Subgroups — C₁₃×#35014 #15721353

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2848	C₂	1	2	yes	maximal
4	C₁₃×#2646	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2626	C₂	1	2	yes	maximal
6	C₁₃×#2589	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2587	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2497	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2492	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2429	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2423	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2312	C₂	1	2	yes	maximal
14	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#400	C₂²	1	4	yes	complemented
29	C₁₃×#400	C₂²	1	4	yes	complemented
30	C₁₃×#399	C₂²	1	4	yes	—
31	C₁₃×#398	C₂²	1	4	yes	complemented
32	C₁₃×#398	C₂²	1	4	yes	complemented
33	C₁₃×#396	C₂²	1	4	yes	—
34	C₁₃×#396	C₂²	1	4	yes	—
35	C₁₃×#393	C₂²	1	4	yes	—
36	C₁₃×#391	C₂²	1	2	yes	complemented
37	C₁₃×#391	C₂²	1	4	yes	complemented
38	C₁₃×#391	C₂²	1	2	yes	complemented
39	C₁₃×#391	C₂²	1	2	yes	complemented
40	C₁₃×#389	C₂²	1	2	yes	complemented
41	C₁₃×#389	C₂²	1	2	yes	complemented
42	C₁₃×#389	C₂²	1	4	yes	complemented
43	C₁₃×#389	C₂²	1	2	yes	complemented
44	C₁₃×#389	C₂²	1	2	yes	complemented
45	C₁₃×#389	C₂²	1	2	yes	complemented
46	C₁₃×#388	C₂²	1	4	yes	—
47	C₁₃×#388	C₂²	1	4	yes	—
48	C₁₃×#388	C₂²	1	4	yes	—
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#387	C₂²	1	4	yes	complemented
51	C₁₃×#387	C₂²	1	4	yes	complemented
52	C₁₃×#387	C₂²	1	4	yes	complemented
53	C₁₃×#385	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#385	C₂²	1	4	yes	—
56	C₁₃×#385	C₂²	1	4	yes	—
57	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
58	C₁₃×#384	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#380	C₂²	1	2	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₁₃×#380	C₂²	1	2	yes	—
64	C₁₃×#380	C₂²	1	2	yes	—
65	C₁₃×#379	C₂²	1	4	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
73	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
74	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
75	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	—	2	4	no	—
79	C₂³×C₄×C₁₃	—	4	2	no	—
80	C₂³×C₄×C₁₃	—	4	2	no	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊Q₈	—	4	2	no	—
90	C₁₃×C₄⋊Q₈	—	4	2	no	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₁₃×C₂²⋊Q₈	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	—	4	4	no	—
94	C₁₃×C₂²⋊Q₈	—	4	4	no	—
95	C₄×Q₈×C₁₃	—	4	4	no	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
113	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	—	4	2	no	—
125	C₂×C₄²×C₁₃	—	4	2	no	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	2	yes	—
135	C₁₃×#95	C₂³	1	2	yes	—
136	C₁₃×#95	C₂³	1	2	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	4	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	C₁₃×#95	C₂³	1	4	yes	—
146	C₁₃×#95	C₂³	1	4	yes	—
147	C₁₃×#95	C₂³	1	4	yes	—
148	#35014	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	2	no	—
150	C₂⁴×C₁₃	—	2	2	no	—
151	C₂⁴×C₁₃	—	4	1	no	—
152	C₂⁴×C₁₃	—	4	1	no	—
153	C₂⁴×C₁₃	—	4	1	no	—
154	C₂⁴×C₁₃	—	4	1	no	—
155	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
158	C₂×Q₈×C₁₃	—	2	4	no	—
159	C₂×Q₈×C₁₃	—	2	4	no	—
160	C₂×Q₈×C₁₃	—	2	4	no	—
161	C₂×Q₈×C₁₃	—	2	4	no	—
162	C₂×Q₈×C₁₃	—	4	2	no	—
163	C₂×Q₈×C₁₃	—	4	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	4	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	—	4	2	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	—	4	1	no	—
