Subgroups — C₁₃×#60811 #15747150

Order 3328.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	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×#3213	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3211	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×#3045	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
23	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
24	C₁₃×#555	—	2	1	no	—
25	C₁₃×#553	—	2	1	no	—
26	C₁₃×#553	—	2	1	no	—
27	C₁₃×#551	—	2	2	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#546	—	2	2	no	—
30	C₁₃×#544	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#542	C₂²	1	2	yes	complemented
32	C₁₃×#540	C₂²	1	2	yes	complemented
33	C₁₃×#535	—	2	2	no	—
34	C₁₃×#535	—	2	1	no	—
35	C₁₃×#535	—	2	1	no	—
36	C₁₃×#535	C₂²	1	2	yes	—
37	C₁₃×#535	C₂²	1	2	yes	—
38	C₁₃×#535	C₂²	1	4	yes	complemented
39	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	2	yes	complemented
41	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
42	C₁₃×#529	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
44	C₁₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#121	—	2	1	no	—
46	C₂×C₁₃×#121	—	2	1	no	—
47	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#120	—	2	2	no	—
49	C₁₃×#520	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#518	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
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	4	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	complemented
62	C₁₃×#463	C₂²	1	4	yes	complemented
63	C₁₃×#463	C₂²	1	4	yes	complemented
64	C₁₃×#460	C₂²	1	4	yes	complemented
65	C₁₃×#459	C₂²	1	4	yes	complemented
66	C₁₃×#459	C₂²	1	4	yes	complemented
67	C₁₃×#459	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
70	C₁₃×#450	C₂²	1	2	yes	complemented
71	C₁₃×#450	C₂²	1	2	yes	complemented
72	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#449	C₂²	1	4	yes	complemented
74	C₁₃×#449	C₂²	1	2	yes	complemented
75	C₁₃×#448	C₂²	1	2	yes	complemented
76	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
77	C₁₃×#447	C₂²	1	2	yes	—
78	C₁₃×#447	C₂²	1	2	yes	—
79	C₁₃×#447	C₂²	1	2	yes	complemented
80	C₁₃×#447	C₂²	1	2	yes	complemented
81	C₁₃×#447	C₂²	1	4	yes	complemented
82	C₁₃×#447	C₂²	1	2	yes	complemented
83	C₁₃×#447	C₂²	1	1	yes	characteristic, 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×#424	C₂²	1	2	yes	complemented
88	C₁₃×#418	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	complemented
90	C₁₃×#416	C₂²	1	2	yes	complemented
91	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
92	C₁₃×#407	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₁₃×#405	C₂²	1	2	yes	complemented
95	C₂⁵×C₁₃	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	1	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	4	4	no	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	2	yes	—
103	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×D₄×C₁₃	—	2	1	no	—
105	C₂²×D₄×C₁₃	—	2	1	no	—
106	C₂²×D₄×C₁₃	—	2	1	no	—
107	C₂²×D₄×C₁₃	—	2	1	no	—
108	C₂²×D₄×C₁₃	—	2	1	no	—
109	C₂²×D₄×C₁₃	—	2	2	no	—
110	C₂²×D₄×C₁₃	—	2	2	no	—
111	C₂²×D₄×C₁₃	—	4	4	no	—
112	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₁₃	—	2	1	no	—
118	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
120	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
121	C₁₃×#135	—	4	4	no	—
122	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	complemented
123	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
125	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
126	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	complemented
127	C₂×C₁₃×D₈	—	4	4	no	—
128	C₂×C₁₃×D₈	C₂³	1	4	yes	—
129	C₂×C₁₃×D₈	C₂³	1	4	yes	—
130	C₂×C₁₃×D₈	C₂³	1	4	yes	—
131	C₂×C₁₃×D₈	C₂³	1	2	yes	complemented
132	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
133	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
134	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
135	C₁₃×C₄⋊Q₈	—	2	1	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
137	C₁₃×#127	—	2	2	no	—
138	C₁₃×#127	—	2	2	no	—
139	C₁₃×#127	C₂³	1	4	yes	—
140	C₁₃×#127	C₂³	1	4	yes	—
141	C₁₃×#127	C₂³	1	2	yes	complemented
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	complemented
146	C₁₃×#124	—	2	2	no	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	—	2	2	no	—
149	C₁₃×#124	—	2	2	no	—
150	C₁₃×#124	C₂³	1	4	yes	—
