Subgroups — C₁₃×#60836 #15747175

Order 3328.

2072 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3225	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3221	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3218	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×#3206	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3039	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×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3013	C₂	1	2	yes	maximal, complemented
16	C₁₃×#3010	C₂	1	2	yes	maximal, complemented
17	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
19	C₂×C₁₃×#137	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₁₃×#135	C₂²	1	2	yes	—
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	D₄×Q₈×C₁₃	—	2	1	no	—
24	D₄×Q₈×C₁₃	—	2	1	no	—
25	C₁₃×#547	—	2	2	no	—
26	C₁₃×#547	—	2	2	no	—
27	C₁₃×#547	—	2	1	no	—
28	C₁₃×#547	—	2	1	no	—
29	C₁₃×#544	C₂²	1	1	yes	characteristic
30	C₁₃×#542	—	2	1	no	—
31	C₁₃×#542	C₂²	1	2	yes	—
32	C₁₃×#540	—	2	1	no	—
33	C₁₃×#540	C₂²	1	2	yes	—
34	C₁₃×#538	—	2	2	no	—
35	C₁₃×#537	C₂²	1	1	yes	characteristic
36	C₁₃×#536	C₂²	1	2	yes	—
37	C₁₃×#536	C₂²	1	4	yes	complemented
38	C₁₃×#535	C₂²	1	1	yes	characteristic
39	C₁₃×#535	C₂²	1	1	yes	characteristic
40	C₁₃×#532	—	2	1	no	—
41	C₁₃×#532	C₂²	1	1	yes	characteristic
42	C₁₃×#532	C₂²	1	2	yes	—
43	C₁₃×#532	C₂²	1	2	yes	complemented
44	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
46	C₁₃×#529	—	2	1	no	—
47	C₁₃×#529	C₂²	1	2	yes	—
48	C₁₃×#525	—	2	2	no	—
49	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
52	C₁₃×#497	C₂²	1	4	yes	—
53	C₁₃×#496	C₂²	1	4	yes	—
54	C₁₃×#495	C₂²	1	4	yes	—
55	C₁₃×#492	C₂²	1	4	yes	—
56	C₁₃×#491	C₂²	1	4	yes	complemented
57	C₁₃×#489	C₂²	1	4	yes	complemented
58	C₁₃×#488	C₂²	1	4	yes	complemented
59	C₁₃×#487	C₂²	1	4	yes	complemented
60	C₁₃×#464	C₂²	1	2	yes	complemented
61	C₁₃×#463	C₂²	1	4	yes	—
62	C₁₃×#463	C₂²	1	2	yes	complemented
63	C₁₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×#462	C₂²	1	2	yes	complemented
65	C₁₃×#462	C₂²	1	2	yes	complemented
66	C₁₃×#461	C₂²	1	2	yes	—
67	C₁₃×#461	C₂²	1	2	yes	—
68	C₁₃×#461	C₂²	1	4	yes	—
69	C₁₃×#461	C₂²	1	2	yes	—
70	C₁₃×#461	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#461	C₂²	1	2	yes	complemented
72	C₁₃×#461	C₂²	1	2	yes	complemented
73	C₁₃×#460	C₂²	1	1	yes	characteristic, complemented
74	C₁₃×#459	C₂²	1	2	yes	—
75	C₁₃×#459	C₂²	1	1	yes	characteristic, complemented
76	C₁₃×#452	C₂²	1	4	yes	complemented
77	C₁₃×#451	C₂²	1	4	yes	complemented
78	C₁₃×#449	C₂²	1	4	yes	—
79	C₁₃×#449	C₂²	1	4	yes	—
80	C₁₃×#449	C₂²	1	4	yes	complemented
81	C₁₃×#448	C₂²	1	4	yes	—
82	C₁₃×#448	C₂²	1	4	yes	—
83	C₁₃×#448	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
88	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₁₃×#419	C₂²	1	2	yes	—
90	C₁₃×#417	C₂²	1	2	yes	—
91	C₁₃×#416	C₂²	1	2	yes	—
92	C₂×C₁₃×#103	C₂²	1	2	yes	—
93	C₁₃×#408	C₂²	1	2	yes	—
94	C₁₃×#405	C₂²	1	2	yes	—
95	C₁₃×2₋¹⁺⁴	—	4	4	no	—
96	C₁₃×2₋¹⁺⁴	—	4	4	no	—
97	C₂×C₁₃×#41	—	2	4	no	—
98	C₂×C₁₃×#41	—	2	2	no	—
99	C₂×C₁₃×#41	—	2	2	no	—
100	C₂×C₁₃×#41	C₂³	1	2	yes	—
101	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×#41	C₂³	1	4	yes	—
103	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₁₃	—	2	2	no	—
105	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
106	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₃	—	2	1	no	—
109	C₁₃×#137	—	4	4	no	—
110	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
111	C₁₃×#135	—	4	4	no	—
112	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
113	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
114	C₂×C₁₃×SD₁₆	—	4	4	no	—