180	C₂²×C₄×C₁₃	—	4	1	no	—
181	C₂²×C₄×C₁₃	—	4	1	no	—
182	C₂²×C₄×C₁₃	—	4	1	no	—
183	C₂²×C₄×C₁₃	—	4	1	no	—
184	C₂²×C₄×C₁₃	—	4	16	no	—
185	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
187	C₂²×C₄×C₁₃	#41	1	4	yes	—
188	C₂²×C₄×C₁₃	#41	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	8	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	4	2	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	—	4	4	no	—
212	C₁₃×C₄⋊C₄	—	4	4	no	—
213	C₁₃×C₄⋊C₄	—	4	4	no	—
214	C₁₃×C₄⋊C₄	—	4	4	no	—
215	C₁₃×C₄⋊C₄	—	4	2	no	—
216	C₁₃×C₄⋊C₄	—	4	2	no	—
217	C₁₃×C₄⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	—	2	8	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	4	4	no	—
223	C₁₃×C₂²⋊C₄	—	4	4	no	—
224	C₁₃×C₂²⋊C₄	—	4	4	no	—
225	C₁₃×C₂²⋊C₄	—	4	4	no	—
226	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
227	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	2	no	—
231	C₄²×C₁₃	—	4	2	no	—
232	C₄²×C₁₃	—	4	1	no	—
233	C₄²×C₁₃	—	4	1	no	—
234	C₄²×C₁₃	—	4	4	no	—
235	C₄²×C₁₃	—	4	4	no	—
236	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2857	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2848	C₂×C₁₃	1	2	yes	—
239	#2646	C₂×C₁₃	1	2	yes	complemented
240	#2626	C₂×C₁₃	1	2	yes	—
241	#2589	C₂×C₁₃	1	4	yes	complemented
242	#2587	C₂×C₁₃	1	4	yes	complemented
243	#2497	C₂×C₁₃	1	2	yes	complemented
244	#2492	C₂×C₁₃	1	2	yes	complemented
245	#2429	C₂×C₁₃	1	2	yes	complemented
246	#2423	C₂×C₁₃	1	2	yes	complemented
247	#2329	C₂×C₁₃	1	2	yes	complemented
248	#2312	C₂×C₁₃	1	2	yes	—
249	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
250	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
251	C₂³×C₁₃	—	2	1	no	—
252	C₂³×C₁₃	—	2	1	no	—
253	C₂³×C₁₃	—	2	1	no	—
254	C₂³×C₁₃	—	2	1	no	—
255	C₂³×C₁₃	—	2	8	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	4	4	no	—
263	C₂³×C₁₃	—	4	4	no	—
264	C₂³×C₁₃	—	4	4	no	—
265	C₂³×C₁₃	—	4	4	no	—
266	C₂³×C₁₃	—	4	4	no	—
267	C₂³×C₁₃	—	4	4	no	—
268	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
269	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
270	C₂³×C₁₃	C₂×#41	1	2	yes	—
271	C₂³×C₁₃	C₂×#41	1	2	yes	—
272	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
273	Q₈×C₁₃	—	4	8	no	—
274	Q₈×C₁₃	—	8	4	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	8	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	2	4	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	4	4	no	—
307	C₂×C₄×C₁₃	—	4	4	no	—
308	C₂×C₄×C₁₃	—	4	4	no	—
309	C₂×C₄×C₁₃	—	4	8	no	—
310	C₂×C₄×C₁₃	—	4	4	no	—
311	C₂×C₄×C₁₃	—	4	4	no	—
312	C₂×C₄×C₁₃	—	4	8	no	—
313	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
314	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
316	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
320	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
321	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
322	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
324	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
327	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
328	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
329	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
330	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
333	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
334	#400	C₂²×C₁₃	1	4	yes	complemented