151	C₁₃×#124	C₂³	1	4	yes	—
152	C₁₃×#124	C₂³	1	2	yes	complemented
153	C₁₃×#123	—	2	1	no	—
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	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	2	no	—
160	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
161	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	4	no	—
170	C₁₃×#121	—	2	4	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	1	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	1	yes	characteristic
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₁₃×#121	C₂³	1	1	yes	characteristic
179	C₁₃×#120	—	2	1	no	—
180	C₁₃×#120	—	2	4	no	—
181	C₁₃×#120	—	2	4	no	—
182	C₁₃×#120	—	2	4	no	—
183	C₁₃×#120	—	2	4	no	—
184	C₁₃×#120	—	2	2	no	—
185	C₄×Q₈×C₁₃	C₂³	1	2	yes	complemented
186	C₄×D₄×C₁₃	—	2	1	no	—
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	2	no	—
189	C₄×D₄×C₁₃	—	2	1	no	—
190	C₄×D₄×C₁₃	—	2	1	no	—
191	C₄×D₄×C₁₃	—	2	2	no	—
192	C₄×D₄×C₁₃	—	2	2	no	—
193	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
194	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
195	C₄×D₄×C₁₃	C₂³	1	2	yes	complemented
196	C₁₃×#117	—	2	1	no	—
197	C₁₃×#117	—	2	2	no	—
198	C₁₃×#117	D₄	1	2	yes	—
199	C₁₃×#117	D₄	1	1	yes	characteristic
200	C₁₃×#117	D₄	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	1	yes	characteristic
202	C₁₃×#117	C₂³	1	1	yes	characteristic
203	C₁₃×#117	C₂³	1	1	yes	characteristic
204	C₁₃×#117	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
207	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
208	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
209	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
210	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
214	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
216	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
217	C₁₃×#103	C₂³	1	2	yes	complemented
218	C₁₃×#103	C₂³	1	2	yes	complemented
219	C₁₃×#103	C₂³	1	4	yes	complemented
220	C₁₃×#102	C₂³	1	4	yes	—
221	C₁₃×#102	C₂³	1	4	yes	—
222	C₁₃×#102	C₂³	1	4	yes	—
223	C₁₃×#102	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	complemented
225	C₁₃×#102	C₂³	1	2	yes	complemented
226	C₁₃×#102	C₂³	1	4	yes	complemented
227	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₁₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
229	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
231	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
232	C₁₃×#97	C₂³	1	4	yes	complemented
233	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
234	#60811	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	2	no	—
236	C₂⁴×C₁₃	—	2	1	no	—
237	C₂⁴×C₁₃	—	2	1	no	—
238	C₂⁴×C₁₃	—	2	2	no	—
239	C₂⁴×C₁₃	—	2	2	no	—
240	C₂⁴×C₁₃	—	4	4	no	—
241	C₂⁴×C₁₃	—	8	2	no	—
242	C₂⁴×C₁₃	—	8	2	no	—
243	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₁₃×#41	—	2	4	no	—
245	C₁₃×#41	—	2	4	no	—
246	C₁₃×#41	—	2	4	no	—
247	C₁₃×#41	—	4	2	no	—
248	C₁₃×#41	—	4	2	no	—
249	C₁₃×#41	—	4	4	no	—
250	C₁₃×#41	—	4	4	no	—
251	C₁₃×#41	—	8	4	no	—
252	C₂×Q₈×C₁₃	—	2	1	no	—
253	C₂×Q₈×C₁₃	—	2	2	no	—
254	C₂×Q₈×C₁₃	—	4	2	no	—
255	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
256	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₁₃	—	2	1	no	—
258	C₂×D₄×C₁₃	—	2	1	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	1	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	1	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	2	no	—
268	C₂×D₄×C₁₃	—	2	1	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	4	no	—
271	C₂×D₄×C₁₃	—	2	4	no	—
272	C₂×D₄×C₁₃	—	2	4	no	—
273	C₂×D₄×C₁₃	—	2	4	no	—
274	C₂×D₄×C₁₃	—	2	2	no	—
275	C₂×D₄×C₁₃	—	2	4	no	—
276	C₂×D₄×C₁₃	—	2	4	no	—
277	C₂×D₄×C₁₃	—	2	4	no	—
278	C₂×D₄×C₁₃	—	4	4	no	—
279	C₂×D₄×C₁₃	—	4	4	no	—
280	C₂×D₄×C₁₃	—	4	2	no	—
281	C₂×D₄×C₁₃	—	4	4	no	—
282	C₂×D₄×C₁₃	—	4	4	no	—
283	C₂×D₄×C₁₃	—	4	4	no	—
284	C₂×D₄×C₁₃	—	4	4	no	—
285	C₂×D₄×C₁₃	—	8	4	no	—
286	C₂×D₄×C₁₃	—	8	4	no	—
287	C₂×D₄×C₁₃	—	8	2	no	—
288	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
289	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₁₃	—	2	4	no	—
293	C₂²×C₄×C₁₃	—	2	1	no	—
294	C₂²×C₄×C₁₃	—	2	1	no	—
295	C₂²×C₄×C₁₃	—	2	1	no	—
296	C₂²×C₄×C₁₃	—	2	2	no	—
297	C₂²×C₄×C₁₃	—	2	2	no	—
298	C₂²×C₄×C₁₃	—	2	2	no	—
299	C₂²×C₄×C₁₃	—	2	2	no	—
300	C₂²×C₄×C₁₃	—	2	2	no	—
301	C₂²×C₄×C₁₃	—	4	4	no	—
302	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
