Subgroups — C₁₃×#60813 #15747152

Order 3328.

2086 conjugacy classes of subgroups.

The subgroup lattice has 968 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×#536	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×#3213	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3211	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×#3046	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3042	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#448	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×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
21	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₁₃×#135	C₂²	1	2	yes	—
23	C₂²×C₁₃×SD₁₆	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×#536	—	2	2	no	—
34	C₁₃×#536	—	2	1	no	—
35	C₁₃×#536	—	2	1	no	—
36	C₁₃×#536	C₂²	1	2	yes	—
37	C₁₃×#536	C₂²	1	2	yes	—
38	C₁₃×#536	C₂²	1	4	yes	complemented
39	C₁₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#532	C₂²	1	2	yes	—
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₁₃×#529	C₂²	1	2	yes	—
43	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
44	C₁₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#123	—	2	2	no	—
46	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
47	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
48	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
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×#497	C₂²	1	4	yes	complemented
53	C₁₃×#496	C₂²	1	4	yes	complemented
54	C₁₃×#495	C₂²	1	4	yes	complemented
55	C₁₃×#492	C₂²	1	4	yes	complemented
56	C₁₃×#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	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×#462	C₂²	1	4	yes	complemented
65	C₁₃×#461	C₂²	1	4	yes	complemented
66	C₁₃×#461	C₂²	1	4	yes	complemented
67	C₁₃×#461	C₂²	1	4	yes	complemented
68	C₁₃×#452	C₂²	1	2	yes	complemented
69	C₁₃×#451	C₂²	1	2	yes	complemented
70	C₁₃×#451	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×#451	C₂²	1	2	yes	complemented
72	C₁₃×#450	C₂²	1	1	yes	characteristic, complemented
73	C₁₃×#449	C₂²	1	4	yes	—
74	C₁₃×#449	C₂²	1	2	yes	complemented
75	C₁₃×#448	C₂²	1	2	yes	—
76	C₁₃×#448	C₂²	1	2	yes	—
77	C₁₃×#448	C₂²	1	2	yes	—
78	C₁₃×#448	C₂²	1	1	yes	characteristic, complemented
79	C₁₃×#448	C₂²	1	2	yes	complemented
80	C₁₃×#448	C₂²	1	2	yes	complemented
81	C₁₃×#448	C₂²	1	4	yes	complemented
82	C₁₃×#447	C₂²	1	2	yes	—
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×#419	C₂²	1	2	yes	complemented
89	C₁₃×#417	C₂²	1	2	yes	—
90	C₁₃×#416	C₂²	1	2	yes	—
91	C₂×C₁₃×#103	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	C₂×C₁₃×#41	—	2	1	no	—
96	C₂×C₁₃×#41	—	2	1	no	—
97	C₂×C₁₃×#41	—	2	2	no	—
98	C₂×C₁₃×#41	—	4	4	no	—
99	C₂×C₁₃×#41	C₂³	1	2	yes	—
100	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×#41	C₂³	1	2	yes	—
102	C₂²×Q₈×C₁₃	—	2	1	no	—
103	C₂²×Q₈×C₁₃	—	2	1	no	—
104	C₂²×Q₈×C₁₃	—	2	1	no	—
105	C₂²×Q₈×C₁₃	—	4	4	no	—
106	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₁₃	—	2	1	no	—
111	C₂²×D₄×C₁₃	—	2	1	no	—
112	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₃	—	2	1	no	—
115	C₂³×C₄×C₁₃	—	2	1	no	—
116	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#137	—	4	4	no	—
118	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
119	C₁₃×#135	—	4	4	no	—
120	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
121	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
122	C₂×C₁₃×SD₁₆	—	4	4	no	—
123	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
124	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
125	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
126	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
127	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
129	C₂×C₁₃×D₈	C₂³	1	4	yes	—
130	C₂×C₁₃×D₈	C₂³	1	2	yes	—
131	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