115	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
118	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
121	C₂×C₁₃×D₈	C₂³	1	4	yes	—
122	C₂×C₁₃×D₈	C₂³	1	2	yes	—
123	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
124	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
125	C₁₃×C₄⋊Q₈	—	2	1	no	—
126	C₁₃×C₄⋊Q₈	—	2	1	no	—
127	C₁₃×C₄⋊Q₈	—	2	1	no	—
128	C₁₃×C₄⋊Q₈	—	2	2	no	—
129	C₁₃×C₄⋊Q₈	—	2	2	no	—
130	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
132	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
133	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
134	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₁₃×#127	—	2	1	no	—
136	C₁₃×#127	C₂³	1	1	yes	characteristic
137	C₁₃×#127	C₂³	1	2	yes	—
138	C₁₃×#126	—	2	2	no	—
139	C₁₃×#126	—	2	2	no	—
140	C₁₃×#125	—	2	1	no	—
141	C₁₃×#125	C₂³	1	2	yes	—
142	C₁₃×#124	—	2	1	no	—
143	C₁₃×#124	—	2	2	no	—
144	C₁₃×#124	—	2	2	no	—
145	C₁₃×#124	C₂³	1	2	yes	—
146	C₁₃×#124	C₂³	1	4	yes	—
147	C₁₃×#124	C₂³	1	2	yes	—
148	C₁₃×#123	—	2	2	no	—
149	C₁₃×#123	—	2	2	no	—
150	C₁₃×#123	—	2	2	no	—
151	C₁₃×#123	—	2	2	no	—
152	C₁₃×#123	—	2	4	no	—
153	C₁₃×#123	—	2	4	no	—
154	C₁₃×#123	—	2	4	no	—
155	C₁₃×C₂²⋊Q₈	—	2	1	no	—
156	C₁₃×C₂²⋊Q₈	—	2	2	no	—
157	C₁₃×C₂²⋊Q₈	—	2	2	no	—
158	C₁₃×C₂²⋊Q₈	—	2	2	no	—
159	C₁₃×C₂²⋊Q₈	—	2	4	no	—
160	C₁₃×C₂²⋊Q₈	—	2	4	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
163	C₁₃×#121	—	2	2	no	—
164	C₁₃×#121	—	2	1	no	—
165	C₁₃×#121	—	2	2	no	—
166	C₁₃×#121	—	2	1	no	—
167	C₁₃×#121	—	2	1	no	—
168	C₁₃×#121	—	2	2	no	—
169	C₁₃×#121	—	2	2	no	—
170	C₁₃×#121	—	2	1	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	2	no	—
174	C₁₃×#121	C₂³	1	2	yes	—
175	C₁₃×#121	C₂³	1	2	yes	—
176	C₁₃×#121	C₂³	1	2	yes	—
177	C₁₃×#120	—	2	2	no	—
178	C₁₃×#120	—	2	2	no	—
179	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
180	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
181	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
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	—	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	D₄	1	2	yes	—
194	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
195	C₄×D₄×C₁₃	D₄	1	2	yes	—
196	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
197	C₄×D₄×C₁₃	C₂³	1	2	yes	—
198	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
199	C₄×D₄×C₁₃	C₂³	1	2	yes	—
200	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
201	C₁₃×#117	—	2	1	no	—
202	C₁₃×#117	—	2	2	no	—
203	C₁₃×#117	C₂³	1	1	yes	characteristic
204	C₁₃×#117	C₂³	1	1	yes	characteristic
205	C₁₃×#117	C₂³	1	2	yes	—
206	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
209	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	4	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	2	yes	—
223	C₁₃×#103	C₂³	1	2	yes	—
224	C₁₃×#103	C₂³	1	4	yes	—
225	C₁₃×#103	C₂³	1	4	yes	—
226	C₁₃×#103	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×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	#60836	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₁₃×#41	—	2	2	no	—
237	C₁₃×#41	—	2	2	no	—
238	C₁₃×#41	—	2	2	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	2	2	no	—
242	C₁₃×#41	—	4	4	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₁₃×#41	—	4	16	no	—
245	C₁₃×#41	—	4	8	no	—
246	C₁₃×#41	—	8	4	no	—
247	C₂×Q₈×C₁₃	—	2	4	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	2	no	—
250	C₂×Q₈×C₁₃	—	2	4	no	—
251	C₂×Q₈×C₁₃	—	2	4	no	—
252	C₂×Q₈×C₁₃	—	4	4	no	—
253	C₂×Q₈×C₁₃	—	4	4	no	—
254	C₂×Q₈×C₁₃	—	4	8	no	—
255	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
256	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
