Subgroups — C₁₃×#60832 #15747171

Order 3328.

2208 conjugacy classes of subgroups.

The subgroup lattice has 984 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×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3217	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3214	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3155	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×#3036	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3012	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3008	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×AGL(1,ℤ/8)	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×D₈	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	1	no	—
27	D₄²×C₁₃	—	2	2	no	—
28	D₄²×C₁₃	—	2	2	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×#540	—	2	1	no	—
33	C₁₃×#540	C₂²	1	2	yes	complemented
34	C₁₃×#538	—	2	2	no	—
35	C₁₃×#537	C₂²	1	1	yes	characteristic
36	C₁₃×#535	C₂²	1	2	yes	—
37	C₁₃×#535	C₂²	1	1	yes	characteristic
38	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#535	C₂²	1	4	yes	complemented
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	2	yes	complemented
43	C₁₃×#532	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
46	C₁₃×#529	—	2	1	no	—
47	C₁₃×#529	C₂²	1	2	yes	complemented
48	C₁₃×#525	—	2	2	no	—
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₁₃×#496	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	4	yes	complemented
55	C₁₃×#493	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×#463	C₂²	1	2	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×#461	C₂²	1	2	yes	complemented
66	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×#460	C₂²	1	2	yes	complemented
68	C₁₃×#460	C₂²	1	2	yes	complemented
69	C₁₃×#459	C₂²	1	2	yes	complemented
70	C₁₃×#459	C₂²	1	2	yes	complemented
71	C₁₃×#459	C₂²	1	4	yes	complemented
72	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#459	C₂²	1	2	yes	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×#450	C₂²	1	4	yes	complemented
78	C₁₃×#449	C₂²	1	4	yes	complemented
79	C₁₃×#449	C₂²	1	4	yes	complemented
80	C₁₃×#449	C₂²	1	4	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#447	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	—	2	2	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	4	yes	—
102	C₂×C₁₃×#41	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	1	no	—
107	C₂²×D₄×C₁₃	—	2	2	no	—
108	C₂²×D₄×C₁₃	—	2	2	no	—
109	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
112	C₂³×C₄×C₁₃	—	2	1	no	—
113	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
114	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
115	C₁₃×#135	—	4	4	no	—
116	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×D₈	—	4	4	no	—
122	C₂×C₁₃×D₈	C₂³	1	2	yes	—
123	C₂×C₁₃×D₈	C₂³	1	4	yes	—
124	C₂×C₁₃×D₈	C₂³	1	4	yes	—
125	C₂×C₁₃×D₈	C₂³	1	4	yes	—
126	C₂×C₁₃×D₈	C₂³	1	4	yes	—
127	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
128	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
129	C₁₃×C₄⋊Q₈	—	2	1	no	—
130	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×#127	—	2	1	no	—
133	C₁₃×#127	—	2	1	no	—
134	C₁₃×#127	—	2	1	no	—
135	C₁₃×#127	—	2	2	no	—
136	C₁₃×#127	—	2	2	no	—
137	C₁₃×#127	C₂³	1	2	yes	—
138	C₁₃×#127	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	1	yes	characteristic
140	C₁₃×#127	C₂³	1	4	yes	—
141	C₁₃×#127	C₂³	1	2	yes	—
142	C₁₃×#126	—	2	2	no	—
143	C₁₃×#126	—	2	2	no	—
144	C₁₃×#125	—	2	1	no	—
145	C₁₃×#125	C₂³	1	2	yes	—
146	C₁₃×#124	—	2	1	no	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	—	2	2	no	—
149	C₁₃×#124	C₂³	1	2	yes	—
150	C₁₃×#124	C₂³	1	4	yes	—
151	C₁₃×#124	C₂³	1	2	yes	—
152	C₁₃×#123	—	2	2	no	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	2	no	—