132	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
133	C₁₃×C₄⋊Q₈	—	2	1	no	—
134	C₁₃×C₄⋊Q₈	—	2	2	no	—
135	C₁₃×C₄⋊Q₈	—	2	2	no	—
136	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
137	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
138	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₁₃×#127	C₂³	1	2	yes	—
140	C₁₃×#126	—	2	2	no	—
141	C₁₃×#126	—	2	2	no	—
142	C₁₃×#125	—	2	1	no	—
143	C₁₃×#125	C₂³	1	2	yes	—
144	C₁₃×#124	—	2	2	no	—
145	C₁₃×#124	—	2	2	no	—
146	C₁₃×#124	—	2	2	no	—
147	C₁₃×#124	—	2	2	no	—
148	C₁₃×#124	C₂³	1	4	yes	—
149	C₁₃×#124	C₂³	1	4	yes	—
150	C₁₃×#124	C₂³	1	2	yes	—
151	C₁₃×#123	—	2	1	no	—
152	C₁₃×#123	—	2	2	no	—
153	C₁₃×#123	—	2	2	no	—
154	C₁₃×#123	—	2	2	no	—
155	C₁₃×#123	—	2	4	no	—
156	C₁₃×#123	—	2	4	no	—
157	C₁₃×#123	—	2	4	no	—
158	C₁₃×#123	—	2	4	no	—
159	C₁₃×#123	—	2	2	no	—
160	C₁₃×C₂²⋊Q₈	—	2	2	no	—
161	C₁₃×C₂²⋊Q₈	—	2	2	no	—
162	C₁₃×C₂²⋊Q₈	—	2	2	no	—
163	C₁₃×C₂²⋊Q₈	—	2	2	no	—
164	C₁₃×C₂²⋊Q₈	—	2	4	no	—
165	C₁₃×C₂²⋊Q₈	—	2	4	no	—
166	C₁₃×C₂²⋊Q₈	—	2	2	no	—
167	C₁₃×C₂²⋊Q₈	—	2	2	no	—
168	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
169	C₁₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
170	C₁₃×#121	—	2	1	no	—
171	C₁₃×#121	—	2	1	no	—
172	C₁₃×#121	—	2	2	no	—
173	C₁₃×#121	—	2	1	no	—
174	C₁₃×#121	—	2	1	no	—
175	C₁₃×#121	—	2	2	no	—
176	C₁₃×#121	—	2	2	no	—
177	C₁₃×#121	C₂³	1	2	yes	—
178	C₁₃×#121	C₂³	1	1	yes	characteristic
179	C₁₃×#121	C₂³	1	2	yes	—
180	C₁₃×#121	C₂³	1	1	yes	characteristic
181	C₁₃×#120	—	2	1	no	—
182	C₁₃×#120	—	2	2	no	—
183	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	—	2	1	no	—
185	C₄×D₄×C₁₃	—	2	1	no	—
186	C₄×D₄×C₁₃	—	2	2	no	—
187	C₄×D₄×C₁₃	—	2	1	no	—
188	C₄×D₄×C₁₃	—	2	1	no	—
189	C₄×D₄×C₁₃	—	2	2	no	—
190	C₄×D₄×C₁₃	—	2	2	no	—
191	C₄×D₄×C₁₃	C₂³	1	2	yes	—
192	C₄×D₄×C₁₃	C₂³	1	2	yes	—
193	C₄×D₄×C₁₃	C₂³	1	2	yes	—
194	C₁₃×#117	—	2	1	no	—
195	C₁₃×#117	—	2	2	no	—
196	C₁₃×#117	D₄	1	2	yes	—
197	C₁₃×#117	D₄	1	1	yes	characteristic
198	C₁₃×#117	D₄	1	1	yes	characteristic
199	C₁₃×#117	C₂³	1	1	yes	characteristic
200	C₁₃×#117	C₂³	1	1	yes	characteristic
201	C₁₃×#117	C₂³	1	1	yes	characteristic
202	C₁₃×#117	C₂³	1	2	yes	—
203	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
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	1	no	—
210	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₂×C₁₃×C₂²⋊C₄	—	2	2	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	—
216	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	4	yes	—
219	C₁₃×#103	C₂³	1	2	yes	—
220	C₁₃×#103	C₂³	1	2	yes	—
221	C₁₃×#103	C₂³	1	4	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×#102	C₂³	1	4	yes	—
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	—
233	C₄×C₈×C₁₃	C₂³	1	4	yes	—
234	#60813	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂⁴×C₁₃	—	2	1	no	—
236	C₂⁴×C₁₃	—	2	1	no	—
237	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
238	C₁₃×#41	—	2	4	no	—
239	C₁₃×#41	—	2	4	no	—
240	C₁₃×#41	—	2	4	no	—
241	C₁₃×#41	—	4	2	no	—
242	C₁₃×#41	—	4	2	no	—
243	C₁₃×#41	—	4	4	no	—
244	C₁₃×#41	—	4	4	no	—
245	C₁₃×#41	—	8	4	no	—
246	C₂×Q₈×C₁₃	—	2	2	no	—
247	C₂×Q₈×C₁₃	—	2	2	no	—
248	C₂×Q₈×C₁₃	—	2	2	no	—
249	C₂×Q₈×C₁₃	—	2	1	no	—
250	C₂×Q₈×C₁₃	—	2	2	no	—
251	C₂×Q₈×C₁₃	—	2	4	no	—
252	C₂×Q₈×C₁₃	—	2	4	no	—
253	C₂×Q₈×C₁₃	—	4	4	no	—
254	C₂×Q₈×C₁₃	—	4	4	no	—
255	C₂×Q₈×C₁₃	—	4	2	no	—
256	C₂×Q₈×C₁₃	—	4	4	no	—
257	C₂×Q₈×C₁₃	—	4	4	no	—
258	C₂×Q₈×C₁₃	—	4	4	no	—
259	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
260	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
261	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×D₄×C₁₃	—	2	1	no	—
263	C₂×D₄×C₁₃	—	2	1	no	—
264	C₂×D₄×C₁₃	—	2	2	no	—
265	C₂×D₄×C₁₃	—	2	2	no	—
266	C₂×D₄×C₁₃	—	2	2	no	—
267	C₂×D₄×C₁₃	—	2	1	no	—
268	C₂×D₄×C₁₃	—	2	2	no	—
269	C₂×D₄×C₁₃	—	2	1	no	—
270	C₂×D₄×C₁₃	—	2	1	no	—
271	C₂×D₄×C₁₃	—	2	2	no	—
272	C₂×D₄×C₁₃	—	2	2	no	—
