
153	C₁₃×#127	D₄	1	1	yes	characteristic
154	C₁₃×#127	C₂³	1	2	yes	—
155	C₁₃×#127	C₂³	1	2	yes	—
156	C₁₃×#127	C₂³	1	1	yes	characteristic
157	C₁₃×#124	—	2	2	no	—
158	C₁₃×#124	D₄	1	2	yes	—
159	C₁₃×#124	C₂³	1	2	yes	—
160	C₁₃×#123	—	2	4	no	—
161	C₁₃×#123	—	2	4	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
164	C₁₃×#121	—	2	4	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	2	no	—
167	C₁₃×#121	—	2	1	no	—
168	C₁₃×#121	—	2	1	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	2	no	—
172	C₁₃×#121	—	2	4	no	—
173	C₁₃×#121	—	2	4	no	—
174	C₁₃×#121	—	2	4	no	—
175	C₁₃×#121	D₄	1	2	yes	—
176	C₁₃×#121	D₄	1	2	yes	—
177	C₁₃×#121	C₂³	1	4	yes	—
178	C₁₃×#121	C₂³	1	4	yes	—
179	C₁₃×#121	C₂³	1	4	yes	—
180	C₁₃×#120	—	2	4	no	—
181	C₁₃×#120	—	2	4	no	—
182	C₁₃×#120	—	2	4	no	—
183	C₁₃×#120	—	2	4	no	—
184	C₁₃×#120	—	2	4	no	—
185	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
186	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	1	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	1	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
196	C₄×D₄×C₁₃	C₂³	1	2	yes	—
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	2	yes	—
201	C₁₃×#117	—	2	1	no	—
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
205	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₁₃×#107	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×#103	C₂³	1	2	yes	—
215	C₁₃×#103	C₂³	1	2	yes	—
216	C₁₃×#103	C₂³	1	2	yes	—
217	C₁₃×#102	C₂³	1	4	yes	—
218	C₁₃×#102	C₂³	1	4	yes	—
219	C₁₃×#102	C₂³	1	2	yes	—
220	C₁₃×#102	C₂³	1	2	yes	—
221	C₁₃×#102	C₂³	1	2	yes	—
222	C₁₃×#102	C₂³	1	2	yes	—
223	C₁₃×#102	C₂³	1	2	yes	—
224	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₁₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₁₃	C₂³	1	2	yes	—
228	#61093	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂⁴×C₁₃	—	2	1	no	—
230	C₂⁴×C₁₃	—	2	4	no	—
231	C₂⁴×C₁₃	—	2	4	no	—
232	C₂⁴×C₁₃	—	2	2	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	4	no	—
236	C₁₃×#41	—	2	8	no	—
237	C₁₃×#41	—	2	8	no	—
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	4	4	no	—
241	C₁₃×#41	—	4	4	no	—
242	C₁₃×#41	—	4	8	no	—
243	C₁₃×#41	—	4	8	no	—
244	C₁₃×#41	C₂×D₄	1	4	yes	complemented
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	8	no	—
250	C₂×D₄×C₁₃	—	2	8	no	—
251	C₂×D₄×C₁₃	—	2	4	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	4	no	—
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	4	no	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	4	no	—
270	C₂×D₄×C₁₃	—	4	4	no	—
271	C₂×D₄×C₁₃	—	4	4	no	—
272	C₂×D₄×C₁₃	—	4	8	no	—
273	C₂×D₄×C₁₃	—	4	16	no	—
274	C₂×D₄×C₁₃	—	4	8	no	—
275	C₂×D₄×C₁₃	—	4	16	no	—
276	C₂×D₄×C₁₃	—	8	2	no	—
277	C₂×D₄×C₁₃	—	8	4	no	—
278	C₂×D₄×C₁₃	—	8	4	no	—
279	C₂×D₄×C₁₃	—	8	2	no	—
280	C₂×D₄×C₁₃	—	8	4	no	—
281	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
282	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	complemented
286	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	1	no	—
292	C₂²×C₄×C₁₃	—	2	1	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	2	4	no	—
295	C₂²×C₄×C₁₃	—	2	2	no	—
296	C₂²×C₄×C₁₃	—	2	4	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	8	2	no	—
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×Q₁₆	—	2	4	no	—
305	C₁₃×SD₁₆	—	2	4	no	—
306	C₁₃×SD₁₆	—	2	4	no	—
307	C₁₃×SD₁₆	—	2	8	no	—
308	C₁₃×SD₁₆	—	4	4	no	—
309	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
310	C₁₃×D₈	—	2	8	no	—