335	#400	C₂²×C₁₃	1	4	yes	complemented
336	#399	C₂²×C₁₃	1	4	yes	—
337	#398	C₂²×C₁₃	1	4	yes	complemented
338	#398	C₂²×C₁₃	1	4	yes	complemented
339	#396	C₂²×C₁₃	1	4	yes	—
340	#396	C₂²×C₁₃	1	4	yes	—
341	#393	C₂²×C₁₃	1	4	yes	—
342	#391	C₂²×C₁₃	1	4	yes	complemented
343	#391	C₂²×C₁₃	1	2	yes	complemented
344	#391	C₂²×C₁₃	1	2	yes	complemented
345	#391	C₂²×C₁₃	1	2	yes	complemented
346	#389	C₂²×C₁₃	1	4	yes	complemented
347	#389	C₂²×C₁₃	1	2	yes	complemented
348	#389	C₂²×C₁₃	1	2	yes	complemented
349	#389	C₂²×C₁₃	1	2	yes	complemented
350	#389	C₂²×C₁₃	1	2	yes	complemented
351	#389	C₂²×C₁₃	1	2	yes	complemented
352	#388	C₂²×C₁₃	1	4	yes	—
353	#388	C₂²×C₁₃	1	4	yes	—
354	#388	C₂²×C₁₃	1	4	yes	—
355	#388	C₂²×C₁₃	1	4	yes	—
356	#387	C₂²×C₁₃	1	4	yes	complemented
357	#387	C₂²×C₁₃	1	4	yes	complemented
358	#387	C₂²×C₁₃	1	4	yes	complemented
359	#385	C₂²×C₁₃	1	4	yes	—
360	#385	C₂²×C₁₃	1	4	yes	—
361	#385	C₂²×C₁₃	1	4	yes	—
362	#385	C₂²×C₁₃	1	4	yes	—
363	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
364	#384	C₂²×C₁₃	1	1	yes	characteristic, complemented
365	#380	C₂²×C₁₃	1	2	yes	—
366	#380	C₂²×C₁₃	1	2	yes	—
367	#380	C₂²×C₁₃	1	2	yes	—
368	#380	C₂²×C₁₃	1	2	yes	—
369	#380	C₂²×C₁₃	1	2	yes	—
370	#380	C₂²×C₁₃	1	2	yes	—
371	#379	C₂²×C₁₃	1	4	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
374	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
375	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
377	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
380	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	2	no	—
383	C₂²×C₁₃	—	2	2	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	2	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	4	no	—
388	C₂²×C₁₃	—	2	4	no	—
389	C₂²×C₁₃	—	2	4	no	—
390	C₂²×C₁₃	—	4	16	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	—	4	2	no	—
395	C₂²×C₁₃	#533	1	4	yes	—
396	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
397	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
399	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×C₁₃	#585	1	1	yes	characteristic
402	C₂²×C₁₃	#585	1	1	yes	characteristic
403	C₄×C₁₃	—	2	2	no	—
404	C₄×C₁₃	—	2	4	no	—
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	—	2	2	no	—
407	C₄×C₁₃	—	2	2	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	4	2	no	—
410	C₄×C₁₃	—	4	4	no	—
411	C₄×C₁₃	—	4	4	no	—
412	C₄×C₁₃	—	4	4	no	—
413	C₄×C₁₃	—	4	4	no	—
414	C₄×C₁₃	—	4	2	no	—
415	C₄×C₁₃	#538	1	4	yes	—
416	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
418	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
419	C₂³×C₄	—	2	4	no	—
420	C₂³×C₄	—	4	2	no	—
421	C₂³×C₄	—	4	2	no	—
422	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
423	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
427	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₄⋊Q₈	—	4	2	no	—
431	C₄⋊Q₈	—	4	2	no	—
432	C₂²⋊Q₈	—	2	8	no	—
433	C₂²⋊Q₈	—	2	8	no	—
434	C₂²⋊Q₈	—	4	4	no	—
435	C₂²⋊Q₈	—	4	4	no	—
436	C₄×Q₈	—	4	4	no	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
453	C₂×C₂²⋊C₄	—	2	4	no	—
454	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄²	—	4	2	no	—
466	C₂×C₄²	—	4	2	no	—
467	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
471	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
475	#95	C₂³×C₁₃	1	2	yes	—
476	#95	C₂³×C₁₃	1	2	yes	—
477	#95	C₂³×C₁₃	1	2	yes	—
478	#95	C₂³×C₁₃	1	2	yes	—
479	#95	C₂³×C₁₃	1	4	yes	—