273	C₂×D₄×C₁₃	—	2	4	no	—
274	C₂×D₄×C₁₃	—	4	2	no	—
275	C₂×D₄×C₁₃	—	4	4	no	—
276	C₂×D₄×C₁₃	—	8	2	no	—
277	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
279	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₁₃	—	2	4	no	—
281	C₂²×C₄×C₁₃	—	2	2	no	—
282	C₂²×C₄×C₁₃	—	2	1	no	—
283	C₂²×C₄×C₁₃	—	2	2	no	—
284	C₂²×C₄×C₁₃	—	2	2	no	—
285	C₂²×C₄×C₁₃	—	2	1	no	—
286	C₂²×C₄×C₁₃	—	2	1	no	—
287	C₂²×C₄×C₁₃	—	2	2	no	—
288	C₂²×C₄×C₁₃	—	2	2	no	—
289	C₂²×C₄×C₁₃	—	2	2	no	—
290	C₂²×C₄×C₁₃	—	2	2	no	—
291	C₂²×C₄×C₁₃	—	2	2	no	—
292	C₂²×C₄×C₁₃	—	4	4	no	—
293	C₂²×C₄×C₁₃	—	4	4	no	—
294	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
299	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
302	C₁₃×Q₁₆	—	4	2	no	—
303	C₁₃×Q₁₆	—	4	4	no	—
304	C₁₃×SD₁₆	—	4	4	no	—
305	C₁₃×SD₁₆	—	4	4	no	—
306	C₁₃×SD₁₆	—	4	2	no	—
307	C₁₃×SD₁₆	—	4	2	no	—
308	C₁₃×SD₁₆	—	4	4	no	—
309	C₁₃×SD₁₆	—	4	4	no	—
310	C₁₃×D₈	—	4	2	no	—
311	C₁₃×D₈	—	4	4	no	—
312	C₁₃×M₁₆	—	2	4	no	—
313	C₂×C₈×C₁₃	—	2	4	no	—
314	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
315	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
317	C₁₃×C₄⋊C₄	—	2	1	no	—
318	C₁₃×C₄⋊C₄	—	2	2	no	—
319	C₁₃×C₄⋊C₄	—	2	4	no	—
320	C₁₃×C₄⋊C₄	—	2	4	no	—
321	C₁₃×C₄⋊C₄	—	2	4	no	—
322	C₁₃×C₄⋊C₄	—	2	4	no	—
323	C₁₃×C₄⋊C₄	—	2	1	no	—
324	C₁₃×C₄⋊C₄	—	2	2	no	—
325	C₁₃×C₄⋊C₄	—	2	2	no	—
326	C₁₃×C₄⋊C₄	—	2	2	no	—
327	C₁₃×C₄⋊C₄	—	2	1	no	—
328	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
329	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
334	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
335	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
336	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
337	C₁₃×C₂²⋊C₄	—	2	1	no	—
338	C₁₃×C₂²⋊C₄	—	2	1	no	—
339	C₁₃×C₂²⋊C₄	—	2	1	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	2	no	—
344	C₁₃×C₂²⋊C₄	—	2	4	no	—
345	C₁₃×C₂²⋊C₄	—	2	4	no	—
346	C₁₃×C₂²⋊C₄	—	2	4	no	—
347	C₁₃×C₂²⋊C₄	—	2	4	no	—
348	C₁₃×C₂²⋊C₄	—	2	2	no	—
349	C₁₃×C₂²⋊C₄	—	2	2	no	—
350	C₁₃×C₂²⋊C₄	—	2	1	no	—
351	C₁₃×C₂²⋊C₄	—	2	2	no	—
352	C₁₃×C₂²⋊C₄	—	2	1	no	—
353	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
354	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₄²×C₁₃	—	2	2	no	—
358	C₄²×C₁₃	—	2	1	no	—
359	C₄²×C₁₃	C₂×D₄	1	2	yes	—
360	C₄²×C₁₃	C₂×D₄	1	2	yes	—
361	C₄²×C₁₃	C₂⁴	1	2	yes	—
362	C₄²×C₁₃	C₂⁴	1	2	yes	—
363	#3494	C₂×C₁₃	1	1	yes	characteristic, complemented
364	C₂×#536	C₂×C₁₃	1	1	yes	characteristic, complemented
365	#3225	C₂×C₁₃	1	4	yes	complemented
366	#3221	C₂×C₁₃	1	4	yes	complemented
367	#3218	C₂×C₁₃	1	2	yes	complemented
368	#3213	C₂×C₁₃	1	2	yes	complemented
369	#3211	C₂×C₁₃	1	2	yes	complemented
370	#3206	C₂×C₁₃	1	2	yes	complemented
371	#3154	C₂×C₁₃	1	2	yes	complemented
372	#3137	C₂×C₁₃	1	2	yes	complemented
373	#3046	C₂×C₁₃	1	2	yes	complemented
374	#3042	C₂×C₁₃	1	2	yes	complemented
375	#3006	C₂×C₁₃	1	1	yes	characteristic, complemented
376	#3004	C₂×C₁₃	1	1	yes	characteristic, complemented
377	#3002	C₂×C₁₃	1	1	yes	characteristic, complemented
378	C₂×#448	C₂×C₁₃	1	1	yes	characteristic, complemented
379	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
380	C₂³×C₁₃	—	2	2	no	—
381	C₂³×C₁₃	—	2	2	no	—
382	C₂³×C₁₃	—	2	2	no	—
383	C₂³×C₁₃	—	2	2	no	—
384	C₂³×C₁₃	—	2	1	no	—
385	C₂³×C₁₃	—	4	1	no	—
386	C₂³×C₁₃	—	4	2	no	—
387	C₂³×C₁₃	—	4	2	no	—
388	C₂³×C₁₃	—	4	2	no	—
389	C₂³×C₁₃	—	4	2	no	—
390	C₂³×C₁₃	—	8	1	no	—
391	C₂³×C₁₃	—	8	1	no	—
392	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
393	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
395	Q₈×C₁₃	—	2	4	no	—
396	Q₈×C₁₃	—	2	2	no	—
397	Q₈×C₁₃	—	2	2	no	—
398	Q₈×C₁₃	—	2	4	no	—
399	Q₈×C₁₃	—	2	2	no	—
400	Q₈×C₁₃	—	4	4	no	—
401	Q₈×C₁₃	—	4	4	no	—
402	Q₈×C₁₃	—	4	2	no	—
403	Q₈×C₁₃	—	4	4	no	—
404	Q₈×C₁₃	—	8	2	no	—
405	D₄×C₁₃	—	2	2	no	—
406	D₄×C₁₃	—	2	4	no	—
407	D₄×C₁₃	—	2	2	no	—
408	D₄×C₁₃	—	2	2	no	—