156	C₁₃×C₂²⋊Q₈	—	2	1	no	—
157	C₁₃×C₂²⋊Q₈	—	2	2	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
160	C₁₃×#121	—	2	2	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	1	no	—
163	C₁₃×#121	—	2	1	no	—
164	C₁₃×#121	—	2	2	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	4	no	—
172	C₁₃×#121	—	2	4	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	—	2	2	no	—
175	C₁₃×#121	C₂³	1	2	yes	—
176	C₁₃×#121	C₂³	1	2	yes	—
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₁₃×#120	—	2	2	no	—
179	C₁₃×#120	—	2	2	no	—
180	C₁₃×#120	—	2	4	no	—
181	C₁₃×#120	—	2	4	no	—
182	C₁₃×#120	—	2	4	no	—
183	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
184	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
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	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	2	yes	—
198	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
199	C₄×D₄×C₁₃	D₄	1	2	yes	—
200	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
201	C₄×D₄×C₁₃	C₂³	1	2	yes	—
202	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
203	C₄×D₄×C₁₃	C₂³	1	2	yes	—
204	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
205	C₁₃×#117	—	2	1	no	—
206	C₁₃×#117	—	2	2	no	—
207	C₁₃×#117	C₂³	1	1	yes	characteristic
208	C₁₃×#117	C₂³	1	1	yes	characteristic
209	C₁₃×#117	C₂³	1	2	yes	—
210	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₁₃×C₂²⋊C₄	—	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	#60832	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	—	2	4	no	—
237	C₂⁴×C₁₃	—	2	2	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	2	2	no	—
240	C₁₃×#41	—	2	2	no	—
241	C₁₃×#41	—	2	4	no	—
242	C₁₃×#41	—	2	2	no	—
243	C₁₃×#41	—	2	4	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₁₃×#41	—	4	4	no	—
246	C₁₃×#41	—	4	8	no	—
247	C₁₃×#41	—	8	4	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
250	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₁₃	—	2	1	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	2	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	1	no	—
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	1	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	4	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	4	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	4	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	4	no	—
273	C₂×D₄×C₁₃	—	2	2	no	—
274	C₂×D₄×C₁₃	—	2	4	no	—
275	C₂×D₄×C₁₃	—	4	4	no	—
276	C₂×D₄×C₁₃	—	4	4	no	—
277	C₂×D₄×C₁₃	—	4	16	no	—
278	C₂×D₄×C₁₃	—	4	8	no	—
279	C₂×D₄×C₁₃	—	8	2	no	—
280	C₂×D₄×C₁₃	—	8	4	no	—
281	C₂×D₄×C₁₃	—	8	2	no	—
282	C₂×D₄×C₁₃	—	8	4	no	—
283	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
285	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
286	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
287	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	—	2	1	no	—
290	C₂²×C₄×C₁₃	—	2	1	no	—
291	C₂²×C₄×C₁₃	—	2	1	no	—
292	C₂²×C₄×C₁₃	—	2	2	no	—
293	C₂²×C₄×C₁₃	—	2	4	no	—
294	C₂²×C₄×C₁₃	—	2	2	no	—
295	C₂²×C₄×C₁₃	—	2	1	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	8	2	no	—
298	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
302	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₁₃×Q₁₆	—	4	2	no	—
305	C₁₃×SD₁₆	—	4	2	no	—
306	C₁₃×SD₁₆	—	4	2	no	—
307	C₁₃×SD₁₆	—	4	4	no	—
308	C₁₃×SD₁₆	—	4	4	no	—
309	C₁₃×D₈	—	4	4	no	—
310	C₁₃×D₈	—	4	4	no	—
311	C₁₃×D₈	—	4	2	no	—
312	C₁₃×D₈	—	4	4	no	—
313	C₁₃×D₈	—	4	4	no	—
314	C₁₃×M₁₆	—	2	4	no	—
315	C₂×C₈×C₁₃	—	2	4	no	—
316	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
318	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
319	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	2	no	—