480	#95	C₂³×C₁₃	1	4	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	4	yes	—
484	#95	C₂³×C₁₃	1	4	yes	—
485	#95	C₂³×C₁₃	1	4	yes	—
486	#95	C₂³×C₁₃	1	4	yes	—
487	#95	C₂³×C₁₃	1	4	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	C₂×C₁₃	—	2	4	no	—
490	C₂×C₁₃	—	4	4	no	—
491	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
492	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
493	C₂×C₁₃	#3455	1	1	yes	characteristic
494	C₂×C₁₃	#3501	1	1	yes	characteristic
495	C₂×C₁₃	#3501	1	1	yes	characteristic
496	C₂×C₁₃	#3505	1	1	yes	characteristic
497	C₂×C₁₃	#3506	1	1	yes	characteristic
498	C₂⁴	—	2	2	no	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	4	1	no	—
501	C₂⁴	—	4	1	no	—
502	C₂⁴	—	4	1	no	—
503	C₂⁴	—	4	1	no	—
504	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
505	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
506	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
507	C₂×Q₈	—	2	4	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	1	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	16	no	—
534	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
535	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
536	C₂²×C₄	C₁₃×#41	1	4	yes	—
537	C₂²×C₄	C₁₃×#41	1	4	yes	—
538	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
541	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	8	no	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	4	4	no	—
558	C₄⋊C₄	—	4	4	no	—
559	C₄⋊C₄	—	4	4	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₄⋊C₄	—	4	2	no	—
562	C₄⋊C₄	—	4	2	no	—
563	C₄⋊C₄	—	4	2	no	—
564	C₄⋊C₄	—	4	2	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	4	no	—
567	C₂²⋊C₄	—	2	8	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	2	4	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	4	4	no	—
572	C₂²⋊C₄	—	4	4	no	—
573	C₂²⋊C₄	—	4	4	no	—
574	C₂²⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
576	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
577	C₄²	—	2	4	no	—
578	C₄²	—	2	2	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	4	2	no	—
581	C₄²	—	4	1	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	4	no	—
584	C₄²	—	4	4	no	—
585	C₁₃	#35014	1	1	yes	characteristic, direct product factor, Sylow
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	8	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	4	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
604	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
605	C₂³	C₂×C₁₃×#41	1	2	yes	—
606	C₂³	C₂×C₁₃×#41	1	2	yes	—
607	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
608	Q₈	—	4	8	no	—
609	Q₈	—	8	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
649	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
650	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
651	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
652	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
653	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
654	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
655	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
656	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	4	16	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	C₁₃×#533	1	4	yes	—
672	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
673	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
674	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
