Subgroups — C₁₃×#61342 #15747681

Order 3328.

1724 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3377	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3374	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3369	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3364	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3137	C₂	1	2	yes	maximal
11	C₁₃×#3082	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3076	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#3044	C₂	1	2	yes	maximal
14	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2950	C₂	1	2	yes	maximal, complemented
17	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
20	Q₈²×C₁₃	—	2	1	no	—
21	Q₈²×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#557	—	2	1	no	—
23	C₁₃×#557	—	2	2	no	—
24	C₁₃×#557	C₂²	1	2	yes	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	2	yes	—
27	C₁₃×#557	C₂²	1	4	yes	—
28	C₁₃×#556	C₂²	1	2	yes	—
29	C₁₃×#556	C₂²	1	2	yes	—
30	C₁₃×#552	—	2	2	no	—
31	C₁₃×#552	—	2	2	no	—
32	C₁₃×#544	—	2	2	no	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#541	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	1	no	—
37	C₁₃×#533	—	2	1	no	—
38	C₁₃×#533	—	2	2	no	—
39	C₁₃×#533	C₂²	1	1	yes	characteristic
40	C₁₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₁₃×#519	C₂²	1	2	yes	—
44	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₁₃×#491	C₂²	1	4	yes	—
47	C₁₃×#491	C₂²	1	4	yes	—
48	C₁₃×#489	C₂²	1	4	yes	—
49	C₁₃×#488	C₂²	1	4	yes	—
50	C₁₃×#487	C₂²	1	2	yes	—
51	C₁₃×#487	C₂²	1	4	yes	—
52	C₁₃×#487	C₂²	1	2	yes	—
53	C₁₃×#479	C₂²	1	2	yes	—
54	C₁₃×#479	C₂²	1	4	yes	—
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#478	C₂²	1	2	yes	—
57	C₁₃×#477	C₂²	1	1	yes	characteristic
58	C₁₃×#477	C₂²	1	4	yes	—
59	C₁₃×#476	C₂²	1	1	yes	characteristic
60	C₁₃×#475	C₂²	1	1	yes	characteristic
61	C₁₃×#475	C₂²	1	4	yes	—
62	C₁₃×#474	C₂²	1	1	yes	characteristic
63	C₁₃×#464	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	2	yes	—
66	C₁₃×#462	C₂²	1	2	yes	—
67	C₁₃×#462	C₂²	1	4	yes	—
68	C₁₃×#462	C₂²	1	4	yes	—
69	C₁₃×#462	C₂²	1	4	yes	—
70	C₁₃×#446	C₂²	1	2	yes	—
71	C₁₃×#446	C₂²	1	4	yes	—
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
73	C₁₃×#441	C₂²	1	4	yes	—
74	C₁₃×#441	C₂²	1	2	yes	—
75	C₁₃×#441	C₂²	1	4	yes	—
76	C₁₃×#440	C₂²	1	2	yes	—
77	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
78	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
81	C₁₃×#428	C₂²	1	1	yes	characteristic
82	C₁₃×#427	C₂²	1	2	yes	—
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
85	C₁₃×#419	C₂²	1	2	yes	—
86	C₁₃×#419	C₂²	1	2	yes	—
87	C₁₃×#419	C₂²	1	1	yes	characteristic
88	C₁₃×#417	C₂²	1	1	yes	characteristic
89	C₁₃×#416	C₂²	1	2	yes	—
90	C₂×C₁₃×#103	C₂²	1	2	yes	—
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
94	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#137	—	2	4	no	—
97	C₂×C₁₃×Q₁₆	—	2	8	no	—
98	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₁₃×C₄⋊Q₈	—	2	2	no	—
106	C₁₃×C₄⋊Q₈	—	2	4	no	—
107	C₁₃×C₄⋊Q₈	—	2	2	no	—
108	C₁₃×C₄⋊Q₈	—	2	4	no	—
109	C₁₃×C₄⋊Q₈	—	2	2	no	—
110	C₁₃×C₄⋊Q₈	—	2	1	no	—
111	C₁₃×C₄⋊Q₈	—	2	1	no	—
112	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×#126	—	2	4	no	—
121	C₁₃×#126	—	2	4	no	—
122	C₁₃×#125	—	2	2	no	—
