Subgroups — C₁₃×#60929 #15747268

Order 3328.

1868 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3263	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3257	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3253	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3247	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3246	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3084	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3062	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3045	C₂	1	2	yes	maximal, complemented
15	C₁₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×#135	C₂²	1	2	yes	—
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#556	—	2	1	no	—
22	C₁₃×#555	—	2	1	no	—
23	C₁₃×#554	—	2	1	no	—
24	C₁₃×#553	—	2	2	no	—
25	C₁₃×#548	—	2	2	no	—
26	C₁₃×#547	—	2	1	no	—
27	C₁₃×#544	C₂²	1	1	yes	characteristic
28	C₁₃×#542	—	2	1	no	—
29	C₁₃×#542	C₂²	1	2	yes	—
30	C₁₃×#542	C₂²	1	4	yes	complemented
31	C₁₃×#540	—	2	1	no	—
32	C₁₃×#540	C₂²	1	2	yes	—
33	C₁₃×#538	—	2	2	no	—
34	C₁₃×#537	C₂²	1	1	yes	characteristic
35	C₁₃×#537	C₂²	1	2	yes	—
36	C₁₃×#535	C₂²	1	1	yes	characteristic
37	C₁₃×#535	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	2	yes	complemented
39	C₁₃×#532	—	2	1	no	—
40	C₁₃×#532	C₂²	1	1	yes	characteristic
41	C₁₃×#532	C₂²	1	2	yes	—
42	C₁₃×#532	C₂²	1	2	yes	complemented
43	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₃×#529	—	2	1	no	—
45	C₁₃×#529	C₂²	1	2	yes	—
46	C₁₃×#525	—	2	2	no	—
47	C₁₃×#520	C₂²	1	2	yes	—
48	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
51	C₁₃×#479	C₂²	1	4	yes	complemented
52	C₁₃×#478	C₂²	1	4	yes	complemented
53	C₁₃×#477	C₂²	1	2	yes	complemented
54	C₁₃×#476	C₂²	1	4	yes	—
55	C₁₃×#476	C₂²	1	2	yes	—
56	C₁₃×#476	C₂²	1	2	yes	—
57	C₁₃×#476	C₂²	1	4	yes	complemented
58	C₁₃×#476	C₂²	1	2	yes	complemented
59	C₁₃×#475	C₂²	1	2	yes	complemented
60	C₁₃×#475	C₂²	1	4	yes	complemented
61	C₁₃×#474	C₂²	1	2	yes	complemented
62	C₁₃×#470	C₂²	1	4	yes	complemented
63	C₁₃×#469	C₂²	1	4	yes	—
64	C₁₃×#469	C₂²	1	4	yes	complemented
65	C₁₃×#468	C₂²	1	4	yes	—
66	C₁₃×#466	C₂²	1	4	yes	—
67	C₁₃×#465	C₂²	1	4	yes	—
68	C₁₃×#465	C₂²	1	4	yes	complemented
69	C₁₃×#465	C₂²	1	4	yes	complemented
70	C₁₃×#464	C₂²	1	4	yes	—
71	C₁₃×#464	C₂²	1	2	yes	complemented
72	C₁₃×#463	C₂²	1	4	yes	—
73	C₁₃×#463	C₂²	1	4	yes	—
74	C₁₃×#463	C₂²	1	2	yes	complemented
75	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#461	C₂²	1	2	yes	—
77	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#460	C₂²	1	4	yes	—
79	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#459	C₂²	1	2	yes	—
81	C₁₃×#459	C₂²	1	4	yes	—
82	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
83	C₁₃×#428	C₂²	1	2	yes	—
84	C₂×C₁₃×#106	C₂²	1	2	yes	—
85	C₁₃×#424	C₂²	1	2	yes	—
86	C₁₃×#424	C₂²	1	4	yes	complemented
87	C₁₃×#423	C₂²	1	1	yes	characteristic
88	C₁₃×#423	C₂²	1	2	yes	complemented
89	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
91	C₁₃×#417	C₂²	1	2	yes	—
92	C₁₃×#417	C₂²	1	2	yes	—
93	C₁₃×#416	C₂²	1	2	yes	—
94	C₂×C₁₃×#102	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	—	2	2	no	—
96	C₂×C₁₃×#41	—	2	2	no	—
97	C₂×C₁₃×#41	C₂³	1	2	yes	—
98	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₁₃	—	2	1	no	—
101	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₁₃	—	2	1	no	—
