Subgroups — C₁₃×#61328 #15747667

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3507	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×#3375	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3374	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3365	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3364	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3363	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3137	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#3083	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3037	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₁₃×#559	C₂²	1	2	yes	—
21	Q₈²×C₁₃	—	2	1	no	—
22	Q₈²×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#557	—	2	1	no	—
24	C₁₃×#557	—	2	2	no	—
25	C₁₃×#557	C₂²	1	2	yes	—
26	C₁₃×#557	C₂²	1	4	yes	—
27	C₁₃×#557	C₂²	1	2	yes	—
28	C₁₃×#556	—	2	1	no	—
29	C₁₃×#556	C₂²	1	4	yes	—
30	C₁₃×#554	—	2	1	no	—
31	C₁₃×#552	—	2	2	no	—
32	C₁₃×#544	—	2	2	no	—
33	C₁₃×#544	C₂²	1	2	yes	—
34	C₁₃×#539	—	2	2	no	—
35	C₁₃×#536	C₂²	1	2	yes	—
36	C₁₃×#533	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#532	C₂²	1	1	yes	characteristic
40	C₁₃×#529	—	2	2	no	—
41	C₁₃×#520	C₂²	1	2	yes	—
42	C₁₃×#519	C₂²	1	2	yes	—
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₁₃×#491	C₂²	1	4	yes	—
46	C₁₃×#489	C₂²	1	4	yes	—
47	C₁₃×#488	C₂²	1	2	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#488	C₂²	1	2	yes	—
50	C₁₃×#487	C₂²	1	1	yes	characteristic
51	C₁₃×#487	C₂²	1	4	yes	—
52	C₁₃×#487	C₂²	1	1	yes	characteristic
53	C₁₃×#486	C₂²	1	1	yes	characteristic
54	C₁₃×#486	C₂²	1	1	yes	characteristic
55	C₁₃×#479	C₂²	1	4	yes	—
56	C₁₃×#479	C₂²	1	4	yes	—
57	C₁₃×#478	C₂²	1	4	yes	—
58	C₁₃×#477	C₂²	1	2	yes	—
59	C₁₃×#477	C₂²	1	4	yes	—
60	C₁₃×#475	C₂²	1	2	yes	—
61	C₁₃×#474	C₂²	1	4	yes	—
62	C₁₃×#464	C₂²	1	4	yes	—
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	4	yes	—
67	C₁₃×#462	C₂²	1	4	yes	—
68	C₁₃×#460	C₂²	1	2	yes	—
69	C₁₃×#446	C₂²	1	2	yes	—
70	C₁₃×#446	C₂²	1	2	yes	—
71	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
72	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
73	C₁₃×#441	C₂²	1	4	yes	—
74	C₁₃×#440	C₂²	1	4	yes	—
75	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
76	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
77	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
78	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
79	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
80	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	—
81	C₁₃×#428	C₂²	1	2	yes	—
82	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
83	C₁₃×#424	C₂²	1	2	yes	—
84	C₁₃×#423	C₂²	1	1	yes	characteristic
85	C₁₃×#419	C₂²	1	2	yes	—
86	C₁₃×#417	C₂²	1	2	yes	—
87	C₁₃×#416	C₂²	1	2	yes	—
88	C₁₃×#416	C₂²	1	2	yes	—
89	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
90	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
91	C₁₃×#405	C₂²	1	2	yes	—
92	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
93	C₂×C₁₃×#41	C₂³	1	2	yes	—
94	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#137	—	2	8	no	—
97	C₂×C₁₃×Q₁₆	—	2	4	no	—
98	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
101	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
111	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