409	D₄×C₁₃	—	4	2	no	—
410	D₄×C₁₃	—	4	4	no	—
411	D₄×C₁₃	—	4	4	no	—
412	D₄×C₁₃	—	4	2	no	—
413	D₄×C₁₃	—	4	4	no	—
414	D₄×C₁₃	—	4	2	no	—
415	D₄×C₁₃	—	4	2	no	—
416	D₄×C₁₃	—	8	2	no	—
417	D₄×C₁₃	—	8	2	no	—
418	D₄×C₁₃	—	8	1	no	—
419	D₄×C₁₃	—	8	2	no	—
420	C₂×C₄×C₁₃	—	2	2	no	—
421	C₂×C₄×C₁₃	—	2	4	no	—
422	C₂×C₄×C₁₃	—	2	2	no	—
423	C₂×C₄×C₁₃	—	2	2	no	—
424	C₂×C₄×C₁₃	—	2	2	no	—
425	C₂×C₄×C₁₃	—	2	2	no	—
426	C₂×C₄×C₁₃	—	2	1	no	—
427	C₂×C₄×C₁₃	—	2	1	no	—
428	C₂×C₄×C₁₃	—	2	1	no	—
429	C₂×C₄×C₁₃	—	2	2	no	—
430	C₂×C₄×C₁₃	—	2	4	no	—
431	C₂×C₄×C₁₃	—	2	2	no	—
432	C₂×C₄×C₁₃	—	4	2	no	—
433	C₂×C₄×C₁₃	—	4	4	no	—
434	C₂×C₄×C₁₃	—	4	2	no	—
435	C₂×C₄×C₁₃	—	4	4	no	—
436	C₂×C₄×C₁₃	—	4	4	no	—
437	C₂×C₄×C₁₃	—	4	4	no	—
438	C₂×C₄×C₁₃	—	4	4	no	—
439	C₂×C₄×C₁₃	—	4	2	no	—
440	C₂×C₄×C₁₃	—	8	2	no	—
441	C₂×C₄×C₁₃	—	8	2	no	—
442	C₂×C₄×C₁₃	—	8	2	no	—
443	C₂×C₄×C₁₃	—	8	1	no	—
444	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
447	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
452	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
453	C₈×C₁₃	—	2	2	no	—
454	C₈×C₁₃	—	2	2	no	—
455	C₈×C₁₃	—	2	4	no	—
456	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
457	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
458	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
459	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
460	C₂×#135	C₂²×C₁₃	1	2	yes	—
461	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
462	#555	—	2	1	no	—
463	#553	—	2	1	no	—
464	#553	—	2	1	no	—
465	#551	—	2	2	no	—
466	#547	—	2	1	no	—
467	#546	—	2	2	no	—
468	#544	C₂²×C₁₃	1	1	yes	characteristic, complemented
469	#542	C₂²×C₁₃	1	2	yes	complemented
470	#540	C₂²×C₁₃	1	2	yes	complemented
471	#536	—	2	2	no	—
472	#536	—	2	1	no	—
473	#536	—	2	1	no	—
474	#536	C₂²×C₁₃	1	2	yes	—
475	#536	C₂²×C₁₃	1	2	yes	—
476	#536	C₂²×C₁₃	1	4	yes	complemented
477	#535	C₂²×C₁₃	1	1	yes	characteristic, complemented
478	#532	C₂²×C₁₃	1	2	yes	—
479	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
480	#529	C₂²×C₁₃	1	2	yes	—
481	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
482	#525	C₂²×C₁₃	1	1	yes	characteristic
483	C₂×#123	—	2	2	no	—
484	C₂×C₂²⋊Q₈	—	2	1	no	—
485	C₂×C₂²⋊Q₈	—	2	1	no	—
486	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
487	#520	C₂²×C₁₃	1	1	yes	characteristic, complemented
488	#518	C₂²×C₁₃	1	1	yes	characteristic, complemented
489	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
490	#497	C₂²×C₁₃	1	4	yes	complemented
491	#496	C₂²×C₁₃	1	4	yes	complemented
492	#495	C₂²×C₁₃	1	4	yes	complemented
493	#492	C₂²×C₁₃	1	4	yes	complemented
494	#491	C₂²×C₁₃	1	4	yes	complemented
495	#489	C₂²×C₁₃	1	4	yes	complemented
496	#488	C₂²×C₁₃	1	4	yes	complemented
497	#487	C₂²×C₁₃	1	4	yes	complemented
498	#464	C₂²×C₁₃	1	4	yes	complemented
499	#463	C₂²×C₁₃	1	4	yes	complemented
500	#463	C₂²×C₁₃	1	4	yes	complemented
501	#463	C₂²×C₁₃	1	4	yes	complemented
502	#462	C₂²×C₁₃	1	4	yes	complemented
503	#461	C₂²×C₁₃	1	4	yes	complemented
504	#461	C₂²×C₁₃	1	4	yes	complemented
505	#461	C₂²×C₁₃	1	4	yes	complemented
506	#452	C₂²×C₁₃	1	2	yes	complemented
507	#451	C₂²×C₁₃	1	2	yes	complemented
508	#451	C₂²×C₁₃	1	1	yes	characteristic, complemented
509	#451	C₂²×C₁₃	1	2	yes	complemented
510	#450	C₂²×C₁₃	1	1	yes	characteristic, complemented
511	#449	C₂²×C₁₃	1	4	yes	—
512	#449	C₂²×C₁₃	1	2	yes	complemented
513	#448	C₂²×C₁₃	1	2	yes	—
514	#448	C₂²×C₁₃	1	2	yes	—
515	#448	C₂²×C₁₃	1	2	yes	—
516	#448	C₂²×C₁₃	1	1	yes	characteristic, complemented
517	#448	C₂²×C₁₃	1	2	yes	complemented
518	#448	C₂²×C₁₃	1	2	yes	complemented
519	#448	C₂²×C₁₃	1	4	yes	complemented
520	#447	C₂²×C₁₃	1	2	yes	—
521	#447	C₂²×C₁₃	1	1	yes	characteristic, complemented
522	#433	C₂²×C₁₃	1	4	yes	complemented
523	#432	C₂²×C₁₃	1	2	yes	complemented
524	#431	C₂²×C₁₃	1	2	yes	complemented
525	#424	C₂²×C₁₃	1	2	yes	complemented