103	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
104	C₁₃×#135	—	4	4	no	—
105	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×D₈	C₂³	1	2	yes	—
110	C₂×C₁₃×D₈	C₂³	1	4	yes	—
111	C₁₃×#131	—	4	4	no	—
112	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
114	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
115	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	—	2	1	no	—
117	C₁₃×C₄⋊Q₈	—	2	1	no	—
118	C₁₃×C₄⋊Q₈	—	2	1	no	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₁₃×#127	—	2	1	no	—
124	C₁₃×#127	C₂³	1	1	yes	characteristic
125	C₁₃×#127	C₂³	1	2	yes	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	4	no	—
128	C₁₃×#126	—	2	2	no	—
129	C₁₃×#125	—	2	1	no	—
130	C₁₃×#125	—	2	2	no	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#124	—	2	1	no	—
133	C₁₃×#124	—	2	2	no	—
134	C₁₃×#124	—	2	4	no	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	—	2	2	no	—
137	C₁₃×#124	C₂³	1	2	yes	—
138	C₁₃×#124	C₂³	1	2	yes	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×#123	—	2	2	no	—
142	C₁₃×#123	—	2	2	no	—
143	C₁₃×#123	—	2	4	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	2	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	2	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×#121	—	2	2	no	—
153	C₁₃×#121	—	2	1	no	—
154	C₁₃×#121	—	2	2	no	—
155	C₁₃×#121	—	2	4	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	—	2	1	no	—
158	C₁₃×#121	—	2	1	no	—
159	C₁₃×#121	—	2	2	no	—
160	C₁₃×#121	—	2	1	no	—
161	C₁₃×#121	—	2	1	no	—
162	C₁₃×#121	—	2	2	no	—
163	C₁₃×#121	—	2	2	no	—
164	C₁₃×#121	C₂³	1	2	yes	—
165	C₁₃×#121	C₂³	1	2	yes	—
166	C₁₃×#121	C₂³	1	4	yes	—
167	C₁₃×#121	C₂³	1	2	yes	—
168	C₁₃×#120	—	2	2	no	—
169	C₁₃×#120	—	2	2	no	—
170	C₄×Q₈×C₁₃	—	2	2	no	—
171	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
172	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
173	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
174	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₁₃	—	2	1	no	—
177	C₄×D₄×C₁₃	—	2	1	no	—
178	C₄×D₄×C₁₃	—	2	2	no	—
179	C₄×D₄×C₁₃	—	2	4	no	—
180	C₄×D₄×C₁₃	—	2	1	no	—
181	C₄×D₄×C₁₃	—	2	1	no	—
182	C₄×D₄×C₁₃	—	2	2	no	—
183	C₄×D₄×C₁₃	—	2	1	no	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	—	2	2	no	—
186	C₄×D₄×C₁₃	D₄	1	2	yes	—
187	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
188	C₄×D₄×C₁₃	D₄	1	2	yes	—
189	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
190	C₄×D₄×C₁₃	C₂³	1	2	yes	—
191	C₄×D₄×C₁₃	C₂³	1	4	yes	—
192	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₁₃	C₂³	1	2	yes	—
194	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	—	2	2	no	—
197	C₁₃×#117	—	2	1	no	—
198	C₁₃×#117	—	2	2	no	—
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	2	yes	—
202	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
206	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
207	C₂×C₄²×C₁₃	—	2	1	no	—
208	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
210	C₁₃×#107	C₂³	1	4	yes	—
211	C₁₃×#106	C₂³	1	4	yes	—
212	C₁₃×#106	C₂³	1	4	yes	—
213	C₁₃×#106	C₂³	1	4	yes	—
214	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
219	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
220	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#102	C₂³	1	4	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