257	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
258	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×D₄×C₁₃	—	2	1	no	—
260	C₂×D₄×C₁₃	—	2	4	no	—
261	C₂×D₄×C₁₃	—	2	2	no	—
262	C₂×D₄×C₁₃	—	2	2	no	—
263	C₂×D₄×C₁₃	—	2	2	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	1	no	—
266	C₂×D₄×C₁₃	—	2	1	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	2	no	—
270	C₂×D₄×C₁₃	—	2	2	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
273	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
274	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
275	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₁₃	—	2	4	no	—
278	C₂²×C₄×C₁₃	—	2	2	no	—
279	C₂²×C₄×C₁₃	—	2	1	no	—
280	C₂²×C₄×C₁₃	—	2	1	no	—
281	C₂²×C₄×C₁₃	—	2	1	no	—
282	C₂²×C₄×C₁₃	—	2	2	no	—
283	C₂²×C₄×C₁₃	—	2	4	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	2	no	—
287	C₂²×C₄×C₁₃	—	8	2	no	—
288	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
290	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
292	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
294	C₁₃×Q₁₆	—	4	2	no	—
295	C₁₃×Q₁₆	—	4	4	no	—
296	C₁₃×SD₁₆	—	4	4	no	—
297	C₁₃×SD₁₆	—	4	4	no	—
298	C₁₃×SD₁₆	—	4	2	no	—
299	C₁₃×SD₁₆	—	4	2	no	—
300	C₁₃×SD₁₆	—	4	4	no	—
301	C₁₃×SD₁₆	—	4	4	no	—
302	C₁₃×D₈	—	4	2	no	—
303	C₁₃×D₈	—	4	4	no	—
304	C₁₃×M₁₆	—	2	4	no	—
305	C₂×C₈×C₁₃	—	2	4	no	—
306	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
307	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
308	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
309	C₁₃×C₄⋊C₄	—	2	2	no	—
310	C₁₃×C₄⋊C₄	—	2	1	no	—
311	C₁₃×C₄⋊C₄	—	2	2	no	—
312	C₁₃×C₄⋊C₄	—	2	1	no	—
313	C₁₃×C₄⋊C₄	—	2	2	no	—
314	C₁₃×C₄⋊C₄	—	2	4	no	—
315	C₁₃×C₄⋊C₄	—	2	2	no	—
316	C₁₃×C₄⋊C₄	—	2	4	no	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	1	no	—
319	C₁₃×C₄⋊C₄	—	2	1	no	—
320	C₁₃×C₄⋊C₄	—	2	2	no	—
321	C₁₃×C₄⋊C₄	—	2	2	no	—
322	C₁₃×C₄⋊C₄	—	2	2	no	—
323	C₁₃×C₄⋊C₄	—	2	2	no	—
324	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
325	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
326	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
327	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
328	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
331	C₁₃×C₂²⋊C₄	—	2	1	no	—
332	C₁₃×C₂²⋊C₄	—	2	2	no	—
333	C₁₃×C₂²⋊C₄	—	2	2	no	—
334	C₁₃×C₂²⋊C₄	—	2	2	no	—
335	C₁₃×C₂²⋊C₄	—	2	1	no	—
336	C₁₃×C₂²⋊C₄	—	2	1	no	—
337	C₁₃×C₂²⋊C₄	—	2	2	no	—
338	C₁₃×C₂²⋊C₄	—	2	2	no	—
339	C₁₃×C₂²⋊C₄	—	2	2	no	—
340	C₁₃×C₂²⋊C₄	—	2	2	no	—
341	C₁₃×C₂²⋊C₄	—	2	2	no	—
342	C₁₃×C₂²⋊C₄	—	2	2	no	—
343	C₁₃×C₂²⋊C₄	—	2	4	no	—
344	C₁₃×C₂²⋊C₄	—	2	2	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₄²×C₁₃	—	2	1	no	—
350	C₄²×C₁₃	—	2	1	no	—
351	C₄²×C₁₃	—	2	1	no	—
352	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₁₃	C₂×D₄	1	2	yes	—
355	C₄²×C₁₃	C₂×D₄	1	2	yes	—
356	C₄²×C₁₃	C₂⁴	1	2	yes	—
357	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
358	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
359	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
360	#3460	C₂×C₁₃	1	1	yes	characteristic, complemented
361	#3225	C₂×C₁₃	1	4	yes	complemented
362	#3221	C₂×C₁₃	1	4	yes	complemented
363	#3218	C₂×C₁₃	1	2	yes	complemented
364	#3214	C₂×C₁₃	1	2	yes	complemented
365	#3212	C₂×C₁₃	1	2	yes	complemented
366	#3206	C₂×C₁₃	1	2	yes	complemented
367	#3154	C₂×C₁₃	1	2	yes	complemented
368	#3137	C₂×C₁₃	1	2	yes	complemented
369	#3039	C₂×C₁₃	1	1	yes	characteristic, complemented
370	#3036	C₂×C₁₃	1	1	yes	characteristic, complemented
371	#3035	C₂×C₁₃	1	1	yes	characteristic, complemented
372	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
373	#3013	C₂×C₁₃	1	2	yes	complemented
