Subgroups — C₁₃×#61106 #15747445

Order 3328.

2656 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3585	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3292	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3290	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3288	C₂	1	8	yes	maximal, complemented
7	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3068	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3067	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3021	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3019	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#585	C₂²	1	2	yes	complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₁₃×#578	—	2	1	no	—
18	C₁₃×#578	C₂²	1	2	yes	complemented
19	C₁₃×#577	—	2	4	no	—
20	C₁₃×#577	—	2	2	no	—
21	C₁₃×#577	C₂²	1	8	yes	complemented
22	C₁₃×#577	C₂²	1	4	yes	complemented
23	C₁₃×#576	—	2	4	no	—
24	C₁₃×#576	—	2	2	no	—
25	C₁₃×#576	—	2	2	no	—
26	C₁₃×#576	—	2	1	no	—
27	C₁₃×#576	C₂²	1	4	yes	complemented
28	C₁₃×#576	C₂²	1	4	yes	complemented
29	C₁₃×#576	C₂²	1	8	yes	complemented
30	C₁₃×#576	C₂²	1	2	yes	complemented
31	C₁₃×#575	—	2	4	no	—
32	C₁₃×#575	—	2	2	no	—
33	C₁₃×#575	C₂²	1	1	yes	characteristic
34	C₁₃×#575	C₂²	1	2	yes	complemented
35	C₁₃×#575	C₂²	1	2	yes	complemented
36	C₂×C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
37	C₂×C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
38	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
39	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
40	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#135	—	2	2	no	—
42	C₂×C₁₃×#135	—	2	1	no	—
43	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₁₃×D₈	—	2	1	no	—
46	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#568	C₂²	1	2	yes	complemented
48	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#535	C₂²	1	2	yes	complemented
51	C₁₃×#496	C₂²	1	4	yes	complemented
52	C₁₃×#495	C₂²	1	2	yes	complemented
53	C₁₃×#493	C₂²	1	2	yes	complemented
54	C₁₃×#473	C₂²	1	2	yes	complemented
55	C₁₃×#472	C₂²	1	2	yes	complemented
56	C₁₃×#472	C₂²	1	4	yes	complemented
57	C₁₃×#472	C₂²	1	4	yes	complemented
58	C₁₃×#472	C₂²	1	8	yes	complemented
59	C₁₃×#471	C₂²	1	4	yes	complemented
60	C₁₃×#471	C₂²	1	8	yes	complemented
61	C₁₃×#455	C₂²	1	8	yes	complemented
62	C₁₃×#454	C₂²	1	8	yes	complemented
63	C₁₃×#453	C₂²	1	8	yes	complemented
64	C₁₃×#453	C₂²	1	8	yes	complemented
65	C₁₃×#444	C₂²	1	4	yes	complemented
66	C₁₃×#444	C₂²	1	4	yes	complemented
67	C₁₃×#443	C₂²	1	4	yes	complemented
68	C₁₃×#443	C₂²	1	4	yes	complemented
69	C₁₃×#430	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#421	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×#421	C₂²	1	2	yes	complemented
73	C₁₃×#421	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#413	C₂²	1	2	yes	complemented
75	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
76	C₁₃×#405	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×2₋¹⁺⁴	—	2	2	no	—
78	C₁₃×2₋¹⁺⁴	—	2	2	no	—
79	C₁₃×2₋¹⁺⁴	C₂³	1	4	yes	complemented
80	C₁₃×H(5,𝔽₂)	—	2	4	no	—
81	C₁₃×H(5,𝔽₂)	—	2	4	no	—
82	C₁₃×H(5,𝔽₂)	—	2	2	no	—
83	C₁₃×H(5,𝔽₂)	—	2	2	no	—
84	C₁₃×H(5,𝔽₂)	—	4	2	no	—
85	C₁₃×H(5,𝔽₂)	—	4	2	no	—
86	C₁₃×H(5,𝔽₂)	C₂³	1	8	yes	—
87	C₁₃×H(5,𝔽₂)	C₂³	1	4	yes	complemented
88	C₂×C₁₃×#41	—	2	4	no	—
89	C₂×C₁₃×#41	—	2	4	no	—
90	C₂×C₁₃×#41	—	2	2	no	—
91	C₂×C₁₃×#41	—	2	2	no	—
92	C₂×C₁₃×#41	—	4	2	no	—
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×#41	C₂³	1	2	yes	—
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×D₄×C₁₃	—	2	2	no	—
98	C₂²×D₄×C₁₃	—	2	2	no	—
99	C₂²×D₄×C₁₃	—	4	2	no	—
100	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
101	C₁₃×#137	—	2	2	no	—
102	C₁₃×#137	—	2	2	no	—
103	C₁₃×#137	—	2	8	no	—
104	C₁₃×#137	—	2	4	no	—
105	C₁₃×#137	—	2	4	no	—
106	C₁₃×#137	D₄	1	2	yes	complemented
107	C₁₃×#137	D₄	1	2	yes	complemented
108	C₁₃×#137	C₂³	1	4	yes	—
109	C₁₃×#137	C₂³	1	4	yes	complemented
110	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
111	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
112	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
113	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
114	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
115	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
116	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
