Subgroups — C₁₃×#60833 #15747172

Order 3328.

2144 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3216	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3136	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3009	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#550	—	2	1	no	—
25	D₄²×C₁₃	—	2	1	no	—
26	D₄²×C₁₃	—	2	2	no	—
27	D₄²×C₁₃	—	2	2	no	—
28	D₄²×C₁₃	—	2	1	no	—
29	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#542	—	2	1	no	—
31	C₁₃×#542	C₂²	1	2	yes	complemented
32	C₁₃×#541	—	2	1	no	—
33	C₁₃×#541	C₂²	1	2	yes	complemented
34	C₁₃×#539	—	2	2	no	—
35	C₁₃×#537	C₂²	1	1	yes	characteristic
36	C₁₃×#536	C₂²	1	1	yes	characteristic
37	C₁₃×#536	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#535	C₂²	1	2	yes	—
39	C₁₃×#535	C₂²	1	4	yes	—
40	C₁₃×#533	—	2	1	no	—
41	C₁₃×#533	C₂²	1	2	yes	complemented
42	C₁₃×#532	C₂²	1	1	yes	characteristic
43	C₁₃×#532	C₂²	1	2	yes	—
44	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#127	C₂²	1	2	yes	—
46	C₁₃×#529	—	2	2	no	—
47	C₁₃×#529	—	2	1	no	—
48	C₁₃×#529	C₂²	1	2	yes	complemented
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#497	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	4	yes	complemented
55	C₁₃×#492	C₂²	1	4	yes	complemented
56	C₁₃×#490	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	4	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	complemented
59	C₁₃×#486	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	2	yes	complemented
61	C₁₃×#464	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	2	yes	complemented
63	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#462	C₂²	1	2	yes	complemented
65	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×#460	C₂²	1	2	yes	complemented
67	C₁₃×#460	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	4	yes	complemented
69	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#460	C₂²	1	2	yes	complemented
71	C₁₃×#460	C₂²	1	2	yes	complemented
72	C₁₃×#460	C₂²	1	2	yes	complemented
73	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#459	C₂²	1	2	yes	complemented
75	C₁₃×#459	C₂²	1	2	yes	complemented
76	C₁₃×#452	C₂²	1	4	yes	complemented
77	C₁₃×#452	C₂²	1	4	yes	complemented
78	C₁₃×#452	C₂²	1	4	yes	complemented
79	C₁₃×#450	C₂²	1	4	yes	complemented
80	C₁₃×#450	C₂²	1	4	yes	complemented
81	C₁₃×#450	C₂²	1	4	yes	complemented
82	C₁₃×#449	C₂²	1	4	yes	complemented
83	C₁₃×#447	C₂²	1	4	yes	complemented
84	C₁₃×#433	C₂²	1	4	yes	complemented
85	C₁₃×#432	C₂²	1	2	yes	complemented
86	C₁₃×#431	C₂²	1	2	yes	complemented
87	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₁₃×#418	C₂²	1	2	yes	complemented
90	C₁₃×#417	C₂²	1	2	yes	complemented
91	C₁₃×#416	C₂²	1	2	yes	complemented
92	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
93	C₁₃×#408	C₂²	1	2	yes	—
94	C₁₃×#405	C₂²	1	2	yes	complemented
95	C₁₃×H(5,𝔽₂)	—	4	4	no	—
96	C₁₃×H(5,𝔽₂)	—	4	4	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	C₂³	1	2	yes	—
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×#41	C₂³	1	4	yes	—
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₁₃	—	2	4	no	—
104	C₂²×D₄×C₁₃	—	2	2	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	2	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	—	2	2	no	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
111	C₁₃×#137	—	4	4	no	—
112	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
113	C₁₃×#135	—	4	4	no	—
114	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₁₃×SD₁₆	—	4	4	no	—
117	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
123	C₂×C₁₃×D₈	C₂³	1	2	yes	—
124	C₂×C₁₃×D₈	C₂³	1	4	yes	—
125	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
126	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