526	#419	C₂²×C₁₃	1	2	yes	complemented
527	#417	C₂²×C₁₃	1	2	yes	—
528	#416	C₂²×C₁₃	1	2	yes	—
529	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
530	#407	C₂²×C₁₃	1	1	yes	characteristic
531	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
532	#405	C₂²×C₁₃	1	2	yes	complemented
533	C₂²×C₁₃	—	2	1	no	—
534	C₂²×C₁₃	—	2	1	no	—
535	C₂²×C₁₃	—	2	1	no	—
536	C₂²×C₁₃	—	2	1	no	—
537	C₂²×C₁₃	—	2	1	no	—
538	C₂²×C₁₃	—	2	1	no	—
539	C₂²×C₁₃	—	2	1	no	—
540	C₂²×C₁₃	—	4	4	no	—
541	C₂²×C₁₃	—	4	2	no	—
542	C₂²×C₁₃	—	4	1	no	—
543	C₂²×C₁₃	—	4	2	no	—
544	C₂²×C₁₃	—	4	2	no	—
545	C₂²×C₁₃	—	4	1	no	—
546	C₂²×C₁₃	—	4	2	no	—
547	C₂²×C₁₃	—	4	1	no	—
548	C₂²×C₁₃	—	4	2	no	—
549	C₂²×C₁₃	—	4	2	no	—
550	C₂²×C₁₃	—	8	4	no	—
551	C₂²×C₁₃	—	16	2	no	—
552	C₂²×C₁₃	#535	1	2	yes	—
553	C₂²×C₁₃	#577	1	2	yes	—
554	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₁₃	—	2	2	no	—
556	C₄×C₁₃	—	2	2	no	—
557	C₄×C₁₃	—	2	1	no	—
558	C₄×C₁₃	—	2	1	no	—
559	C₄×C₁₃	—	2	2	no	—
560	C₄×C₁₃	—	2	2	no	—
561	C₄×C₁₃	—	4	1	no	—
562	C₄×C₁₃	—	4	2	no	—
563	C₄×C₁₃	—	4	4	no	—
564	C₄×C₁₃	—	4	1	no	—
565	C₄×C₁₃	—	4	2	no	—
566	C₄×C₁₃	—	4	1	no	—
567	C₄×C₁₃	#535	1	2	yes	—
568	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
569	C₂×#41	—	2	1	no	—
570	C₂×#41	—	2	1	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	4	4	no	—
573	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
574	C₂×#41	C₂³×C₁₃	1	2	yes	—
575	C₂×#41	C₂³×C₁₃	1	2	yes	—
576	C₂²×Q₈	—	2	1	no	—
577	C₂²×Q₈	—	2	1	no	—
578	C₂²×Q₈	—	2	1	no	—
579	C₂²×Q₈	—	4	4	no	—
580	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
581	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
582	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
583	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
587	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
588	C₂³×C₄	—	2	1	no	—
589	C₂³×C₄	—	2	1	no	—
590	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
591	#137	—	4	4	no	—
592	AGL(1,ℤ/8)	—	4	4	no	—
593	#135	—	4	4	no	—
594	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
595	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
596	C₂×SD₁₆	—	4	4	no	—
597	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
598	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
599	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
602	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
603	C₂×D₈	C₂³×C₁₃	1	2	yes	—
604	C₂×D₈	C₂³×C₁₃	1	4	yes	—
605	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
606	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
607	C₄⋊Q₈	—	2	1	no	—
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	—	2	2	no	—
610	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
611	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
612	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
613	#127	C₂³×C₁₃	1	2	yes	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#125	—	2	1	no	—
617	#125	C₂³×C₁₃	1	2	yes	—
618	#124	—	2	2	no	—
619	#124	—	2	2	no	—
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	C₂³×C₁₃	1	4	yes	—
623	#124	C₂³×C₁₃	1	4	yes	—
624	#124	C₂³×C₁₃	1	2	yes	—
625	#123	—	2	1	no	—
626	#123	—	2	2	no	—
627	#123	—	2	2	no	—
628	#123	—	2	2	no	—
629	#123	—	2	4	no	—
630	#123	—	2	4	no	—
631	#123	—	2	4	no	—
632	#123	—	2	4	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	4	no	—
639	C₂²⋊Q₈	—	2	4	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
643	C₂²⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
644	#121	—	2	1	no	—
645	#121	—	2	1	no	—
646	#121	—	2	2	no	—
647	#121	—	2	1	no	—
648	#121	—	2	1	no	—
649	#121	—	2	2	no	—
650	#121	—	2	2	no	—
651	#121	C₂³×C₁₃	1	2	yes	—
652	#121	C₂³×C₁₃	1	2	yes	—
653	#121	C₂³×C₁₃	1	1	yes	characteristic
654	#121	C₂³×C₁₃	1	1	yes	characteristic
655	#120	—	2	1	no	—
656	#120	—	2	2	no	—
657	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