117	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
118	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
119	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
120	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
121	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
122	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
123	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
124	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	complemented
125	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	—
126	C₁₃×AGL(1,ℤ/8)	C₂³	1	8	yes	—
127	C₁₃×AGL(1,ℤ/8)	C₂³	1	4	yes	complemented
128	C₁₃×AGL(1,ℤ/8)	C₂³	1	8	yes	complemented
129	C₁₃×#135	—	2	4	no	—
130	C₁₃×#135	—	2	4	no	—
131	C₁₃×#135	—	2	4	no	—
132	C₁₃×#135	—	2	4	no	—
133	C₁₃×#135	—	2	2	no	—
134	C₁₃×#135	—	2	8	no	—
135	C₁₃×#135	—	2	4	no	—
136	C₁₃×#135	—	2	8	no	—
137	C₁₃×#135	—	2	2	no	—
138	C₁₃×#135	—	2	1	no	—
139	C₁₃×#135	—	2	1	no	—
140	C₁₃×#135	—	2	1	no	—
141	C₁₃×#135	—	2	1	no	—
142	C₁₃×#135	D₄	1	2	yes	complemented
143	C₁₃×#135	D₄	1	2	yes	complemented
144	C₁₃×#135	C₂³	1	2	yes	—
145	C₁₃×#135	C₂³	1	4	yes	—
146	C₁₃×#135	C₂³	1	2	yes	—
147	C₂×C₁₃×Q₁₆	—	2	2	no	—
148	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
149	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
150	C₂×C₁₃×SD₁₆	—	2	2	no	—
151	C₂×C₁₃×SD₁₆	—	2	2	no	—
152	C₂×C₁₃×SD₁₆	—	2	4	no	—
153	C₂×C₁₃×SD₁₆	—	2	8	no	—
154	C₂×C₁₃×SD₁₆	D₄	1	2	yes	complemented
155	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
156	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
157	C₂×C₁₃×D₈	—	2	2	no	—
158	C₂×C₁₃×D₈	—	2	2	no	—
159	C₂×C₁₃×D₈	—	2	4	no	—
160	C₂×C₁₃×D₈	—	2	4	no	—
161	C₂×C₁₃×D₈	—	2	2	no	—
162	C₂×C₁₃×D₈	—	2	8	no	—
163	C₂×C₁₃×D₈	—	2	1	no	—
164	C₂×C₁₃×D₈	—	2	1	no	—
165	C₂×C₁₃×D₈	—	2	1	no	—
166	C₂×C₁₃×D₈	—	2	1	no	—
167	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic, complemented
168	C₂×C₁₃×D₈	C₂³	1	2	yes	—
169	C₂×C₁₃×D₈	C₂³	1	2	yes	—
170	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic, complemented
171	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
172	C₁₃×#131	—	2	4	no	—
173	C₁₃×#131	—	2	1	no	—
174	C₁₃×#131	—	2	1	no	—
175	C₁₃×#131	—	2	1	no	—
176	C₁₃×#131	—	2	1	no	—
177	C₁₃×#131	C₂³	1	2	yes	—
178	C₁₃×#131	C₂³	1	2	yes	—
179	C₁₃×#131	C₂³	1	2	yes	complemented
180	C₁₃×#131	C₂³	1	8	yes	complemented
181	C₁₃×#131	C₂³	1	2	yes	complemented
182	C₂×C₁₃×M₁₆	—	2	4	no	—
183	C₂×C₁₃×M₁₆	—	2	1	no	—
184	C₂×C₁₃×M₁₆	—	2	1	no	—
185	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
186	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
187	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
188	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₁₃	—	2	1	no	—
190	C₂²×C₈×C₁₃	—	2	1	no	—
191	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
192	C₁₃×#127	C₂³	1	4	yes	complemented
193	C₁₃×#124	C₂³	1	4	yes	complemented
194	C₁₃×#121	—	4	2	no	—
195	C₁₃×#120	—	4	2	no	—
196	C₁₃×#117	C₂³	1	1	yes	characteristic
197	C₁₃×#108	C₂³	1	2	yes	complemented
198	C₁₃×#108	C₂³	1	2	yes	complemented
199	C₁₃×#108	C₂³	1	4	yes	complemented
200	C₁₃×#104	C₂³	1	4	yes	—
201	C₁₃×#104	C₂³	1	4	yes	complemented
202	C₁₃×#104	C₂³	1	8	yes	complemented
203	C₁₃×#101	C₂³	1	4	yes	complemented
204	C₁₃×#100	C₂³	1	8	yes	complemented
205	C₁₃×#100	C₂³	1	4	yes	complemented
206	C₁₃×#97	C₂³	1	2	yes	complemented
207	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
208	#61106	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂⁴×C₁₃	—	2	2	no	—
210	C₂⁴×C₁₃	—	4	2	no	—
211	C₁₃×#41	—	2	1	no	—
212	C₁₃×#41	—	2	2	no	—
213	C₁₃×#41	—	2	1	no	—
214	C₁₃×#41	—	2	1	no	—
215	C₁₃×#41	—	2	2	no	—
216	C₁₃×#41	—	2	1	no	—
217	C₁₃×#41	—	2	8	no	—
218	C₁₃×#41	—	2	4	no	—
219	C₁₃×#41	—	2	8	no	—
220	C₁₃×#41	—	2	4	no	—
221	C₁₃×#41	—	2	4	no	—
222	C₁₃×#41	—	2	4	no	—
223	C₁₃×#41	—	2	2	no	—
224	C₁₃×#41	—	2	2	no	—
225	C₁₃×#41	—	2	2	no	—
226	C₁₃×#41	—	2	2	no	—
227	C₁₃×#41	—	4	4	no	—
228	C₁₃×#41	—	4	4	no	—
229	C₁₃×#41	—	4	4	no	—
230	C₁₃×#41	—	4	4	no	—
231	C₁₃×#41	—	4	4	no	—
232	C₁₃×#41	—	4	4	no	—
233	C₁₃×#41	—	4	2	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₁₃×#41	C₂×D₄	1	2	yes	—
236	C₁₃×#41	C₂×D₄	1	4	yes	—
237	C₁₃×#41	C₂×D₄	1	2	yes	—
238	C₁₃×#41	C₂⁴	1	2	yes	—
239	C₁₃×#41	C₂⁴	1	4	yes	—
240	C₁₃×#41	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₁₃	—	2	4	no	—