311	C₁₃×D₈	—	2	4	no	—
312	C₁₃×D₈	—	2	8	no	—
313	C₁₃×D₈	—	2	8	no	—
314	C₁₃×D₈	—	4	4	no	—
315	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
316	C₁₃×M₁₆	—	2	2	no	—
317	C₁₃×M₁₆	—	2	8	no	—
318	C₁₃×M₁₆	C₂×D₄	1	4	yes	complemented
319	C₂×C₈×C₁₃	—	2	4	no	—
320	C₂×C₈×C₁₃	—	2	8	no	—
321	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	4	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	—	2	1	no	—
329	C₁₃×C₄⋊C₄	—	2	1	no	—
330	C₁₃×C₄⋊C₄	—	2	1	no	—
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
335	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
336	C₁₃×C₂²⋊C₄	—	2	4	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	4	no	—
342	C₁₃×C₂²⋊C₄	—	2	1	no	—
343	C₁₃×C₂²⋊C₄	—	2	1	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
348	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
349	C₄²×C₁₃	—	2	1	no	—
350	C₄²×C₁₃	—	2	1	no	—
351	C₄²×C₁₃	—	2	1	no	—
352	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
355	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
356	C₂×#576	C₂×C₁₃	1	2	yes	complemented
357	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#3284	C₂×C₁₃	1	2	yes	complemented
360	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
361	#3274	C₂×C₁₃	1	2	yes	complemented
362	#3272	C₂×C₁₃	1	2	yes	complemented
363	#3268	C₂×C₁₃	1	4	yes	complemented
364	#3264	C₂×C₁₃	1	4	yes	complemented
365	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
366	#3062	C₂×C₁₃	1	2	yes	complemented
367	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#3012	C₂×C₁₃	1	2	yes	complemented
370	#3008	C₂×C₁₃	1	2	yes	complemented
371	C₄×AGL(1,ℤ/8)	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#2935	C₂×C₁₃	1	1	yes	characteristic, complemented
373	C₂³×C₁₃	—	2	2	no	—
374	C₂³×C₁₃	—	2	1	no	—
375	C₂³×C₁₃	—	2	4	no	—
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	4	no	—
378	C₂³×C₁₃	—	4	8	no	—
379	C₂³×C₁₃	—	4	8	no	—
380	C₂³×C₁₃	—	4	4	no	—
381	C₂³×C₁₃	—	8	1	no	—
382	C₂³×C₁₃	—	8	1	no	—
383	C₂³×C₁₃	—	8	2	no	—
384	C₂³×C₁₃	—	8	2	no	—
385	C₂³×C₁₃	—	8	4	no	—
386	C₂³×C₁₃	—	8	4	no	—
387	C₂³×C₁₃	—	8	4	no	—
388	C₂³×C₁₃	—	8	4	no	—
389	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
390	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
391	Q₈×C₁₃	—	2	4	no	—
392	Q₈×C₁₃	—	2	1	no	—
393	Q₈×C₁₃	—	2	2	no	—
394	Q₈×C₁₃	—	2	2	no	—
395	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
396	D₄×C₁₃	—	2	4	no	—
397	D₄×C₁₃	—	2	8	no	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	2	4	no	—
400	D₄×C₁₃	—	2	4	no	—
401	D₄×C₁₃	—	2	4	no	—
402	D₄×C₁₃	—	2	2	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	2	1	no	—
405	D₄×C₁₃	—	2	2	no	—
406	D₄×C₁₃	—	2	4	no	—
407	D₄×C₁₃	—	4	2	no	—
408	D₄×C₁₃	—	4	8	no	—
409	D₄×C₁₃	—	4	8	no	—
410	D₄×C₁₃	—	4	8	no	—
411	D₄×C₁₃	—	4	4	no	—
412	D₄×C₁₃	—	4	8	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	4	no	—
415	D₄×C₁₃	—	4	2	no	—
416	D₄×C₁₃	—	4	4	no	—
417	D₄×C₁₃	—	8	1	no	—
418	D₄×C₁₃	—	8	2	no	—
419	D₄×C₁₃	—	8	2	no	—
420	D₄×C₁₃	—	8	4	no	—
421	D₄×C₁₃	—	8	4	no	—
422	D₄×C₁₃	—	8	4	no	—
423	D₄×C₁₃	C₂²×D₄	1	4	yes	—
424	D₄×C₁₃	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₁₃	—	2	1	no	—
426	C₂×C₄×C₁₃	—	2	4	no	—
427	C₂×C₄×C₁₃	—	2	2	no	—
428	C₂×C₄×C₁₃	—	2	4	no	—
429	C₂×C₄×C₁₃	—	2	4	no	—
430	C₂×C₄×C₁₃	—	2	1	no	—
431	C₂×C₄×C₁₃	—	2	1	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	4	1	no	—
435	C₂×C₄×C₁₃	—	4	8	no	—
436	C₂×C₄×C₁₃	—	4	8	no	—