658	C₄×D₄	—	2	1	no	—
659	C₄×D₄	—	2	1	no	—
660	C₄×D₄	—	2	2	no	—
661	C₄×D₄	—	2	1	no	—
662	C₄×D₄	—	2	1	no	—
663	C₄×D₄	—	2	2	no	—
664	C₄×D₄	—	2	2	no	—
665	C₄×D₄	C₂³×C₁₃	1	2	yes	—
666	C₄×D₄	C₂³×C₁₃	1	2	yes	—
667	C₄×D₄	C₂³×C₁₃	1	2	yes	—
668	#117	—	2	1	no	—
669	#117	—	2	2	no	—
670	#117	D₄×C₁₃	1	2	yes	—
671	#117	D₄×C₁₃	1	1	yes	characteristic
672	#117	D₄×C₁₃	1	1	yes	characteristic
673	#117	C₂³×C₁₃	1	1	yes	characteristic
674	#117	C₂³×C₁₃	1	1	yes	characteristic
675	#117	C₂³×C₁₃	1	1	yes	characteristic
676	#117	C₂³×C₁₃	1	2	yes	—
677	C₂×C₄⋊C₄	—	2	2	no	—
678	C₂×C₄⋊C₄	—	2	2	no	—
679	C₂×C₄⋊C₄	—	2	1	no	—
680	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	—	2	1	no	—
684	C₂×C₂²⋊C₄	—	2	2	no	—
685	C₂×C₂²⋊C₄	—	2	2	no	—
686	C₂×C₂²⋊C₄	—	2	2	no	—
687	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
688	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
689	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
690	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
691	#103	C₂³×C₁₃	1	4	yes	—
692	#103	C₂³×C₁₃	1	4	yes	—
693	#103	C₂³×C₁₃	1	2	yes	—
694	#103	C₂³×C₁₃	1	2	yes	—
695	#103	C₂³×C₁₃	1	4	yes	—
696	#103	C₂³×C₁₃	1	4	yes	—
697	#103	C₂³×C₁₃	1	4	yes	—
698	#102	C₂³×C₁₃	1	2	yes	—
699	#102	C₂³×C₁₃	1	2	yes	—
700	#102	C₂³×C₁₃	1	4	yes	—
701	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
702	C₂²⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
703	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
704	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
705	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
706	#97	C₂³×C₁₃	1	4	yes	—
707	C₄×C₈	C₂³×C₁₃	1	4	yes	—
708	C₂×C₁₃	—	2	2	no	—
709	C₂×C₁₃	—	2	2	no	—
710	C₂×C₁₃	—	4	1	no	—
711	C₂×C₁₃	—	8	1	no	—
712	C₂×C₁₃	—	8	2	no	—
713	C₂×C₁₃	—	8	2	no	—
714	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
715	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
716	C₂×C₁₃	#3586	1	1	yes	characteristic
717	C₂⁴	—	2	1	no	—
718	C₂⁴	—	2	1	no	—
719	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
720	#41	—	2	4	no	—
721	#41	—	2	4	no	—
722	#41	—	2	4	no	—
723	#41	—	4	2	no	—
724	#41	—	4	2	no	—
725	#41	—	4	4	no	—
726	#41	—	4	4	no	—
727	#41	—	8	4	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	—	2	1	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	4	no	—
734	C₂×Q₈	—	2	4	no	—
735	C₂×Q₈	—	4	4	no	—
736	C₂×Q₈	—	4	4	no	—
737	C₂×Q₈	—	4	2	no	—
738	C₂×Q₈	—	4	4	no	—
739	C₂×Q₈	—	4	4	no	—
740	C₂×Q₈	—	4	4	no	—
741	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
742	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
743	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
744	C₂×D₄	—	2	1	no	—
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	1	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	1	no	—
752	C₂×D₄	—	2	1	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	4	no	—
756	C₂×D₄	—	4	2	no	—
757	C₂×D₄	—	4	4	no	—
758	C₂×D₄	—	8	2	no	—
759	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
760	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
761	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	2	1	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	4	4	no	—
775	C₂²×C₄	—	4	4	no	—
776	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
777	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
778	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
779	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
784	Q₁₆	—	4	2	no	—
785	Q₁₆	—	4	4	no	—
786	SD₁₆	—	4	4	no	—
787	SD₁₆	—	4	4	no	—
788	SD₁₆	—	4	2	no	—
789	SD₁₆	—	4	2	no	—
790	SD₁₆	—	4	4	no	—
791	SD₁₆	—	4	4	no	—
792	D₈	—	4	2	no	—
793	D₈	—	4	4	no	—
794	M₁₆	—	2	4	no	—
795	C₂×C₈	—	2	4	no	—
796	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
797	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
798	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	4	no	—