242	C₂×Q₈×C₁₃	—	2	4	no	—
243	C₂×Q₈×C₁₃	—	4	2	no	—
244	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
245	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	2	8	no	—
252	C₂×D₄×C₁₃	—	2	4	no	—
253	C₂×D₄×C₁₃	—	2	8	no	—
254	C₂×D₄×C₁₃	—	2	4	no	—
255	C₂×D₄×C₁₃	—	2	2	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	4	4	no	—
262	C₂×D₄×C₁₃	—	4	4	no	—
263	C₂×D₄×C₁₃	—	4	2	no	—
264	C₂×D₄×C₁₃	—	4	2	no	—
265	C₂×D₄×C₁₃	—	4	4	no	—
266	C₂×D₄×C₁₃	—	4	8	no	—
267	C₂×D₄×C₁₃	—	4	4	no	—
268	C₂×D₄×C₁₃	—	4	8	no	—
269	C₂×D₄×C₁₃	—	4	2	no	—
270	C₂×D₄×C₁₃	—	4	4	no	—
271	C₂×D₄×C₁₃	—	4	4	no	—
272	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
273	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
274	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
275	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₁₃	—	2	1	no	—
278	C₂²×C₄×C₁₃	—	2	1	no	—
279	C₂²×C₄×C₁₃	—	2	2	no	—
280	C₂²×C₄×C₁₃	—	2	2	no	—
281	C₂²×C₄×C₁₃	—	4	2	no	—
282	C₂²×C₄×C₁₃	—	4	4	no	—
283	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₁₃×Q₁₆	—	2	4	no	—
285	C₁₃×Q₁₆	—	2	4	no	—
286	C₁₃×Q₁₆	—	2	1	no	—
287	C₁₃×Q₁₆	—	2	1	no	—
288	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
289	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
290	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
291	C₁₃×SD₁₆	—	2	8	no	—
292	C₁₃×SD₁₆	—	2	8	no	—
293	C₁₃×SD₁₆	—	2	4	no	—
294	C₁₃×SD₁₆	—	2	4	no	—
295	C₁₃×SD₁₆	—	2	4	no	—
296	C₁₃×SD₁₆	—	2	4	no	—
297	C₁₃×SD₁₆	—	2	2	no	—
298	C₁₃×SD₁₆	—	2	8	no	—
299	C₁₃×SD₁₆	—	2	2	no	—
300	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
301	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
302	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
303	C₁₃×SD₁₆	C₂×D₄	1	4	yes	—
304	C₁₃×D₈	—	2	8	no	—
305	C₁₃×D₈	—	2	4	no	—
306	C₁₃×D₈	—	2	8	no	—
307	C₁₃×D₈	—	2	4	no	—
308	C₁₃×D₈	—	2	2	no	—
309	C₁₃×D₈	—	2	2	no	—
310	C₁₃×D₈	—	2	2	no	—
311	C₁₃×D₈	—	2	2	no	—
312	C₁₃×D₈	—	2	1	no	—
313	C₁₃×D₈	—	2	8	no	—
314	C₁₃×D₈	—	2	1	no	—
315	C₁₃×D₈	C₂×D₄	1	2	yes	—
316	C₁₃×D₈	C₂×D₄	1	2	yes	—
317	C₁₃×D₈	C₂×D₄	1	4	yes	—
318	C₁₃×M₁₆	—	2	2	no	—
319	C₁₃×M₁₆	—	2	1	no	—
320	C₁₃×M₁₆	—	2	1	no	—
321	C₁₃×M₁₆	—	2	2	no	—
322	C₁₃×M₁₆	—	2	2	no	—
323	C₁₃×M₁₆	—	2	8	no	—
324	C₁₃×M₁₆	—	2	2	no	—
325	C₁₃×M₁₆	—	2	2	no	—
326	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
327	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
328	C₁₃×M₁₆	C₂⁴	1	2	yes	—
329	C₁₃×M₁₆	C₂⁴	1	4	yes	—
330	C₁₃×M₁₆	C₂⁴	1	2	yes	—
331	C₂×C₈×C₁₃	—	2	1	no	—
332	C₂×C₈×C₁₃	—	2	1	no	—
333	C₂×C₈×C₁₃	—	2	2	no	—
334	C₂×C₈×C₁₃	—	2	2	no	—
335	C₂×C₈×C₁₃	—	2	2	no	—
336	C₂×C₈×C₁₃	—	2	2	no	—
337	C₂×C₈×C₁₃	—	2	2	no	—
338	C₂×C₈×C₁₃	—	2	8	no	—
339	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
342	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
345	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₁₃×C₄⋊C₄	—	2	1	no	—
347	C₁₃×C₂²⋊C₄	—	2	1	no	—
348	C₁₃×C₂²⋊C₄	—	4	4	no	—
349	C₄²×C₁₃	C₂⁴	1	2	yes	—
350	#3585	C₂×C₁₃	1	2	yes	complemented
351	#3584	C₂×C₁₃	1	1	yes	characteristic, complemented
352	C₂×#576	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3292	C₂×C₁₃	1	4	yes	complemented
354	#3290	C₂×C₁₃	1	4	yes	complemented
355	#3288	C₂×C₁₃	1	8	yes	complemented
356	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3068	C₂×C₁₃	1	2	yes	complemented
358	#3067	C₂×C₁₃	1	1	yes	characteristic, complemented
359	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3021	C₂×C₁₃	1	2	yes	complemented
361	#3019	C₂×C₁₃	1	2	yes	complemented
362	#2957	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2955	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂³×C₁₃	—	2	1	no	—
365	C₂³×C₁₃	—	2	1	no	—
366	C₂³×C₁₃	—	2	2	no	—
367	C₂³×C₁₃	—	2	4	no	—
368	C₂³×C₁₃	—	2	2	no	—
369	C₂³×C₁₃	—	4	4	no	—
370	C₂³×C₁₃	—	4	8	no	—
371	C₂³×C₁₃	—	4	2	no	—
372	C₂³×C₁₃	—	4	2	no	—
373	C₂³×C₁₃	—	16	2	no	—
374	C₂³×C₁₃	—	16	4	no	—
375	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
376	Q₈×C₁₃	—	2	1	no	—
377	Q₈×C₁₃	—	2	2	no	—
378	Q₈×C₁₃	—	2	1	no	—
379	Q₈×C₁₃	—	2	2	no	—
380	Q₈×C₁₃	—	2	2	no	—
381	Q₈×C₁₃	—	4	4	no	—
382	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
383	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
384	Q₈×C₁₃	C₂²×D₄	1	2	yes	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	4	no	—
387	D₄×C₁₃	—	2	2	no	—
388	D₄×C₁₃	—	2	2	no	—