123	C₁₃×#125	—	2	2	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	4	no	—
126	C₁₃×#125	—	2	4	no	—
127	C₁₃×#125	—	2	4	no	—
128	C₁₃×#125	—	2	4	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	D₄	1	2	yes	—
131	C₁₃×#125	C₂³	1	2	yes	—
132	C₁₃×#125	C₂³	1	4	yes	—
133	C₁₃×#124	C₂³	1	4	yes	—
134	C₁₃×#123	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	2	no	—
136	C₁₃×C₂²⋊Q₈	—	2	2	no	—
137	C₁₃×C₂²⋊Q₈	—	2	1	no	—
138	C₁₃×C₂²⋊Q₈	—	2	1	no	—
139	C₁₃×C₂²⋊Q₈	—	2	2	no	—
140	C₁₃×C₂²⋊Q₈	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	4	no	—
142	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
143	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
144	C₄×Q₈×C₁₃	—	2	2	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	—	2	2	no	—
147	C₄×Q₈×C₁₃	—	2	2	no	—
148	C₄×Q₈×C₁₃	—	2	2	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	2	no	—
151	C₄×Q₈×C₁₃	—	2	4	no	—
152	C₄×Q₈×C₁₃	—	2	2	no	—
153	C₄×Q₈×C₁₃	—	2	1	no	—
154	C₄×Q₈×C₁₃	—	2	1	no	—
155	C₄×Q₈×C₁₃	—	2	1	no	—
156	C₄×Q₈×C₁₃	—	2	1	no	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
161	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
162	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
163	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
165	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
170	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
171	C₁₃×#117	—	2	2	no	—
172	C₁₃×#117	—	2	2	no	—
173	C₁₃×#117	—	2	4	no	—
174	C₁₃×#117	—	2	4	no	—
175	C₁₃×#117	—	2	1	no	—
176	C₁₃×#117	C₂³	1	2	yes	—
177	C₁₃×#117	C₂³	1	1	yes	characteristic
178	C₁₃×#117	C₂³	1	2	yes	—
179	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₁₃	—	2	1	no	—
184	C₂×C₄²×C₁₃	—	2	1	no	—
185	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
186	C₁₃×#107	C₂³	1	2	yes	—
187	C₁₃×#107	C₂³	1	2	yes	—
188	C₁₃×#107	C₂³	1	2	yes	—
189	C₁₃×#106	C₂³	1	2	yes	—
190	C₁₃×#106	C₂³	1	2	yes	—
191	C₁₃×#106	C₂³	1	2	yes	—
192	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
194	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
195	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
196	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
197	C₁₃×#103	C₂³	1	4	yes	—
198	C₁₃×#103	C₂³	1	4	yes	—
199	C₁₃×#103	C₂³	1	2	yes	—
200	C₁₃×#103	C₂³	1	2	yes	—
201	C₁₃×#103	C₂³	1	2	yes	—
202	C₁₃×#103	C₂³	1	2	yes	—
203	C₁₃×#103	C₂³	1	2	yes	—
204	C₁₃×#103	C₂³	1	4	yes	—
205	C₁₃×#103	C₂³	1	4	yes	—
206	C₁₃×#103	C₂³	1	4	yes	—
207	C₁₃×#103	C₂³	1	4	yes	—
208	C₁₃×#102	C₂³	1	2	yes	—
209	C₁₃×#102	C₂³	1	2	yes	—
210	C₁₃×#102	C₂³	1	2	yes	—
211	C₁₃×#97	C₂³	1	2	yes	—
212	C₁₃×#97	C₂³	1	4	yes	—
213	C₄×C₈×C₁₃	C₂³	1	2	yes	—
214	C₄×C₈×C₁₃	C₂³	1	4	yes	—
215	#61342	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₁₃×#41	—	2	2	no	—
217	C₁₃×#41	—	2	2	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	2	no	—
221	C₂×Q₈×C₁₃	—	2	1	no	—
222	C₂×Q₈×C₁₃	—	2	4	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	—	2	4	no	—
225	C₂×Q₈×C₁₃	—	2	4	no	—
226	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
227	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
228	C₂×Q₈×C₁₃	#41	1	4	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
230	C₂×Q₈×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	2	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	1	no	—