227	C₁₃×#102	C₂³	1	2	yes	—
228	C₁₃×#102	C₂³	1	2	yes	—
229	C₁₃×#102	C₂³	1	4	yes	—
230	C₁₃×#102	C₂³	1	4	yes	—
231	#60929	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂⁴×C₁₃	—	2	1	no	—
233	C₁₃×#41	—	2	2	no	—
234	C₁₃×#41	—	2	2	no	—
235	C₁₃×#41	—	2	2	no	—
236	C₁₃×#41	—	2	4	no	—
237	C₁₃×#41	—	2	4	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	8	4	no	—
240	C₁₃×#41	—	8	4	no	—
241	C₂×Q₈×C₁₃	—	2	2	no	—
242	C₂×Q₈×C₁₃	—	2	2	no	—
243	C₂×Q₈×C₁₃	—	2	2	no	—
244	C₂×Q₈×C₁₃	—	8	2	no	—
245	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×D₄×C₁₃	—	2	1	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	2	no	—
251	C₂×D₄×C₁₃	—	2	2	no	—
252	C₂×D₄×C₁₃	—	2	2	no	—
253	C₂×D₄×C₁₃	—	2	4	no	—
254	C₂×D₄×C₁₃	—	2	1	no	—
255	C₂×D₄×C₁₃	—	2	1	no	—
256	C₂×D₄×C₁₃	—	2	1	no	—
257	C₂×D₄×C₁₃	—	2	2	no	—
258	C₂×D₄×C₁₃	—	2	2	no	—
259	C₂×D₄×C₁₃	—	2	2	no	—
260	C₂×D₄×C₁₃	—	2	2	no	—
261	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
262	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
264	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₁₃	—	2	1	no	—
267	C₂²×C₄×C₁₃	—	2	2	no	—
268	C₂²×C₄×C₁₃	—	2	1	no	—
269	C₂²×C₄×C₁₃	—	2	1	no	—
270	C₂²×C₄×C₁₃	—	2	2	no	—
271	C₂²×C₄×C₁₃	—	2	2	no	—
272	C₂²×C₄×C₁₃	—	2	1	no	—
273	C₂²×C₄×C₁₃	—	2	4	no	—
274	C₂²×C₄×C₁₃	—	2	2	no	—
275	C₂²×C₄×C₁₃	—	8	2	no	—
276	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
278	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₁₃×Q₁₆	—	4	2	no	—
283	C₁₃×SD₁₆	—	4	2	no	—
284	C₁₃×SD₁₆	—	4	2	no	—
285	C₁₃×SD₁₆	—	4	4	no	—
286	C₁₃×D₈	—	4	2	no	—
287	C₁₃×D₈	—	4	4	no	—
288	C₁₃×M₁₆	—	2	4	no	—
289	C₁₃×M₁₆	—	4	4	no	—
290	C₂×C₈×C₁₃	—	2	4	no	—
291	C₂×C₈×C₁₃	—	4	4	no	—
292	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
293	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
294	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	2	no	—
297	C₁₃×C₄⋊C₄	—	2	4	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	1	no	—
300	C₁₃×C₄⋊C₄	—	2	1	no	—
301	C₁₃×C₄⋊C₄	—	2	1	no	—
302	C₁₃×C₄⋊C₄	—	2	1	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	2	no	—
305	C₁₃×C₄⋊C₄	—	2	1	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	—	2	2	no	—
308	C₁₃×C₄⋊C₄	—	2	4	no	—
309	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
310	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
316	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
317	C₁₃×C₂²⋊C₄	—	2	4	no	—
318	C₁₃×C₂²⋊C₄	—	2	1	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	2	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	1	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	4	no	—
325	C₁₃×C₂²⋊C₄	—	2	2	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	—	2	2	no	—
329	C₁₃×C₂²⋊C₄	—	2	4	no	—
330	C₁₃×C₂²⋊C₄	—	2	2	no	—
331	C₁₃×C₂²⋊C₄	—	2	2	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
335	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
336	C₄²×C₁₃	—	2	1	no	—
337	C₄²×C₁₃	—	2	1	no	—
338	C₄²×C₁₃	—	2	1	no	—
339	C₄²×C₁₃	—	2	4	no	—
340	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₁₃	C₂×D₄	1	2	yes	—
342	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₁₃	C₂×D₄	1	2	yes	—
344	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
346	C₄²×C₁₃	C₂⁴	1	2	yes	—
347	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
348	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