112	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₁₃×#127	C₂³	1	1	yes	characteristic
118	C₁₃×#126	—	2	4	no	—
119	C₁₃×#126	—	2	4	no	—
120	C₁₃×#125	—	2	2	no	—
121	C₁₃×#125	—	2	4	no	—
122	C₁₃×#125	—	2	4	no	—
123	C₁₃×#125	—	2	4	no	—
124	C₁₃×#125	—	2	4	no	—
125	C₁₃×#125	—	2	2	no	—
126	C₁₃×#125	D₄	1	2	yes	—
127	C₁₃×#125	C₂³	1	4	yes	—
128	C₁₃×#125	C₂³	1	2	yes	—
129	C₁₃×#124	—	2	2	no	—
130	C₁₃×#124	C₂³	1	2	yes	—
131	C₁₃×#124	C₂³	1	4	yes	—
132	C₁₃×#123	—	2	4	no	—
133	C₁₃×#123	—	2	4	no	—
134	C₁₃×C₂²⋊Q₈	—	2	4	no	—
135	C₁₃×C₂²⋊Q₈	—	2	1	no	—
136	C₁₃×C₂²⋊Q₈	—	2	1	no	—
137	C₁₃×C₂²⋊Q₈	—	2	2	no	—
138	C₁₃×C₂²⋊Q₈	—	2	2	no	—
139	C₁₃×C₂²⋊Q₈	—	2	4	no	—
140	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
141	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
142	C₁₃×#121	—	2	1	no	—
143	C₁₃×#121	—	2	1	no	—
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	4	no	—
149	C₄×Q₈×C₁₃	—	2	2	no	—
150	C₄×Q₈×C₁₃	—	2	1	no	—
151	C₄×Q₈×C₁₃	—	2	1	no	—
152	C₄×Q₈×C₁₃	—	2	1	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	C₂³	1	4	yes	—
157	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₁₃	C₂³	1	2	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	2	yes	—
165	C₄×D₄×C₁₃	—	2	2	no	—
166	C₄×D₄×C₁₃	—	2	4	no	—
167	C₄×D₄×C₁₃	—	2	1	no	—
168	C₄×D₄×C₁₃	—	2	1	no	—
169	C₄×D₄×C₁₃	C₂³	1	4	yes	—
170	C₁₃×#117	—	2	2	no	—
171	C₁₃×#117	—	2	4	no	—
172	C₁₃×#117	—	2	4	no	—
173	C₁₃×#117	C₂³	1	2	yes	—
174	C₁₃×#117	C₂³	1	2	yes	—
175	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₁₃	—	2	1	no	—
181	C₂×C₄²×C₁₃	—	2	1	no	—
182	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
183	C₁₃×#107	C₂³	1	2	yes	—
184	C₁₃×#107	C₂³	1	2	yes	—
185	C₁₃×#107	C₂³	1	4	yes	—
186	C₁₃×#106	C₂³	1	4	yes	—
187	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
188	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
189	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
190	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
191	C₁₃×#103	C₂³	1	2	yes	—
192	C₁₃×#103	C₂³	1	2	yes	—
193	C₁₃×#103	C₂³	1	2	yes	—
194	C₁₃×#103	C₂³	1	2	yes	—
195	C₁₃×#103	C₂³	1	2	yes	—
196	C₁₃×#103	C₂³	1	2	yes	—
197	C₁₃×#103	C₂³	1	2	yes	—
198	C₁₃×#103	C₂³	1	2	yes	—
199	C₁₃×#103	C₂³	1	4	yes	—
200	C₁₃×#103	C₂³	1	4	yes	—
201	C₁₃×#103	C₂³	1	4	yes	—
202	C₁₃×#102	C₂³	1	2	yes	—
203	C₁₃×#102	C₂³	1	2	yes	—
204	C₁₃×#102	C₂³	1	2	yes	—
205	C₁₃×#102	C₂³	1	2	yes	—
206	C₁₃×#102	C₂³	1	4	yes	—
207	C₁₃×#97	C₂³	1	4	yes	—
208	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
210	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
211	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
212	C₄×C₈×C₁₃	C₂³	1	4	yes	—
213	#61328	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₁₃×#41	—	2	4	no	—
215	C₁₃×#41	—	2	4	no	—
216	C₂×Q₈×C₁₃	—	2	1	no	—
217	C₂×Q₈×C₁₃	—	2	1	no	—
218	C₂×Q₈×C₁₃	—	2	1	no	—
219	C₂×Q₈×C₁₃	—	2	1	no	—
220	C₂×Q₈×C₁₃	—	2	4	no	—
221	C₂×Q₈×C₁₃	—	2	2	no	—
222	C₂×Q₈×C₁₃	—	2	2	no	—
223	C₂×Q₈×C₁₃	—	2	2	no	—
224	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
225	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
226	C₂×Q₈×C₁₃	#41	1	4	yes	—
227	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
228	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
229	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₁₃	—	2	2	no	—