675	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂²	C₁₃×#585	1	1	yes	characteristic
678	C₂²	C₁₃×#585	1	1	yes	characteristic
679	C₄	—	2	2	no	—
680	C₄	—	2	4	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	4	4	no	—
687	C₄	—	4	4	no	—
688	C₄	—	4	4	no	—
689	C₄	—	4	4	no	—
690	C₄	—	4	2	no	—
691	C₄	C₁₃×#538	1	4	yes	—
692	C₂	—	2	4	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
695	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
696	C₂	C₁₃×#3455	1	1	yes	characteristic
697	C₂	C₁₃×#3501	1	1	yes	characteristic
698	C₂	C₁₃×#3501	1	1	yes	characteristic
699	C₂	C₁₃×#3505	1	1	yes	characteristic
700	C₂	C₁₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2857	C₂	semidirect
2. C₁₃×#2857	C₂	semidirect
4. C₁₃×#2646	C₂	semidirect
6. C₁₃×#2589	C₂	semidirect
7. C₁₃×#2587	C₂	semidirect
8. C₁₃×#2497	C₂	semidirect
9. C₁₃×#2492	C₂	semidirect
10. C₁₃×#2429	C₂	semidirect
11. C₁₃×#2423	C₂	semidirect
12. C₁₃×#2329	C₂	semidirect
14. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₁₃×#400	C₂²	semidirect
29. C₁₃×#400	C₂²	semidirect
31. C₁₃×#398	C₂²	semidirect
32. C₁₃×#398	C₂²	semidirect
36. C₁₃×#391	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#391	C₂²	semidirect
39. C₁₃×#391	C₂²	semidirect
40. C₁₃×#389	C₂²	semidirect
41. C₁₃×#389	C₂²	semidirect
42. C₁₃×#389	C₂²	semidirect
43. C₁₃×#389	C₂²	semidirect
44. C₁₃×#389	C₂²	semidirect
45. C₁₃×#389	C₂²	semidirect
50. C₁₃×#387	C₂²	semidirect
51. C₁₃×#387	C₂²	semidirect
52. C₁₃×#387	C₂²	semidirect
57. C₁₃×#384	C₂²	semidirect
58. C₁₃×#384	C₂²	semidirect
66. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
67. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
113. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
148. #35014	C₁₃	direct (N × H)
236. #2857	C₂×C₁₃	semidirect
237. #2857	C₂×C₁₃	semidirect
239. #2646	C₂×C₁₃	semidirect
241. #2589	C₂×C₁₃	semidirect
242. #2587	C₂×C₁₃	semidirect
243. #2497	C₂×C₁₃	semidirect
244. #2492	C₂×C₁₃	semidirect
245. #2429	C₂×C₁₃	semidirect
246. #2423	C₂×C₁₃	semidirect
247. #2329	C₂×C₁₃	semidirect
249. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
323. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
324. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
329. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
334. #400	C₂²×C₁₃	semidirect
335. #400	C₂²×C₁₃	semidirect
337. #398	C₂²×C₁₃	semidirect
338. #398	C₂²×C₁₃	semidirect
342. #391	C₂²×C₁₃	semidirect
343. #391	C₂²×C₁₃	semidirect
344. #391	C₂²×C₁₃	semidirect
345. #391	C₂²×C₁₃	semidirect
346. #389	C₂²×C₁₃	semidirect
347. #389	C₂²×C₁₃	semidirect
348. #389	C₂²×C₁₃	semidirect
349. #389	C₂²×C₁₃	semidirect
350. #389	C₂²×C₁₃	semidirect
351. #389	C₂²×C₁₃	semidirect
356. #387	C₂²×C₁₃	semidirect
357. #387	C₂²×C₁₃	semidirect
358. #387	C₂²×C₁₃	semidirect
363. #384	C₂²×C₁₃	semidirect
364. #384	C₂²×C₁₃	semidirect
372. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
373. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
454. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
585. C₁₃	#35014	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×#2857	2
C₁₃×#2848	2
C₁₃×#2646	2
C₁₃×#2626	2
C₁₃×#2589	2
C₁₃×#2587	2
C₁₃×#2497	2
C₁₃×#2492	2
C₁₃×#2429	2
C₁₃×#2423	2
C₁₃×#2329	2
C₁₃×#2312	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35014	13

Subgroups — C13×#35014 #15721353

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35014 #15721353