349	#3263	C₂×C₁₃	1	4	yes	complemented
350	#3257	C₂×C₁₃	1	4	yes	complemented
351	#3253	C₂×C₁₃	1	2	yes	complemented
352	#3252	C₂×C₁₃	1	2	yes	complemented
353	#3247	C₂×C₁₃	1	2	yes	complemented
354	#3246	C₂×C₁₃	1	2	yes	complemented
355	#3084	C₂×C₁₃	1	2	yes	complemented
356	#3079	C₂×C₁₃	1	1	yes	characteristic, complemented
357	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
358	#3062	C₂×C₁₃	1	2	yes	complemented
359	#3060	C₂×C₁₃	1	2	yes	complemented
360	#3045	C₂×C₁₃	1	2	yes	complemented
361	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
362	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
363	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂³×C₁₃	—	2	2	no	—
365	C₂³×C₁₃	—	2	2	no	—
366	C₂³×C₁₃	—	2	1	no	—
367	C₂³×C₁₃	—	4	2	no	—
368	C₂³×C₁₃	—	8	1	no	—
369	C₂³×C₁₃	—	8	1	no	—
370	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
371	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	2	2	no	—
374	Q₈×C₁₃	—	2	1	no	—
375	Q₈×C₁₃	—	2	1	no	—
376	Q₈×C₁₃	—	2	2	no	—
377	Q₈×C₁₃	—	4	4	no	—
378	Q₈×C₁₃	—	8	2	no	—
379	Q₈×C₁₃	—	8	2	no	—
380	D₄×C₁₃	—	2	4	no	—
381	D₄×C₁₃	—	2	2	no	—
382	D₄×C₁₃	—	2	2	no	—
383	D₄×C₁₃	—	2	2	no	—
384	D₄×C₁₃	—	2	1	no	—
385	D₄×C₁₃	—	2	2	no	—
386	D₄×C₁₃	—	2	2	no	—
387	D₄×C₁₃	—	2	1	no	—
388	D₄×C₁₃	—	4	2	no	—
389	D₄×C₁₃	—	4	2	no	—
390	D₄×C₁₃	—	4	4	no	—
391	D₄×C₁₃	—	4	2	no	—
392	D₄×C₁₃	—	4	2	no	—
393	D₄×C₁₃	—	8	2	no	—
394	D₄×C₁₃	—	8	2	no	—
395	D₄×C₁₃	—	8	2	no	—
396	D₄×C₁₃	—	8	4	no	—
397	D₄×C₁₃	—	8	2	no	—
398	D₄×C₁₃	—	8	2	no	—
399	C₂×C₄×C₁₃	—	2	2	no	—
400	C₂×C₄×C₁₃	—	2	4	no	—
401	C₂×C₄×C₁₃	—	2	2	no	—
402	C₂×C₄×C₁₃	—	2	2	no	—
403	C₂×C₄×C₁₃	—	2	1	no	—
404	C₂×C₄×C₁₃	—	2	2	no	—
405	C₂×C₄×C₁₃	—	2	1	no	—
406	C₂×C₄×C₁₃	—	2	1	no	—
407	C₂×C₄×C₁₃	—	2	4	no	—
408	C₂×C₄×C₁₃	—	2	2	no	—
409	C₂×C₄×C₁₃	—	4	1	no	—
410	C₂×C₄×C₁₃	—	4	2	no	—
411	C₂×C₄×C₁₃	—	4	2	no	—
412	C₂×C₄×C₁₃	—	4	4	no	—
413	C₂×C₄×C₁₃	—	4	4	no	—
414	C₂×C₄×C₁₃	—	4	2	no	—
415	C₂×C₄×C₁₃	—	8	1	no	—
416	C₂×C₄×C₁₃	—	8	2	no	—
417	C₂×C₄×C₁₃	—	8	4	no	—
418	C₂×C₄×C₁₃	—	8	1	no	—
419	C₂×C₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
430	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
431	C₈×C₁₃	—	2	2	no	—
432	C₈×C₁₃	—	2	2	no	—
433	C₈×C₁₃	—	2	4	no	—
434	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
435	C₂×#135	C₂²×C₁₃	1	2	yes	—
436	C₂×#131	C₂²×C₁₃	1	2	yes	—
437	#556	—	2	1	no	—
438	#555	—	2	1	no	—
439	#554	—	2	1	no	—
440	#553	—	2	2	no	—
441	#548	—	2	2	no	—
442	#547	—	2	1	no	—
443	#544	C₂²×C₁₃	1	1	yes	characteristic
444	#542	—	2	1	no	—
445	#542	C₂²×C₁₃	1	2	yes	—
446	#542	C₂²×C₁₃	1	4	yes	complemented
447	#540	—	2	1	no	—
448	#540	C₂²×C₁₃	1	2	yes	—
449	#538	—	2	2	no	—
450	#537	C₂²×C₁₃	1	1	yes	characteristic
451	#537	C₂²×C₁₃	1	2	yes	—
452	#535	C₂²×C₁₃	1	1	yes	characteristic
453	#535	C₂²×C₁₃	1	1	yes	characteristic
454	#533	C₂²×C₁₃	1	2	yes	complemented
455	#532	—	2	1	no	—
456	#532	C₂²×C₁₃	1	1	yes	characteristic
457	#532	C₂²×C₁₃	1	2	yes	—
458	#532	C₂²×C₁₃	1	2	yes	complemented
459	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
460	#529	—	2	1	no	—
461	#529	C₂²×C₁₃	1	2	yes	—
462	#525	—	2	2	no	—
463	#520	C₂²×C₁₃	1	2	yes	—
464	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
465	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
467	#479	C₂²×C₁₃	1	4	yes	complemented