127	C₁₃×C₄⋊Q₈	—	2	1	no	—
128	C₁₃×C₄⋊Q₈	—	2	1	no	—
129	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
130	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#127	—	2	1	no	—
133	C₁₃×#127	—	2	1	no	—
134	C₁₃×#127	—	2	2	no	—
135	C₁₃×#127	—	2	2	no	—
136	C₁₃×#127	C₂³	1	1	yes	characteristic
137	C₁₃×#127	C₂³	1	2	yes	—
138	C₁₃×#127	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	4	yes	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#125	—	2	2	no	—
145	C₁₃×#125	—	2	1	no	—
146	C₁₃×#125	—	2	2	no	—
147	C₁₃×#125	—	2	2	no	—
148	C₁₃×#125	C₂³	1	2	yes	—
149	C₁₃×#124	—	2	1	no	—
150	C₁₃×#124	—	2	2	no	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#124	C₂³	1	4	yes	—
153	C₁₃×#124	C₂³	1	2	yes	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×#123	—	2	2	no	—
157	C₁₃×#123	—	2	2	no	—
158	C₁₃×C₂²⋊Q₈	—	2	1	no	—
159	C₁₃×C₂²⋊Q₈	—	2	2	no	—
160	C₁₃×C₂²⋊Q₈	—	2	1	no	—
161	C₁₃×C₂²⋊Q₈	—	2	1	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₁₃×#121	—	2	2	no	—
168	C₁₃×#121	—	2	1	no	—
169	C₁₃×#121	—	2	1	no	—
170	C₁₃×#121	—	2	2	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	4	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	4	no	—
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₁₃×#120	—	2	4	no	—
179	C₁₃×#120	—	2	4	no	—
180	C₁₃×#120	—	2	4	no	—
181	C₄×Q₈×C₁₃	—	2	1	no	—
182	C₄×Q₈×C₁₃	—	2	1	no	—
183	C₄×Q₈×C₁₃	—	2	2	no	—
184	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
186	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
188	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	1	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	—	2	1	no	—
194	C₄×D₄×C₁₃	—	2	1	no	—
195	C₄×D₄×C₁₃	—	2	2	no	—
196	C₄×D₄×C₁₃	—	2	2	no	—
197	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
198	C₄×D₄×C₁₃	D₄	1	2	yes	—
199	C₄×D₄×C₁₃	D₄	1	2	yes	—
200	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
201	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
202	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₁₃×#117	—	2	2	no	—
204	C₁₃×#117	—	2	1	no	—
205	C₁₃×#117	—	2	2	no	—
206	C₁₃×#117	C₂³	1	1	yes	characteristic
207	C₁₃×#117	C₂³	1	1	yes	characteristic
208	C₁₃×#117	C₂³	1	2	yes	—
209	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₁₃	—	2	1	no	—
212	C₂×C₄²×C₁₃	—	2	1	no	—
213	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	2	yes	—
227	C₁₃×#102	C₂³	1	4	yes	—
228	C₁₃×#102	C₂³	1	4	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₁₃×#97	C₂³	1	4	yes	—
233	C₄×C₈×C₁₃	C₂³	1	4	yes	—
234	#60833	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	4	no	—
236	C₂⁴×C₁₃	—	2	2	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	2	2	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	2	no	—
242	C₁₃×#41	—	2	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₁₃×#41	—	4	8	no	—
246	C₂×Q₈×C₁₃	—	2	1	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
251	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	4	no	—
256	C₂×D₄×C₁₃	—	2	2	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	1	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	4	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	4	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	4	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	16	no	—
273	C₂×D₄×C₁₃	—	4	8	no	—
274	C₂×D₄×C₁₃	—	8	2	no	—
275	C₂×D₄×C₁₃	—	8	4	no	—
276	C₂×D₄×C₁₃	—	8	2	no	—
277	C₂×D₄×C₁₃	—	8	4	no	—
278	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
279	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
281	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
282	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₁₃	—	2	1	no	—