239	C₂²×C₄×C₁₃	—	2	1	no	—
240	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₁₃×Q₁₆	—	2	8	no	—
244	C₁₃×Q₁₆	—	2	8	no	—
245	C₁₃×Q₁₆	—	2	4	no	—
246	C₁₃×SD₁₆	—	2	4	no	—
247	C₁₃×M₁₆	—	2	2	no	—
248	C₁₃×M₁₆	—	2	2	no	—
249	C₂×C₈×C₁₃	—	2	4	no	—
250	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
254	C₁₃×C₄⋊C₄	—	2	2	no	—
255	C₁₃×C₄⋊C₄	—	2	2	no	—
256	C₁₃×C₄⋊C₄	—	2	2	no	—
257	C₁₃×C₄⋊C₄	—	2	2	no	—
258	C₁₃×C₄⋊C₄	—	2	2	no	—
259	C₁₃×C₄⋊C₄	—	2	2	no	—
260	C₁₃×C₄⋊C₄	—	2	1	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	1	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	4	no	—
266	C₁₃×C₄⋊C₄	—	2	4	no	—
267	C₁₃×C₄⋊C₄	—	2	2	no	—
268	C₁₃×C₄⋊C₄	—	2	1	no	—
269	C₁₃×C₄⋊C₄	—	2	4	no	—
270	C₁₃×C₄⋊C₄	—	2	4	no	—
271	C₁₃×C₄⋊C₄	—	2	1	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	4	no	—
274	C₁₃×C₄⋊C₄	—	2	2	no	—
275	C₁₃×C₄⋊C₄	—	2	4	no	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
281	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
282	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
285	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
286	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
287	C₁₃×C₂²⋊C₄	—	2	1	no	—
288	C₁₃×C₂²⋊C₄	—	2	2	no	—
289	C₁₃×C₂²⋊C₄	—	2	1	no	—
290	C₁₃×C₂²⋊C₄	—	2	1	no	—
291	C₁₃×C₂²⋊C₄	—	2	4	no	—
292	C₁₃×C₂²⋊C₄	—	2	4	no	—
293	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
294	C₄²×C₁₃	—	2	1	no	—
295	C₄²×C₁₃	—	2	1	no	—
296	C₄²×C₁₃	—	2	1	no	—
297	C₄²×C₁₃	—	2	2	no	—
298	C₄²×C₁₃	—	2	2	no	—
299	C₄²×C₁₃	—	2	4	no	—
300	C₄²×C₁₃	—	2	4	no	—
301	C₄²×C₁₃	—	2	4	no	—
302	C₄²×C₁₃	—	2	4	no	—
303	C₄²×C₁₃	—	2	2	no	—
304	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
307	C₄²×C₁₃	C₂⁴	1	4	yes	—
308	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
309	#3509	C₂×C₁₃	1	1	yes	characteristic
310	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#3377	C₂×C₁₃	1	4	yes	complemented
312	#3374	C₂×C₁₃	1	2	yes	complemented
313	#3374	C₂×C₁₃	1	4	yes	complemented
314	#3369	C₂×C₁₃	1	2	yes	complemented
315	#3364	C₂×C₁₃	1	2	yes	complemented
316	#3363	C₂×C₁₃	1	2	yes	complemented
317	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
318	#3137	C₂×C₁₃	1	2	yes	—
319	#3082	C₂×C₁₃	1	2	yes	complemented
320	#3076	C₂×C₁₃	1	1	yes	characteristic
321	#3044	C₂×C₁₃	1	2	yes	—
322	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
323	#2962	C₂×C₁₃	1	1	yes	characteristic, complemented
324	#2950	C₂×C₁₃	1	2	yes	complemented
325	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
326	C₂³×C₁₃	—	2	1	no	—
327	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
328	Q₈×C₁₃	—	2	4	no	—
329	Q₈×C₁₃	—	2	4	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	2	4	no	—
332	Q₈×C₁₃	—	2	1	no	—
333	Q₈×C₁₃	—	2	4	no	—
334	Q₈×C₁₃	—	2	1	no	—
335	Q₈×C₁₃	—	4	2	no	—
336	Q₈×C₁₃	—	4	4	no	—
337	Q₈×C₁₃	—	4	2	no	—
338	Q₈×C₁₃	—	8	1	no	—
339	Q₈×C₁₃	—	8	4	no	—
340	Q₈×C₁₃	C₂×#41	1	4	yes	—
341	D₄×C₁₃	—	2	1	no	—
342	D₄×C₁₃	—	2	1	no	—
343	D₄×C₁₃	—	4	2	no	—
344	C₂×C₄×C₁₃	—	2	4	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	1	no	—
348	C₂×C₄×C₁₃	—	2	1	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	2	4	no	—
352	C₂×C₄×C₁₃	—	2	1	no	—
353	C₂×C₄×C₁₃	—	2	2	no	—
354	C₂×C₄×C₁₃	—	4	1	no	—