389	D₄×C₁₃	—	2	4	no	—
390	D₄×C₁₃	—	2	2	no	—
391	D₄×C₁₃	—	2	1	no	—
392	D₄×C₁₃	—	2	2	no	—
393	D₄×C₁₃	—	2	1	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	4	no	—
397	D₄×C₁₃	—	2	2	no	—
398	D₄×C₁₃	—	4	8	no	—
399	D₄×C₁₃	—	4	8	no	—
400	D₄×C₁₃	—	4	4	no	—
401	D₄×C₁₃	—	4	4	no	—
402	D₄×C₁₃	—	4	4	no	—
403	D₄×C₁₃	—	4	2	no	—
404	D₄×C₁₃	—	4	2	no	—
405	D₄×C₁₃	—	4	2	no	—
406	D₄×C₁₃	—	4	2	no	—
407	D₄×C₁₃	—	16	4	no	—
408	D₄×C₁₃	C₂²×D₄	1	2	yes	—
409	D₄×C₁₃	C₂²×D₄	1	4	yes	—
410	D₄×C₁₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₁₃	—	2	1	no	—
412	C₂×C₄×C₁₃	—	2	2	no	—
413	C₂×C₄×C₁₃	—	2	1	no	—
414	C₂×C₄×C₁₃	—	2	2	no	—
415	C₂×C₄×C₁₃	—	2	4	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	2	no	—
418	C₂×C₄×C₁₃	—	2	4	no	—
419	C₂×C₄×C₁₃	—	2	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	2	no	—
422	C₂×C₄×C₁₃	—	4	8	no	—
423	C₂×C₄×C₁₃	—	4	4	no	—
424	C₂×C₄×C₁₃	—	4	4	no	—
425	C₂×C₄×C₁₃	—	4	4	no	—
426	C₂×C₄×C₁₃	—	4	2	no	—
427	C₂×C₄×C₁₃	—	4	2	no	—
428	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
433	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
434	C₈×C₁₃	—	2	2	no	—
435	C₈×C₁₃	—	2	4	no	—
436	C₈×C₁₃	—	2	2	no	—
437	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
438	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
439	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₈×C₁₃	C₂²×D₄	1	4	yes	—
441	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	#585	C₂²×C₁₃	1	2	yes	complemented
443	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
444	#578	—	2	1	no	—
445	#578	C₂²×C₁₃	1	2	yes	complemented
446	#577	—	2	4	no	—
447	#577	—	2	2	no	—
448	#577	C₂²×C₁₃	1	8	yes	complemented
449	#577	C₂²×C₁₃	1	4	yes	complemented
450	#576	—	2	4	no	—
451	#576	—	2	2	no	—
452	#576	—	2	2	no	—
453	#576	—	2	1	no	—
454	#576	C₂²×C₁₃	1	4	yes	complemented
455	#576	C₂²×C₁₃	1	4	yes	complemented
456	#576	C₂²×C₁₃	1	8	yes	complemented
457	#576	C₂²×C₁₃	1	2	yes	complemented
458	#575	—	2	4	no	—
459	#575	—	2	2	no	—
460	#575	C₂²×C₁₃	1	1	yes	characteristic
461	#575	C₂²×C₁₃	1	2	yes	complemented
462	#575	C₂²×C₁₃	1	2	yes	complemented
463	C₂×AGL(1,ℤ/8)	—	2	4	no	—
464	C₂×AGL(1,ℤ/8)	—	2	2	no	—
465	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
466	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
467	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
468	C₂×#135	—	2	2	no	—
469	C₂×#135	—	2	1	no	—
470	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
471	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic, complemented
472	C₂²×D₈	—	2	1	no	—
473	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
474	#568	C₂²×C₁₃	1	2	yes	complemented
475	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
476	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic, complemented
477	#535	C₂²×C₁₃	1	2	yes	complemented
478	#496	C₂²×C₁₃	1	4	yes	complemented
479	#495	C₂²×C₁₃	1	2	yes	complemented
480	#493	C₂²×C₁₃	1	2	yes	complemented
481	#473	C₂²×C₁₃	1	2	yes	complemented
482	#472	C₂²×C₁₃	1	2	yes	complemented
483	#472	C₂²×C₁₃	1	4	yes	complemented
484	#472	C₂²×C₁₃	1	4	yes	complemented
485	#472	C₂²×C₁₃	1	8	yes	complemented
486	#471	C₂²×C₁₃	1	4	yes	complemented
487	#471	C₂²×C₁₃	1	8	yes	complemented
488	#455	C₂²×C₁₃	1	8	yes	complemented
489	#454	C₂²×C₁₃	1	8	yes	complemented
490	#453	C₂²×C₁₃	1	8	yes	complemented
491	#453	C₂²×C₁₃	1	8	yes	complemented
492	#444	C₂²×C₁₃	1	4	yes	complemented
493	#444	C₂²×C₁₃	1	4	yes	complemented
494	#443	C₂²×C₁₃	1	4	yes	complemented
495	#443	C₂²×C₁₃	1	4	yes	complemented
496	#430	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic, complemented
498	#421	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#421	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#421	C₂²×C₁₃	1	2	yes	complemented
501	#413	C₂²×C₁₃	1	2	yes	complemented
502	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
503	#405	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	4	no	—
506	C₂²×C₁₃	—	2	2	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	2	no	—
509	C₂²×C₁₃	—	4	2	no	—
510	C₂²×C₁₃	—	4	4	no	—
511	C₂²×C₁₃	—	8	1	no	—
512	C₂²×C₁₃	—	8	2	no	—
513	C₂²×C₁₃	—	8	2	no	—
514	C₂²×C₁₃	—	8	4	no	—
515	C₂²×C₁₃	—	8	4	no	—
516	C₂²×C₁₃	—	16	2	no	—
517	C₂²×C₁₃	—	16	4	no	—
518	C₂²×C₁₃	—	16	8	no	—
519	C₂²×C₁₃	D₄²	1	1	yes	characteristic
520	C₂²×C₁₃	D₄²	1	1	yes	characteristic