328	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
331	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
332	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
334	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	2	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	1	no	—
340	C₁₃×C₂²⋊C₄	—	2	1	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	2	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
351	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
352	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
353	C₄²×C₁₃	—	2	1	no	—
354	C₄²×C₁₃	—	2	1	no	—
355	C₄²×C₁₃	—	2	1	no	—
356	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
357	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
358	C₄²×C₁₃	C₂×D₄	1	2	yes	—
359	C₄²×C₁₃	C₂×D₄	1	2	yes	—
360	C₄²×C₁₃	C₂⁴	1	2	yes	—
361	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
362	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
363	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
364	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3224	C₂×C₁₃	1	4	yes	complemented
366	#3220	C₂×C₁₃	1	4	yes	complemented
367	#3217	C₂×C₁₃	1	2	yes	complemented
368	#3214	C₂×C₁₃	1	2	yes	complemented
369	#3212	C₂×C₁₃	1	2	yes	complemented
370	#3205	C₂×C₁₃	1	2	yes	complemented
371	#3155	C₂×C₁₃	1	2	yes	complemented
372	#3136	C₂×C₁₃	1	2	yes	complemented
373	#3038	C₂×C₁₃	1	1	yes	characteristic, complemented
374	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
375	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
376	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#3012	C₂×C₁₃	1	2	yes	complemented
378	#3008	C₂×C₁₃	1	2	yes	complemented
379	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	1	no	—
382	C₂³×C₁₃	—	2	4	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	4	8	no	—
385	C₂³×C₁₃	—	4	2	no	—
386	C₂³×C₁₃	—	4	4	no	—
387	C₂³×C₁₃	—	8	1	no	—
388	C₂³×C₁₃	—	8	1	no	—
389	C₂³×C₁₃	—	8	2	no	—
390	C₂³×C₁₃	—	8	2	no	—
391	C₂³×C₁₃	—	8	4	no	—
392	C₂³×C₁₃	—	8	4	no	—
393	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
394	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	Q₈×C₁₃	—	2	2	no	—
396	Q₈×C₁₃	—	2	1	no	—
397	Q₈×C₁₃	—	2	1	no	—
398	Q₈×C₁₃	—	2	2	no	—
399	Q₈×C₁₃	—	2	2	no	—
400	Q₈×C₁₃	—	8	2	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	1	no	—
407	D₄×C₁₃	—	2	4	no	—
408	D₄×C₁₃	—	2	2	no	—
409	D₄×C₁₃	—	2	4	no	—
410	D₄×C₁₃	—	2	2	no	—
411	D₄×C₁₃	—	4	8	no	—
412	D₄×C₁₃	—	4	2	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	8	no	—
415	D₄×C₁₃	—	4	4	no	—
416	D₄×C₁₃	—	4	2	no	—
417	D₄×C₁₃	—	4	2	no	—
418	D₄×C₁₃	—	4	4	no	—
419	D₄×C₁₃	—	4	2	no	—
420	D₄×C₁₃	—	4	4	no	—
421	D₄×C₁₃	—	8	2	no	—
422	D₄×C₁₃	—	8	2	no	—
423	D₄×C₁₃	—	8	4	no	—
424	D₄×C₁₃	—	8	2	no	—
425	D₄×C₁₃	—	8	4	no	—
426	D₄×C₁₃	—	8	2	no	—
427	D₄×C₁₃	—	8	2	no	—
428	D₄×C₁₃	—	8	2	no	—
429	D₄×C₁₃	—	8	2	no	—
430	C₂×C₄×C₁₃	—	2	2	no	—
431	C₂×C₄×C₁₃	—	2	4	no	—
432	C₂×C₄×C₁₃	—	2	2	no	—
433	C₂×C₄×C₁₃	—	2	2	no	—
434	C₂×C₄×C₁₃	—	2	1	no	—
435	C₂×C₄×C₁₃	—	2	1	no	—
436	C₂×C₄×C₁₃	—	2	1	no	—
437	C₂×C₄×C₁₃	—	2	2	no	—
438	C₂×C₄×C₁₃	—	2	2	no	—
439	C₂×C₄×C₁₃	—	4	1	no	—
440	C₂×C₄×C₁₃	—	4	2	no	—
441	C₂×C₄×C₁₃	—	4	8	no	—
442	C₂×C₄×C₁₃	—	4	4	no	—
443	C₂×C₄×C₁₃	—	4	2	no	—
444	C₂×C₄×C₁₃	—	4	4	no	—
445	C₂×C₄×C₁₃	—	4	2	no	—
446	C₂×C₄×C₁₃	—	8	1	no	—
447	C₂×C₄×C₁₃	—	8	2	no	—
448	C₂×C₄×C₁₃	—	8	1	no	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
459	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
460	C₈×C₁₃	—	2	2	no	—
461	C₈×C₁₃	—	2	2	no	—
462	C₈×C₁₃	—	2	4	no	—
463	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
464	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
465	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