355	C₂×C₄×C₁₃	—	4	2	no	—
356	C₂×C₄×C₁₃	—	4	4	no	—
357	C₂×C₄×C₁₃	—	4	2	no	—
358	C₂×C₄×C₁₃	—	4	2	no	—
359	C₂×C₄×C₁₃	—	8	1	no	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
362	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
368	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
369	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
370	C₈×C₁₃	—	2	2	no	—
371	C₈×C₁₃	—	2	2	no	—
372	C₈×C₁₃	—	2	2	no	—
373	C₈×C₁₃	—	2	2	no	—
374	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
375	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
376	Q₈²	—	2	1	no	—
377	Q₈²	C₂²×C₁₃	1	2	yes	—
378	#557	—	2	1	no	—
379	#557	—	2	2	no	—
380	#557	C₂²×C₁₃	1	2	yes	—
381	#557	C₂²×C₁₃	1	2	yes	—
382	#557	C₂²×C₁₃	1	2	yes	—
383	#557	C₂²×C₁₃	1	4	yes	—
384	#556	C₂²×C₁₃	1	2	yes	—
385	#556	C₂²×C₁₃	1	2	yes	—
386	#552	—	2	2	no	—
387	#552	—	2	2	no	—
388	#544	—	2	2	no	—
389	#544	C₂²×C₁₃	1	2	yes	—
390	#541	—	2	2	no	—
391	#536	C₂²×C₁₃	1	2	yes	—
392	#533	—	2	1	no	—
393	#533	—	2	1	no	—
394	#533	—	2	2	no	—
395	#533	C₂²×C₁₃	1	1	yes	characteristic
396	#533	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	#519	C₂²×C₁₃	1	2	yes	—
399	#519	C₂²×C₁₃	1	2	yes	—
400	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
402	#491	C₂²×C₁₃	1	4	yes	—
403	#491	C₂²×C₁₃	1	4	yes	—
404	#489	C₂²×C₁₃	1	4	yes	—
405	#488	C₂²×C₁₃	1	4	yes	—
406	#487	C₂²×C₁₃	1	2	yes	—
407	#487	C₂²×C₁₃	1	4	yes	—
408	#487	C₂²×C₁₃	1	2	yes	—
409	#479	C₂²×C₁₃	1	2	yes	—
410	#479	C₂²×C₁₃	1	4	yes	—
411	#479	C₂²×C₁₃	1	4	yes	—
412	#478	C₂²×C₁₃	1	2	yes	—
413	#477	C₂²×C₁₃	1	1	yes	characteristic
414	#477	C₂²×C₁₃	1	4	yes	—
415	#476	C₂²×C₁₃	1	1	yes	characteristic
416	#475	C₂²×C₁₃	1	1	yes	characteristic
417	#475	C₂²×C₁₃	1	4	yes	—
418	#474	C₂²×C₁₃	1	1	yes	characteristic
419	#464	C₂²×C₁₃	1	4	yes	—
420	#464	C₂²×C₁₃	1	4	yes	—
421	#462	C₂²×C₁₃	1	2	yes	—
422	#462	C₂²×C₁₃	1	4	yes	—
423	#462	C₂²×C₁₃	1	2	yes	—
424	#462	C₂²×C₁₃	1	4	yes	—
425	#462	C₂²×C₁₃	1	4	yes	—
426	#446	C₂²×C₁₃	1	2	yes	—
427	#446	C₂²×C₁₃	1	4	yes	—
428	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
429	#441	C₂²×C₁₃	1	4	yes	—
430	#441	C₂²×C₁₃	1	2	yes	—
431	#441	C₂²×C₁₃	1	4	yes	—
432	#440	C₂²×C₁₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
434	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
435	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
436	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
437	#428	C₂²×C₁₃	1	1	yes	characteristic
438	#427	C₂²×C₁₃	1	2	yes	—
439	#424	C₂²×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
441	#419	C₂²×C₁₃	1	2	yes	—
442	#419	C₂²×C₁₃	1	2	yes	—
443	#419	C₂²×C₁₃	1	1	yes	characteristic
444	#417	C₂²×C₁₃	1	1	yes	characteristic
445	#416	C₂²×C₁₃	1	2	yes	—
446	C₂×#103	C₂²×C₁₃	1	2	yes	—
447	#405	C₂²×C₁₃	1	2	yes	—
448	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
449	C₂²×C₁₃	—	2	1	no	—
450	C₂²×C₁₃	—	2	1	no	—
451	C₂²×C₁₃	—	4	1	no	—
452	C₂²×C₁₃	—	4	1	no	—
453	C₂²×C₁₃	—	4	1	no	—
454	C₂²×C₁₃	#548	1	2	yes	—
455	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
456	C₄×C₁₃	—	2	1	no	—
457	C₄×C₁₃	—	2	1	no	—
458	C₄×C₁₃	—	2	4	no	—
459	C₄×C₁₃	—	2	4	no	—
460	C₄×C₁₃	—	2	1	no	—
461	C₄×C₁₃	—	2	4	no	—
462	C₄×C₁₃	—	4	1	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	1	no	—