303	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
310	C₁₃×Q₁₆	—	4	2	no	—
311	C₁₃×SD₁₆	—	4	4	no	—
312	C₁₃×SD₁₆	—	4	2	no	—
313	C₁₃×SD₁₆	—	4	2	no	—
314	C₁₃×SD₁₆	—	4	4	no	—
315	C₁₃×D₈	—	4	4	no	—
316	C₁₃×D₈	—	4	4	no	—
317	C₁₃×D₈	—	4	4	no	—
318	C₁₃×D₈	—	4	2	no	—
319	C₁₃×D₈	—	4	4	no	—
320	C₁₃×M₁₆	—	2	4	no	—
321	C₂×C₈×C₁₃	—	2	4	no	—
322	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
323	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
324	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
325	C₁₃×C₄⋊C₄	—	2	1	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	—	2	2	no	—
329	C₁₃×C₄⋊C₄	—	2	2	no	—
330	C₁₃×C₄⋊C₄	—	2	2	no	—
331	C₁₃×C₄⋊C₄	—	2	1	no	—
332	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
333	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
334	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
335	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
336	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
338	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
340	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
341	C₁₃×C₂²⋊C₄	—	2	1	no	—
342	C₁₃×C₂²⋊C₄	—	2	1	no	—
343	C₁₃×C₂²⋊C₄	—	2	1	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	2	no	—
346	C₁₃×C₂²⋊C₄	—	2	2	no	—
347	C₁₃×C₂²⋊C₄	—	2	4	no	—
348	C₁₃×C₂²⋊C₄	—	2	4	no	—
349	C₁₃×C₂²⋊C₄	—	2	4	no	—
350	C₁₃×C₂²⋊C₄	—	2	4	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	2	no	—
353	C₁₃×C₂²⋊C₄	—	2	2	no	—
354	C₁₃×C₂²⋊C₄	—	2	1	no	—
355	C₁₃×C₂²⋊C₄	—	2	2	no	—
356	C₁₃×C₂²⋊C₄	—	2	1	no	—
357	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
358	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
359	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
360	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
361	C₄²×C₁₃	—	2	2	no	—
362	C₄²×C₁₃	—	2	1	no	—
363	C₄²×C₁₃	C₂×D₄	1	2	yes	—
364	C₄²×C₁₃	C₂×D₄	1	2	yes	—
365	C₄²×C₁₃	C₂⁴	1	2	yes	—
366	C₄²×C₁₃	C₂⁴	1	2	yes	—
367	#3494	C₂×C₁₃	1	1	yes	characteristic, complemented
368	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
369	#3224	C₂×C₁₃	1	4	yes	complemented
370	#3220	C₂×C₁₃	1	4	yes	complemented
371	#3217	C₂×C₁₃	1	2	yes	complemented
372	#3213	C₂×C₁₃	1	2	yes	complemented
373	#3211	C₂×C₁₃	1	2	yes	complemented
374	#3205	C₂×C₁₃	1	2	yes	complemented
375	#3155	C₂×C₁₃	1	2	yes	complemented
376	#3136	C₂×C₁₃	1	2	yes	complemented
377	#3045	C₂×C₁₃	1	2	yes	complemented
378	#3041	C₂×C₁₃	1	2	yes	complemented
379	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
380	#3003	C₂×C₁₃	1	1	yes	characteristic, complemented
381	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
382	C₂×#447	C₂×C₁₃	1	1	yes	characteristic, complemented
383	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
384	C₂³×C₁₃	—	2	2	no	—
385	C₂³×C₁₃	—	2	2	no	—
386	C₂³×C₁₃	—	2	2	no	—
387	C₂³×C₁₃	—	2	1	no	—
388	C₂³×C₁₃	—	2	4	no	—
389	C₂³×C₁₃	—	2	2	no	—
390	C₂³×C₁₃	—	4	1	no	—
391	C₂³×C₁₃	—	4	2	no	—
392	C₂³×C₁₃	—	4	4	no	—
393	C₂³×C₁₃	—	4	4	no	—
394	C₂³×C₁₃	—	4	2	no	—
395	C₂³×C₁₃	—	4	4	no	—
396	C₂³×C₁₃	—	4	4	no	—
397	C₂³×C₁₃	—	4	2	no	—
398	C₂³×C₁₃	—	4	4	no	—
399	C₂³×C₁₃	—	4	2	no	—
400	C₂³×C₁₃	—	8	2	no	—
401	C₂³×C₁₃	—	8	2	no	—
402	C₂³×C₁₃	—	8	2	no	—
403	C₂³×C₁₃	—	8	2	no	—
404	C₂³×C₁₃	—	8	1	no	—
405	C₂³×C₁₃	—	8	1	no	—
406	C₂³×C₁₃	—	8	16	no	—
407	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
408	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
409	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₁₃	—	2	2	no	—
411	Q₈×C₁₃	—	2	2	no	—
412	Q₈×C₁₃	—	2	2	no	—
413	Q₈×C₁₃	—	4	2	no	—
414	Q₈×C₁₃	—	8	2	no	—
415	D₄×C₁₃	—	2	4	no	—
416	D₄×C₁₃	—	2	2	no	—
417	D₄×C₁₃	—	2	4	no	—
418	D₄×C₁₃	—	2	2	no	—
419	D₄×C₁₃	—	2	4	no	—
420	D₄×C₁₃	—	2	2	no	—
421	D₄×C₁₃	—	4	4	no	—
422	D₄×C₁₃	—	4	4	no	—
423	D₄×C₁₃	—	4	2	no	—
424	D₄×C₁₃	—	4	4	no	—
425	D₄×C₁₃	—	4	4	no	—
426	D₄×C₁₃	—	4	2	no	—
427	D₄×C₁₃	—	4	4	no	—
428	D₄×C₁₃	—	4	2	no	—
429	D₄×C₁₃	—	4	2	no	—
430	D₄×C₁₃	—	4	4	no	—
431	D₄×C₁₃	—	8	2	no	—
432	D₄×C₁₃	—	8	4	no	—
433	D₄×C₁₃	—	8	4	no	—
434	D₄×C₁₃	—	8	4	no	—
435	D₄×C₁₃	—	8	4	no	—
436	D₄×C₁₃	—	8	2	no	—
437	D₄×C₁₃	—	8	1	no	—
438	D₄×C₁₃	—	8	2	no	—
439	C₂×C₄×C₁₃	—	2	2	no	—
440	C₂×C₄×C₁₃	—	2	4	no	—
441	C₂×C₄×C₁₃	—	2	2	no	—
442	C₂×C₄×C₁₃	—	2	2	no	—
443	C₂×C₄×C₁₃	—	2	2	no	—
444	C₂×C₄×C₁₃	—	2	2	no	—
445	C₂×C₄×C₁₃	—	2	1	no	—
446	C₂×C₄×C₁₃	—	2	1	no	—
447	C₂×C₄×C₁₃	—	2	1	no	—