466	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
467	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
468	#550	—	2	1	no	—
469	#550	—	2	1	no	—
470	D₄²	—	2	1	no	—
471	D₄²	—	2	1	no	—
472	D₄²	—	2	2	no	—
473	D₄²	—	2	2	no	—
474	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
475	#542	—	2	1	no	—
476	#542	C₂²×C₁₃	1	2	yes	complemented
477	#540	—	2	1	no	—
478	#540	C₂²×C₁₃	1	2	yes	complemented
479	#538	—	2	2	no	—
480	#537	C₂²×C₁₃	1	1	yes	characteristic
481	#535	C₂²×C₁₃	1	2	yes	—
482	#535	C₂²×C₁₃	1	1	yes	characteristic
483	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#535	C₂²×C₁₃	1	4	yes	complemented
485	#532	—	2	1	no	—
486	#532	C₂²×C₁₃	1	1	yes	characteristic
487	#532	C₂²×C₁₃	1	2	yes	complemented
488	#532	C₂²×C₁₃	1	2	yes	complemented
489	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
490	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
491	#529	—	2	1	no	—
492	#529	C₂²×C₁₃	1	2	yes	complemented
493	#525	—	2	2	no	—
494	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
495	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
497	#496	C₂²×C₁₃	1	4	yes	complemented
498	#496	C₂²×C₁₃	1	4	yes	complemented
499	#495	C₂²×C₁₃	1	4	yes	complemented
500	#493	C₂²×C₁₃	1	4	yes	complemented
501	#490	C₂²×C₁₃	1	4	yes	complemented
502	#489	C₂²×C₁₃	1	4	yes	complemented
503	#488	C₂²×C₁₃	1	4	yes	complemented
504	#486	C₂²×C₁₃	1	4	yes	complemented
505	#464	C₂²×C₁₃	1	2	yes	complemented
506	#463	C₂²×C₁₃	1	2	yes	complemented
507	#463	C₂²×C₁₃	1	4	yes	complemented
508	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#461	C₂²×C₁₃	1	2	yes	complemented
510	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#460	C₂²×C₁₃	1	2	yes	complemented
512	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
513	#460	C₂²×C₁₃	1	2	yes	complemented
514	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
515	#459	C₂²×C₁₃	1	2	yes	complemented
516	#459	C₂²×C₁₃	1	2	yes	complemented
517	#459	C₂²×C₁₃	1	2	yes	complemented
518	#459	C₂²×C₁₃	1	2	yes	complemented
519	#459	C₂²×C₁₃	1	2	yes	complemented
520	#459	C₂²×C₁₃	1	4	yes	complemented
521	#452	C₂²×C₁₃	1	4	yes	complemented
522	#450	C₂²×C₁₃	1	4	yes	complemented
523	#449	C₂²×C₁₃	1	4	yes	complemented
524	#449	C₂²×C₁₃	1	4	yes	complemented
525	#449	C₂²×C₁₃	1	4	yes	complemented
526	#447	C₂²×C₁₃	1	4	yes	complemented
527	#447	C₂²×C₁₃	1	4	yes	complemented
528	#447	C₂²×C₁₃	1	4	yes	complemented
529	#433	C₂²×C₁₃	1	4	yes	complemented
530	#432	C₂²×C₁₃	1	2	yes	complemented
531	#431	C₂²×C₁₃	1	2	yes	complemented
532	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
533	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
534	#418	C₂²×C₁₃	1	2	yes	complemented
535	#417	C₂²×C₁₃	1	2	yes	complemented
536	#416	C₂²×C₁₃	1	2	yes	complemented
537	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
538	#408	C₂²×C₁₃	1	2	yes	—
539	#405	C₂²×C₁₃	1	2	yes	complemented
540	C₂²×C₁₃	—	2	1	no	—
541	C₂²×C₁₃	—	2	1	no	—
542	C₂²×C₁₃	—	2	2	no	—
543	C₂²×C₁₃	—	2	2	no	—
544	C₂²×C₁₃	—	2	2	no	—
545	C₂²×C₁₃	—	4	1	no	—
546	C₂²×C₁₃	—	4	4	no	—
547	C₂²×C₁₃	—	4	2	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	4	no	—
550	C₂²×C₁₃	—	4	2	no	—
551	C₂²×C₁₃	—	4	1	no	—
552	C₂²×C₁₃	—	4	2	no	—
553	C₂²×C₁₃	—	4	2	no	—
554	C₂²×C₁₃	—	4	1	no	—
555	C₂²×C₁₃	—	4	4	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	8	4	no	—
558	C₂²×C₁₃	—	16	4	no	—
559	C₂²×C₁₃	—	16	8	no	—
560	C₂²×C₁₃	#535	1	2	yes	—
561	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
562	C₄×C₁₃	—	2	1	no	—
563	C₄×C₁₃	—	2	1	no	—
564	C₄×C₁₃	—	2	2	no	—
565	C₄×C₁₃	—	2	2	no	—
566	C₄×C₁₃	—	2	1	no	—
567	C₄×C₁₃	—	2	2	no	—
568	C₄×C₁₃	—	4	1	no	—
569	C₄×C₁₃	—	4	2	no	—
570	C₄×C₁₃	—	4	1	no	—
571	C₄×C₁₃	—	4	2	no	—