466	C₄×C₁₃	—	4	4	no	—
467	C₄×C₁₃	—	4	1	no	—
468	C₄×C₁₃	—	4	2	no	—
469	C₄×C₁₃	#548	1	2	yes	—
470	C₄×C₁₃	#578	1	2	yes	—
471	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
472	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
475	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
476	#137	—	2	4	no	—
477	C₂×Q₁₆	—	2	8	no	—
478	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
479	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
480	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
481	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
482	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
483	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
485	C₄⋊Q₈	—	2	2	no	—
486	C₄⋊Q₈	—	2	4	no	—
487	C₄⋊Q₈	—	2	2	no	—
488	C₄⋊Q₈	—	2	4	no	—
489	C₄⋊Q₈	—	2	2	no	—
490	C₄⋊Q₈	—	2	1	no	—
491	C₄⋊Q₈	—	2	1	no	—
492	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
493	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
494	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
495	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
496	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
497	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
498	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
499	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
500	#126	—	2	4	no	—
501	#126	—	2	4	no	—
502	#125	—	2	2	no	—
503	#125	—	2	2	no	—
504	#125	—	2	4	no	—
505	#125	—	2	4	no	—
506	#125	—	2	4	no	—
507	#125	—	2	4	no	—
508	#125	—	2	4	no	—
509	#125	—	2	2	no	—
510	#125	D₄×C₁₃	1	2	yes	—
511	#125	C₂³×C₁₃	1	2	yes	—
512	#125	C₂³×C₁₃	1	4	yes	—
513	#124	C₂³×C₁₃	1	4	yes	—
514	#123	—	2	4	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	2	1	no	—
518	C₂²⋊Q₈	—	2	1	no	—
519	C₂²⋊Q₈	—	2	2	no	—
520	C₂²⋊Q₈	—	2	2	no	—
521	C₂²⋊Q₈	—	2	4	no	—
522	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
523	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	2	no	—
529	C₄×Q₈	—	2	2	no	—
530	C₄×Q₈	—	2	2	no	—
531	C₄×Q₈	—	2	4	no	—
532	C₄×Q₈	—	2	2	no	—
533	C₄×Q₈	—	2	1	no	—
534	C₄×Q₈	—	2	1	no	—
535	C₄×Q₈	—	2	1	no	—
536	C₄×Q₈	—	2	1	no	—
537	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
538	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
539	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
540	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
541	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
542	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
543	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
544	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
545	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
546	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
547	C₄×D₄	—	2	1	no	—
548	C₄×D₄	—	2	1	no	—
549	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	—	2	4	no	—
554	#117	—	2	4	no	—
555	#117	—	2	1	no	—
556	#117	C₂³×C₁₃	1	1	yes	characteristic
557	#117	C₂³×C₁₃	1	2	yes	—
558	#117	C₂³×C₁₃	1	2	yes	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	—	2	1	no	—
561	C₂×C₄⋊C₄	—	2	1	no	—
562	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
563	C₂×C₄²	—	2	1	no	—
564	C₂×C₄²	—	2	1	no	—
565	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
566	#107	C₂³×C₁₃	1	2	yes	—