521	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₄×C₁₃	—	2	2	no	—
523	C₄×C₁₃	—	2	4	no	—
524	C₄×C₁₃	—	2	2	no	—
525	C₄×C₁₃	—	4	2	no	—
526	C₄×C₁₃	—	4	2	no	—
527	C₄×C₁₃	D₄²	1	1	yes	characteristic
528	C₄×C₁₃	D₄²	1	1	yes	characteristic
529	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
530	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
531	2₋¹⁺⁴	—	2	2	no	—
532	2₋¹⁺⁴	—	2	2	no	—
533	2₋¹⁺⁴	C₂³×C₁₃	1	4	yes	complemented
534	H(5,𝔽₂)	—	2	4	no	—
535	H(5,𝔽₂)	—	2	4	no	—
536	H(5,𝔽₂)	—	2	2	no	—
537	H(5,𝔽₂)	—	2	2	no	—
538	H(5,𝔽₂)	—	4	2	no	—
539	H(5,𝔽₂)	—	4	2	no	—
540	H(5,𝔽₂)	C₂³×C₁₃	1	8	yes	—
541	H(5,𝔽₂)	C₂³×C₁₃	1	4	yes	complemented
542	C₂×#41	—	2	4	no	—
543	C₂×#41	—	2	4	no	—
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	—	4	2	no	—
547	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
548	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
549	C₂×#41	C₂³×C₁₃	1	2	yes	—
550	C₂×#41	C₂³×C₁₃	1	2	yes	—
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	4	2	no	—
554	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
555	#137	—	2	2	no	—
556	#137	—	2	2	no	—
557	#137	—	2	8	no	—
558	#137	—	2	4	no	—
559	#137	—	2	4	no	—
560	#137	D₄×C₁₃	1	2	yes	complemented
561	#137	D₄×C₁₃	1	2	yes	complemented
562	#137	C₂³×C₁₃	1	4	yes	—
563	#137	C₂³×C₁₃	1	4	yes	complemented
564	AGL(1,ℤ/8)	—	2	4	no	—
565	AGL(1,ℤ/8)	—	2	4	no	—
566	AGL(1,ℤ/8)	—	2	2	no	—
567	AGL(1,ℤ/8)	—	2	2	no	—
568	AGL(1,ℤ/8)	—	2	8	no	—
569	AGL(1,ℤ/8)	—	2	8	no	—
570	AGL(1,ℤ/8)	—	2	8	no	—
571	AGL(1,ℤ/8)	—	2	8	no	—
572	AGL(1,ℤ/8)	—	2	4	no	—
573	AGL(1,ℤ/8)	—	2	8	no	—
574	AGL(1,ℤ/8)	—	2	4	no	—
575	AGL(1,ℤ/8)	—	2	4	no	—
576	AGL(1,ℤ/8)	—	2	4	no	—
577	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	complemented
578	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	complemented
579	AGL(1,ℤ/8)	C₂³×C₁₃	1	8	yes	—
580	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	—
581	AGL(1,ℤ/8)	C₂³×C₁₃	1	8	yes	complemented
582	AGL(1,ℤ/8)	C₂³×C₁₃	1	4	yes	complemented
583	#135	—	2	4	no	—
584	#135	—	2	4	no	—
585	#135	—	2	4	no	—
586	#135	—	2	4	no	—
587	#135	—	2	2	no	—
588	#135	—	2	8	no	—
589	#135	—	2	4	no	—
590	#135	—	2	8	no	—
591	#135	—	2	2	no	—
592	#135	—	2	1	no	—
593	#135	—	2	1	no	—
594	#135	—	2	1	no	—
595	#135	—	2	1	no	—
596	#135	D₄×C₁₃	1	2	yes	complemented
597	#135	D₄×C₁₃	1	2	yes	complemented
598	#135	C₂³×C₁₃	1	2	yes	—
599	#135	C₂³×C₁₃	1	2	yes	—
600	#135	C₂³×C₁₃	1	4	yes	—
601	C₂×Q₁₆	—	2	2	no	—
602	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic, complemented
603	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic, complemented
604	C₂×SD₁₆	—	2	2	no	—
605	C₂×SD₁₆	—	2	2	no	—
606	C₂×SD₁₆	—	2	4	no	—
607	C₂×SD₁₆	—	2	8	no	—
608	C₂×SD₁₆	D₄×C₁₃	1	2	yes	complemented
609	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
610	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
611	C₂×D₈	—	2	2	no	—
612	C₂×D₈	—	2	2	no	—
613	C₂×D₈	—	2	4	no	—
614	C₂×D₈	—	2	4	no	—
615	C₂×D₈	—	2	2	no	—
616	C₂×D₈	—	2	8	no	—
617	C₂×D₈	—	2	1	no	—
618	C₂×D₈	—	2	1	no	—
619	C₂×D₈	—	2	1	no	—
620	C₂×D₈	—	2	1	no	—
621	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic, complemented
622	C₂×D₈	C₂³×C₁₃	1	2	yes	—
623	C₂×D₈	C₂³×C₁₃	1	2	yes	—
624	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
625	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
626	#131	—	2	4	no	—
627	#131	—	2	1	no	—
628	#131	—	2	1	no	—
629	#131	—	2	1	no	—
630	#131	—	2	1	no	—
631	#131	C₂³×C₁₃	1	2	yes	—
632	#131	C₂³×C₁₃	1	2	yes	—
633	#131	C₂³×C₁₃	1	2	yes	complemented
634	#131	C₂³×C₁₃	1	2	yes	complemented
635	#131	C₂³×C₁₃	1	8	yes	complemented
636	C₂×M₁₆	—	2	4	no	—
637	C₂×M₁₆	—	2	1	no	—
638	C₂×M₁₆	—	2	1	no	—
639	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
640	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
641	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
642	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
643	C₂²×C₈	—	2	1	no	—
644	C₂²×C₈	—	2	1	no	—
645	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
646	#127	C₂³×C₁₃	1	4	yes	complemented
647	#124	C₂³×C₁₃	1	4	yes	complemented
648	#121	—	4	2	no	—
649	#120	—	4	2	no	—
650	#117	C₂³×C₁₃	1	1	yes	characteristic
651	#108	C₂³×C₁₃	1	2	yes	complemented
652	#108	C₂³×C₁₃	1	2	yes	complemented
653	#108	C₂³×C₁₃	1	4	yes	complemented
654	#104	C₂³×C₁₃	1	4	yes	—
655	#104	C₂³×C₁₃	1	4	yes	complemented