468	#478	C₂²×C₁₃	1	4	yes	complemented
469	#477	C₂²×C₁₃	1	2	yes	complemented
470	#476	C₂²×C₁₃	1	2	yes	—
471	#476	C₂²×C₁₃	1	2	yes	—
472	#476	C₂²×C₁₃	1	4	yes	—
473	#476	C₂²×C₁₃	1	2	yes	complemented
474	#476	C₂²×C₁₃	1	4	yes	complemented
475	#475	C₂²×C₁₃	1	2	yes	complemented
476	#475	C₂²×C₁₃	1	4	yes	complemented
477	#474	C₂²×C₁₃	1	2	yes	complemented
478	#470	C₂²×C₁₃	1	4	yes	complemented
479	#469	C₂²×C₁₃	1	4	yes	—
480	#469	C₂²×C₁₃	1	4	yes	complemented
481	#468	C₂²×C₁₃	1	4	yes	—
482	#466	C₂²×C₁₃	1	4	yes	—
483	#465	C₂²×C₁₃	1	4	yes	—
484	#465	C₂²×C₁₃	1	4	yes	complemented
485	#465	C₂²×C₁₃	1	4	yes	complemented
486	#464	C₂²×C₁₃	1	4	yes	—
487	#464	C₂²×C₁₃	1	2	yes	complemented
488	#463	C₂²×C₁₃	1	4	yes	—
489	#463	C₂²×C₁₃	1	4	yes	—
490	#463	C₂²×C₁₃	1	2	yes	complemented
491	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
492	#461	C₂²×C₁₃	1	2	yes	—
493	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
494	#460	C₂²×C₁₃	1	4	yes	—
495	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#459	C₂²×C₁₃	1	2	yes	—
497	#459	C₂²×C₁₃	1	4	yes	—
498	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
499	#428	C₂²×C₁₃	1	2	yes	—
500	C₂×#106	C₂²×C₁₃	1	2	yes	—
501	#424	C₂²×C₁₃	1	2	yes	—
502	#424	C₂²×C₁₃	1	4	yes	complemented
503	#423	C₂²×C₁₃	1	1	yes	characteristic
504	#423	C₂²×C₁₃	1	2	yes	complemented
505	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
506	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
507	#417	C₂²×C₁₃	1	2	yes	—
508	#417	C₂²×C₁₃	1	2	yes	—
509	#416	C₂²×C₁₃	1	2	yes	—
510	C₂×#102	C₂²×C₁₃	1	2	yes	—
511	C₂²×C₁₃	—	2	1	no	—
512	C₂²×C₁₃	—	2	1	no	—
513	C₂²×C₁₃	—	2	2	no	—
514	C₂²×C₁₃	—	2	2	no	—
515	C₂²×C₁₃	—	2	2	no	—
516	C₂²×C₁₃	—	4	2	no	—
517	C₂²×C₁₃	—	4	1	no	—
518	C₂²×C₁₃	—	4	2	no	—
519	C₂²×C₁₃	—	4	2	no	—
520	C₂²×C₁₃	—	4	1	no	—
521	C₂²×C₁₃	—	4	2	no	—
522	C₂²×C₁₃	—	4	2	no	—
523	C₂²×C₁₃	—	4	1	no	—
524	C₂²×C₁₃	—	4	2	no	—
525	C₂²×C₁₃	—	8	4	no	—
526	C₂²×C₁₃	#537	1	2	yes	—
527	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
528	C₄×C₁₃	—	2	1	no	—
529	C₄×C₁₃	—	2	2	no	—
530	C₄×C₁₃	—	2	1	no	—
531	C₄×C₁₃	—	2	2	no	—
532	C₄×C₁₃	—	2	1	no	—
533	C₄×C₁₃	—	2	2	no	—
534	C₄×C₁₃	—	4	4	no	—
535	C₄×C₁₃	—	4	1	no	—
536	C₄×C₁₃	—	4	1	no	—
537	C₄×C₁₃	—	4	2	no	—
538	C₄×C₁₃	—	4	2	no	—
539	C₄×C₁₃	—	4	1	no	—
540	C₄×C₁₃	#537	1	2	yes	—
541	C₄×C₁₃	#577	1	2	yes	—
542	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
543	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	C₂×#41	—	2	2	no	—
545	C₂×#41	—	2	2	no	—
546	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
547	C₂×#41	C₂³×C₁₃	1	2	yes	—
548	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²×Q₈	—	2	1	no	—
550	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
551	C₂³×C₄	—	2	1	no	—
552	AGL(1,ℤ/8)	—	4	4	no	—
553	#135	—	4	4	no	—
554	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
557	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
558	C₂×D₈	C₂³×C₁₃	1	2	yes	—
559	C₂×D₈	C₂³×C₁₃	1	4	yes	—
560	#131	—	4	4	no	—
561	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
562	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
563	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
564	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	—	2	1	no	—
567	C₄⋊Q₈	—	2	1	no	—
568	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