231	C₂×D₄×C₁₃	—	2	1	no	—
232	C₂×D₄×C₁₃	—	2	1	no	—
233	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₁₃	—	2	1	no	—
235	C₂²×C₄×C₁₃	—	2	1	no	—
236	C₂²×C₄×C₁₃	—	2	1	no	—
237	C₂²×C₄×C₁₃	—	2	1	no	—
238	C₂²×C₄×C₁₃	—	2	2	no	—
239	C₂²×C₄×C₁₃	—	2	4	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	4	no	—
244	C₁₃×Q₁₆	—	2	4	no	—
245	C₁₃×Q₁₆	—	2	8	no	—
246	C₁₃×SD₁₆	—	2	8	no	—
247	C₁₃×M₁₆	—	2	4	no	—
248	C₂×C₈×C₁₃	—	2	2	no	—
249	C₂×C₈×C₁₃	—	2	2	no	—
250	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	4	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	2	no	—
261	C₁₃×C₄⋊C₄	—	2	1	no	—
262	C₁₃×C₄⋊C₄	—	2	4	no	—
263	C₁₃×C₄⋊C₄	—	2	4	no	—
264	C₁₃×C₄⋊C₄	—	2	4	no	—
265	C₁₃×C₄⋊C₄	—	2	1	no	—
266	C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
271	C₁₃×C₄⋊C₄	—	2	4	no	—
272	C₁₃×C₄⋊C₄	—	2	4	no	—
273	C₁₃×C₄⋊C₄	—	2	2	no	—
274	C₁₃×C₄⋊C₄	—	2	4	no	—
275	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
277	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
278	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
279	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
280	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₁₃×C₄⋊C₄	C₂⁴	1	2	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×C₂²⋊C₄	—	2	2	no	—
286	C₁₃×C₂²⋊C₄	—	2	2	no	—
287	C₁₃×C₂²⋊C₄	—	2	4	no	—
288	C₁₃×C₂²⋊C₄	—	2	4	no	—
289	C₁₃×C₂²⋊C₄	—	2	2	no	—
290	C₁₃×C₂²⋊C₄	—	2	4	no	—
291	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
292	C₄²×C₁₃	—	2	2	no	—
293	C₄²×C₁₃	—	2	2	no	—
294	C₄²×C₁₃	—	2	2	no	—
295	C₄²×C₁₃	—	2	2	no	—
296	C₄²×C₁₃	—	2	4	no	—
297	C₄²×C₁₃	—	2	4	no	—
298	C₄²×C₁₃	—	2	4	no	—
299	C₄²×C₁₃	—	2	2	no	—
300	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
303	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
304	C₄²×C₁₃	C₂⁴	1	4	yes	—
305	#3507	C₂×C₁₃	1	1	yes	characteristic
306	#3502	C₂×C₁₃	1	1	yes	characteristic, complemented
307	#3377	C₂×C₁₃	1	4	yes	complemented
308	#3375	C₂×C₁₃	1	2	yes	complemented
309	#3374	C₂×C₁₃	1	2	yes	complemented
310	#3365	C₂×C₁₃	1	2	yes	complemented
311	#3364	C₂×C₁₃	1	4	yes	complemented
312	#3363	C₂×C₁₃	1	2	yes	complemented
313	#3137	C₂×C₁₃	1	2	yes	complemented
314	#3131	C₂×C₁₃	1	1	yes	characteristic
315	#3083	C₂×C₁₃	1	2	yes	complemented
316	#3078	C₂×C₁₃	1	1	yes	characteristic, complemented
317	#3044	C₂×C₁₃	1	2	yes	complemented
318	#3037	C₂×C₁₃	1	1	yes	characteristic
319	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
320	#2947	C₂×C₁₃	1	2	yes	complemented
321	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
322	C₂³×C₁₃	—	2	2	no	—
323	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
324	Q₈×C₁₃	—	2	4	no	—
325	Q₈×C₁₃	—	2	4	no	—
326	Q₈×C₁₃	—	2	2	no	—
327	Q₈×C₁₃	—	2	2	no	—
328	Q₈×C₁₃	—	2	2	no	—
329	Q₈×C₁₃	—	2	2	no	—
330	Q₈×C₁₃	—	2	2	no	—
331	Q₈×C₁₃	—	4	2	no	—
332	Q₈×C₁₃	—	4	2	no	—
333	Q₈×C₁₃	—	4	2	no	—
334	Q₈×C₁₃	—	8	1	no	—
335	Q₈×C₁₃	—	8	4	no	—
336	Q₈×C₁₃	C₂×#41	1	4	yes	—
337	D₄×C₁₃	—	2	2	no	—
338	D₄×C₁₃	—	2	2	no	—
339	D₄×C₁₃	—	4	4	no	—
340	D₄×C₁₃	—	4	2	no	—
341	D₄×C₁₃	—	8	1	no	—
342	C₂×C₄×C₁₃	—	2	4	no	—
343	C₂×C₄×C₁₃	—	2	2	no	—
344	C₂×C₄×C₁₃	—	2	2	no	—
345	C₂×C₄×C₁₃	—	2	2	no	—
346	C₂×C₄×C₁₃	—	2	2	no	—
347	C₂×C₄×C₁₃	—	2	2	no	—
348	C₂×C₄×C₁₃	—	2	2	no	—
349	C₂×C₄×C₁₃	—	2	2	no	—