437	C₂×C₄×C₁₃	—	4	2	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	4	4	no	—
440	C₂×C₄×C₁₃	—	4	2	no	—
441	C₂×C₄×C₁₃	—	8	2	no	—
442	C₂×C₄×C₁₃	—	8	1	no	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
451	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
452	C₈×C₁₃	—	2	2	no	—
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	2	no	—
455	C₈×C₁₃	C₂²×D₄	1	4	yes	—
456	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
457	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
458	#576	—	2	16	no	—
459	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
460	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
461	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
462	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
463	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
464	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
465	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
466	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
467	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
468	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
469	#550	C₂²×C₁₃	1	2	yes	complemented
470	#550	C₂²×C₁₃	1	2	yes	complemented
471	#547	—	2	1	no	—
472	#547	C₂²×C₁₃	1	2	yes	complemented
473	#546	—	2	2	no	—
474	#546	C₂²×C₁₃	1	4	yes	complemented
475	D₄²	—	2	1	no	—
476	D₄²	—	2	2	no	—
477	D₄²	—	2	2	no	—
478	D₄²	C₂²×C₁₃	1	2	yes	complemented
479	D₄²	C₂²×C₁₃	1	2	yes	complemented
480	D₄²	C₂²×C₁₃	1	2	yes	complemented
481	#537	C₂²×C₁₃	1	2	yes	complemented
482	#535	—	2	2	no	—
483	#535	C₂²×C₁₃	1	2	yes	complemented
484	#534	—	2	2	no	—
485	#532	—	2	1	no	—
486	#532	C₂²×C₁₃	1	1	yes	characteristic
487	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	C₂×#127	—	2	1	no	—
489	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic, complemented
490	C₂×#121	—	2	2	no	—
491	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#496	C₂²×C₁₃	1	4	yes	complemented
494	#493	C₂²×C₁₃	1	2	yes	complemented
495	#492	C₂²×C₁₃	1	2	yes	complemented
496	#469	C₂²×C₁₃	1	4	yes	complemented
497	#468	C₂²×C₁₃	1	4	yes	complemented
498	#466	C₂²×C₁₃	1	4	yes	complemented
499	#465	C₂²×C₁₃	1	4	yes	complemented
500	#464	C₂²×C₁₃	1	2	yes	complemented
501	#463	C₂²×C₁₃	1	2	yes	complemented
502	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#459	C₂²×C₁₃	1	4	yes	complemented
506	#459	C₂²×C₁₃	1	2	yes	complemented
507	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
508	#459	C₂²×C₁₃	1	2	yes	complemented
509	#452	C₂²×C₁₃	1	4	yes	complemented
510	#450	C₂²×C₁₃	1	4	yes	complemented
511	#449	C₂²×C₁₃	1	4	yes	complemented
512	#449	C₂²×C₁₃	1	4	yes	complemented
513	#449	C₂²×C₁₃	1	4	yes	complemented
514	#447	C₂²×C₁₃	1	4	yes	complemented
515	#447	C₂²×C₁₃	1	4	yes	complemented
516	#447	C₂²×C₁₃	1	4	yes	complemented
517	#442	C₂²×C₁₃	1	2	yes	complemented
518	#440	C₂²×C₁₃	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
520	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
521	#436	C₂²×C₁₃	1	2	yes	complemented
522	#435	C₂²×C₁₃	1	4	yes	complemented
523	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
524	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
525	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
527	#417	C₂²×C₁₃	1	1	yes	characteristic, complemented
528	#416	C₂²×C₁₃	1	2	yes	complemented
529	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
530	#408	C₂²×C₁₃	1	2	yes	complemented