567	#107	C₂³×C₁₃	1	2	yes	—
568	#107	C₂³×C₁₃	1	2	yes	—
569	#106	C₂³×C₁₃	1	2	yes	—
570	#106	C₂³×C₁₃	1	2	yes	—
571	#106	C₂³×C₁₃	1	2	yes	—
572	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
573	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
574	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
575	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
576	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
577	#103	C₂³×C₁₃	1	4	yes	—
578	#103	C₂³×C₁₃	1	4	yes	—
579	#103	C₂³×C₁₃	1	2	yes	—
580	#103	C₂³×C₁₃	1	2	yes	—
581	#103	C₂³×C₁₃	1	2	yes	—
582	#103	C₂³×C₁₃	1	2	yes	—
583	#103	C₂³×C₁₃	1	2	yes	—
584	#103	C₂³×C₁₃	1	4	yes	—
585	#103	C₂³×C₁₃	1	4	yes	—
586	#103	C₂³×C₁₃	1	4	yes	—
587	#103	C₂³×C₁₃	1	4	yes	—
588	#102	C₂³×C₁₃	1	2	yes	—
589	#102	C₂³×C₁₃	1	2	yes	—
590	#102	C₂³×C₁₃	1	2	yes	—
591	#97	C₂³×C₁₃	1	2	yes	—
592	#97	C₂³×C₁₃	1	4	yes	—
593	C₄×C₈	C₂³×C₁₃	1	2	yes	—
594	C₄×C₈	C₂³×C₁₃	1	4	yes	—
595	C₂×C₁₃	—	2	2	no	—
596	C₂×C₁₃	—	8	1	no	—
597	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
598	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
599	C₂×C₁₃	#3586	1	1	yes	characteristic
600	#41	—	2	2	no	—
601	#41	—	2	2	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	2	4	no	—
607	C₂×Q₈	—	2	2	no	—
608	C₂×Q₈	—	2	4	no	—
609	C₂×Q₈	—	2	4	no	—
610	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
611	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
612	C₂×Q₈	C₁₃×#41	1	4	yes	—
613	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
614	C₂×Q₈	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
616	C₂×D₄	—	2	1	no	—
617	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
625	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
626	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	Q₁₆	—	2	8	no	—
628	Q₁₆	—	2	8	no	—
629	Q₁₆	—	2	4	no	—
630	SD₁₆	—	2	4	no	—
631	M₁₆	—	2	2	no	—
632	M₁₆	—	2	2	no	—
633	C₂×C₈	—	2	4	no	—
634	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
635	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
636	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
637	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
638	C₄⋊C₄	—	2	2	no	—
639	C₄⋊C₄	—	2	2	no	—
640	C₄⋊C₄	—	2	2	no	—
641	C₄⋊C₄	—	2	2	no	—
642	C₄⋊C₄	—	2	2	no	—
643	C₄⋊C₄	—	2	2	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	4	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	2	no	—
652	C₄⋊C₄	—	2	1	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	2	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
661	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
663	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
665	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
666	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
667	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
668	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
669	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
670	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
671	C₂²⋊C₄	—	2	1	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	2	1	no	—
674	C₂²⋊C₄	—	2	1	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
678	C₄²	—	2	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	2	no	—