284	C₂²×C₄×C₁₃	—	2	1	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	4	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	1	no	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
294	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
296	C₁₃×Q₁₆	—	4	2	no	—
297	C₁₃×Q₁₆	—	4	4	no	—
298	C₁₃×SD₁₆	—	4	4	no	—
299	C₁₃×SD₁₆	—	4	4	no	—
300	C₁₃×SD₁₆	—	4	2	no	—
301	C₁₃×SD₁₆	—	4	2	no	—
302	C₁₃×SD₁₆	—	4	4	no	—
303	C₁₃×SD₁₆	—	4	4	no	—
304	C₁₃×D₈	—	4	2	no	—
305	C₁₃×D₈	—	4	4	no	—
306	C₁₃×M₁₆	—	2	4	no	—
307	C₂×C₈×C₁₃	—	2	4	no	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
310	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	2	no	—
313	C₁₃×C₄⋊C₄	—	2	1	no	—
314	C₁₃×C₄⋊C₄	—	2	1	no	—
315	C₁₃×C₄⋊C₄	—	2	1	no	—
316	C₁₃×C₄⋊C₄	—	2	2	no	—
317	C₁₃×C₄⋊C₄	—	2	2	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	2	no	—
320	C₁₃×C₄⋊C₄	—	2	1	no	—
321	C₁₃×C₄⋊C₄	—	2	1	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
328	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
329	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
332	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₄²×C₁₃	—	2	2	no	—
350	C₄²×C₁₃	—	2	1	no	—
351	C₄²×C₁₃	—	2	1	no	—
352	C₄²×C₁₃	—	2	1	no	—
353	C₄²×C₁₃	—	2	2	no	—
354	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
356	C₄²×C₁₃	C₂×D₄	1	2	yes	—
357	C₄²×C₁₃	C₂×D₄	1	2	yes	—
358	C₄²×C₁₃	C₂⁴	1	2	yes	—
359	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
360	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
361	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3461	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#3224	C₂×C₁₃	1	4	yes	complemented
364	#3222	C₂×C₁₃	1	4	yes	complemented
365	#3217	C₂×C₁₃	1	2	yes	complemented
366	#3216	C₂×C₁₃	1	2	yes	complemented
367	#3212	C₂×C₁₃	1	2	yes	complemented
368	#3208	C₂×C₁₃	1	2	yes	complemented
369	#3154	C₂×C₁₃	1	2	yes	complemented
370	#3136	C₂×C₁₃	1	2	yes	complemented
371	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
372	#3037	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
374	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3012	C₂×C₁₃	1	2	yes	complemented
376	#3009	C₂×C₁₃	1	2	yes	complemented
377	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
378	C₂³×C₁₃	—	2	1	no	—
379	C₂³×C₁₃	—	2	4	no	—
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	4	8	no	—
382	C₂³×C₁₃	—	4	4	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	C₂²×D₄	1	2	yes	—
388	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
389	Q₈×C₁₃	—	2	2	no	—
390	Q₈×C₁₃	—	2	2	no	—
391	Q₈×C₁₃	—	2	1	no	—
392	Q₈×C₁₃	—	2	2	no	—
393	Q₈×C₁₃	—	2	1	no	—
394	Q₈×C₁₃	—	2	2	no	—
395	Q₈×C₁₃	—	2	2	no	—
396	Q₈×C₁₃	—	4	2	no	—
397	Q₈×C₁₃	—	8	2	no	—
398	D₄×C₁₃	—	2	4	no	—
399	D₄×C₁₃	—	2	2	no	—
400	D₄×C₁₃	—	2	1	no	—
401	D₄×C₁₃	—	2	1	no	—
402	D₄×C₁₃	—	2	4	no	—
403	D₄×C₁₃	—	2	2	no	—
404	D₄×C₁₃	—	2	4	no	—
405	D₄×C₁₃	—	2	2	no	—
406	D₄×C₁₃	—	4	8	no	—
407	D₄×C₁₃	—	4	4	no	—
408	D₄×C₁₃	—	4	2	no	—
409	D₄×C₁₃	—	4	8	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	4	2	no	—
412	D₄×C₁₃	—	4	4	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	2	no	—
415	D₄×C₁₃	—	8	2	no	—
416	D₄×C₁₃	—	8	4	no	—
417	D₄×C₁₃	—	8	2	no	—
418	D₄×C₁₃	—	8	4	no	—
419	D₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	1	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	2	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	4	1	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	4	8	no	—
433	C₂×C₄×C₁₃	—	4	2	no	—
434	C₂×C₄×C₁₃	—	4	4	no	—
435	C₂×C₄×C₁₃	—	4	2	no	—
436	C₂×C₄×C₁₃	—	4	2	no	—
437	C₂×C₄×C₁₃	—	8	1	no	—
438	C₂×C₄×C₁₃	—	8	1	no	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
443	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