531	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
532	C₂²×C₁₃	—	2	1	no	—
533	C₂²×C₁₃	—	2	1	no	—
534	C₂²×C₁₃	—	2	4	no	—
535	C₂²×C₁₃	—	2	4	no	—
536	C₂²×C₁₃	—	2	2	no	—
537	C₂²×C₁₃	—	2	4	no	—
538	C₂²×C₁₃	—	2	4	no	—
539	C₂²×C₁₃	—	4	1	no	—
540	C₂²×C₁₃	—	4	2	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	1	no	—
543	C₂²×C₁₃	—	4	4	no	—
544	C₂²×C₁₃	—	4	2	no	—
545	C₂²×C₁₃	—	4	4	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	4	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	8	4	no	—
550	C₂²×C₁₃	—	16	4	no	—
551	C₂²×C₁₃	—	16	8	no	—
552	C₂²×C₁₃	—	16	8	no	—
553	C₂²×C₁₃	D₄²	1	2	yes	—
554	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₁₃	—	2	1	no	—
556	C₄×C₁₃	—	2	1	no	—
557	C₄×C₁₃	—	2	2	no	—
558	C₄×C₁₃	—	2	4	no	—
559	C₄×C₁₃	—	2	1	no	—
560	C₄×C₁₃	—	4	1	no	—
561	C₄×C₁₃	—	4	2	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	—	4	1	no	—
564	C₄×C₁₃	D₄²	1	2	yes	—
565	C₄×C₁₃	#576	1	2	yes	complemented
566	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
567	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
568	H(5,𝔽₂)	—	2	8	no	—
569	H(5,𝔽₂)	—	2	8	no	—
570	H(5,𝔽₂)	—	4	4	no	—
571	H(5,𝔽₂)	—	4	4	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	C₂³×C₁₃	1	2	yes	—
575	C₂×#41	C₂³×C₁₃	1	4	yes	—
576	C₂×#41	C₂³×C₁₃	1	4	yes	—
577	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
578	C₂×#41	C₂³×C₁₃	1	2	yes	—
579	C₂²×D₄	—	2	4	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	4	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	1	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
589	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
590	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
591	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂³×C₄	—	2	1	no	—
593	AGL(1,ℤ/8)	—	2	16	no	—
594	AGL(1,ℤ/8)	—	2	16	no	—
595	AGL(1,ℤ/8)	—	2	8	no	—
596	AGL(1,ℤ/8)	—	4	4	no	—
597	AGL(1,ℤ/8)	D₄×C₁₃	1	8	yes	complemented
598	#135	—	2	8	no	—
599	#135	—	2	16	no	—
600	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
604	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
605	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂×D₈	—	2	8	no	—
607	C₂×D₈	—	2	16	no	—
608	C₂×D₈	C₂³×C₁₃	1	2	yes	—
609	C₂×D₈	C₂³×C₁₃	1	4	yes	—
610	C₂×D₈	C₂³×C₁₃	1	4	yes	—
611	C₂×D₈	C₂³×C₁₃	1	4	yes	—
612	C₂×D₈	C₂³×C₁₃	1	4	yes	—
613	C₂×D₈	C₂³×C₁₃	1	2	yes	—
614	#131	—	2	8	no	—
615	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
616	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
617	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
619	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
620	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
621	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
622	#127	—	2	2	no	—
623	#127	—	2	2	no	—
624	#127	—	2	2	no	—
625	#127	—	2	1	no	—
626	#127	—	2	1	no	—
627	#127	D₄×C₁₃	1	1	yes	characteristic
628	#127	C₂³×C₁₃	1	2	yes	—
629	#127	C₂³×C₁₃	1	2	yes	—
630	#127	C₂³×C₁₃	1	1	yes	characteristic
631	#124	—	2	2	no	—
632	#124	D₄×C₁₃	1	2	yes	—
633	#124	C₂³×C₁₃	1	2	yes	—
634	#123	—	2	4	no	—
635	#123	—	2	4	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
638	#121	—	2	4	no	—
639	#121	—	2	2	no	—
640	#121	—	2	2	no	—
641	#121	—	2	1	no	—
642	#121	—	2	1	no	—
643	#121	—	2	2	no	—
644	#121	—	2	2	no	—
645	#121	—	2	2	no	—
646	#121	—	2	4	no	—
647	#121	—	2	4	no	—
648	#121	—	2	4	no	—
649	#121	D₄×C₁₃	1	2	yes	—
650	#121	D₄×C₁₃	1	2	yes	—
651	#121	C₂³×C₁₃	1	4	yes	—