448	C₂×C₄×C₁₃	—	2	2	no	—
449	C₂×C₄×C₁₃	—	2	2	no	—
450	C₂×C₄×C₁₃	—	4	2	no	—
451	C₂×C₄×C₁₃	—	4	4	no	—
452	C₂×C₄×C₁₃	—	4	2	no	—
453	C₂×C₄×C₁₃	—	4	4	no	—
454	C₂×C₄×C₁₃	—	4	2	no	—
455	C₂×C₄×C₁₃	—	8	2	no	—
456	C₂×C₄×C₁₃	—	8	2	no	—
457	C₂×C₄×C₁₃	—	8	2	no	—
458	C₂×C₄×C₁₃	—	8	1	no	—
459	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
460	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
467	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
468	C₈×C₁₃	—	2	2	no	—
469	C₈×C₁₃	—	2	2	no	—
470	C₈×C₁₃	—	2	4	no	—
471	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
472	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
473	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
474	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
475	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
476	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
477	#555	—	2	1	no	—
478	#553	—	2	1	no	—
479	#553	—	2	1	no	—
480	#551	—	2	2	no	—
481	#547	—	2	1	no	—
482	#546	—	2	2	no	—
483	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
484	#542	C₂²×C₁₃	1	2	yes	complemented
485	#540	C₂²×C₁₃	1	2	yes	complemented
486	#535	—	2	2	no	—
487	#535	—	2	1	no	—
488	#535	—	2	1	no	—
489	#535	C₂²×C₁₃	1	2	yes	—
490	#535	C₂²×C₁₃	1	2	yes	—
491	#535	C₂²×C₁₃	1	4	yes	complemented
492	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
493	#532	C₂²×C₁₃	1	2	yes	complemented
494	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
495	#529	C₂²×C₁₃	1	2	yes	complemented
496	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
497	#525	C₂²×C₁₃	1	1	yes	characteristic
498	C₂×#121	—	2	1	no	—
499	C₂×#121	—	2	1	no	—
500	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
501	C₂×#120	—	2	2	no	—
502	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
503	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
504	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
505	#496	C₂²×C₁₃	1	4	yes	complemented
506	#496	C₂²×C₁₃	1	4	yes	complemented
507	#495	C₂²×C₁₃	1	4	yes	complemented
508	#493	C₂²×C₁₃	1	4	yes	complemented
509	#490	C₂²×C₁₃	1	4	yes	complemented
510	#489	C₂²×C₁₃	1	4	yes	complemented
511	#488	C₂²×C₁₃	1	4	yes	complemented
512	#486	C₂²×C₁₃	1	4	yes	complemented
513	#464	C₂²×C₁₃	1	4	yes	complemented
514	#463	C₂²×C₁₃	1	4	yes	complemented
515	#463	C₂²×C₁₃	1	4	yes	complemented
516	#463	C₂²×C₁₃	1	4	yes	complemented
517	#460	C₂²×C₁₃	1	4	yes	complemented
518	#459	C₂²×C₁₃	1	4	yes	complemented
519	#459	C₂²×C₁₃	1	4	yes	complemented
520	#459	C₂²×C₁₃	1	4	yes	complemented
521	#452	C₂²×C₁₃	1	2	yes	complemented
522	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
523	#450	C₂²×C₁₃	1	2	yes	complemented
524	#450	C₂²×C₁₃	1	2	yes	complemented
525	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
526	#449	C₂²×C₁₃	1	2	yes	complemented
527	#449	C₂²×C₁₃	1	4	yes	complemented
528	#448	C₂²×C₁₃	1	2	yes	complemented
529	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
530	#447	C₂²×C₁₃	1	2	yes	—
531	#447	C₂²×C₁₃	1	2	yes	—
532	#447	C₂²×C₁₃	1	2	yes	complemented
533	#447	C₂²×C₁₃	1	2	yes	complemented
534	#447	C₂²×C₁₃	1	4	yes	complemented
535	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
536	#447	C₂²×C₁₃	1	2	yes	complemented
537	#433	C₂²×C₁₃	1	4	yes	complemented
538	#432	C₂²×C₁₃	1	2	yes	complemented
539	#431	C₂²×C₁₃	1	2	yes	complemented
540	#424	C₂²×C₁₃	1	2	yes	complemented
541	#418	C₂²×C₁₃	1	2	yes	complemented
542	#417	C₂²×C₁₃	1	2	yes	complemented
543	#416	C₂²×C₁₃	1	2	yes	complemented
544	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
545	#407	C₂²×C₁₃	1	1	yes	characteristic
546	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
547	#405	C₂²×C₁₃	1	2	yes	complemented
548	C₂²×C₁₃	—	2	1	no	—
549	C₂²×C₁₃	—	2	1	no	—
550	C₂²×C₁₃	—	2	1	no	—
551	C₂²×C₁₃	—	2	1	no	—
552	C₂²×C₁₃	—	2	1	no	—
553	C₂²×C₁₃	—	2	1	no	—
554	C₂²×C₁₃	—	2	1	no	—
555	C₂²×C₁₃	—	4	4	no	—
556	C₂²×C₁₃	—	4	2	no	—
557	C₂²×C₁₃	—	4	2	no	—
558	C₂²×C₁₃	—	4	1	no	—
559	C₂²×C₁₃	—	4	4	no	—
560	C₂²×C₁₃	—	4	2	no	—
561	C₂²×C₁₃	—	4	1	no	—
562	C₂²×C₁₃	—	4	4	no	—
563	C₂²×C₁₃	—	4	2	no	—
564	C₂²×C₁₃	—	4	1	no	—
565	C₂²×C₁₃	—	4	2	no	—
566	C₂²×C₁₃	—	4	2	no	—
567	C₂²×C₁₃	—	4	4	no	—
568	C₂²×C₁₃	—	8	4	no	—
569	C₂²×C₁₃	—	8	8	no	—
570	C₂²×C₁₃	—	8	8	no	—
571	C₂²×C₁₃	—	8	8	no	—
572	C₂²×C₁₃	—	16	2	no	—
573	C₂²×C₁₃	#535	1	2	yes	—
574	C₂²×C₁₃	#576	1	2	yes	—