448	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
449	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
450	C₈×C₁₃	—	2	2	no	—
451	C₈×C₁₃	—	2	2	no	—
452	C₈×C₁₃	—	2	4	no	—
453	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
454	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
455	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
456	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
457	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
458	#550	—	2	1	no	—
459	#550	—	2	1	no	—
460	D₄²	—	2	1	no	—
461	D₄²	—	2	2	no	—
462	D₄²	—	2	2	no	—
463	D₄²	—	2	1	no	—
464	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
465	#542	—	2	1	no	—
466	#542	C₂²×C₁₃	1	2	yes	complemented
467	#541	—	2	1	no	—
468	#541	C₂²×C₁₃	1	2	yes	complemented
469	#539	—	2	2	no	—
470	#537	C₂²×C₁₃	1	1	yes	characteristic
471	#536	C₂²×C₁₃	1	1	yes	characteristic
472	#536	C₂²×C₁₃	1	1	yes	characteristic, complemented
473	#535	C₂²×C₁₃	1	2	yes	—
474	#535	C₂²×C₁₃	1	4	yes	—
475	#533	—	2	1	no	—
476	#533	C₂²×C₁₃	1	2	yes	complemented
477	#532	C₂²×C₁₃	1	2	yes	—
478	#532	C₂²×C₁₃	1	1	yes	characteristic
479	C₂×#127	C₂²×C₁₃	1	2	yes	—
480	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
481	#529	—	2	2	no	—
482	#529	—	2	1	no	—
483	#529	C₂²×C₁₃	1	2	yes	complemented
484	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
485	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
486	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
487	#497	C₂²×C₁₃	1	4	yes	complemented
488	#496	C₂²×C₁₃	1	4	yes	complemented
489	#495	C₂²×C₁₃	1	4	yes	complemented
490	#492	C₂²×C₁₃	1	4	yes	complemented
491	#490	C₂²×C₁₃	1	4	yes	complemented
492	#489	C₂²×C₁₃	1	4	yes	complemented
493	#488	C₂²×C₁₃	1	4	yes	complemented
494	#486	C₂²×C₁₃	1	4	yes	complemented
495	#464	C₂²×C₁₃	1	2	yes	complemented
496	#464	C₂²×C₁₃	1	4	yes	complemented
497	#463	C₂²×C₁₃	1	2	yes	complemented
498	#462	C₂²×C₁₃	1	2	yes	complemented
499	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
500	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
501	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#460	C₂²×C₁₃	1	2	yes	complemented
503	#460	C₂²×C₁₃	1	2	yes	complemented
504	#460	C₂²×C₁₃	1	2	yes	complemented
505	#460	C₂²×C₁₃	1	2	yes	complemented
506	#460	C₂²×C₁₃	1	2	yes	complemented
507	#460	C₂²×C₁₃	1	4	yes	complemented
508	#459	C₂²×C₁₃	1	2	yes	complemented
509	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
510	#459	C₂²×C₁₃	1	2	yes	complemented
511	#452	C₂²×C₁₃	1	4	yes	complemented
512	#452	C₂²×C₁₃	1	4	yes	complemented
513	#452	C₂²×C₁₃	1	4	yes	complemented
514	#450	C₂²×C₁₃	1	4	yes	complemented
515	#450	C₂²×C₁₃	1	4	yes	complemented
516	#450	C₂²×C₁₃	1	4	yes	complemented
517	#449	C₂²×C₁₃	1	4	yes	complemented
518	#447	C₂²×C₁₃	1	4	yes	complemented
519	#433	C₂²×C₁₃	1	4	yes	complemented
520	#432	C₂²×C₁₃	1	2	yes	complemented
521	#431	C₂²×C₁₃	1	2	yes	complemented
522	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
524	#418	C₂²×C₁₃	1	2	yes	complemented
525	#417	C₂²×C₁₃	1	2	yes	complemented
526	#416	C₂²×C₁₃	1	2	yes	complemented
527	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
528	#408	C₂²×C₁₃	1	2	yes	—
529	#405	C₂²×C₁₃	1	2	yes	complemented
530	C₂²×C₁₃	—	2	1	no	—
531	C₂²×C₁₃	—	2	1	no	—
532	C₂²×C₁₃	—	2	2	no	—
533	C₂²×C₁₃	—	2	2	no	—
534	C₂²×C₁₃	—	2	2	no	—
535	C₂²×C₁₃	—	4	1	no	—
536	C₂²×C₁₃	—	4	4	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	4	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	4	1	no	—
541	C₂²×C₁₃	—	4	1	no	—
542	C₂²×C₁₃	—	4	4	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	16	4	no	—
545	C₂²×C₁₃	—	16	8	no	—
546	C₂²×C₁₃	#535	1	2	yes	—
547	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