374	#3010	C₂×C₁₃	1	2	yes	complemented
375	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
376	C₂³×C₁₃	—	2	2	no	—
377	C₂³×C₁₃	—	2	2	no	—
378	C₂³×C₁₃	—	2	1	no	—
379	C₂³×C₁₃	—	4	2	no	—
380	C₂³×C₁₃	—	8	1	no	—
381	C₂³×C₁₃	—	8	1	no	—
382	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
383	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
384	Q₈×C₁₃	—	2	2	no	—
385	Q₈×C₁₃	—	2	1	no	—
386	Q₈×C₁₃	—	2	4	no	—
387	Q₈×C₁₃	—	2	2	no	—
388	Q₈×C₁₃	—	2	4	no	—
389	Q₈×C₁₃	—	2	2	no	—
390	Q₈×C₁₃	—	2	1	no	—
391	Q₈×C₁₃	—	4	8	no	—
392	Q₈×C₁₃	—	4	4	no	—
393	Q₈×C₁₃	—	8	2	no	—
394	D₄×C₁₃	—	2	4	no	—
395	D₄×C₁₃	—	2	2	no	—
396	D₄×C₁₃	—	2	2	no	—
397	D₄×C₁₃	—	2	1	no	—
398	D₄×C₁₃	—	2	2	no	—
399	D₄×C₁₃	—	2	2	no	—
400	D₄×C₁₃	—	2	2	no	—
401	D₄×C₁₃	—	2	1	no	—
402	D₄×C₁₃	—	4	2	no	—
403	D₄×C₁₃	—	4	8	no	—
404	D₄×C₁₃	—	4	2	no	—
405	D₄×C₁₃	—	4	4	no	—
406	D₄×C₁₃	—	4	2	no	—
407	D₄×C₁₃	—	4	2	no	—
408	D₄×C₁₃	—	8	2	no	—
409	D₄×C₁₃	—	8	2	no	—
410	D₄×C₁₃	—	8	2	no	—
411	D₄×C₁₃	—	8	2	no	—
412	D₄×C₁₃	—	8	2	no	—
413	C₂×C₄×C₁₃	—	2	2	no	—
414	C₂×C₄×C₁₃	—	2	4	no	—
415	C₂×C₄×C₁₃	—	2	2	no	—
416	C₂×C₄×C₁₃	—	2	2	no	—
417	C₂×C₄×C₁₃	—	2	1	no	—
418	C₂×C₄×C₁₃	—	2	1	no	—
419	C₂×C₄×C₁₃	—	2	1	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	4	1	no	—
424	C₂×C₄×C₁₃	—	4	2	no	—
425	C₂×C₄×C₁₃	—	4	8	no	—
426	C₂×C₄×C₁₃	—	4	8	no	—
427	C₂×C₄×C₁₃	—	4	4	no	—
428	C₂×C₄×C₁₃	—	4	4	no	—
429	C₂×C₄×C₁₃	—	4	2	no	—
430	C₂×C₄×C₁₃	—	4	4	no	—
431	C₂×C₄×C₁₃	—	4	2	no	—
432	C₂×C₄×C₁₃	—	8	1	no	—
433	C₂×C₄×C₁₃	—	8	2	no	—
434	C₂×C₄×C₁₃	—	8	1	no	—
435	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
438	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
439	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
444	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
445	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
446	C₈×C₁₃	—	2	2	no	—
447	C₈×C₁₃	—	2	2	no	—
448	C₈×C₁₃	—	2	4	no	—
449	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
450	C₂×#137	C₂²×C₁₃	1	2	yes	—
451	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
452	C₂×#135	C₂²×C₁₃	1	2	yes	—
453	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
454	D₄×Q₈	—	2	1	no	—
455	D₄×Q₈	—	2	1	no	—
456	#547	—	2	2	no	—
457	#547	—	2	2	no	—
458	#547	—	2	1	no	—
459	#547	—	2	1	no	—
460	#544	C₂²×C₁₃	1	1	yes	characteristic
461	#542	—	2	1	no	—
462	#542	C₂²×C₁₃	1	2	yes	—
463	#540	—	2	1	no	—
464	#540	C₂²×C₁₃	1	2	yes	—
465	#538	—	2	2	no	—
466	#537	C₂²×C₁₃	1	1	yes	characteristic
467	#536	C₂²×C₁₃	1	2	yes	—
468	#536	C₂²×C₁₃	1	4	yes	complemented
469	#535	C₂²×C₁₃	1	1	yes	characteristic
470	#535	C₂²×C₁₃	1	1	yes	characteristic
471	#532	—	2	1	no	—
472	#532	C₂²×C₁₃	1	1	yes	characteristic
473	#532	C₂²×C₁₃	1	2	yes	—
474	#532	C₂²×C₁₃	1	2	yes	complemented
475	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
476	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
477	#529	—	2	1	no	—
478	#529	C₂²×C₁₃	1	2	yes	—
479	#525	—	2	2	no	—
480	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
481	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
482	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
483	#497	C₂²×C₁₃	1	4	yes	—
484	#496	C₂²×C₁₃	1	4	yes	—
485	#495	C₂²×C₁₃	1	4	yes	—
486	#492	C₂²×C₁₃	1	4	yes	—
487	#491	C₂²×C₁₃	1	4	yes	complemented
488	#489	C₂²×C₁₃	1	4	yes	complemented
489	#488	C₂²×C₁₃	1	4	yes	complemented
490	#487	C₂²×C₁₃	1	4	yes	complemented
491	#464	C₂²×C₁₃	1	2	yes	complemented
492	#463	C₂²×C₁₃	1	4	yes	—
493	#463	C₂²×C₁₃	1	2	yes	complemented
494	#462	C₂²×C₁₃	1	2	yes	complemented
495	#462	C₂²×C₁₃	1	1	yes	characteristic, complemented
496	#462	C₂²×C₁₃	1	2	yes	complemented
497	#461	C₂²×C₁₃	1	2	yes	—