682	C₄²	—	2	2	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	2	no	—
688	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
689	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
690	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
691	C₄²	C₂⁴×C₁₃	1	4	yes	—
692	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
693	C₁₃	#61342	1	1	yes	characteristic, direct product factor, Sylow
694	C₂³	—	2	1	no	—
695	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
696	Q₈	—	2	4	no	—
697	Q₈	—	2	4	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	4	no	—
700	Q₈	—	2	1	no	—
701	Q₈	—	2	4	no	—
702	Q₈	—	2	1	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	4	4	no	—
705	Q₈	—	4	2	no	—
706	Q₈	—	8	1	no	—
707	Q₈	—	8	4	no	—
708	Q₈	C₂×C₁₃×#41	1	4	yes	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	4	2	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	4	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	8	1	no	—
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
730	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
731	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
732	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
735	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
736	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
737	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
738	C₈	—	2	2	no	—
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	4	1	no	—
745	C₂²	—	4	1	no	—
746	C₂²	—	4	1	no	—
747	C₂²	C₁₃×#548	1	2	yes	—
748	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
749	C₄	—	2	1	no	—
750	C₄	—	2	4	no	—
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	4	1	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	4	4	no	—
762	C₄	C₁₃×#548	1	2	yes	—
763	C₄	C₁₃×#578	1	2	yes	—
764	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
765	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
766	C₂	—	2	2	no	—
767	C₂	—	8	1	no	—
768	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
769	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
770	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3502	C₂	semidirect
3. C₁₃×#3377	C₂	semidirect
4. C₁₃×#3374	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3369	C₂	semidirect
7. C₁₃×#3364	C₂	semidirect
8. C₁₃×#3363	C₂	semidirect
9. C₁₃×#3139	C₂	semidirect
11. C₁₃×#3082	C₂	semidirect
14. C₂×C₁₃×#462	C₂	semidirect
15. C₁₃×#2962	C₂	semidirect
16. C₁₃×#2950	C₂	semidirect
215. #61342	C₁₃	direct (N × H)
310. #3502	C₂×C₁₃	semidirect
311. #3377	C₂×C₁₃	semidirect
312. #3374	C₂×C₁₃	semidirect
313. #3374	C₂×C₁₃	semidirect
314. #3369	C₂×C₁₃	semidirect
315. #3364	C₂×C₁₃	semidirect
316. #3363	C₂×C₁₃	semidirect
317. #3139	C₂×C₁₃	semidirect
319. #3082	C₂×C₁₃	semidirect
322. C₂×#462	C₂×C₁₃	semidirect
323. #2962	C₂×C₁₃	semidirect
324. #2950	C₂×C₁₃	semidirect
693. C₁₃	#61342	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×#3509	2
C₁₃×#3502	2
C₁₃×#3377	2
C₁₃×#3374	2
C₁₃×#3369	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3139	2
C₁₃×#3137	2
C₁₃×#3082	2
C₁₃×#3076	2
C₁₃×#3044	2
C₂×C₁₃×#462	2
C₁₃×#2962	2
C₁₃×#2950	2
C₄×C₁₃×#137	2
#61342	13

Subgroups — C13×#61342 #15747681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61342 #15747681