652	#121	C₂³×C₁₃	1	4	yes	—
653	#121	C₂³×C₁₃	1	4	yes	—
654	#120	—	2	4	no	—
655	#120	—	2	4	no	—
656	#120	—	2	4	no	—
657	#120	—	2	4	no	—
658	#120	—	2	4	no	—
659	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
660	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	—	2	1	no	—
666	C₄×D₄	—	2	1	no	—
667	C₄×D₄	—	2	1	no	—
668	C₄×D₄	—	2	1	no	—
669	C₄×D₄	C₂³×C₁₃	1	2	yes	—
670	C₄×D₄	C₂³×C₁₃	1	2	yes	—
671	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
672	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
673	C₄×D₄	C₂³×C₁₃	1	2	yes	—
674	C₄×D₄	C₂³×C₁₃	1	2	yes	—
675	#117	—	2	1	no	—
676	#117	C₂³×C₁₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	—	2	1	no	—
680	C₂×C₂²⋊C₄	—	2	4	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	#107	C₂³×C₁₃	1	2	yes	—
684	#106	C₂³×C₁₃	1	2	yes	—
685	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
686	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
687	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
688	#103	C₂³×C₁₃	1	2	yes	—
689	#103	C₂³×C₁₃	1	2	yes	—
690	#103	C₂³×C₁₃	1	2	yes	—
691	#102	C₂³×C₁₃	1	4	yes	—
692	#102	C₂³×C₁₃	1	4	yes	—
693	#102	C₂³×C₁₃	1	2	yes	—
694	#102	C₂³×C₁₃	1	2	yes	—
695	#102	C₂³×C₁₃	1	2	yes	—
696	#102	C₂³×C₁₃	1	2	yes	—
697	#102	C₂³×C₁₃	1	2	yes	—
698	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
699	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
700	#97	C₂³×C₁₃	1	2	yes	—
701	C₄×C₈	C₂³×C₁₃	1	2	yes	—
702	C₂×C₁₃	—	2	2	no	—
703	C₂×C₁₃	—	4	4	no	—
704	C₂×C₁₃	—	4	4	no	—
705	C₂×C₁₃	—	4	2	no	—
706	C₂×C₁₃	—	8	4	no	—
707	C₂×C₁₃	—	8	2	no	—
708	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
709	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
710	C₂×C₁₃	#3585	1	1	yes	characteristic
711	C₂⁴	—	2	1	no	—
712	C₂⁴	—	2	4	no	—
713	C₂⁴	—	2	4	no	—
714	C₂⁴	—	2	2	no	—
715	#41	—	2	4	no	—
716	#41	—	2	2	no	—
717	#41	—	2	4	no	—
718	#41	—	2	8	no	—
719	#41	—	2	8	no	—
720	#41	—	2	4	no	—
721	#41	—	2	4	no	—
722	#41	—	4	4	no	—
723	#41	—	4	4	no	—
724	#41	—	4	8	no	—
725	#41	—	4	8	no	—
726	#41	C₂×D₄×C₁₃	1	4	yes	complemented
727	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
728	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	8	no	—
732	C₂×D₄	—	2	8	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	4	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	1	no	—
740	C₂×D₄	—	2	4	no	—
741	C₂×D₄	—	2	1	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	2	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	1	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	4	4	no	—
753	C₂×D₄	—	4	4	no	—
754	C₂×D₄	—	4	8	no	—
755	C₂×D₄	—	4	16	no	—
756	C₂×D₄	—	4	8	no	—
757	C₂×D₄	—	4	16	no	—
758	C₂×D₄	—	8	2	no	—
759	C₂×D₄	—	8	4	no	—
760	C₂×D₄	—	8	4	no	—
761	C₂×D₄	—	8	2	no	—
762	C₂×D₄	—	8	4	no	—
763	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
764	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
765	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
766	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
767	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	complemented
768	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
769	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
770	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
771	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	1	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	4	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	8	2	no	—