569	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
570	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
571	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
572	#127	—	2	1	no	—
573	#127	C₂³×C₁₃	1	1	yes	characteristic
574	#127	C₂³×C₁₃	1	2	yes	—
575	#126	—	2	2	no	—
576	#126	—	2	4	no	—
577	#126	—	2	2	no	—
578	#125	—	2	1	no	—
579	#125	—	2	2	no	—
580	#125	C₂³×C₁₃	1	2	yes	—
581	#124	—	2	1	no	—
582	#124	—	2	2	no	—
583	#124	—	2	4	no	—
584	#124	—	2	2	no	—
585	#124	—	2	2	no	—
586	#124	C₂³×C₁₃	1	2	yes	—
587	#124	C₂³×C₁₃	1	2	yes	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	4	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	4	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
601	#121	—	2	2	no	—
602	#121	—	2	1	no	—
603	#121	—	2	2	no	—
604	#121	—	2	4	no	—
605	#121	—	2	2	no	—
606	#121	—	2	1	no	—
607	#121	—	2	1	no	—
608	#121	—	2	2	no	—
609	#121	—	2	1	no	—
610	#121	—	2	1	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	C₂³×C₁₃	1	2	yes	—
614	#121	C₂³×C₁₃	1	2	yes	—
615	#121	C₂³×C₁₃	1	2	yes	—
616	#121	C₂³×C₁₃	1	4	yes	—
617	#120	—	2	2	no	—
618	#120	—	2	2	no	—
619	C₄×Q₈	—	2	2	no	—
620	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
621	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
622	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
623	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	4	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	D₄×C₁₃	1	2	yes	—
636	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
637	C₄×D₄	D₄×C₁₃	1	2	yes	—
638	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
639	C₄×D₄	C₂³×C₁₃	1	2	yes	—
640	C₄×D₄	C₂³×C₁₃	1	2	yes	—
641	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
643	C₄×D₄	C₂³×C₁₃	1	4	yes	—
644	#117	—	2	2	no	—
645	#117	—	2	2	no	—
646	#117	—	2	1	no	—
647	#117	—	2	2	no	—
648	#117	C₂³×C₁₃	1	1	yes	characteristic
649	#117	C₂³×C₁₃	1	1	yes	characteristic
650	#117	C₂³×C₁₃	1	2	yes	—
651	C₂×C₄⋊C₄	—	2	1	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
659	#107	C₂³×C₁₃	1	4	yes	—
660	#106	C₂³×C₁₃	1	4	yes	—
661	#106	C₂³×C₁₃	1	4	yes	—
662	#106	C₂³×C₁₃	1	4	yes	—
663	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
664	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
665	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
666	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
667	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
668	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
670	#103	C₂³×C₁₃	1	2	yes	—
671	#103	C₂³×C₁₃	1	2	yes	—
672	#103	C₂³×C₁₃	1	4	yes	—
673	#103	C₂³×C₁₃	1	4	yes	—
674	#102	C₂³×C₁₃	1	4	yes	—
675	#102	C₂³×C₁₃	1	4	yes	—
676	#102	C₂³×C₁₃	1	2	yes	—
677	#102	C₂³×C₁₃	1	2	yes	—
678	#102	C₂³×C₁₃	1	4	yes	—
679	#102	C₂³×C₁₃	1	4	yes	—
680	C₂×C₁₃	—	2	2	no	—
681	C₂×C₁₃	—	4	2	no	—
682	C₂×C₁₃	—	8	2	no	—
683	C₂×C₁₃	—	8	1	no	—
684	C₂×C₁₃	—	8	2	no	—
685	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
686	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
687	C₂×C₁₃	#3585	1	1	yes	characteristic
688	C₂⁴	—	2	1	no	—
689	#41	—	2	2	no	—
690	#41	—	2	2	no	—
691	#41	—	2	2	no	—
692	#41	—	2	4	no	—
693	#41	—	2	2	no	—
694	#41	—	2	4	no	—
695	#41	—	8	4	no	—
696	#41	—	8	4	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	8	2	no	—