572	C₄×C₁₃	—	4	1	no	—
573	C₄×C₁₃	#535	1	2	yes	—
574	C₄×C₁₃	#576	1	2	yes	—
575	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
576	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	H(5,𝔽₂)	—	4	4	no	—
578	H(5,𝔽₂)	—	4	4	no	—
579	C₂×#41	—	2	2	no	—
580	C₂×#41	—	2	2	no	—
581	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
582	C₂×#41	C₂³×C₁₃	1	2	yes	—
583	C₂×#41	C₂³×C₁₃	1	4	yes	—
584	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
585	C₂²×D₄	—	2	4	no	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	—	2	1	no	—
589	C₂²×D₄	—	2	2	no	—
590	C₂²×D₄	—	2	2	no	—
591	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
593	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
594	C₂³×C₄	—	2	1	no	—
595	AGL(1,ℤ/8)	—	4	4	no	—
596	AGL(1,ℤ/8)	—	4	4	no	—
597	#135	—	4	4	no	—
598	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
599	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
603	C₂×D₈	—	4	4	no	—
604	C₂×D₈	C₂³×C₁₃	1	4	yes	—
605	C₂×D₈	C₂³×C₁₃	1	4	yes	—
606	C₂×D₈	C₂³×C₁₃	1	2	yes	—
607	C₂×D₈	C₂³×C₁₃	1	4	yes	—
608	C₂×D₈	C₂³×C₁₃	1	4	yes	—
609	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
610	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
611	C₄⋊Q₈	—	2	1	no	—
612	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
613	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
614	#127	—	2	1	no	—
615	#127	—	2	1	no	—
616	#127	—	2	1	no	—
617	#127	—	2	2	no	—
618	#127	—	2	2	no	—
619	#127	C₂³×C₁₃	1	2	yes	—
620	#127	C₂³×C₁₃	1	2	yes	—
621	#127	C₂³×C₁₃	1	1	yes	characteristic
622	#127	C₂³×C₁₃	1	4	yes	—
623	#127	C₂³×C₁₃	1	2	yes	—
624	#126	—	2	2	no	—
625	#126	—	2	2	no	—
626	#125	—	2	1	no	—
627	#125	C₂³×C₁₃	1	2	yes	—
628	#124	—	2	1	no	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	C₂³×C₁₃	1	2	yes	—
632	#124	C₂³×C₁₃	1	2	yes	—
633	#124	C₂³×C₁₃	1	4	yes	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	C₂²⋊Q₈	—	2	1	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
642	#121	—	2	2	no	—
643	#121	—	2	1	no	—
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	2	no	—
647	#121	—	2	2	no	—
648	#121	—	2	2	no	—
649	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	4	no	—
654	#121	—	2	4	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	C₂³×C₁₃	1	2	yes	—
658	#121	C₂³×C₁₃	1	2	yes	—
659	#121	C₂³×C₁₃	1	2	yes	—
660	#120	—	2	2	no	—
661	#120	—	2	2	no	—
662	#120	—	2	4	no	—
663	#120	—	2	4	no	—
664	#120	—	2	4	no	—
665	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
666	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
667	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
668	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
669	C₄×D₄	—	2	1	no	—
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	1	no	—
676	C₄×D₄	—	2	1	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	D₄×C₁₃	1	2	yes	—
680	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
681	C₄×D₄	D₄×C₁₃	1	2	yes	—
682	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
683	C₄×D₄	C₂³×C₁₃	1	2	yes	—
684	C₄×D₄	C₂³×C₁₃	1	2	yes	—
685	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
686	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
687	#117	—	2	1	no	—
688	#117	—	2	2	no	—
689	#117	C₂³×C₁₃	1	1	yes	characteristic
690	#117	C₂³×C₁₃	1	1	yes	characteristic
691	#117	C₂³×C₁₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	—	2	1	no	—
694	C₂×C₄²	—	2	1	no	—
695	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
697	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
698	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
699	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
700	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