782	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
785	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
786	Q₁₆	—	2	4	no	—
787	SD₁₆	—	2	4	no	—
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	8	no	—
790	SD₁₆	—	4	4	no	—
791	SD₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
792	D₈	—	2	8	no	—
793	D₈	—	2	4	no	—
794	D₈	—	2	8	no	—
795	D₈	—	2	8	no	—
796	D₈	—	4	4	no	—
797	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
798	M₁₆	—	2	2	no	—
799	M₁₆	—	2	8	no	—
800	M₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
801	C₂×C₈	—	2	4	no	—
802	C₂×C₈	—	2	8	no	—
803	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
804	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
805	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
806	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
807	C₄⋊C₄	—	2	1	no	—
808	C₄⋊C₄	—	2	4	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	C₂×D₄×C₁₃	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
817	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	1	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	1	no	—
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
830	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
831	C₄²	—	2	1	no	—
832	C₄²	—	2	1	no	—
833	C₄²	—	2	1	no	—
834	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
835	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
838	C₁₃	#61093	1	1	yes	characteristic, direct product factor, Sylow
839	C₂³	—	2	2	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	4	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	4	no	—
844	C₂³	—	4	8	no	—
845	C₂³	—	4	8	no	—
846	C₂³	—	4	4	no	—
847	C₂³	—	8	1	no	—
848	C₂³	—	8	1	no	—
849	C₂³	—	8	2	no	—
850	C₂³	—	8	2	no	—
851	C₂³	—	8	4	no	—
852	C₂³	—	8	4	no	—
853	C₂³	—	8	4	no	—
854	C₂³	—	8	4	no	—
855	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
856	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
857	Q₈	—	2	4	no	—
858	Q₈	—	2	1	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
862	D₄	—	2	4	no	—
863	D₄	—	2	8	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	4	no	—
866	D₄	—	2	4	no	—
867	D₄	—	2	4	no	—
868	D₄	—	2	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	1	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	4	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	8	no	—
876	D₄	—	4	8	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	2	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	1	no	—
886	D₄	—	8	4	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	C₂²×D₄×C₁₃	1	4	yes	—
890	D₄	C₂²×D₄×C₁₃	1	2	yes	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	4	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	4	no	—
895	C₂×C₄	—	2	4	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	8	no	—
902	C₂×C₄	—	4	8	no	—
903	C₂×C₄	—	4	2	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	1	no	—
909	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
913	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
916	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
917	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
918	C₈	—	2	2	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	C₂²×D₄×C₁₃	1	4	yes	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	4	no	—