575	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
576	C₄×C₁₃	—	2	2	no	—
577	C₄×C₁₃	—	2	2	no	—
578	C₄×C₁₃	—	2	1	no	—
579	C₄×C₁₃	—	2	1	no	—
580	C₄×C₁₃	—	2	2	no	—
581	C₄×C₁₃	—	2	2	no	—
582	C₄×C₁₃	—	4	1	no	—
583	C₄×C₁₃	—	4	2	no	—
584	C₄×C₁₃	—	4	1	no	—
585	C₄×C₁₃	—	4	2	no	—
586	C₄×C₁₃	—	4	1	no	—
587	C₄×C₁₃	#535	1	2	yes	—
588	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
589	C₂⁵	—	2	1	no	—
590	C₂×#41	—	2	1	no	—
591	C₂×#41	—	2	1	no	—
592	C₂×#41	—	2	2	no	—
593	C₂×#41	—	4	4	no	—
594	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
595	C₂×#41	C₂³×C₁₃	1	2	yes	—
596	C₂×#41	C₂³×C₁₃	1	2	yes	—
597	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
598	C₂²×D₄	—	2	1	no	—
599	C₂²×D₄	—	2	1	no	—
600	C₂²×D₄	—	2	1	no	—
601	C₂²×D₄	—	2	1	no	—
602	C₂²×D₄	—	2	1	no	—
603	C₂²×D₄	—	2	2	no	—
604	C₂²×D₄	—	2	2	no	—
605	C₂²×D₄	—	4	4	no	—
606	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
607	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
608	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
609	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
611	C₂³×C₄	—	2	1	no	—
612	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
613	AGL(1,ℤ/8)	—	4	4	no	—
614	AGL(1,ℤ/8)	—	4	4	no	—
615	#135	—	4	4	no	—
616	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	complemented
617	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
618	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
619	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	complemented
620	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
621	C₂×D₈	—	4	4	no	—
622	C₂×D₈	C₂³×C₁₃	1	4	yes	—
623	C₂×D₈	C₂³×C₁₃	1	4	yes	—
624	C₂×D₈	C₂³×C₁₃	1	4	yes	—
625	C₂×D₈	C₂³×C₁₃	1	2	yes	complemented
626	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
627	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
628	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
629	C₄⋊Q₈	—	2	1	no	—
630	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
631	#127	—	2	2	no	—
632	#127	—	2	2	no	—
633	#127	C₂³×C₁₃	1	4	yes	—
634	#127	C₂³×C₁₃	1	4	yes	—
635	#127	C₂³×C₁₃	1	2	yes	complemented
636	#126	—	2	2	no	—
637	#126	—	2	2	no	—
638	#125	—	2	1	no	—
639	#125	C₂³×C₁₃	1	2	yes	complemented
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	—	2	2	no	—
643	#124	—	2	2	no	—
644	#124	C₂³×C₁₃	1	4	yes	—
645	#124	C₂³×C₁₃	1	4	yes	—
646	#124	C₂³×C₁₃	1	2	yes	complemented
647	#123	—	2	1	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
655	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
656	#121	—	2	1	no	—
657	#121	—	2	1	no	—
658	#121	—	2	2	no	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	4	no	—
664	#121	—	2	4	no	—
665	#121	—	2	1	no	—
666	#121	—	2	1	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	C₂³×C₁₃	1	2	yes	—
670	#121	C₂³×C₁₃	1	2	yes	—
671	#121	C₂³×C₁₃	1	1	yes	characteristic
672	#121	C₂³×C₁₃	1	1	yes	characteristic
673	#120	—	2	1	no	—
674	#120	—	2	4	no	—
675	#120	—	2	4	no	—
676	#120	—	2	4	no	—
677	#120	—	2	4	no	—
678	#120	—	2	2	no	—
679	C₄×Q₈	C₂³×C₁₃	1	2	yes	complemented
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
688	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
689	C₄×D₄	C₂³×C₁₃	1	2	yes	complemented
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	D₄×C₁₃	1	2	yes	—
693	#117	D₄×C₁₃	1	1	yes	characteristic
694	#117	D₄×C₁₃	1	1	yes	characteristic
695	#117	C₂³×C₁₃	1	1	yes	characteristic
696	#117	C₂³×C₁₃	1	1	yes	characteristic
697	#117	C₂³×C₁₃	1	1	yes	characteristic
698	#117	C₂³×C₁₃	1	2	yes	—
699	C₂×C₄⋊C₄	—	2	1	no	—
700	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
703	C₂×C₂²⋊C₄	—	2	2	no	—
704	C₂×C₂²⋊C₄	—	2	2	no	—
705	C₂×C₂²⋊C₄	—	2	1	no	—
706	C₂×C₂²⋊C₄	—	2	2	no	—
707	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
708	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
709	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
710	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
711	#103	C₂³×C₁₃	1	2	yes	complemented
712	#103	C₂³×C₁₃	1	2	yes	complemented
713	#103	C₂³×C₁₃	1	4	yes	complemented
714	#102	C₂³×C₁₃	1	4	yes	—
715	#102	C₂³×C₁₃	1	4	yes	—
716	#102	C₂³×C₁₃	1	4	yes	—
717	#102	C₂³×C₁₃	1	4	yes	—
718	#102	C₂³×C₁₃	1	2	yes	complemented
719	#102	C₂³×C₁₃	1	2	yes	complemented
720	#102	C₂³×C₁₃	1	4	yes	complemented
721	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