350	C₂×C₄×C₁₃	—	2	2	no	—
351	C₂×C₄×C₁₃	—	4	1	no	—
352	C₂×C₄×C₁₃	—	4	2	no	—
353	C₂×C₄×C₁₃	—	4	4	no	—
354	C₂×C₄×C₁₃	—	8	4	no	—
355	C₂×C₄×C₁₃	—	8	1	no	—
356	C₂×C₄×C₁₃	—	8	1	no	—
357	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
359	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
360	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
365	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
366	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
367	C₈×C₁₃	—	2	1	no	—
368	C₈×C₁₃	—	2	1	no	—
369	C₈×C₁₃	—	2	4	no	—
370	C₈×C₁₃	—	2	1	no	—
371	C₈×C₁₃	—	2	1	no	—
372	C₂×#137	C₂²×C₁₃	1	2	yes	—
373	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
374	#559	C₂²×C₁₃	1	2	yes	—
375	Q₈²	—	2	1	no	—
376	Q₈²	C₂²×C₁₃	1	2	yes	—
377	#557	—	2	1	no	—
378	#557	—	2	2	no	—
379	#557	C₂²×C₁₃	1	2	yes	—
380	#557	C₂²×C₁₃	1	4	yes	—
381	#557	C₂²×C₁₃	1	2	yes	—
382	#556	—	2	1	no	—
383	#556	C₂²×C₁₃	1	4	yes	—
384	#554	—	2	1	no	—
385	#552	—	2	2	no	—
386	#544	—	2	2	no	—
387	#544	C₂²×C₁₃	1	2	yes	—
388	#539	—	2	2	no	—
389	#536	C₂²×C₁₃	1	2	yes	—
390	#533	—	2	2	no	—
391	#533	C₂²×C₁₃	1	1	yes	characteristic
392	#533	C₂²×C₁₃	1	1	yes	characteristic
393	#532	C₂²×C₁₃	1	1	yes	characteristic
394	#529	—	2	2	no	—
395	#520	C₂²×C₁₃	1	2	yes	—
396	#519	C₂²×C₁₃	1	2	yes	—
397	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
399	#491	C₂²×C₁₃	1	4	yes	—
400	#489	C₂²×C₁₃	1	4	yes	—
401	#488	C₂²×C₁₃	1	2	yes	—
402	#488	C₂²×C₁₃	1	4	yes	—
403	#488	C₂²×C₁₃	1	2	yes	—
404	#487	C₂²×C₁₃	1	1	yes	characteristic
405	#487	C₂²×C₁₃	1	4	yes	—
406	#487	C₂²×C₁₃	1	1	yes	characteristic
407	#486	C₂²×C₁₃	1	1	yes	characteristic
408	#486	C₂²×C₁₃	1	1	yes	characteristic
409	#479	C₂²×C₁₃	1	4	yes	—
410	#479	C₂²×C₁₃	1	4	yes	—
411	#478	C₂²×C₁₃	1	4	yes	—
412	#477	C₂²×C₁₃	1	2	yes	—
413	#477	C₂²×C₁₃	1	4	yes	—
414	#475	C₂²×C₁₃	1	2	yes	—
415	#474	C₂²×C₁₃	1	4	yes	—
416	#464	C₂²×C₁₃	1	4	yes	—
417	#464	C₂²×C₁₃	1	4	yes	—
418	#464	C₂²×C₁₃	1	4	yes	—
419	#462	C₂²×C₁₃	1	2	yes	—
420	#462	C₂²×C₁₃	1	4	yes	—
421	#462	C₂²×C₁₃	1	4	yes	—
422	#460	C₂²×C₁₃	1	2	yes	—
423	#446	C₂²×C₁₃	1	2	yes	—
424	#446	C₂²×C₁₃	1	2	yes	—
425	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
426	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
427	#441	C₂²×C₁₃	1	4	yes	—
428	#440	C₂²×C₁₃	1	4	yes	—
429	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	—
430	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
432	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
433	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
434	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	—
435	#428	C₂²×C₁₃	1	2	yes	—
436	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
437	#424	C₂²×C₁₃	1	2	yes	—
438	#423	C₂²×C₁₃	1	1	yes	characteristic
439	#419	C₂²×C₁₃	1	2	yes	—
440	#417	C₂²×C₁₃	1	2	yes	—
441	#416	C₂²×C₁₃	1	2	yes	—
442	#416	C₂²×C₁₃	1	2	yes	—
443	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
444	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
445	#405	C₂²×C₁₃	1	2	yes	—
446	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
447	C₂²×C₁₃	—	2	1	no	—
448	C₂²×C₁₃	—	2	1	no	—
449	C₂²×C₁₃	—	4	2	no	—
450	C₂²×C₁₃	—	4	2	no	—
451	C₂²×C₁₃	—	4	2	no	—
452	C₂²×C₁₃	#548	1	2	yes	—
453	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₁₃	—	2	1	no	—