701	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
702	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
703	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
720	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
721	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	8	2	no	—
732	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
738	Q₁₆	—	4	2	no	—
739	SD₁₆	—	4	2	no	—
740	SD₁₆	—	4	2	no	—
741	SD₁₆	—	4	4	no	—
742	D₈	—	4	2	no	—
743	D₈	—	4	4	no	—
744	M₁₆	—	2	4	no	—
745	M₁₆	—	4	4	no	—
746	C₂×C₈	—	2	4	no	—
747	C₂×C₈	—	4	4	no	—
748	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
749	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
750	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
769	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
770	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
771	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	1	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
791	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
792	C₄²	—	2	1	no	—
793	C₄²	—	2	1	no	—
794	C₄²	—	2	1	no	—
795	C₄²	—	2	4	no	—
796	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₄²	C₂×D₄×C₁₃	1	2	yes	—
798	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₁₃	1	2	yes	—
800	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
801	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₄²	C₂⁴×C₁₃	1	2	yes	—
803	C₁₃	#60929	1	1	yes	characteristic, direct product factor, Sylow
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	8	1	no	—
809	C₂³	—	8	1	no	—
810	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
811	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
812	Q₈	—	2	2	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	1	no	—
815	Q₈	—	2	1	no	—
816	Q₈	—	2	2	no	—
817	Q₈	—	4	4	no	—
818	Q₈	—	8	2	no	—
819	Q₈	—	8	2	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	1	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	1	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	2	no	—
830	D₄	—	4	4	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	2	no	—
833	D₄	—	8	2	no	—
834	D₄	—	8	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	4	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	4	1	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	4	no	—
853	C₂×C₄	—	4	4	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	—	8	1	no	—
857	C₂×C₄	—	8	4	no	—
858	C₂×C₄	—	8	1	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
864	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
865	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
868	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
869	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
870	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
871	C₈	—	2	2	no	—
872	C₈	—	2	2	no	—
873	C₈	—	2	4	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	1	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	1	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	1	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	8	4	no	—
889	C₂²	C₁₃×#537	1	2	yes	—
890	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
891	C₄	—	2	1	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	1	no	—
899	C₄	—	4	4	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	C₁₃×#537	1	2	yes	—