722	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
723	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
724	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
725	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
726	#97	C₂³×C₁₃	1	4	yes	complemented
727	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
728	C₂×C₁₃	—	2	2	no	—
729	C₂×C₁₃	—	2	2	no	—
730	C₂×C₁₃	—	4	1	no	—
731	C₂×C₁₃	—	8	1	no	—
732	C₂×C₁₃	—	8	2	no	—
733	C₂×C₁₃	—	8	4	no	—
734	C₂×C₁₃	—	8	2	no	—
735	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
736	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
737	C₂×C₁₃	#3585	1	1	yes	characteristic
738	C₂⁴	—	2	2	no	—
739	C₂⁴	—	2	1	no	—
740	C₂⁴	—	2	1	no	—
741	C₂⁴	—	2	2	no	—
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	4	4	no	—
744	C₂⁴	—	8	2	no	—
745	C₂⁴	—	8	2	no	—
746	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
747	#41	—	2	4	no	—
748	#41	—	2	4	no	—
749	#41	—	2	4	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	4	no	—
753	#41	—	4	4	no	—
754	#41	—	8	4	no	—
755	C₂×Q₈	—	2	1	no	—
756	C₂×Q₈	—	2	2	no	—
757	C₂×Q₈	—	4	2	no	—
758	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
759	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
760	C₂×D₄	—	2	1	no	—
761	C₂×D₄	—	2	1	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	1	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	2	4	no	—
775	C₂×D₄	—	2	4	no	—
776	C₂×D₄	—	2	4	no	—
777	C₂×D₄	—	2	2	no	—
778	C₂×D₄	—	2	4	no	—
779	C₂×D₄	—	2	4	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	4	4	no	—
782	C₂×D₄	—	4	4	no	—
783	C₂×D₄	—	4	2	no	—
784	C₂×D₄	—	4	4	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	4	no	—
787	C₂×D₄	—	4	4	no	—
788	C₂×D₄	—	8	4	no	—
789	C₂×D₄	—	8	4	no	—
790	C₂×D₄	—	8	2	no	—
791	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
792	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
793	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
794	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	1	no	—
797	C₂²×C₄	—	2	1	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	2	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	no	—
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	4	4	no	—
805	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
806	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
807	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
808	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
809	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
813	Q₁₆	—	4	2	no	—
814	SD₁₆	—	4	4	no	—
815	SD₁₆	—	4	2	no	—
816	SD₁₆	—	4	2	no	—
817	SD₁₆	—	4	4	no	—
818	D₈	—	4	4	no	—
819	D₈	—	4	4	no	—
820	D₈	—	4	4	no	—
821	D₈	—	4	2	no	—
822	D₈	—	4	4	no	—
823	M₁₆	—	2	4	no	—
824	C₂×C₈	—	2	4	no	—
825	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
826	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
827	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
828	C₄⋊C₄	—	2	1	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	1	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	1	no	—
835	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
836	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
837	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
838	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
839	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
840	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
841	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
842	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
843	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
844	C₂²⋊C₄	—	2	1	no	—
845	C₂²⋊C₄	—	2	1	no	—
846	C₂²⋊C₄	—	2	1	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	4	no	—
851	C₂²⋊C₄	—	2	4	no	—
852	C₂²⋊C₄	—	2	4	no	—
853	C₂²⋊C₄	—	2	4	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	1	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	1	no	—
860	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
861	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
862	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
863	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
864	C₄²	—	2	2	no	—
865	C₄²	—	2	1	no	—
866	C₄²	C₂×D₄×C₁₃	1	2	yes	—
867	C₄²	C₂×D₄×C₁₃	1	2	yes	—
868	C₄²	C₂⁴×C₁₃	1	2	yes	—
869	C₄²	C₂⁴×C₁₃	1	2	yes	—
870	C₁₃	#60811	1	1	yes	characteristic, direct product factor, Sylow