498	#461	C₂²×C₁₃	1	2	yes	—
499	#461	C₂²×C₁₃	1	2	yes	—
500	#461	C₂²×C₁₃	1	4	yes	—
501	#461	C₂²×C₁₃	1	1	yes	characteristic, complemented
502	#461	C₂²×C₁₃	1	2	yes	complemented
503	#461	C₂²×C₁₃	1	2	yes	complemented
504	#460	C₂²×C₁₃	1	1	yes	characteristic, complemented
505	#459	C₂²×C₁₃	1	2	yes	—
506	#459	C₂²×C₁₃	1	1	yes	characteristic, complemented
507	#452	C₂²×C₁₃	1	4	yes	complemented
508	#451	C₂²×C₁₃	1	4	yes	complemented
509	#449	C₂²×C₁₃	1	4	yes	—
510	#449	C₂²×C₁₃	1	4	yes	—
511	#449	C₂²×C₁₃	1	4	yes	complemented
512	#448	C₂²×C₁₃	1	4	yes	—
513	#448	C₂²×C₁₃	1	4	yes	—
514	#448	C₂²×C₁₃	1	4	yes	complemented
515	#433	C₂²×C₁₃	1	4	yes	complemented
516	#432	C₂²×C₁₃	1	2	yes	complemented
517	#431	C₂²×C₁₃	1	2	yes	complemented
518	#423	C₂²×C₁₃	1	1	yes	characteristic
519	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
520	#419	C₂²×C₁₃	1	2	yes	—
521	#417	C₂²×C₁₃	1	2	yes	—
522	#416	C₂²×C₁₃	1	2	yes	—
523	C₂×#103	C₂²×C₁₃	1	2	yes	—
524	#408	C₂²×C₁₃	1	2	yes	—
525	#405	C₂²×C₁₃	1	2	yes	—
526	C₂²×C₁₃	—	2	1	no	—
527	C₂²×C₁₃	—	2	1	no	—
528	C₂²×C₁₃	—	2	2	no	—
529	C₂²×C₁₃	—	2	2	no	—
530	C₂²×C₁₃	—	2	2	no	—
531	C₂²×C₁₃	—	4	1	no	—
532	C₂²×C₁₃	—	4	2	no	—
533	C₂²×C₁₃	—	4	2	no	—
534	C₂²×C₁₃	—	4	2	no	—
535	C₂²×C₁₃	—	4	1	no	—
536	C₂²×C₁₃	—	4	2	no	—
537	C₂²×C₁₃	—	4	2	no	—
538	C₂²×C₁₃	—	4	1	no	—
539	C₂²×C₁₃	—	4	2	no	—
540	C₂²×C₁₃	—	8	4	no	—
541	C₂²×C₁₃	#535	1	2	yes	—
542	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
543	C₄×C₁₃	—	2	1	no	—
544	C₄×C₁₃	—	2	1	no	—
545	C₄×C₁₃	—	2	2	no	—
546	C₄×C₁₃	—	2	2	no	—
547	C₄×C₁₃	—	2	1	no	—
548	C₄×C₁₃	—	2	2	no	—
549	C₄×C₁₃	—	4	1	no	—
550	C₄×C₁₃	—	4	4	no	—
551	C₄×C₁₃	—	4	2	no	—
552	C₄×C₁₃	—	4	1	no	—
553	C₄×C₁₃	—	4	2	no	—
554	C₄×C₁₃	—	4	1	no	—
555	C₄×C₁₃	#535	1	2	yes	—
556	C₄×C₁₃	#577	1	2	yes	—
557	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
558	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
559	2₋¹⁺⁴	—	4	4	no	—
560	2₋¹⁺⁴	—	4	4	no	—
561	C₂×#41	—	2	4	no	—
562	C₂×#41	—	2	2	no	—
563	C₂×#41	—	2	2	no	—
564	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
565	C₂×#41	C₂³×C₁₃	1	2	yes	—
566	C₂×#41	C₂³×C₁₃	1	4	yes	—
567	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
568	C₂²×Q₈	—	2	2	no	—
569	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
570	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
571	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
572	C₂³×C₄	—	2	1	no	—
573	#137	—	4	4	no	—
574	AGL(1,ℤ/8)	—	4	4	no	—
575	#135	—	4	4	no	—
576	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
577	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
578	C₂×SD₁₆	—	4	4	no	—
579	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
580	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
584	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
585	C₂×D₈	C₂³×C₁₃	1	2	yes	—
586	C₂×D₈	C₂³×C₁₃	1	4	yes	—
587	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
588	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
589	C₄⋊Q₈	—	2	1	no	—
590	C₄⋊Q₈	—	2	1	no	—
591	C₄⋊Q₈	—	2	1	no	—
592	C₄⋊Q₈	—	2	2	no	—
593	C₄⋊Q₈	—	2	2	no	—
594	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
595	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
596	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
597	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
598	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
599	#127	—	2	1	no	—
600	#127	C₂³×C₁₃	1	1	yes	characteristic
601	#127	C₂³×C₁₃	1	2	yes	—
602	#126	—	2	2	no	—
603	#126	—	2	2	no	—
604	#125	—	2	1	no	—
605	#125	C₂³×C₁₃	1	2	yes	—
606	#124	—	2	1	no	—
607	#124	—	2	2	no	—
608	#124	—	2	2	no	—
609	#124	C₂³×C₁₃	1	2	yes	—