904	C₄	C₁₃×#577	1	2	yes	—
905	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
906	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
907	C₂	—	2	2	no	—
908	C₂	—	4	2	no	—
909	C₂	—	8	2	no	—
910	C₂	—	8	1	no	—
911	C₂	—	8	2	no	—
912	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
913	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
914	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×#3511	C₂	semidirect
2. C₁₃×#3460	C₂	semidirect
3. C₁₃×#3263	C₂	semidirect
4. C₁₃×#3257	C₂	semidirect
5. C₁₃×#3253	C₂	semidirect
6. C₁₃×#3252	C₂	semidirect
7. C₁₃×#3247	C₂	semidirect
8. C₁₃×#3246	C₂	semidirect
9. C₁₃×#3084	C₂	semidirect
10. C₁₃×#3079	C₂	semidirect
11. C₂×C₁₃×#476	C₂	semidirect
12. C₁₃×#3062	C₂	semidirect
13. C₁₃×#3060	C₂	semidirect
14. C₁₃×#3045	C₂	semidirect
15. C₁₃×#3036	C₂	semidirect
16. C₁₃×#3035	C₂	semidirect
17. C₁₃×#2906	C₂	semidirect
30. C₁₃×#542	C₂²	semidirect
38. C₁₃×#533	C₂²	semidirect
42. C₁₃×#532	C₂²	semidirect
51. C₁₃×#479	C₂²	semidirect
52. C₁₃×#478	C₂²	semidirect
53. C₁₃×#477	C₂²	semidirect
57. C₁₃×#476	C₂²	semidirect
58. C₁₃×#476	C₂²	semidirect
59. C₁₃×#475	C₂²	semidirect
60. C₁₃×#475	C₂²	semidirect
61. C₁₃×#474	C₂²	semidirect
62. C₁₃×#470	C₂²	semidirect
64. C₁₃×#469	C₂²	semidirect
68. C₁₃×#465	C₂²	semidirect
69. C₁₃×#465	C₂²	semidirect
71. C₁₃×#464	C₂²	semidirect
74. C₁₃×#463	C₂²	semidirect
75. C₁₃×#462	C₂²	semidirect
77. C₁₃×#461	C₂²	semidirect
79. C₁₃×#460	C₂²	semidirect
82. C₁₃×#459	C₂²	semidirect
86. C₁₃×#424	C₂²	semidirect
88. C₁₃×#423	C₂²	semidirect
90. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
231. #60929	C₁₃	direct (N × H)
347. #3511	C₂×C₁₃	semidirect
348. #3460	C₂×C₁₃	semidirect
349. #3263	C₂×C₁₃	semidirect
350. #3257	C₂×C₁₃	semidirect
351. #3253	C₂×C₁₃	semidirect
352. #3252	C₂×C₁₃	semidirect
353. #3247	C₂×C₁₃	semidirect
354. #3246	C₂×C₁₃	semidirect
355. #3084	C₂×C₁₃	semidirect
356. #3079	C₂×C₁₃	semidirect
357. C₂×#476	C₂×C₁₃	semidirect
358. #3062	C₂×C₁₃	semidirect
359. #3060	C₂×C₁₃	semidirect
360. #3045	C₂×C₁₃	semidirect
361. #3036	C₂×C₁₃	semidirect
362. #3035	C₂×C₁₃	semidirect
363. #2906	C₂×C₁₃	semidirect
446. #542	C₂²×C₁₃	semidirect
454. #533	C₂²×C₁₃	semidirect
458. #532	C₂²×C₁₃	semidirect
467. #479	C₂²×C₁₃	semidirect
468. #478	C₂²×C₁₃	semidirect
469. #477	C₂²×C₁₃	semidirect
473. #476	C₂²×C₁₃	semidirect
474. #476	C₂²×C₁₃	semidirect
475. #475	C₂²×C₁₃	semidirect
476. #475	C₂²×C₁₃	semidirect
477. #474	C₂²×C₁₃	semidirect
478. #470	C₂²×C₁₃	semidirect
480. #469	C₂²×C₁₃	semidirect
484. #465	C₂²×C₁₃	semidirect
485. #465	C₂²×C₁₃	semidirect
487. #464	C₂²×C₁₃	semidirect
490. #463	C₂²×C₁₃	semidirect
491. #462	C₂²×C₁₃	semidirect
493. #461	C₂²×C₁₃	semidirect
495. #460	C₂²×C₁₃	semidirect
498. #459	C₂²×C₁₃	semidirect
502. #424	C₂²×C₁₃	semidirect
504. #423	C₂²×C₁₃	semidirect
506. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
803. C₁₃	#60929	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×#3511	2
C₁₃×#3460	2
C₁₃×#3263	2
C₁₃×#3257	2
C₁₃×#3253	2
C₁₃×#3252	2
C₁₃×#3247	2
C₁₃×#3246	2
C₁₃×#3084	2
C₁₃×#3079	2
C₂×C₁₃×#476	2
C₁₃×#3062	2
C₁₃×#3060	2
C₁₃×#3045	2
C₁₃×#3036	2
C₁₃×#3035	2
C₁₃×#2906	2
#60929	13

Subgroups — C13×#60929 #15747268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60929 #15747268