455	C₄×C₁₃	—	2	1	no	—
456	C₄×C₁₃	—	2	4	no	—
457	C₄×C₁₃	—	2	4	no	—
458	C₄×C₁₃	—	2	1	no	—
459	C₄×C₁₃	—	2	4	no	—
460	C₄×C₁₃	—	4	2	no	—
461	C₄×C₁₃	—	4	2	no	—
462	C₄×C₁₃	—	4	2	no	—
463	C₄×C₁₃	—	4	2	no	—
464	C₄×C₁₃	—	4	2	no	—
465	C₄×C₁₃	—	4	2	no	—
466	C₄×C₁₃	#548	1	2	yes	—
467	C₄×C₁₃	#578	1	2	yes	—
468	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
469	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	C₂×#41	C₂³×C₁₃	1	2	yes	—
471	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
473	#137	—	2	8	no	—
474	C₂×Q₁₆	—	2	4	no	—
475	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
476	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
477	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
478	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
479	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
480	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
482	C₄⋊Q₈	—	2	2	no	—
483	C₄⋊Q₈	—	2	4	no	—
484	C₄⋊Q₈	—	2	2	no	—
485	C₄⋊Q₈	—	2	4	no	—
486	C₄⋊Q₈	—	2	2	no	—
487	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
488	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
489	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
490	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
491	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
492	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
493	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
494	#127	C₂³×C₁₃	1	1	yes	characteristic
495	#126	—	2	4	no	—
496	#126	—	2	4	no	—
497	#125	—	2	2	no	—
498	#125	—	2	4	no	—
499	#125	—	2	4	no	—
500	#125	—	2	4	no	—
501	#125	—	2	4	no	—
502	#125	—	2	2	no	—
503	#125	D₄×C₁₃	1	2	yes	—
504	#125	C₂³×C₁₃	1	2	yes	—
505	#125	C₂³×C₁₃	1	4	yes	—
506	#124	—	2	2	no	—
507	#124	C₂³×C₁₃	1	2	yes	—
508	#124	C₂³×C₁₃	1	4	yes	—
509	#123	—	2	4	no	—
510	#123	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂²⋊Q₈	—	2	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	4	no	—
517	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
518	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
519	#121	—	2	1	no	—
520	#121	—	2	1	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	4	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	1	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	—	2	1	no	—
533	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
535	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
536	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
537	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
538	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
539	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
540	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
541	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
542	C₄×D₄	—	2	2	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	2	1	no	—
545	C₄×D₄	—	2	1	no	—
546	C₄×D₄	C₂³×C₁₃	1	4	yes	—
547	#117	—	2	2	no	—
548	#117	—	2	4	no	—
549	#117	—	2	4	no	—
550	#117	C₂³×C₁₃	1	2	yes	—
551	#117	C₂³×C₁₃	1	2	yes	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	2	no	—
555	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₂×C₄²	—	2	1	no	—
558	C₂×C₄²	—	2	1	no	—
559	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	#107	C₂³×C₁₃	1	2	yes	—