610	#124	C₂³×C₁₃	1	2	yes	—
611	#124	C₂³×C₁₃	1	4	yes	—
612	#123	—	2	2	no	—
613	#123	—	2	2	no	—
614	#123	—	2	2	no	—
615	#123	—	2	2	no	—
616	#123	—	2	4	no	—
617	#123	—	2	4	no	—
618	#123	—	2	4	no	—
619	C₂²⋊Q₈	—	2	1	no	—
620	C₂²⋊Q₈	—	2	2	no	—
621	C₂²⋊Q₈	—	2	2	no	—
622	C₂²⋊Q₈	—	2	2	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	C₂²⋊Q₈	—	2	4	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
627	#121	—	2	2	no	—
628	#121	—	2	1	no	—
629	#121	—	2	2	no	—
630	#121	—	2	1	no	—
631	#121	—	2	1	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	1	no	—
635	#121	—	2	1	no	—
636	#121	—	2	2	no	—
637	#121	—	2	2	no	—
638	#121	C₂³×C₁₃	1	2	yes	—
639	#121	C₂³×C₁₃	1	2	yes	—
640	#121	C₂³×C₁₃	1	2	yes	—
641	#120	—	2	2	no	—
642	#120	—	2	2	no	—
643	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
644	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
645	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
646	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	—	2	1	no	—
652	C₄×D₄	—	2	2	no	—
653	C₄×D₄	—	2	1	no	—
654	C₄×D₄	—	2	1	no	—
655	C₄×D₄	—	2	2	no	—
656	C₄×D₄	—	2	2	no	—
657	C₄×D₄	D₄×C₁₃	1	2	yes	—
658	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
659	C₄×D₄	D₄×C₁₃	1	2	yes	—
660	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
661	C₄×D₄	C₂³×C₁₃	1	2	yes	—
662	C₄×D₄	C₂³×C₁₃	1	2	yes	—
663	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
664	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
665	#117	—	2	1	no	—
666	#117	—	2	2	no	—
667	#117	C₂³×C₁₃	1	1	yes	characteristic
668	#117	C₂³×C₁₃	1	1	yes	characteristic
669	#117	C₂³×C₁₃	1	2	yes	—
670	C₂×C₄⋊C₄	—	2	1	no	—
671	C₂×C₄⋊C₄	—	2	1	no	—
672	C₂×C₄⋊C₄	—	2	2	no	—
673	C₂×C₄⋊C₄	—	2	2	no	—
674	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	—	2	1	no	—
676	C₂×C₄²	—	2	1	no	—
677	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
678	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
679	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
680	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
681	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
682	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
683	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
684	#103	C₂³×C₁₃	1	4	yes	—
685	#103	C₂³×C₁₃	1	4	yes	—
686	#103	C₂³×C₁₃	1	2	yes	—
687	#103	C₂³×C₁₃	1	2	yes	—
688	#103	C₂³×C₁₃	1	4	yes	—
689	#103	C₂³×C₁₃	1	4	yes	—
690	#103	C₂³×C₁₃	1	4	yes	—
691	#102	C₂³×C₁₃	1	2	yes	—
692	#102	C₂³×C₁₃	1	2	yes	—
693	#102	C₂³×C₁₃	1	4	yes	—
694	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
696	#97	C₂³×C₁₃	1	4	yes	—
697	C₄×C₈	C₂³×C₁₃	1	4	yes	—
698	C₂×C₁₃	—	2	2	no	—
699	C₂×C₁₃	—	4	2	no	—
700	C₂×C₁₃	—	8	1	no	—
701	C₂×C₁₃	—	8	2	no	—
702	C₂×C₁₃	—	8	2	no	—
703	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
704	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
705	C₂×C₁₃	#3586	1	1	yes	characteristic
706	C₂⁴	—	2	1	no	—
707	#41	—	2	2	no	—
708	#41	—	2	2	no	—
709	#41	—	2	2	no	—
710	#41	—	2	4	no	—
711	#41	—	2	4	no	—
712	#41	—	2	2	no	—
713	#41	—	4	4	no	—
714	#41	—	4	4	no	—
715	#41	—	4	16	no	—
716	#41	—	4	8	no	—
717	#41	—	8	4	no	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	2	no	—
721	C₂×Q₈	—	2	4	no	—
722	C₂×Q₈	—	2	4	no	—
723	C₂×Q₈	—	4	4	no	—
724	C₂×Q₈	—	4	4	no	—
725	C₂×Q₈	—	4	8	no	—
726	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
727	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
728	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
729	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
730	C₂×D₄	—	2	1	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	2	1	no	—
737	C₂×D₄	—	2	1	no	—