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	4	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	1	no	—
878	C₂³	—	4	2	no	—
879	C₂³	—	4	4	no	—
880	C₂³	—	4	4	no	—
881	C₂³	—	4	2	no	—
882	C₂³	—	4	4	no	—
883	C₂³	—	4	4	no	—
884	C₂³	—	4	2	no	—
885	C₂³	—	4	4	no	—
886	C₂³	—	4	2	no	—
887	C₂³	—	8	2	no	—
888	C₂³	—	8	2	no	—
889	C₂³	—	8	2	no	—
890	C₂³	—	8	2	no	—
891	C₂³	—	8	1	no	—
892	C₂³	—	8	1	no	—
893	C₂³	—	8	16	no	—
894	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
896	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
897	Q₈	—	2	2	no	—
898	Q₈	—	2	2	no	—
899	Q₈	—	2	2	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	8	2	no	—
902	D₄	—	2	4	no	—
903	D₄	—	2	2	no	—
904	D₄	—	2	4	no	—
905	D₄	—	2	2	no	—
906	D₄	—	2	4	no	—
907	D₄	—	2	2	no	—
908	D₄	—	4	4	no	—
909	D₄	—	4	4	no	—
910	D₄	—	4	2	no	—
911	D₄	—	4	4	no	—
912	D₄	—	4	4	no	—
913	D₄	—	4	2	no	—
914	D₄	—	4	4	no	—
915	D₄	—	4	2	no	—
916	D₄	—	4	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	8	4	no	—
919	D₄	—	8	4	no	—
920	D₄	—	8	4	no	—
921	D₄	—	8	4	no	—
922	D₄	—	8	2	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	2	no	—
925	D₄	—	8	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	4	2	no	—
938	C₂×C₄	—	4	4	no	—
939	C₂×C₄	—	4	2	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	4	2	no	—
942	C₂×C₄	—	8	2	no	—
943	C₂×C₄	—	8	2	no	—
944	C₂×C₄	—	8	2	no	—
945	C₂×C₄	—	8	1	no	—
946	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
947	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
949	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
950	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
952	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
953	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
954	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
955	C₈	—	2	2	no	—
956	C₈	—	2	2	no	—
957	C₈	—	2	4	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	2	1	no	—
963	C₂²	—	2	1	no	—
964	C₂²	—	2	1	no	—
965	C₂²	—	4	4	no	—
966	C₂²	—	4	1	no	—
967	C₂²	—	4	2	no	—
968	C₂²	—	4	2	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	4	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	4	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	1	no	—
976	C₂²	—	4	4	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	8	4	no	—
979	C₂²	—	8	8	no	—
980	C₂²	—	8	8	no	—
981	C₂²	—	8	8	no	—
982	C₂²	—	16	2	no	—
983	C₂²	C₁₃×#535	1	2	yes	—
984	C₂²	C₁₃×#576	1	2	yes	—
985	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
986	C₄	—	2	2	no	—
987	C₄	—	2	2	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	2	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	1	no	—
994	C₄	—	4	1	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	1	no	—
997	C₄	C₁₃×#535	1	2	yes	—
998	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	2	no	—
1001	C₂	—	4	1	no	—
1002	C₂	—	8	4	no	—
1003	C₂	—	8	2	no	—
1004	C₂	—	8	2	no	—
1005	C₂	—	8	1	no	—
1006	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
1007	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
1008	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3494	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3220	C₂	semidirect
5. C₁₃×#3217	C₂	semidirect
6. C₁₃×#3213	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3205	C₂	semidirect
9. C₁₃×#3155	C₂	semidirect
10. C₁₃×#3136	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3041	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#3003	C₂	semidirect
15. C₁₃×#3002	C₂	semidirect
16. C₂×C₁₃×#447	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₁₃×#135	C₂²	semidirect
23. C₂²×C₁₃×D₈	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#540	C₂²	semidirect
38. C₁₃×#535	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
40. C₁₃×#532	C₂²	semidirect
41. C₂×C₁₃×#127	C₂²	semidirect
42. C₁₃×#529	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#518	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×#463	C₂²	semidirect
64. C₁₃×#460	C₂²	semidirect
65. C₁₃×#459	C₂²	semidirect
66. C₁₃×#459	C₂²	semidirect
67. C₁₃×#459	C₂²	semidirect
68. C₁₃×#452	C₂²	semidirect
69. C₁₃×#451	C₂²	semidirect
70. C₁₃×#450	C₂²	semidirect
71. C₁₃×#450	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
73. C₁₃×#449	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
75. C₁₃×#448	C₂²	semidirect
76. C₁₃×#448	C₂²	semidirect
79. C₁₃×#447	C₂²	semidirect