561	#107	C₂³×C₁₃	1	2	yes	—
562	#107	C₂³×C₁₃	1	4	yes	—
563	#106	C₂³×C₁₃	1	4	yes	—
564	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
565	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
566	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
567	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
568	#103	C₂³×C₁₃	1	2	yes	—
569	#103	C₂³×C₁₃	1	2	yes	—
570	#103	C₂³×C₁₃	1	2	yes	—
571	#103	C₂³×C₁₃	1	2	yes	—
572	#103	C₂³×C₁₃	1	2	yes	—
573	#103	C₂³×C₁₃	1	2	yes	—
574	#103	C₂³×C₁₃	1	2	yes	—
575	#103	C₂³×C₁₃	1	2	yes	—
576	#103	C₂³×C₁₃	1	4	yes	—
577	#103	C₂³×C₁₃	1	4	yes	—
578	#103	C₂³×C₁₃	1	4	yes	—
579	#102	C₂³×C₁₃	1	2	yes	—
580	#102	C₂³×C₁₃	1	2	yes	—
581	#102	C₂³×C₁₃	1	2	yes	—
582	#102	C₂³×C₁₃	1	2	yes	—
583	#102	C₂³×C₁₃	1	4	yes	—
584	#97	C₂³×C₁₃	1	4	yes	—
585	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
586	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
587	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
588	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
589	C₄×C₈	C₂³×C₁₃	1	4	yes	—
590	C₂×C₁₃	—	2	2	no	—
591	C₂×C₁₃	—	8	2	no	—
592	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
593	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
594	C₂×C₁₃	#3584	1	1	yes	characteristic
595	#41	—	2	4	no	—
596	#41	—	2	4	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	4	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
606	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
607	C₂×Q₈	C₁₃×#41	1	4	yes	—
608	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
609	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
610	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
611	C₂×D₄	—	2	2	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
623	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
624	Q₁₆	—	2	4	no	—
625	Q₁₆	—	2	4	no	—
626	Q₁₆	—	2	8	no	—
627	SD₁₆	—	2	8	no	—
628	M₁₆	—	2	4	no	—
629	C₂×C₈	—	2	2	no	—
630	C₂×C₈	—	2	2	no	—
631	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
632	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
633	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
634	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
635	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
636	C₄⋊C₄	—	2	1	no	—
637	C₄⋊C₄	—	2	4	no	—
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	1	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	2	1	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	1	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
659	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
660	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
661	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
662	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
663	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
664	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
665	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
666	C₂²⋊C₄	—	2	2	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
673	C₄²	—	2	2	no	—
674	C₄²	—	2	2	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₄²	—	2	4	no	—
678	C₄²	—	2	4	no	—
679	C₄²	—	2	4	no	—
680	C₄²	—	2	2	no	—
681	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
682	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