656	#104	C₂³×C₁₃	1	8	yes	complemented
657	#101	C₂³×C₁₃	1	4	yes	complemented
658	#100	C₂³×C₁₃	1	8	yes	complemented
659	#100	C₂³×C₁₃	1	4	yes	complemented
660	#97	C₂³×C₁₃	1	2	yes	complemented
661	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
662	C₂×C₁₃	—	2	1	no	—
663	C₂×C₁₃	—	2	1	no	—
664	C₂×C₁₃	—	2	1	no	—
665	C₂×C₁₃	—	4	2	no	—
666	C₂×C₁₃	—	4	2	no	—
667	C₂×C₁₃	—	4	4	no	—
668	C₂×C₁₃	—	8	4	no	—
669	C₂×C₁₃	—	8	2	no	—
670	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
671	C₂⁴	—	2	2	no	—
672	C₂⁴	—	4	2	no	—
673	#41	—	2	1	no	—
674	#41	—	2	2	no	—
675	#41	—	2	1	no	—
676	#41	—	2	1	no	—
677	#41	—	2	2	no	—
678	#41	—	2	1	no	—
679	#41	—	2	8	no	—
680	#41	—	2	4	no	—
681	#41	—	2	8	no	—
682	#41	—	2	4	no	—
683	#41	—	2	4	no	—
684	#41	—	2	4	no	—
685	#41	—	2	2	no	—
686	#41	—	2	2	no	—
687	#41	—	2	2	no	—
688	#41	—	2	2	no	—
689	#41	—	4	4	no	—
690	#41	—	4	4	no	—
691	#41	—	4	4	no	—
692	#41	—	4	4	no	—
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	4	2	no	—
696	#41	—	4	2	no	—
697	#41	C₂×D₄×C₁₃	1	2	yes	—
698	#41	C₂×D₄×C₁₃	1	4	yes	—
699	#41	C₂×D₄×C₁₃	1	2	yes	—
700	#41	C₂⁴×C₁₃	1	2	yes	—
701	#41	C₂⁴×C₁₃	1	4	yes	—
702	#41	C₂⁴×C₁₃	1	2	yes	—
703	C₂×Q₈	—	2	4	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	4	2	no	—
706	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
707	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
708	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
709	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	8	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	2	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	4	4	no	—
724	C₂×D₄	—	4	4	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	4	4	no	—
728	C₂×D₄	—	4	8	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	—	4	8	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
738	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	1	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	4	no	—
745	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
746	Q₁₆	—	2	4	no	—
747	Q₁₆	—	2	4	no	—
748	Q₁₆	—	2	1	no	—
749	Q₁₆	—	2	1	no	—
750	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
751	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
752	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
753	SD₁₆	—	2	8	no	—
754	SD₁₆	—	2	8	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	2	4	no	—
757	SD₁₆	—	2	4	no	—
758	SD₁₆	—	2	4	no	—
759	SD₁₆	—	2	2	no	—
760	SD₁₆	—	2	8	no	—
761	SD₁₆	—	2	2	no	—
762	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
763	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
764	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
765	SD₁₆	C₂×D₄×C₁₃	1	4	yes	—
766	D₈	—	2	8	no	—
767	D₈	—	2	4	no	—
768	D₈	—	2	8	no	—
769	D₈	—	2	4	no	—
770	D₈	—	2	2	no	—
771	D₈	—	2	2	no	—
772	D₈	—	2	2	no	—
773	D₈	—	2	2	no	—
774	D₈	—	2	1	no	—
775	D₈	—	2	8	no	—
776	D₈	—	2	1	no	—
777	D₈	C₂×D₄×C₁₃	1	2	yes	—
778	D₈	C₂×D₄×C₁₃	1	2	yes	—
779	D₈	C₂×D₄×C₁₃	1	4	yes	—
780	M₁₆	—	2	2	no	—
781	M₁₆	—	2	1	no	—
782	M₁₆	—	2	1	no	—
783	M₁₆	—	2	2	no	—
784	M₁₆	—	2	2	no	—
785	M₁₆	—	2	8	no	—
786	M₁₆	—	2	2	no	—
787	M₁₆	—	2	2	no	—
788	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
789	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
790	M₁₆	C₂⁴×C₁₃	1	2	yes	—
791	M₁₆	C₂⁴×C₁₃	1	4	yes	—
792	M₁₆	C₂⁴×C₁₃	1	2	yes	—
793	C₂×C₈	—	2	1	no	—
794	C₂×C₈	—	2	1	no	—
795	C₂×C₈	—	2	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	2	2	no	—
798	C₂×C₈	—	2	2	no	—
799	C₂×C₈	—	2	2	no	—
800	C₂×C₈	—	2	8	no	—
801	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
802	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
803	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
804	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
806	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
807	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₄⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	1	no	—
810	C₂²⋊C₄	—	4	4	no	—
811	C₄²	C₂⁴×C₁₃	1	2	yes	—
812	C₁₃	#61106	1	1	yes	characteristic, direct product factor, Sylow
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	4	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	2	no	—
821	C₂³	—	4	2	no	—
822	C₂³	—	16	2	no	—
823	C₂³	—	16	4	no	—
824	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