738	C₂×D₄	—	2	1	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂×D₄	—	2	2	no	—
741	C₂×D₄	—	2	2	no	—
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
744	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
745	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
746	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
747	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	4	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	8	2	no	—
759	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
761	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
765	Q₁₆	—	4	2	no	—
766	Q₁₆	—	4	4	no	—
767	SD₁₆	—	4	4	no	—
768	SD₁₆	—	4	4	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	2	no	—
771	SD₁₆	—	4	4	no	—
772	SD₁₆	—	4	4	no	—
773	D₈	—	4	2	no	—
774	D₈	—	4	4	no	—
775	M₁₆	—	2	4	no	—
776	C₂×C₈	—	2	4	no	—
777	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
778	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
779	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
796	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
797	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
798	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
800	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
801	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	1	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	—	2	2	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	2	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
818	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
819	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
820	C₄²	—	2	1	no	—
821	C₄²	—	2	1	no	—
822	C₄²	—	2	1	no	—
823	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
824	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
825	C₄²	C₂×D₄×C₁₃	1	2	yes	—
826	C₄²	C₂×D₄×C₁₃	1	2	yes	—
827	C₄²	C₂⁴×C₁₃	1	2	yes	—
828	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
829	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
830	C₁₃	#60836	1	1	yes	characteristic, direct product factor, Sylow
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	4	2	no	—
835	C₂³	—	8	1	no	—
836	C₂³	—	8	1	no	—
837	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
838	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
839	Q₈	—	2	2	no	—
840	Q₈	—	2	1	no	—
841	Q₈	—	2	4	no	—
842	Q₈	—	2	2	no	—
843	Q₈	—	2	4	no	—
844	Q₈	—	2	2	no	—
845	Q₈	—	2	1	no	—
846	Q₈	—	4	8	no	—
847	Q₈	—	4	4	no	—
848	Q₈	—	8	2	no	—
849	D₄	—	2	4	no	—
850	D₄	—	2	2	no	—
851	D₄	—	2	2	no	—
852	D₄	—	2	1	no	—
853	D₄	—	2	2	no	—
854	D₄	—	2	2	no	—
855	D₄	—	2	2	no	—
856	D₄	—	2	1	no	—
857	D₄	—	4	2	no	—
858	D₄	—	4	8	no	—
859	D₄	—	4	2	no	—
860	D₄	—	4	4	no	—
861	D₄	—	4	2	no	—
862	D₄	—	4	2	no	—
863	D₄	—	8	2	no	—
864	D₄	—	8	2	no	—
865	D₄	—	8	2	no	—
866	D₄	—	8	2	no	—
867	D₄	—	8	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	4	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	8	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	2	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	4	2	no	—
887	C₂×C₄	—	8	2	no	—
888	C₂×C₄	—	8	1	no	—
889	C₂×C₄	—	8	1	no	—
890	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
891	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
892	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
894	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
895	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
896	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
897	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
898	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
899	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