805	C₄⋊C₄	—	2	1	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	1	no	—
810	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
811	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
812	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
813	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
814	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
816	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
818	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
819	C₂²⋊C₄	—	2	1	no	—
820	C₂²⋊C₄	—	2	1	no	—
821	C₂²⋊C₄	—	2	1	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	4	no	—
829	C₂²⋊C₄	—	2	4	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	1	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	1	no	—
835	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
836	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
837	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
838	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	1	no	—
841	C₄²	C₂×D₄×C₁₃	1	2	yes	—
842	C₄²	C₂×D₄×C₁₃	1	2	yes	—
843	C₄²	C₂⁴×C₁₃	1	2	yes	—
844	C₄²	C₂⁴×C₁₃	1	2	yes	—
845	C₁₃	#60813	1	1	yes	characteristic, direct product factor, Sylow
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	2	no	—
853	C₂³	—	4	2	no	—
854	C₂³	—	4	2	no	—
855	C₂³	—	4	2	no	—
856	C₂³	—	8	1	no	—
857	C₂³	—	8	1	no	—
858	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
859	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
860	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
861	Q₈	—	2	4	no	—
862	Q₈	—	2	2	no	—
863	Q₈	—	2	2	no	—
864	Q₈	—	2	4	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	4	4	no	—
867	Q₈	—	4	4	no	—
868	Q₈	—	4	2	no	—
869	Q₈	—	4	4	no	—
870	Q₈	—	8	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	2	4	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	4	2	no	—
876	D₄	—	4	4	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	4	no	—
880	D₄	—	4	2	no	—
881	D₄	—	4	2	no	—
882	D₄	—	8	2	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	—	8	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	4	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	4	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	2	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	—	4	2	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	2	no	—
906	C₂×C₄	—	8	2	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	—	8	1	no	—
910	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
911	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
912	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
914	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
915	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
916	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
917	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
918	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
919	C₈	—	2	2	no	—
920	C₈	—	2	2	no	—
921	C₈	—	2	4	no	—
922	C₂²	—	2	1	no	—
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	4	4	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	4	2	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	8	4	no	—
940	C₂²	—	16	2	no	—
941	C₂²	C₁₃×#535	1	2	yes	—
942	C₂²	C₁₃×#577	1	2	yes	—
943	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	2	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	1	no	—
952	C₄	—	4	1	no	—
953	C₄	—	4	2	no	—
954	C₄	—	4	4	no	—
955	C₄	—	4	1	no	—
956	C₄	C₁₃×#535	1	2	yes	—
957	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
958	C₂	—	2	2	no	—
959	C₂	—	2	2	no	—
960	C₂	—	4	1	no	—
961	C₂	—	8	2	no	—
962	C₂	—	8	2	no	—
963	C₂	—	8	1	no	—
964	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
965	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
966	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 ◁ 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×#536	C₂	semidirect