683	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
684	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
685	C₄²	C₂⁴×C₁₃	1	4	yes	—
686	C₁₃	#61328	1	1	yes	characteristic, direct product factor, Sylow
687	C₂³	—	2	2	no	—
688	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
689	Q₈	—	2	4	no	—
690	Q₈	—	2	4	no	—
691	Q₈	—	2	2	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	—	4	2	no	—
698	Q₈	—	4	2	no	—
699	Q₈	—	8	1	no	—
700	Q₈	—	8	4	no	—
701	Q₈	C₂×C₁₃×#41	1	4	yes	—
702	D₄	—	2	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	4	4	no	—
705	D₄	—	4	2	no	—
706	D₄	—	8	1	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	8	4	no	—
720	C₂×C₄	—	8	1	no	—
721	C₂×C₄	—	8	1	no	—
722	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
723	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
724	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
725	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
727	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
728	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
729	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
730	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
732	C₈	—	2	1	no	—
733	C₈	—	2	1	no	—
734	C₈	—	2	4	no	—
735	C₈	—	2	1	no	—
736	C₈	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	C₁₃×#548	1	2	yes	—
743	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
744	C₄	—	2	1	no	—
745	C₄	—	2	4	no	—
746	C₄	—	2	1	no	—
747	C₄	—	2	1	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	4	2	no	—
751	C₄	—	4	2	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	C₁₃×#548	1	2	yes	—
757	C₄	C₁₃×#578	1	2	yes	—
758	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
759	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
760	C₂	—	2	2	no	—
761	C₂	—	8	2	no	—
762	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
763	C₂	C₂×C₁₃×#578	1	1	yes	characteristic
764	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#532	C₂²
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×#3375	C₂	semidirect
5. C₁₃×#3374	C₂	semidirect
6. C₁₃×#3365	C₂	semidirect
7. C₁₃×#3364	C₂	semidirect
8. C₁₃×#3363	C₂	semidirect
9. C₁₃×#3137	C₂	semidirect
11. C₁₃×#3083	C₂	semidirect
12. C₁₃×#3078	C₂	semidirect
13. C₁₃×#3044	C₂	semidirect
15. C₁₃×#2960	C₂	semidirect
16. C₁₃×#2947	C₂	semidirect
17. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
213. #61328	C₁₃	direct (N × H)
306. #3502	C₂×C₁₃	semidirect
307. #3377	C₂×C₁₃	semidirect
308. #3375	C₂×C₁₃	semidirect
309. #3374	C₂×C₁₃	semidirect
310. #3365	C₂×C₁₃	semidirect
311. #3364	C₂×C₁₃	semidirect
312. #3363	C₂×C₁₃	semidirect
313. #3137	C₂×C₁₃	semidirect
315. #3083	C₂×C₁₃	semidirect
316. #3078	C₂×C₁₃	semidirect
317. #3044	C₂×C₁₃	semidirect
319. #2960	C₂×C₁₃	semidirect
320. #2947	C₂×C₁₃	semidirect
321. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
686. C₁₃	#61328	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×#3507	2
C₁₃×#3502	2
C₁₃×#3377	2
C₁₃×#3375	2
C₁₃×#3374	2
C₁₃×#3365	2
C₁₃×#3364	2
C₁₃×#3363	2
C₁₃×#3137	2
C₁₃×#3131	2
C₁₃×#3083	2
C₁₃×#3078	2
C₁₃×#3044	2
C₁₃×#3037	2
C₁₃×#2960	2
C₁₃×#2947	2
C₂×C₄×C₁₃×Q₁₆	2
#61328	13

Subgroups — C13×#61328 #15747667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61328 #15747667