701	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
702	#103	C₂³×C₁₃	1	2	yes	—
703	#103	C₂³×C₁₃	1	2	yes	—
704	#103	C₂³×C₁₃	1	4	yes	—
705	#102	C₂³×C₁₃	1	4	yes	—
706	#102	C₂³×C₁₃	1	4	yes	—
707	#102	C₂³×C₁₃	1	2	yes	—
708	#102	C₂³×C₁₃	1	2	yes	—
709	#102	C₂³×C₁₃	1	4	yes	—
710	#102	C₂³×C₁₃	1	4	yes	—
711	#102	C₂³×C₁₃	1	4	yes	—
712	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
713	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
714	#97	C₂³×C₁₃	1	4	yes	—
715	C₄×C₈	C₂³×C₁₃	1	4	yes	—
716	C₂×C₁₃	—	2	2	no	—
717	C₂×C₁₃	—	4	2	no	—
718	C₂×C₁₃	—	8	1	no	—
719	C₂×C₁₃	—	8	2	no	—
720	C₂×C₁₃	—	8	4	no	—
721	C₂×C₁₃	—	8	2	no	—
722	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
723	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
724	C₂×C₁₃	#3585	1	1	yes	characteristic
725	C₂⁴	—	2	1	no	—
726	C₂⁴	—	2	4	no	—
727	C₂⁴	—	2	2	no	—
728	#41	—	2	2	no	—
729	#41	—	2	2	no	—
730	#41	—	2	2	no	—
731	#41	—	2	4	no	—
732	#41	—	2	2	no	—
733	#41	—	2	4	no	—
734	#41	—	4	4	no	—
735	#41	—	4	4	no	—
736	#41	—	4	8	no	—
737	#41	—	8	4	no	—
738	C₂×Q₈	—	2	2	no	—
739	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
740	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
741	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
742	C₂×D₄	—	2	1	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	2	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	1	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	2	no	—
753	C₂×D₄	—	2	4	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	4	4	no	—
766	C₂×D₄	—	4	4	no	—
767	C₂×D₄	—	4	16	no	—
768	C₂×D₄	—	4	8	no	—
769	C₂×D₄	—	8	2	no	—
770	C₂×D₄	—	8	4	no	—
771	C₂×D₄	—	8	2	no	—
772	C₂×D₄	—	8	4	no	—
773	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
774	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
775	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
776	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
777	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
778	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	—	2	1	no	—
780	C₂²×C₄	—	2	1	no	—
781	C₂²×C₄	—	2	1	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	4	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	8	2	no	—
788	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
793	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
794	Q₁₆	—	4	2	no	—
795	SD₁₆	—	4	2	no	—
796	SD₁₆	—	4	2	no	—
797	SD₁₆	—	4	4	no	—
798	SD₁₆	—	4	4	no	—
799	D₈	—	4	4	no	—
800	D₈	—	4	4	no	—
801	D₈	—	4	2	no	—
802	D₈	—	4	4	no	—
803	D₈	—	4	4	no	—
804	M₁₆	—	2	4	no	—
805	C₂×C₈	—	2	4	no	—
806	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
807	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
808	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	—	2	1	no	—
811	C₄⋊C₄	—	2	1	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	1	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
819	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
820	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
822	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
823	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
824	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
825	C₂²⋊C₄	—	2	1	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	1	no	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	4	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
843	C₄²	—	2	1	no	—
844	C₄²	—	2	1	no	—
845	C₄²	—	2	1	no	—
846	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
847	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
848	C₄²	C₂×D₄×C₁₃	1	2	yes	—
849	C₄²	C₂×D₄×C₁₃	1	2	yes	—
850	C₄²	C₂⁴×C₁₃	1	2	yes	—
851	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