900	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
901	C₈	—	2	2	no	—
902	C₈	—	2	2	no	—
903	C₈	—	2	4	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	8	4	no	—
919	C₂²	C₁₃×#535	1	2	yes	—
920	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
921	C₄	—	2	1	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	4	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	1	no	—
933	C₄	C₁₃×#535	1	2	yes	—
934	C₄	C₁₃×#577	1	2	yes	—
935	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
936	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	8	2	no	—
940	C₂	—	8	1	no	—
941	C₂	—	8	2	no	—
942	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
943	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
944	C₂	C₁₃×#3586	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×#3499	C₂	semidirect
2. C₁₃×#3460	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3221	C₂	semidirect
5. C₁₃×#3218	C₂	semidirect
6. C₁₃×#3214	C₂	semidirect
7. C₁₃×#3212	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3039	C₂	semidirect
12. C₁₃×#3036	C₂	semidirect
13. C₁₃×#3035	C₂	semidirect
14. C₂×C₁₃×#461	C₂	semidirect
15. C₁₃×#3013	C₂	semidirect
16. C₁₃×#3010	C₂	semidirect
17. C₁₃×#2925	C₂	semidirect
37. C₁₃×#536	C₂²	semidirect
43. C₁₃×#532	C₂²	semidirect
45. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
56. C₁₃×#491	C₂²	semidirect
57. C₁₃×#489	C₂²	semidirect
58. C₁₃×#488	C₂²	semidirect
59. C₁₃×#487	C₂²	semidirect
60. C₁₃×#464	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#462	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
70. C₁₃×#461	C₂²	semidirect
71. C₁₃×#461	C₂²	semidirect
72. C₁₃×#461	C₂²	semidirect
73. C₁₃×#460	C₂²	semidirect
75. C₁₃×#459	C₂²	semidirect
76. C₁₃×#452	C₂²	semidirect
77. C₁₃×#451	C₂²	semidirect
80. C₁₃×#449	C₂²	semidirect
83. C₁₃×#448	C₂²	semidirect
84. C₁₃×#433	C₂²	semidirect
85. C₁₃×#432	C₂²	semidirect
86. C₁₃×#431	C₂²	semidirect
234. #60836	C₁₃	direct (N × H)
359. #3499	C₂×C₁₃	semidirect
360. #3460	C₂×C₁₃	semidirect
361. #3225	C₂×C₁₃	semidirect
362. #3221	C₂×C₁₃	semidirect
363. #3218	C₂×C₁₃	semidirect
364. #3214	C₂×C₁₃	semidirect
365. #3212	C₂×C₁₃	semidirect
366. #3206	C₂×C₁₃	semidirect
367. #3154	C₂×C₁₃	semidirect
368. #3137	C₂×C₁₃	semidirect
369. #3039	C₂×C₁₃	semidirect
370. #3036	C₂×C₁₃	semidirect
371. #3035	C₂×C₁₃	semidirect
372. C₂×#461	C₂×C₁₃	semidirect
373. #3013	C₂×C₁₃	semidirect
374. #3010	C₂×C₁₃	semidirect
375. #2925	C₂×C₁₃	semidirect
468. #536	C₂²×C₁₃	semidirect
474. #532	C₂²×C₁₃	semidirect
476. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
487. #491	C₂²×C₁₃	semidirect
488. #489	C₂²×C₁₃	semidirect
489. #488	C₂²×C₁₃	semidirect
490. #487	C₂²×C₁₃	semidirect
491. #464	C₂²×C₁₃	semidirect
493. #463	C₂²×C₁₃	semidirect
494. #462	C₂²×C₁₃	semidirect
495. #462	C₂²×C₁₃	semidirect
496. #462	C₂²×C₁₃	semidirect
501. #461	C₂²×C₁₃	semidirect
502. #461	C₂²×C₁₃	semidirect
503. #461	C₂²×C₁₃	semidirect
504. #460	C₂²×C₁₃	semidirect
506. #459	C₂²×C₁₃	semidirect
507. #452	C₂²×C₁₃	semidirect
508. #451	C₂²×C₁₃	semidirect
511. #449	C₂²×C₁₃	semidirect
514. #448	C₂²×C₁₃	semidirect
515. #433	C₂²×C₁₃	semidirect
516. #432	C₂²×C₁₃	semidirect
517. #431	C₂²×C₁₃	semidirect
830. C₁₃	#60836	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×#3499	2
C₁₃×#3460	2
C₁₃×#3225	2
C₁₃×#3221	2
C₁₃×#3218	2
C₁₃×#3214	2
C₁₃×#3212	2
C₁₃×#3206	2
C₁₃×#3154	2
C₁₃×#3137	2
C₁₃×#3039	2
C₁₃×#3036	2
C₁₃×#3035	2
C₂×C₁₃×#461	2
C₁₃×#3013	2
C₁₃×#3010	2
C₁₃×#2925	2
#60836	13

Subgroups — C13×#60836 #15747175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60836 #15747175