925	C₂²	—	2	4	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	4	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	1	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	4	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	4	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	4	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	8	4	no	—
940	C₂²	—	16	4	no	—
941	C₂²	—	16	8	no	—
942	C₂²	—	16	8	no	—
943	C₂²	D₄²×C₁₃	1	2	yes	—
944	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
945	C₄	—	2	1	no	—
946	C₄	—	2	1	no	—
947	C₄	—	2	1	no	—
948	C₄	—	2	2	no	—
949	C₄	—	2	4	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	D₄²×C₁₃	1	2	yes	—
955	C₄	C₁₃×#576	1	2	yes	complemented
956	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
957	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
958	C₂	—	2	2	no	—
959	C₂	—	4	4	no	—
960	C₂	—	4	4	no	—
961	C₂	—	4	2	no	—
962	C₂	—	8	4	no	—
963	C₂	—	8	2	no	—
964	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
965	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
966	C₂	C₁₃×#3585	1	1	yes	characteristic

	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×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3496	C₂	semidirect
4. C₁₃×#3284	C₂	semidirect
5. D₄×C₁₃×D₈	C₂	semidirect
6. C₁₃×#3274	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₁₃×#3268	C₂	semidirect
9. C₁₃×#3264	C₂	semidirect
10. C₁₃×#3151	C₂	semidirect
11. C₁₃×#3062	C₂	semidirect
12. C₁₃×#3035	C₂	semidirect
13. C₂×C₁₃×#459	C₂	semidirect
14. C₁₃×#3012	C₂	semidirect
15. C₁₃×#3008	C₂	semidirect
16. C₄×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
17. C₁₃×#2935	C₂	semidirect
18. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
19. C₂×C₁₃×H(5,𝔽₂)	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×#135	C₂²	semidirect
27. C₂×C₁₃×#135	C₂²	semidirect
28. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₂×C₁₃×#131	C₂²	semidirect
31. C₁₃×#550	C₂²	semidirect
32. C₁₃×#550	C₂²	semidirect
34. C₁₃×#547	C₂²	semidirect
36. C₁₃×#546	C₂²	semidirect
40. D₄²×C₁₃	C₂²	semidirect
41. D₄²×C₁₃	C₂²	semidirect
42. D₄²×C₁₃	C₂²	semidirect
43. C₁₃×#537	C₂²	semidirect
45. C₁₃×#535	C₂²	semidirect
49. C₁₃×#532	C₂²	semidirect
51. C₂×C₁₃×#127	C₂²	semidirect
53. C₄×C₁₃×#41	C₂²	semidirect
54. C₂×C₄×D₄×C₁₃	C₂²	semidirect
55. C₁₃×#496	C₂²	semidirect
56. C₁₃×#493	C₂²	semidirect
57. C₁₃×#492	C₂²	semidirect
58. C₁₃×#469	C₂²	semidirect
59. C₁₃×#468	C₂²	semidirect
60. C₁₃×#466	C₂²	semidirect
61. C₁₃×#465	C₂²	semidirect
62. C₁₃×#464	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#459	C₂²	semidirect
68. C₁₃×#459	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#452	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#449	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
75. C₁₃×#449	C₂²	semidirect
76. C₁₃×#447	C₂²	semidirect
77. C₁₃×#447	C₂²	semidirect
78. C₁₃×#447	C₂²	semidirect
79. C₁₃×#442	C₂²	semidirect
80. C₁₃×#440	C₂²	semidirect
81. C₄×C₁₃×SD₁₆	C₂²	semidirect
82. C₄×C₁₃×D₈	C₂²	semidirect
83. C₁₃×#436	C₂²	semidirect
84. C₁₃×#435	C₂²	semidirect
85. C₈×D₄×C₁₃	C₂²	semidirect
86. C₁₃×#428	C₂²	semidirect
87. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
88. C₁₃×#418	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#416	C₂²	semidirect
91. C₂×C₁₃×#102	C₂²	semidirect
92. C₁₃×#408	C₂²	semidirect
93. C₄×C₁₃×M₁₆	C₂²	semidirect
123. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
228. #61093	C₁₃	direct (N × H)
244. C₁₃×#41	C₂×D₄	semidirect
285. C₂×D₄×C₁₃	C₂×D₄	semidirect