548	C₄×C₁₃	—	2	1	no	—
549	C₄×C₁₃	—	2	1	no	—
550	C₄×C₁₃	—	2	2	no	—
551	C₄×C₁₃	—	2	2	no	—
552	C₄×C₁₃	—	2	1	no	—
553	C₄×C₁₃	—	2	2	no	—
554	C₄×C₁₃	—	4	2	no	—
555	C₄×C₁₃	—	4	1	no	—
556	C₄×C₁₃	—	4	2	no	—
557	C₄×C₁₃	—	4	1	no	—
558	C₄×C₁₃	—	4	2	no	—
559	C₄×C₁₃	—	4	1	no	—
560	C₄×C₁₃	#535	1	2	yes	—
561	C₄×C₁₃	#577	1	2	yes	—
562	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
563	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
564	H(5,𝔽₂)	—	4	4	no	—
565	H(5,𝔽₂)	—	4	4	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
568	C₂×#41	C₂³×C₁₃	1	2	yes	—
569	C₂×#41	C₂³×C₁₃	1	4	yes	—
570	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
571	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
572	C₂²×D₄	—	2	4	no	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	1	no	—
575	C₂²×D₄	—	2	2	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	2	no	—
578	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
579	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
580	#137	—	4	4	no	—
581	AGL(1,ℤ/8)	—	4	4	no	—
582	#135	—	4	4	no	—
583	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
584	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂×SD₁₆	—	4	4	no	—
586	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
587	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
589	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
590	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
591	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
592	C₂×D₈	C₂³×C₁₃	1	2	yes	—
593	C₂×D₈	C₂³×C₁₃	1	4	yes	—
594	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
596	C₄⋊Q₈	—	2	1	no	—
597	C₄⋊Q₈	—	2	1	no	—
598	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
599	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
600	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
601	#127	—	2	1	no	—
602	#127	—	2	2	no	—
603	#127	—	2	1	no	—
604	#127	—	2	2	no	—
605	#127	C₂³×C₁₃	1	1	yes	characteristic
606	#127	C₂³×C₁₃	1	2	yes	—
607	#127	C₂³×C₁₃	1	2	yes	—
608	#127	C₂³×C₁₃	1	4	yes	—
609	#126	—	2	2	no	—
610	#126	—	2	2	no	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#125	—	2	2	no	—
614	#125	—	2	1	no	—
615	#125	—	2	2	no	—
616	#125	—	2	2	no	—
617	#125	C₂³×C₁₃	1	2	yes	—
618	#124	—	2	1	no	—
619	#124	—	2	2	no	—
620	#124	C₂³×C₁₃	1	2	yes	—
621	#124	C₂³×C₁₃	1	2	yes	—
622	#124	C₂³×C₁₃	1	4	yes	—
623	#123	—	2	2	no	—
624	#123	—	2	2	no	—
625	#123	—	2	2	no	—
626	#123	—	2	2	no	—
627	C₂²⋊Q₈	—	2	1	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	2	1	no	—
630	C₂²⋊Q₈	—	2	1	no	—
631	C₂²⋊Q₈	—	2	2	no	—
632	C₂²⋊Q₈	—	2	2	no	—
633	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
634	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
635	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
636	#121	—	2	2	no	—
637	#121	—	2	1	no	—
638	#121	—	2	1	no	—
639	#121	—	2	2	no	—
640	#121	—	2	1	no	—
641	#121	—	2	2	no	—
642	#121	—	2	2	no	—
643	#121	—	2	4	no	—
644	#121	—	2	2	no	—
645	#121	—	2	4	no	—
646	#121	C₂³×C₁₃	1	2	yes	—
647	#120	—	2	4	no	—
648	#120	—	2	4	no	—
649	#120	—	2	4	no	—
650	C₄×Q₈	—	2	1	no	—
651	C₄×Q₈	—	2	1	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
654	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
655	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
656	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
658	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	1	no	—
661	C₄×D₄	—	2	2	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	1	no	—
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
667	C₄×D₄	D₄×C₁₃	1	2	yes	—
668	C₄×D₄	D₄×C₁₃	1	2	yes	—
669	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
