Subgroups — C₁₃×#34739 #15721078

Order 3328.

2598 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2442	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2441	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2440	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2439	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2438	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2437	C₂	1	4	yes	maximal
9	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic
15	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#533	—	2	8	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#117	—	2	8	no	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₁₃×#117	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
37	C₁₃×#400	C₂²	1	4	yes	complemented
38	C₁₃×#399	C₂²	1	4	yes	—
39	C₁₃×#398	C₂²	1	4	yes	complemented
40	C₁₃×#398	C₂²	1	4	yes	complemented
41	C₁₃×#396	C₂²	1	4	yes	—
42	C₁₃×#396	C₂²	1	4	yes	—
43	C₁₃×#395	C₂²	1	4	yes	complemented
44	C₁₃×#393	C₂²	1	4	yes	—
45	C₁₃×#391	C₂²	1	4	yes	complemented
46	C₁₃×#389	C₂²	1	2	yes	complemented
47	C₁₃×#389	C₂²	1	2	yes	complemented
48	C₁₃×#389	C₂²	1	2	yes	complemented
49	C₁₃×#389	C₂²	1	2	yes	complemented
50	C₁₃×#389	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	2	yes	complemented
58	C₁₃×#382	C₂²	1	2	yes	complemented
59	C₁₃×#381	C₂²	1	2	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	4	yes	—
63	C₁₃×#380	C₂²	1	4	yes	—
64	C₁₃×#379	C₂²	1	2	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	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	1	yes	characteristic
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
72	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
73	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
74	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
75	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
76	C₂×C₁₃×#95	C₂²	1	2	yes	—
77	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	—	2	4	no	—
80	C₂³×C₄×C₁₃	—	2	4	no	—
81	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	—	2	8	no	—
92	C₁₃×#125	—	2	8	no	—
93	C₁₃×C₂²⋊Q₈	—	2	16	no	—
94	C₁₃×C₂²⋊Q₈	—	2	16	no	—
95	C₄×Q₈×C₁₃	—	2	16	no	—
96	C₁₃×#117	—	2	4	no	—
97	C₁₃×#117	—	2	4	no	—
98	C₁₃×#117	—	2	4	no	—
99	C₁₃×#117	—	2	8	no	—
100	C₁₃×#117	—	2	8	no	—
101	C₁₃×#117	—	2	8	no	—
102	C₁₃×#117	D₄	1	8	yes	—
103	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	—	2	4	no	—
132	C₂×C₄²×C₁₃	—	2	4	no	—
133	C₂×C₄²×C₁₃	—	2	8	no	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
145	C₁₃×#95	C₂³	1	2	yes	—
146	C₁₃×#95	C₂³	1	2	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	4	yes	—
152	C₁₃×#95	C₂³	1	4	yes	—
153	C₁₃×#95	C₂³	1	4	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	#34739	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂⁴×C₁₃	—	2	2	no	—
159	C₂⁴×C₁₃	—	2	4	no	—
160	C₂⁴×C₁₃	—	2	2	no	—
161	C₂⁴×C₁₃	—	4	2	no	—
162	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
163	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×Q₈×C₁₃	—	2	8	no	—
167	C₂×Q₈×C₁₃	—	2	8	no	—
168	C₂×Q₈×C₁₃	—	4	4	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	32	no	—
172	C₂²×C₄×C₁₃	—	2	2	no	—
173	C₂²×C₄×C₁₃	—	2	2	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	2	2	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	2	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	8	no	—
183	C₂²×C₄×C₁₃	—	2	8	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	4	2	no	—
187	C₂²×C₄×C₁₃	—	4	4	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
193	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
195	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
196	C₂²×C₄×C₁₃	#41	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
205	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	—	2	8	no	—
210	C₁₃×C₄⋊C₄	—	2	4	no	—
211	C₁₃×C₄⋊C₄	—	2	4	no	—
212	C₁₃×C₄⋊C₄	—	2	8	no	—
213	C₁₃×C₄⋊C₄	—	2	8	no	—
214	C₁₃×C₄⋊C₄	—	2	8	no	—
215	C₁₃×C₄⋊C₄	—	2	4	no	—
216	C₁₃×C₄⋊C₄	—	2	8	no	—
217	C₁₃×C₄⋊C₄	—	2	8	no	—
218	C₁₃×C₄⋊C₄	—	2	8	no	—
219	C₁₃×C₄⋊C₄	—	4	4	no	—
220	C₁₃×C₄⋊C₄	—	4	4	no	—
221	C₁₃×C₄⋊C₄	—	4	4	no	—
222	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	4	no	—
226	C₁₃×C₂²⋊C₄	—	2	4	no	—
227	C₁₃×C₂²⋊C₄	—	2	8	no	—
228	C₁₃×C₂²⋊C₄	—	2	8	no	—
229	C₁₃×C₂²⋊C₄	—	2	4	no	—
230	C₁₃×C₂²⋊C₄	—	2	4	no	—
231	C₁₃×C₂²⋊C₄	—	4	4	no	—
232	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
233	C₁₃×C₂²⋊C₄	#41	1	8	yes	—
234	C₄²×C₁₃	—	2	8	no	—
235	C₄²×C₁₃	—	2	4	no	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	2	no	—
238	C₄²×C₁₃	—	2	2	no	—
239	C₄²×C₁₃	—	2	4	no	—
240	C₄²×C₁₃	—	2	2	no	—
241	C₄²×C₁₃	—	2	4	no	—
242	C₄²×C₁₃	—	2	2	no	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	C₂×D₄	1	8	yes	—
245	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
246	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