852	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
853	C₁₃	#60832	1	1	yes	characteristic, direct product factor, Sylow
854	C₂³	—	2	2	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	4	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	8	no	—
859	C₂³	—	4	2	no	—
860	C₂³	—	4	4	no	—
861	C₂³	—	8	1	no	—
862	C₂³	—	8	1	no	—
863	C₂³	—	8	2	no	—
864	C₂³	—	8	2	no	—
865	C₂³	—	8	4	no	—
866	C₂³	—	8	4	no	—
867	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
868	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
869	Q₈	—	2	2	no	—
870	Q₈	—	2	1	no	—
871	Q₈	—	2	1	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	2	2	no	—
874	Q₈	—	8	2	no	—
875	D₄	—	2	4	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	2	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	1	no	—
881	D₄	—	2	4	no	—
882	D₄	—	2	2	no	—
883	D₄	—	2	4	no	—
884	D₄	—	2	2	no	—
885	D₄	—	4	8	no	—
886	D₄	—	4	2	no	—
887	D₄	—	4	4	no	—
888	D₄	—	4	8	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	2	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	2	no	—
893	D₄	—	4	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	4	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	4	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	D₄	—	8	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	4	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	8	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	2	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	1	no	—
922	C₂×C₄	—	8	1	no	—
923	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
924	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
925	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
929	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
931	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
932	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
933	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₈	—	2	4	no	—
937	C₂²	—	2	1	no	—
938	C₂²	—	2	1	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	4	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	4	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	4	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	4	no	—
955	C₂²	—	16	4	no	—
956	C₂²	—	16	8	no	—
957	C₂²	C₁₃×#535	1	2	yes	—
958	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
959	C₄	—	2	1	no	—
960	C₄	—	2	2	no	—
961	C₄	—	2	1	no	—
962	C₄	—	2	1	no	—
963	C₄	—	2	2	no	—
964	C₄	—	2	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	1	no	—
967	C₄	—	4	1	no	—
968	C₄	—	4	2	no	—
969	C₄	—	4	1	no	—
970	C₄	C₁₃×#535	1	2	yes	—
971	C₄	C₁₃×#576	1	2	yes	—
972	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
973	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
974	C₂	—	2	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	8	2	no	—
977	C₂	—	8	4	no	—
978	C₂	—	8	2	no	—
979	C₂	—	8	1	no	—
980	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
981	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
982	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×#3460	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3220	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3214	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3155	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3038	C₂	semidirect
12. C₁₃×#3036	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#459	C₂	semidirect
15. C₁₃×#3012	C₂	semidirect
16. C₁₃×#3008	C₂	semidirect
17. C₁₃×#2925	C₂	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×D₈	C₂²	semidirect
29. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
33. C₁₃×#540	C₂²	semidirect
38. C₁₃×#535	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