670	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
671	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
672	#117	—	2	2	no	—
673	#117	—	2	1	no	—
674	#117	—	2	2	no	—
675	#117	C₂³×C₁₃	1	1	yes	characteristic
676	#117	C₂³×C₁₃	1	1	yes	characteristic
677	#117	C₂³×C₁₃	1	2	yes	—
678	C₂×C₄⋊C₄	—	2	1	no	—
679	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
680	C₂×C₄²	—	2	1	no	—
681	C₂×C₄²	—	2	1	no	—
682	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
684	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
685	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
686	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
687	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
688	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
689	#103	C₂³×C₁₃	1	2	yes	—
690	#103	C₂³×C₁₃	1	2	yes	—
691	#103	C₂³×C₁₃	1	4	yes	—
692	#102	C₂³×C₁₃	1	4	yes	—
693	#102	C₂³×C₁₃	1	4	yes	—
694	#102	C₂³×C₁₃	1	2	yes	—
695	#102	C₂³×C₁₃	1	2	yes	—
696	#102	C₂³×C₁₃	1	4	yes	—
697	#102	C₂³×C₁₃	1	4	yes	—
698	#102	C₂³×C₁₃	1	4	yes	—
699	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
700	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
701	#97	C₂³×C₁₃	1	4	yes	—
702	C₄×C₈	C₂³×C₁₃	1	4	yes	—
703	C₂×C₁₃	—	2	2	no	—
704	C₂×C₁₃	—	4	2	no	—
705	C₂×C₁₃	—	8	1	no	—
706	C₂×C₁₃	—	8	4	no	—
707	C₂×C₁₃	—	8	2	no	—
708	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
709	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
710	C₂×C₁₃	#3585	1	1	yes	characteristic
711	C₂⁴	—	2	4	no	—
712	C₂⁴	—	2	2	no	—
713	#41	—	2	2	no	—
714	#41	—	2	2	no	—
715	#41	—	2	2	no	—
716	#41	—	2	4	no	—
717	#41	—	2	2	no	—
718	#41	—	2	4	no	—
719	#41	—	4	4	no	—
720	#41	—	4	4	no	—
721	#41	—	4	8	no	—
722	C₂×Q₈	—	2	1	no	—
723	C₂×Q₈	—	2	2	no	—
724	C₂×Q₈	—	2	2	no	—
725	C₂×Q₈	—	2	2	no	—
726	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂×Q₈	C₂⁴×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	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	1	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	4	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	4	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	4	4	no	—
747	C₂×D₄	—	4	4	no	—
748	C₂×D₄	—	4	16	no	—
749	C₂×D₄	—	4	8	no	—
750	C₂×D₄	—	8	2	no	—
751	C₂×D₄	—	8	4	no	—
752	C₂×D₄	—	8	2	no	—
753	C₂×D₄	—	8	4	no	—
754	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
755	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
756	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
757	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
758	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	—	2	1	no	—
763	C₂²×C₄	—	2	4	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
769	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	Q₁₆	—	4	2	no	—
773	Q₁₆	—	4	4	no	—
774	SD₁₆	—	4	4	no	—
775	SD₁₆	—	4	4	no	—
776	SD₁₆	—	4	2	no	—
777	SD₁₆	—	4	2	no	—
778	SD₁₆	—	4	4	no	—
779	SD₁₆	—	4	4	no	—
780	D₈	—	4	2	no	—
781	D₈	—	4	4	no	—
782	M₁₆	—	2	4	no	—
783	C₂×C₈	—	2	4	no	—
784	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
785	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
786	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	1	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
803	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
804	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
805	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
807	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
808	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	1	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	1	no	—
814	C₂²⋊C₄	—	2	1	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	2	no	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	2	no	—