309. C₁₃×SD₁₆	C₂×D₄	semidirect
315. C₁₃×D₈	C₂×D₄	semidirect
318. C₁₃×M₁₆	C₂×D₄	semidirect
356. C₂×#576	C₂×C₁₃	semidirect
357. #3498	C₂×C₁₃	semidirect
358. #3496	C₂×C₁₃	semidirect
359. #3284	C₂×C₁₃	semidirect
360. D₄×D₈	C₂×C₁₃	semidirect
361. #3274	C₂×C₁₃	semidirect
362. #3272	C₂×C₁₃	semidirect
363. #3268	C₂×C₁₃	semidirect
364. #3264	C₂×C₁₃	semidirect
365. #3151	C₂×C₁₃	semidirect
366. #3062	C₂×C₁₃	semidirect
367. #3035	C₂×C₁₃	semidirect
368. C₂×#459	C₂×C₁₃	semidirect
369. #3012	C₂×C₁₃	semidirect
370. #3008	C₂×C₁₃	semidirect
371. C₄×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
372. #2935	C₂×C₁₃	semidirect
456. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
457. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
460. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
461. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
462. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
463. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
464. C₂×#135	C₂²×C₁₃	semidirect
465. C₂×#135	C₂²×C₁₃	semidirect
466. C₂²×D₈	C₂²×C₁₃	semidirect
467. C₂²×D₈	C₂²×C₁₃	semidirect
468. C₂×#131	C₂²×C₁₃	semidirect
469. #550	C₂²×C₁₃	semidirect
470. #550	C₂²×C₁₃	semidirect
472. #547	C₂²×C₁₃	semidirect
474. #546	C₂²×C₁₃	semidirect
478. D₄²	C₂²×C₁₃	semidirect
479. D₄²	C₂²×C₁₃	semidirect
480. D₄²	C₂²×C₁₃	semidirect
481. #537	C₂²×C₁₃	semidirect
483. #535	C₂²×C₁₃	semidirect
487. #532	C₂²×C₁₃	semidirect
489. C₂×#127	C₂²×C₁₃	semidirect
491. C₄×#41	C₂²×C₁₃	semidirect
492. C₂×C₄×D₄	C₂²×C₁₃	semidirect
493. #496	C₂²×C₁₃	semidirect
494. #493	C₂²×C₁₃	semidirect
495. #492	C₂²×C₁₃	semidirect
496. #469	C₂²×C₁₃	semidirect
497. #468	C₂²×C₁₃	semidirect
498. #466	C₂²×C₁₃	semidirect
499. #465	C₂²×C₁₃	semidirect
500. #464	C₂²×C₁₃	semidirect
501. #463	C₂²×C₁₃	semidirect
502. #462	C₂²×C₁₃	semidirect
503. #461	C₂²×C₁₃	semidirect
504. #460	C₂²×C₁₃	semidirect
505. #459	C₂²×C₁₃	semidirect
506. #459	C₂²×C₁₃	semidirect
507. #459	C₂²×C₁₃	semidirect
508. #459	C₂²×C₁₃	semidirect
509. #452	C₂²×C₁₃	semidirect
510. #450	C₂²×C₁₃	semidirect
511. #449	C₂²×C₁₃	semidirect
512. #449	C₂²×C₁₃	semidirect
513. #449	C₂²×C₁₃	semidirect
514. #447	C₂²×C₁₃	semidirect
515. #447	C₂²×C₁₃	semidirect
516. #447	C₂²×C₁₃	semidirect
517. #442	C₂²×C₁₃	semidirect
518. #440	C₂²×C₁₃	semidirect
519. C₄×SD₁₆	C₂²×C₁₃	semidirect
520. C₄×D₈	C₂²×C₁₃	semidirect
521. #436	C₂²×C₁₃	semidirect
522. #435	C₂²×C₁₃	semidirect
523. C₈×D₄	C₂²×C₁₃	semidirect
524. #428	C₂²×C₁₃	semidirect
525. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
526. #418	C₂²×C₁₃	semidirect
527. #417	C₂²×C₁₃	semidirect
528. #416	C₂²×C₁₃	semidirect
529. C₂×#102	C₂²×C₁₃	semidirect
530. #408	C₂²×C₁₃	semidirect
531. C₄×M₁₆	C₂²×C₁₃	semidirect
565. C₄×C₁₃	#576	semidirect
597. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
726. #41	C₂×D₄×C₁₃	semidirect
767. C₂×D₄	C₂×D₄×C₁₃	semidirect
791. SD₁₆	C₂×D₄×C₁₃	semidirect
797. D₈	C₂×D₄×C₁₃	semidirect
800. M₁₆	C₂×D₄×C₁₃	semidirect
838. C₁₃	#61093	direct (N × H)
955. C₄	C₁₃×#576	semidirect

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
C₁₃×#3498	2
C₁₃×#3496	2
C₁₃×#3284	2
D₄×C₁₃×D₈	2
C₁₃×#3274	2
C₁₃×#3272	2
C₁₃×#3268	2
C₁₃×#3264	2
C₁₃×#3151	2
C₁₃×#3062	2
C₁₃×#3035	2
C₂×C₁₃×#459	2
C₁₃×#3012	2
C₁₃×#3008	2
C₄×C₁₃×AGL(1,ℤ/8)	2
C₁₃×#2935	2
#61093	13

Subgroups — C13×#61093 #15747432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61093 #15747432