42. C₁₃×#532	C₂²	semidirect
43. C₁₃×#532	C₂²	semidirect
45. C₂×C₁₃×#127	C₂²	semidirect
47. C₁₃×#529	C₂²	semidirect
50. C₄×C₁₃×#41	C₂²	semidirect
51. C₂×C₄×D₄×C₁₃	C₂²	semidirect
52. C₁₃×#496	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#493	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×#463	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
64. C₁₃×#461	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#460	C₂²	semidirect
67. C₁₃×#460	C₂²	semidirect
68. C₁₃×#460	C₂²	semidirect
69. C₁₃×#459	C₂²	semidirect
70. C₁₃×#459	C₂²	semidirect
71. C₁₃×#459	C₂²	semidirect
72. C₁₃×#459	C₂²	semidirect
73. C₁₃×#459	C₂²	semidirect
74. C₁₃×#459	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#452	C₂²	semidirect
77. C₁₃×#450	C₂²	semidirect
78. C₁₃×#449	C₂²	semidirect
79. C₁₃×#449	C₂²	semidirect
80. C₁₃×#449	C₂²	semidirect
81. C₁₃×#447	C₂²	semidirect
82. C₁₃×#447	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. #60832	C₁₃	direct (N × H)
363. #3498	C₂×C₁₃	semidirect
364. #3460	C₂×C₁₃	semidirect
365. #3224	C₂×C₁₃	semidirect
366. #3220	C₂×C₁₃	semidirect
367. #3217	C₂×C₁₃	semidirect
368. #3214	C₂×C₁₃	semidirect
369. #3212	C₂×C₁₃	semidirect
370. #3205	C₂×C₁₃	semidirect
371. #3155	C₂×C₁₃	semidirect
372. #3136	C₂×C₁₃	semidirect
373. #3038	C₂×C₁₃	semidirect
374. #3036	C₂×C₁₃	semidirect
375. #3035	C₂×C₁₃	semidirect
376. C₂×#459	C₂×C₁₃	semidirect
377. #3012	C₂×C₁₃	semidirect
378. #3008	C₂×C₁₃	semidirect
379. #2925	C₂×C₁₃	semidirect
464. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
465. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
466. C₂×#135	C₂²×C₁₃	semidirect
467. C₂²×D₈	C₂²×C₁₃	semidirect
474. #544	C₂²×C₁₃	semidirect
476. #542	C₂²×C₁₃	semidirect
478. #540	C₂²×C₁₃	semidirect
483. #535	C₂²×C₁₃	semidirect
484. #535	C₂²×C₁₃	semidirect
487. #532	C₂²×C₁₃	semidirect
488. #532	C₂²×C₁₃	semidirect
490. C₂×#127	C₂²×C₁₃	semidirect
492. #529	C₂²×C₁₃	semidirect
495. C₄×#41	C₂²×C₁₃	semidirect
496. C₂×C₄×D₄	C₂²×C₁₃	semidirect
497. #496	C₂²×C₁₃	semidirect
498. #496	C₂²×C₁₃	semidirect
499. #495	C₂²×C₁₃	semidirect
500. #493	C₂²×C₁₃	semidirect
501. #490	C₂²×C₁₃	semidirect
502. #489	C₂²×C₁₃	semidirect
503. #488	C₂²×C₁₃	semidirect
504. #486	C₂²×C₁₃	semidirect
505. #464	C₂²×C₁₃	semidirect
506. #463	C₂²×C₁₃	semidirect
507. #463	C₂²×C₁₃	semidirect
508. #462	C₂²×C₁₃	semidirect
509. #461	C₂²×C₁₃	semidirect
510. #461	C₂²×C₁₃	semidirect
511. #460	C₂²×C₁₃	semidirect
512. #460	C₂²×C₁₃	semidirect
513. #460	C₂²×C₁₃	semidirect
514. #459	C₂²×C₁₃	semidirect
515. #459	C₂²×C₁₃	semidirect
516. #459	C₂²×C₁₃	semidirect
517. #459	C₂²×C₁₃	semidirect
518. #459	C₂²×C₁₃	semidirect
519. #459	C₂²×C₁₃	semidirect
520. #459	C₂²×C₁₃	semidirect
521. #452	C₂²×C₁₃	semidirect
522. #450	C₂²×C₁₃	semidirect
523. #449	C₂²×C₁₃	semidirect
524. #449	C₂²×C₁₃	semidirect
525. #449	C₂²×C₁₃	semidirect
526. #447	C₂²×C₁₃	semidirect
527. #447	C₂²×C₁₃	semidirect
528. #447	C₂²×C₁₃	semidirect
529. #433	C₂²×C₁₃	semidirect
530. #432	C₂²×C₁₃	semidirect
531. #431	C₂²×C₁₃	semidirect
532. #423	C₂²×C₁₃	semidirect
533. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
534. #418	C₂²×C₁₃	semidirect
535. #417	C₂²×C₁₃	semidirect
536. #416	C₂²×C₁₃	semidirect
537. C₂×#102	C₂²×C₁₃	semidirect
539. #405	C₂²×C₁₃	semidirect
853. C₁₃	#60832	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×#3460	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3217	2
C₁₃×#3214	2
C₁₃×#3212	2
C₁₃×#3205	2
C₁₃×#3155	2
C₁₃×#3136	2
C₁₃×#3038	2
C₁₃×#3036	2
C₁₃×#3035	2
C₂×C₁₃×#459	2
C₁₃×#3012	2
C₁₃×#3008	2
C₁₃×#2925	2
#60832	13

Subgroups — C13×#60832 #15747171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60832 #15747171