819	C₂²⋊C₄	—	2	4	no	—
820	C₂²⋊C₄	—	2	4	no	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
823	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
824	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	1	no	—
827	C₄²	—	2	1	no	—
828	C₄²	—	2	1	no	—
829	C₄²	—	2	2	no	—
830	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
831	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
832	C₄²	C₂×D₄×C₁₃	1	2	yes	—
833	C₄²	C₂×D₄×C₁₃	1	2	yes	—
834	C₄²	C₂⁴×C₁₃	1	2	yes	—
835	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
836	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
837	C₁₃	#60833	1	1	yes	characteristic, direct product factor, Sylow
838	C₂³	—	2	1	no	—
839	C₂³	—	2	4	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	4	8	no	—
842	C₂³	—	4	4	no	—
843	C₂³	—	8	2	no	—
844	C₂³	—	8	2	no	—
845	C₂³	—	8	4	no	—
846	C₂³	—	8	4	no	—
847	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
848	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
849	Q₈	—	2	2	no	—
850	Q₈	—	2	2	no	—
851	Q₈	—	2	1	no	—
852	Q₈	—	2	2	no	—
853	Q₈	—	2	1	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	2	2	no	—
856	Q₈	—	4	2	no	—
857	Q₈	—	8	2	no	—
858	D₄	—	2	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	1	no	—
861	D₄	—	2	1	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	4	no	—
865	D₄	—	2	2	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	4	no	—
868	D₄	—	4	2	no	—
869	D₄	—	4	8	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	2	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	4	no	—
874	D₄	—	4	2	no	—
875	D₄	—	8	2	no	—
876	D₄	—	8	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	4	no	—
879	D₄	—	8	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	2	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	2	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	4	2	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	—	8	1	no	—
899	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
903	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
904	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
905	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
906	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
907	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
908	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
909	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
910	C₈	—	2	2	no	—
911	C₈	—	2	2	no	—
912	C₈	—	2	4	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	4	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₁₃×#535	1	2	yes	—
930	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	C₁₃×#535	1	2	yes	—
944	C₄	C₁₃×#577	1	2	yes	—
945	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
946	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
947	C₂	—	2	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	1	no	—
952	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
953	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
954	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3498	C₂	semidirect
2. C₁₃×#3461	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3222	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3216	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3208	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3038	C₂	semidirect
12. C₁₃×#3037	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#460	C₂	semidirect
15. C₁₃×#3012	C₂	semidirect
16. C₁₃×#3009	C₂	semidirect
17. C₁₃×#2925	C₂	semidirect
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×SD₁₆	C₂²	semidirect
29. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
33. C₁₃×#541	C₂²	semidirect
37. C₁₃×#536	C₂²	semidirect