825	Q₈	—	2	1	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	1	no	—
828	Q₈	—	2	2	no	—
829	Q₈	—	2	2	no	—
830	Q₈	—	4	4	no	—
831	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
832	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
833	Q₈	C₂²×D₄×C₁₃	1	2	yes	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	2	no	—
837	D₄	—	2	2	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	1	no	—
841	D₄	—	2	2	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	4	no	—
846	D₄	—	2	2	no	—
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	4	no	—
850	D₄	—	4	4	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	2	no	—
853	D₄	—	4	2	no	—
854	D₄	—	4	2	no	—
855	D₄	—	4	2	no	—
856	D₄	—	16	4	no	—
857	D₄	C₂²×D₄×C₁₃	1	2	yes	—
858	D₄	C₂²×D₄×C₁₃	1	4	yes	—
859	D₄	C₂²×D₄×C₁₃	1	2	yes	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	4	8	no	—
872	C₂×C₄	—	4	4	no	—
873	C₂×C₄	—	4	4	no	—
874	C₂×C₄	—	4	4	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
881	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
882	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
883	C₈	—	2	2	no	—
884	C₈	—	2	4	no	—
885	C₈	—	2	2	no	—
886	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
887	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
888	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
889	C₈	C₂²×D₄×C₁₃	1	4	yes	—
890	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
891	C₂²	—	2	2	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	8	1	no	—
899	C₂²	—	8	2	no	—
900	C₂²	—	8	2	no	—
901	C₂²	—	8	4	no	—
902	C₂²	—	8	4	no	—
903	C₂²	—	16	2	no	—
904	C₂²	—	16	4	no	—
905	C₂²	—	16	8	no	—
906	C₂²	D₄²×C₁₃	1	1	yes	characteristic
907	C₂²	D₄²×C₁₃	1	1	yes	characteristic
908	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	2	no	—
912	C₄	—	4	2	no	—
913	C₄	—	4	2	no	—
914	C₄	D₄²×C₁₃	1	1	yes	characteristic
915	C₄	D₄²×C₁₃	1	1	yes	characteristic
916	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
917	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
918	C₂	—	2	1	no	—
919	C₂	—	2	1	no	—
920	C₂	—	2	1	no	—
921	C₂	—	4	2	no	—
922	C₂	—	4	4	no	—
923	C₂	—	4	2	no	—
924	C₂	—	8	4	no	—
925	C₂	—	8	2	no	—
926	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂×D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3585	C₂	semidirect
2. C₁₃×#3584	C₂	semidirect
3. C₂×C₁₃×#576	C₂	semidirect
4. C₁₃×#3292	C₂	semidirect
5. C₁₃×#3290	C₂	semidirect
6. C₁₃×#3288	C₂	semidirect
7. C₁₃×#3155	C₂	semidirect
8. C₁₃×#3068	C₂	semidirect
9. C₁₃×#3067	C₂	semidirect
10. C₂×C₁₃×#472	C₂	semidirect
11. C₁₃×#3021	C₂	semidirect
12. C₁₃×#3019	C₂	semidirect
13. C₁₃×#2957	C₂	semidirect
14. C₁₃×#2955	C₂	semidirect
15. C₁₃×#585	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₁₃×#578	C₂²	semidirect
21. C₁₃×#577	C₂²	semidirect
22. C₁₃×#577	C₂²	semidirect
27. C₁₃×#576	C₂²	semidirect
28. C₁₃×#576	C₂²	semidirect
29. C₁₃×#576	C₂²	semidirect
30. C₁₃×#576	C₂²	semidirect
34. C₁₃×#575	C₂²	semidirect
35. C₁₃×#575	C₂²	semidirect
38. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
39. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
40. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
44. C₂×C₁₃×#135	C₂²	semidirect
46. C₂²×C₁₃×D₈	C₂²	semidirect
47. C₁₃×#568	C₂²	semidirect
48. C₂×C₁₃×#131	C₂²	semidirect
49. C₂×C₁₃×#131	C₂²	semidirect
50. C₁₃×#535	C₂²	semidirect
51. C₁₃×#496	C₂²	semidirect
52. C₁₃×#495	C₂²	semidirect
53. C₁₃×#493	C₂²	semidirect
54. C₁₃×#473	C₂²	semidirect
55. C₁₃×#472	C₂²	semidirect
56. C₁₃×#472	C₂²	semidirect
57. C₁₃×#472	C₂²	semidirect
58. C₁₃×#472	C₂²	semidirect
59. C₁₃×#471	C₂²	semidirect
60. C₁₃×#471	C₂²	semidirect
61. C₁₃×#455	C₂²	semidirect
62. C₁₃×#454	C₂²	semidirect
63. C₁₃×#453	C₂²	semidirect
64. C₁₃×#453	C₂²	semidirect
65. C₁₃×#444	C₂²	semidirect
66. C₁₃×#444	C₂²	semidirect
67. C₁₃×#443	C₂²	semidirect
68. C₁₃×#443	C₂²	semidirect
69. C₁₃×#430	C₂²	semidirect
70. C₂×C₁₃×#108	C₂²	semidirect
71. C₁₃×#421	C₂²	semidirect
72. C₁₃×#421	C₂²	semidirect
73. C₁₃×#421	C₂²	semidirect
74. C₁₃×#413	C₂²	semidirect
75. C₂×C₁₃×#100	C₂²	semidirect
76. C₁₃×#405	C₂²	semidirect
79. C₁₃×2₋¹⁺⁴	C₂³	semidirect
87. C₁₃×H(5,𝔽₂)	C₂³	semidirect
106. C₁₃×#137	D₄	semidirect
107. C₁₃×#137	D₄	semidirect
109. C₁₃×#137	C₂³	semidirect
123. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
124. C₁₃×AGL(1,ℤ/8)	D₄	semidirect
127. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
128. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
142. C₁₃×#135	D₄	semidirect
143. C₁₃×#135	D₄	semidirect
148. C₂×C₁₃×Q₁₆	D₄	semidirect
149. C₂×C₁₃×Q₁₆	C₂³	semidirect
154. C₂×C₁₃×SD₁₆	D₄	semidirect
155. C₂×C₁₃×SD₁₆	C₂³	semidirect
156. C₂×C₁₃×SD₁₆	C₂³	semidirect
167. C₂×C₁₃×D₈	D₄	semidirect
170. C₂×C₁₃×D₈	C₂³	semidirect
171. C₂×C₁₃×D₈	C₂³	semidirect
179. C₁₃×#131	C₂³	semidirect
180. C₁₃×#131	C₂³	semidirect
181. C₁₃×#131	C₂³	semidirect
192. C₁₃×#127	C₂³	semidirect
193. C₁₃×#124	C₂³	semidirect
197. C₁₃×#108	C₂³	semidirect
198. C₁₃×#108	C₂³	semidirect
199. C₁₃×#108	C₂³	semidirect
201. C₁₃×#104	C₂³	semidirect
202. C₁₃×#104	C₂³	semidirect
203. C₁₃×#101	C₂³	semidirect
204. C₁₃×#100	C₂³	semidirect
205. C₁₃×#100	C₂³	semidirect
206. C₁₃×#97	C₂³	semidirect
207. C₄×C₈×C₁₃	C₂³	semidirect
208. #61106	C₁₃	direct (N × H)
350. #3585	C₂×C₁₃	semidirect
351. #3584	C₂×C₁₃	semidirect
352. C₂×#576	C₂×C₁₃	semidirect
353. #3292	C₂×C₁₃	semidirect
354. #3290	C₂×C₁₃	semidirect
355. #3288	C₂×C₁₃	semidirect
356. #3155	C₂×C₁₃	semidirect
357. #3068	C₂×C₁₃	semidirect
358. #3067	C₂×C₁₃	semidirect
359. C₂×#472	C₂×C₁₃	semidirect
360. #3021	C₂×C₁₃	semidirect
361. #3019	C₂×C₁₃	semidirect
362. #2957	C₂×C₁₃	semidirect
363. #2955	C₂×C₁₃	semidirect
442. #585	C₂²×C₁₃	semidirect
443. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
445. #578	C₂²×C₁₃	semidirect
448. #577	C₂²×C₁₃	semidirect
449. #577	C₂²×C₁₃	semidirect
454. #576	C₂²×C₁₃	semidirect
455. #576	C₂²×C₁₃	semidirect
456. #576	C₂²×C₁₃	semidirect
457. #576	C₂²×C₁₃	semidirect
461. #575	C₂²×C₁₃	semidirect
462. #575	C₂²×C₁₃	semidirect
465. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
466. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
467. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
471. C₂×#135	C₂²×C₁₃	semidirect
473. C₂²×D₈	C₂²×C₁₃	semidirect
474. #568	C₂²×C₁₃	semidirect
475. C₂×#131	C₂²×C₁₃	semidirect
476. C₂×#131	C₂²×C₁₃	semidirect
477. #535	C₂²×C₁₃	semidirect
478. #496	C₂²×C₁₃	semidirect
479. #495	C₂²×C₁₃	semidirect
480. #493	C₂²×C₁₃	semidirect
481. #473	C₂²×C₁₃	semidirect
482. #472	C₂²×C₁₃	semidirect
483. #472	C₂²×C₁₃	semidirect
484. #472	C₂²×C₁₃	semidirect
485. #472	C₂²×C₁₃	semidirect
486. #471	C₂²×C₁₃	semidirect
487. #471	C₂²×C₁₃	semidirect
488. #455	C₂²×C₁₃	semidirect
489. #454	C₂²×C₁₃	semidirect
490. #453	C₂²×C₁₃	semidirect
491. #453	C₂²×C₁₃	semidirect
492. #444	C₂²×C₁₃	semidirect
493. #444	C₂²×C₁₃	semidirect
494. #443	C₂²×C₁₃	semidirect
495. #443	C₂²×C₁₃	semidirect
496. #430	C₂²×C₁₃	semidirect
497. C₂×#108	C₂²×C₁₃	semidirect
498. #421	C₂²×C₁₃	semidirect
499. #421	C₂²×C₁₃	semidirect
500. #421	C₂²×C₁₃	semidirect
501. #413	C₂²×C₁₃	semidirect
502. C₂×#100	C₂²×C₁₃	semidirect
503. #405	C₂²×C₁₃	semidirect
533. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
541. H(5,𝔽₂)	C₂³×C₁₃	semidirect
560. #137	D₄×C₁₃	semidirect
561. #137	D₄×C₁₃	semidirect
563. #137	C₂³×C₁₃	semidirect
577. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
578. AGL(1,ℤ/8)	D₄×C₁₃	semidirect
581. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
582. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
596. #135	D₄×C₁₃	semidirect
597. #135	D₄×C₁₃	semidirect
602. C₂×Q₁₆	D₄×C₁₃	semidirect
603. C₂×Q₁₆	C₂³×C₁₃	semidirect
608. C₂×SD₁₆	D₄×C₁₃	semidirect
609. C₂×SD₁₆	C₂³×C₁₃	semidirect
610. C₂×SD₁₆	C₂³×C₁₃	semidirect
621. C₂×D₈	D₄×C₁₃	semidirect
624. C₂×D₈	C₂³×C₁₃	semidirect
625. C₂×D₈	C₂³×C₁₃	semidirect
633. #131	C₂³×C₁₃	semidirect
634. #131	C₂³×C₁₃	semidirect
635. #131	C₂³×C₁₃	semidirect
646. #127	C₂³×C₁₃	semidirect
647. #124	C₂³×C₁₃	semidirect
651. #108	C₂³×C₁₃	semidirect
652. #108	C₂³×C₁₃	semidirect
653. #108	C₂³×C₁₃	semidirect
655. #104	C₂³×C₁₃	semidirect
656. #104	C₂³×C₁₃	semidirect
657. #101	C₂³×C₁₃	semidirect
658. #100	C₂³×C₁₃	semidirect
659. #100	C₂³×C₁₃	semidirect
660. #97	C₂³×C₁₃	semidirect
661. C₄×C₈	C₂³×C₁₃	semidirect
812. C₁₃	#61106	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×#3585	2
C₁₃×#3584	2
C₂×C₁₃×#576	2
C₁₃×#3292	2
C₁₃×#3290	2
C₁₃×#3288	2
C₁₃×#3155	2
C₁₃×#3068	2
C₁₃×#3067	2
C₂×C₁₃×#472	2
C₁₃×#3021	2
C₁₃×#3019	2
C₁₃×#2957	2
C₁₃×#2955	2
#61106	13

Subgroups — C13×#61106 #15747445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61106 #15747445