80. C₁₃×#447	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×#424	C₂²	semidirect
88. C₁₃×#418	C₂²	semidirect
89. C₁₃×#417	C₂²	semidirect
90. C₁₃×#416	C₂²	semidirect
91. C₂×C₁₃×#102	C₂²	semidirect
94. C₁₃×#405	C₂²	semidirect
122. C₂×C₁₃×Q₁₆	C₂³	semidirect
124. C₂×C₁₃×SD₁₆	C₂³	semidirect
125. C₂×C₁₃×SD₁₆	C₂³	semidirect
126. C₂×C₁₃×SD₁₆	C₂³	semidirect
131. C₂×C₁₃×D₈	C₂³	semidirect
132. C₂×C₁₃×D₈	C₂³	semidirect
136. C₁₃×C₄⋊Q₈	C₂³	semidirect
141. C₁₃×#127	C₂³	semidirect
145. C₁₃×#125	C₂³	semidirect
152. C₁₃×#124	C₂³	semidirect
185. C₄×Q₈×C₁₃	C₂³	semidirect
193. C₄×D₄×C₁₃	C₂³	semidirect
194. C₄×D₄×C₁₃	C₂³	semidirect
195. C₄×D₄×C₁₃	C₂³	semidirect
215. C₁₃×C₄⋊C₈	C₂³	semidirect
216. C₁₃×C₄⋊C₈	C₂³	semidirect
217. C₁₃×#103	C₂³	semidirect
218. C₁₃×#103	C₂³	semidirect
219. C₁₃×#103	C₂³	semidirect
224. C₁₃×#102	C₂³	semidirect
225. C₁₃×#102	C₂³	semidirect
226. C₁₃×#102	C₂³	semidirect
232. C₁₃×#97	C₂³	semidirect
233. C₄×C₈×C₁₃	C₂³	semidirect
234. #60811	C₁₃	direct (N × H)
367. #3494	C₂×C₁₃	semidirect
368. C₂×#535	C₂×C₁₃	semidirect
369. #3224	C₂×C₁₃	semidirect
370. #3220	C₂×C₁₃	semidirect
371. #3217	C₂×C₁₃	semidirect
372. #3213	C₂×C₁₃	semidirect
373. #3211	C₂×C₁₃	semidirect
374. #3205	C₂×C₁₃	semidirect
375. #3155	C₂×C₁₃	semidirect
376. #3136	C₂×C₁₃	semidirect
377. #3045	C₂×C₁₃	semidirect
378. #3041	C₂×C₁₃	semidirect
379. #3006	C₂×C₁₃	semidirect
380. #3003	C₂×C₁₃	semidirect
381. #3002	C₂×C₁₃	semidirect
382. C₂×#447	C₂×C₁₃	semidirect
383. #2924	C₂×C₁₃	semidirect
473. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
474. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
475. C₂×#135	C₂²×C₁₃	semidirect
476. C₂²×D₈	C₂²×C₁₃	semidirect
483. #544	C₂²×C₁₃	semidirect
484. #542	C₂²×C₁₃	semidirect
485. #540	C₂²×C₁₃	semidirect
491. #535	C₂²×C₁₃	semidirect
492. #535	C₂²×C₁₃	semidirect
493. #532	C₂²×C₁₃	semidirect
494. C₂×#127	C₂²×C₁₃	semidirect
495. #529	C₂²×C₁₃	semidirect
496. C₂×#124	C₂²×C₁₃	semidirect
502. #520	C₂²×C₁₃	semidirect
503. #518	C₂²×C₁₃	semidirect
505. #496	C₂²×C₁₃	semidirect
506. #496	C₂²×C₁₃	semidirect
507. #495	C₂²×C₁₃	semidirect
508. #493	C₂²×C₁₃	semidirect
509. #490	C₂²×C₁₃	semidirect
510. #489	C₂²×C₁₃	semidirect
511. #488	C₂²×C₁₃	semidirect
512. #486	C₂²×C₁₃	semidirect
513. #464	C₂²×C₁₃	semidirect
514. #463	C₂²×C₁₃	semidirect
515. #463	C₂²×C₁₃	semidirect
516. #463	C₂²×C₁₃	semidirect
517. #460	C₂²×C₁₃	semidirect
518. #459	C₂²×C₁₃	semidirect
519. #459	C₂²×C₁₃	semidirect
520. #459	C₂²×C₁₃	semidirect
521. #452	C₂²×C₁₃	semidirect
522. #451	C₂²×C₁₃	semidirect
523. #450	C₂²×C₁₃	semidirect
524. #450	C₂²×C₁₃	semidirect
525. #450	C₂²×C₁₃	semidirect
526. #449	C₂²×C₁₃	semidirect
527. #449	C₂²×C₁₃	semidirect
528. #448	C₂²×C₁₃	semidirect
529. #448	C₂²×C₁₃	semidirect
532. #447	C₂²×C₁₃	semidirect
533. #447	C₂²×C₁₃	semidirect
534. #447	C₂²×C₁₃	semidirect
535. #447	C₂²×C₁₃	semidirect
536. #447	C₂²×C₁₃	semidirect
537. #433	C₂²×C₁₃	semidirect
538. #432	C₂²×C₁₃	semidirect
539. #431	C₂²×C₁₃	semidirect
540. #424	C₂²×C₁₃	semidirect
541. #418	C₂²×C₁₃	semidirect
542. #417	C₂²×C₁₃	semidirect
543. #416	C₂²×C₁₃	semidirect
544. C₂×#102	C₂²×C₁₃	semidirect
547. #405	C₂²×C₁₃	semidirect
616. C₂×Q₁₆	C₂³×C₁₃	semidirect
618. C₂×SD₁₆	C₂³×C₁₃	semidirect
619. C₂×SD₁₆	C₂³×C₁₃	semidirect
620. C₂×SD₁₆	C₂³×C₁₃	semidirect
625. C₂×D₈	C₂³×C₁₃	semidirect
626. C₂×D₈	C₂³×C₁₃	semidirect
630. C₄⋊Q₈	C₂³×C₁₃	semidirect
635. #127	C₂³×C₁₃	semidirect
639. #125	C₂³×C₁₃	semidirect
646. #124	C₂³×C₁₃	semidirect
679. C₄×Q₈	C₂³×C₁₃	semidirect
687. C₄×D₄	C₂³×C₁₃	semidirect
688. C₄×D₄	C₂³×C₁₃	semidirect
689. C₄×D₄	C₂³×C₁₃	semidirect
709. C₄⋊C₈	C₂³×C₁₃	semidirect
710. C₄⋊C₈	C₂³×C₁₃	semidirect
711. #103	C₂³×C₁₃	semidirect
712. #103	C₂³×C₁₃	semidirect
713. #103	C₂³×C₁₃	semidirect
718. #102	C₂³×C₁₃	semidirect
719. #102	C₂³×C₁₃	semidirect
720. #102	C₂³×C₁₃	semidirect
726. #97	C₂³×C₁₃	semidirect
727. C₄×C₈	C₂³×C₁₃	semidirect
870. C₁₃	#60811	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×#3494	2
C₂×C₁₃×#535	2
C₁₃×#3224	2
C₁₃×#3220	2
C₁₃×#3217	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3205	2
C₁₃×#3155	2
C₁₃×#3136	2
C₁₃×#3045	2
C₁₃×#3041	2
C₁₃×#3006	2
C₁₃×#3003	2
C₁₃×#3002	2
C₂×C₁₃×#447	2
C₁₃×#2924	2
#60811	13

Subgroups — C13×#60811 #15747150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60811 #15747150