41. C₁₃×#533	C₂²	semidirect
48. C₁₃×#529	C₂²	semidirect
50. C₄×C₁₃×#41	C₂²	semidirect
51. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#492	C₂²	semidirect
56. C₁₃×#490	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#486	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
61. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#460	C₂²	semidirect
70. C₁₃×#460	C₂²	semidirect
71. C₁₃×#460	C₂²	semidirect
72. C₁₃×#460	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#452	C₂²	semidirect
77. C₁₃×#452	C₂²	semidirect
78. C₁₃×#452	C₂²	semidirect
79. C₁₃×#450	C₂²	semidirect
80. C₁₃×#450	C₂²	semidirect
81. C₁₃×#450	C₂²	semidirect
82. C₁₃×#449	C₂²	semidirect
83. C₁₃×#447	C₂²	semidirect
84. C₁₃×#433	C₂²	semidirect
85. C₁₃×#432	C₂²	semidirect
86. C₁₃×#431	C₂²	semidirect
87. C₁₃×#423	C₂²	semidirect
88. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
89. C₁₃×#418	C₂²	semidirect
90. C₁₃×#417	C₂²	semidirect
91. C₁₃×#416	C₂²	semidirect
92. C₂×C₁₃×#102	C₂²	semidirect
94. C₁₃×#405	C₂²	semidirect
234. #60833	C₁₃	direct (N × H)
361. #3498	C₂×C₁₃	semidirect
362. #3461	C₂×C₁₃	semidirect
363. #3224	C₂×C₁₃	semidirect
364. #3222	C₂×C₁₃	semidirect
365. #3217	C₂×C₁₃	semidirect
366. #3216	C₂×C₁₃	semidirect
367. #3212	C₂×C₁₃	semidirect
368. #3208	C₂×C₁₃	semidirect
369. #3154	C₂×C₁₃	semidirect
370. #3136	C₂×C₁₃	semidirect
371. #3038	C₂×C₁₃	semidirect
372. #3037	C₂×C₁₃	semidirect
373. #3035	C₂×C₁₃	semidirect
374. C₂×#460	C₂×C₁₃	semidirect
375. #3012	C₂×C₁₃	semidirect
376. #3009	C₂×C₁₃	semidirect
377. #2925	C₂×C₁₃	semidirect
454. C₂×#137	C₂²×C₁₃	semidirect
455. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
456. C₂×#135	C₂²×C₁₃	semidirect
457. C₂²×SD₁₆	C₂²×C₁₃	semidirect
464. #544	C₂²×C₁₃	semidirect
466. #542	C₂²×C₁₃	semidirect
468. #541	C₂²×C₁₃	semidirect
472. #536	C₂²×C₁₃	semidirect
476. #533	C₂²×C₁₃	semidirect
483. #529	C₂²×C₁₃	semidirect
485. C₄×#41	C₂²×C₁₃	semidirect
486. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
487. #497	C₂²×C₁₃	semidirect
488. #496	C₂²×C₁₃	semidirect
489. #495	C₂²×C₁₃	semidirect
490. #492	C₂²×C₁₃	semidirect
491. #490	C₂²×C₁₃	semidirect
492. #489	C₂²×C₁₃	semidirect
493. #488	C₂²×C₁₃	semidirect
494. #486	C₂²×C₁₃	semidirect
495. #464	C₂²×C₁₃	semidirect
496. #464	C₂²×C₁₃	semidirect
497. #463	C₂²×C₁₃	semidirect
498. #462	C₂²×C₁₃	semidirect
499. #462	C₂²×C₁₃	semidirect
500. #461	C₂²×C₁₃	semidirect
501. #460	C₂²×C₁₃	semidirect
502. #460	C₂²×C₁₃	semidirect
503. #460	C₂²×C₁₃	semidirect
504. #460	C₂²×C₁₃	semidirect
505. #460	C₂²×C₁₃	semidirect
506. #460	C₂²×C₁₃	semidirect
507. #460	C₂²×C₁₃	semidirect
508. #459	C₂²×C₁₃	semidirect
509. #459	C₂²×C₁₃	semidirect
510. #459	C₂²×C₁₃	semidirect
511. #452	C₂²×C₁₃	semidirect
512. #452	C₂²×C₁₃	semidirect
513. #452	C₂²×C₁₃	semidirect
514. #450	C₂²×C₁₃	semidirect
515. #450	C₂²×C₁₃	semidirect
516. #450	C₂²×C₁₃	semidirect
517. #449	C₂²×C₁₃	semidirect
518. #447	C₂²×C₁₃	semidirect
519. #433	C₂²×C₁₃	semidirect
520. #432	C₂²×C₁₃	semidirect
521. #431	C₂²×C₁₃	semidirect
522. #423	C₂²×C₁₃	semidirect
523. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
524. #418	C₂²×C₁₃	semidirect
525. #417	C₂²×C₁₃	semidirect
526. #416	C₂²×C₁₃	semidirect
527. C₂×#102	C₂²×C₁₃	semidirect
529. #405	C₂²×C₁₃	semidirect
837. C₁₃	#60833	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×#3498	2
C₁₃×#3461	2
C₁₃×#3224	2
C₁₃×#3222	2
C₁₃×#3217	2
C₁₃×#3216	2
C₁₃×#3212	2
C₁₃×#3208	2
C₁₃×#3154	2
C₁₃×#3136	2
C₁₃×#3038	2
C₁₃×#3037	2
C₁₃×#3035	2
C₂×C₁₃×#460	2
C₁₃×#3012	2
C₁₃×#3009	2
C₁₃×#2925	2
#60833	13

Subgroups — C13×#60833 #15747172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60833 #15747172