3. C₁₃×#3225	C₂	semidirect
4. C₁₃×#3221	C₂	semidirect
5. C₁₃×#3218	C₂	semidirect
6. C₁₃×#3213	C₂	semidirect
7. C₁₃×#3211	C₂	semidirect
8. C₁₃×#3206	C₂	semidirect
9. C₁₃×#3154	C₂	semidirect
10. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3042	C₂	semidirect
13. C₁₃×#3006	C₂	semidirect
14. C₁₃×#3004	C₂	semidirect
15. C₁₃×#3002	C₂	semidirect
16. C₂×C₁₃×#448	C₂	semidirect
17. C₁₃×#2924	C₂	semidirect
20. C₂×C₁₃×#137	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
30. C₁₃×#544	C₂²	semidirect
31. C₁₃×#542	C₂²	semidirect
32. C₁₃×#540	C₂²	semidirect
38. C₁₃×#536	C₂²	semidirect
39. C₁₃×#535	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₁₃×#124	C₂²	semidirect
49. C₁₃×#520	C₂²	semidirect
50. C₁₃×#518	C₂²	semidirect
52. C₁₃×#497	C₂²	semidirect
53. C₁₃×#496	C₂²	semidirect
54. C₁₃×#495	C₂²	semidirect
55. C₁₃×#492	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
61. C₁₃×#463	C₂²	semidirect
62. C₁₃×#463	C₂²	semidirect
63. C₁₃×#463	C₂²	semidirect
64. C₁₃×#462	C₂²	semidirect
65. C₁₃×#461	C₂²	semidirect
66. C₁₃×#461	C₂²	semidirect
67. C₁₃×#461	C₂²	semidirect
68. C₁₃×#452	C₂²	semidirect
69. C₁₃×#451	C₂²	semidirect
70. C₁₃×#451	C₂²	semidirect
71. C₁₃×#451	C₂²	semidirect
72. C₁₃×#450	C₂²	semidirect
74. C₁₃×#449	C₂²	semidirect
78. C₁₃×#448	C₂²	semidirect
79. C₁₃×#448	C₂²	semidirect
80. C₁₃×#448	C₂²	semidirect
81. C₁₃×#448	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×#419	C₂²	semidirect
91. C₂×C₁₃×#103	C₂²	semidirect
94. C₁₃×#405	C₂²	semidirect
234. #60813	C₁₃	direct (N × H)
363. #3494	C₂×C₁₃	semidirect
364. C₂×#536	C₂×C₁₃	semidirect
365. #3225	C₂×C₁₃	semidirect
366. #3221	C₂×C₁₃	semidirect
367. #3218	C₂×C₁₃	semidirect
368. #3213	C₂×C₁₃	semidirect
369. #3211	C₂×C₁₃	semidirect
370. #3206	C₂×C₁₃	semidirect
371. #3154	C₂×C₁₃	semidirect
372. #3137	C₂×C₁₃	semidirect
373. #3046	C₂×C₁₃	semidirect
374. #3042	C₂×C₁₃	semidirect
375. #3006	C₂×C₁₃	semidirect
376. #3004	C₂×C₁₃	semidirect
377. #3002	C₂×C₁₃	semidirect
378. C₂×#448	C₂×C₁₃	semidirect
379. #2924	C₂×C₁₃	semidirect
458. C₂×#137	C₂²×C₁₃	semidirect
461. C₂²×SD₁₆	C₂²×C₁₃	semidirect
468. #544	C₂²×C₁₃	semidirect
469. #542	C₂²×C₁₃	semidirect
470. #540	C₂²×C₁₃	semidirect
476. #536	C₂²×C₁₃	semidirect
477. #535	C₂²×C₁₃	semidirect
479. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
481. C₂×#124	C₂²×C₁₃	semidirect
487. #520	C₂²×C₁₃	semidirect
488. #518	C₂²×C₁₃	semidirect
490. #497	C₂²×C₁₃	semidirect
491. #496	C₂²×C₁₃	semidirect
492. #495	C₂²×C₁₃	semidirect
493. #492	C₂²×C₁₃	semidirect
494. #491	C₂²×C₁₃	semidirect
495. #489	C₂²×C₁₃	semidirect
496. #488	C₂²×C₁₃	semidirect
497. #487	C₂²×C₁₃	semidirect
498. #464	C₂²×C₁₃	semidirect
499. #463	C₂²×C₁₃	semidirect
500. #463	C₂²×C₁₃	semidirect
501. #463	C₂²×C₁₃	semidirect
502. #462	C₂²×C₁₃	semidirect
503. #461	C₂²×C₁₃	semidirect
504. #461	C₂²×C₁₃	semidirect
505. #461	C₂²×C₁₃	semidirect
506. #452	C₂²×C₁₃	semidirect
507. #451	C₂²×C₁₃	semidirect
508. #451	C₂²×C₁₃	semidirect
509. #451	C₂²×C₁₃	semidirect
510. #450	C₂²×C₁₃	semidirect
512. #449	C₂²×C₁₃	semidirect
516. #448	C₂²×C₁₃	semidirect
517. #448	C₂²×C₁₃	semidirect
518. #448	C₂²×C₁₃	semidirect
519. #448	C₂²×C₁₃	semidirect
521. #447	C₂²×C₁₃	semidirect
522. #433	C₂²×C₁₃	semidirect
523. #432	C₂²×C₁₃	semidirect
524. #431	C₂²×C₁₃	semidirect
525. #424	C₂²×C₁₃	semidirect
526. #419	C₂²×C₁₃	semidirect
529. C₂×#103	C₂²×C₁₃	semidirect
532. #405	C₂²×C₁₃	semidirect
845. C₁₃	#60813	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×#536	2
C₁₃×#3225	2
C₁₃×#3221	2
C₁₃×#3218	2
C₁₃×#3213	2
C₁₃×#3211	2
C₁₃×#3206	2
C₁₃×#3154	2
C₁₃×#3137	2
C₁₃×#3046	2
C₁₃×#3042	2
C₁₃×#3006	2
C₁₃×#3004	2
C₁₃×#3002	2
C₂×C₁₃×#448	2
C₁₃×#2924	2
#60813	13

Subgroups — C13×#60813 #15747152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60813 #15747152