247	#2442	C₂×C₁₃	1	2	yes	complemented
248	#2441	C₂×C₁₃	1	2	yes	complemented
249	#2440	C₂×C₁₃	1	2	yes	complemented
250	#2439	C₂×C₁₃	1	2	yes	complemented
251	#2438	C₂×C₁₃	1	4	yes	complemented
252	#2437	C₂×C₁₃	1	4	yes	—
253	#2396	C₂×C₁₃	1	4	yes	complemented
254	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
255	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
256	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
257	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#2280	C₂×C₁₃	1	1	yes	characteristic
259	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
260	C₂³×C₁₃	—	2	1	no	—
261	C₂³×C₁₃	—	2	1	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	8	no	—
266	C₂³×C₁₃	—	2	8	no	—
267	C₂³×C₁₃	—	2	1	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	1	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	4	4	no	—
272	C₂³×C₁₃	—	4	8	no	—
273	C₂³×C₁₃	—	4	8	no	—
274	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
276	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
277	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
278	C₂³×C₁₃	C₂×#41	1	2	yes	—
279	C₂³×C₁₃	C₂×#41	1	4	yes	—
280	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
281	Q₈×C₁₃	—	4	16	no	—
282	C₂×C₄×C₁₃	—	2	8	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	4	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	8	no	—
294	C₂×C₄×C₁₃	—	2	8	no	—
295	C₂×C₄×C₁₃	—	2	8	no	—
296	C₂×C₄×C₁₃	—	2	8	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	4	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	4	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	4	no	—
310	C₂×C₄×C₁₃	—	2	2	no	—
311	C₂×C₄×C₁₃	—	2	2	no	—
312	C₂×C₄×C₁₃	—	4	16	no	—
313	C₂×C₄×C₁₃	—	4	8	no	—
314	C₂×C₄×C₁₃	—	4	8	no	—
315	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
316	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
320	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
323	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
324	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
325	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
326	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
327	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
328	#533	—	2	8	no	—
329	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
330	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
331	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
332	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
333	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
334	C₂×#117	—	2	8	no	—
335	C₂×#117	C₂²×C₁₃	1	2	yes	—
336	C₂×#117	C₂²×C₁₃	1	2	yes	—
337	C₂×#117	C₂²×C₁₃	1	2	yes	—
338	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
344	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
345	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
346	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
348	#400	C₂²×C₁₃	1	4	yes	complemented
349	#399	C₂²×C₁₃	1	4	yes	—
350	#398	C₂²×C₁₃	1	4	yes	complemented
351	#398	C₂²×C₁₃	1	4	yes	complemented
352	#396	C₂²×C₁₃	1	4	yes	—
353	#396	C₂²×C₁₃	1	4	yes	—
354	#395	C₂²×C₁₃	1	4	yes	complemented
355	#393	C₂²×C₁₃	1	4	yes	—
356	#391	C₂²×C₁₃	1	4	yes	complemented
357	#389	C₂²×C₁₃	1	4	yes	complemented
358	#389	C₂²×C₁₃	1	2	yes	complemented
359	#389	C₂²×C₁₃	1	2	yes	complemented
360	#389	C₂²×C₁₃	1	2	yes	complemented
361	#389	C₂²×C₁₃	1	2	yes	complemented
362	#387	C₂²×C₁₃	1	4	yes	complemented
363	#387	C₂²×C₁₃	1	4	yes	complemented
364	#385	C₂²×C₁₃	1	4	yes	—
365	#385	C₂²×C₁₃	1	4	yes	—
366	#385	C₂²×C₁₃	1	4	yes	—
367	#385	C₂²×C₁₃	1	4	yes	—
368	#384	C₂²×C₁₃	1	2	yes	complemented
369	#382	C₂²×C₁₃	1	2	yes	complemented
370	#381	C₂²×C₁₃	1	2	yes	—
371	#380	C₂²×C₁₃	1	4	yes	—
372	#380	C₂²×C₁₃	1	4	yes	—
373	#380	C₂²×C₁₃	1	2	yes	—
374	#380	C₂²×C₁₃	1	2	yes	—
375	#379	C₂²×C₁₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
379	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
382	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
383	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
385	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
386	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
387	C₂×#95	C₂²×C₁₃	1	2	yes	—
388	C₂²×C₁₃	—	2	2	no	—
389	C₂²×C₁₃	—	2	2	no	—
390	C₂²×C₁₃	—	2	2	no	—
391	C₂²×C₁₃	—	2	2	no	—
392	C₂²×C₁₃	—	2	4	no	—
393	C₂²×C₁₃	—	2	4	no	—
394	C₂²×C₁₃	—	2	4	no	—
395	C₂²×C₁₃	—	2	4	no	—
396	C₂²×C₁₃	—	2	2	no	—
397	C₂²×C₁₃	—	2	2	no	—
398	C₂²×C₁₃	—	2	2	no	—
399	C₂²×C₁₃	—	4	16	no	—
400	C₂²×C₁₃	—	4	2	no	—
401	C₂²×C₁₃	—	4	2	no	—
402	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
403	C₂²×C₁₃	#533	1	4	yes	complemented
404	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
405	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
406	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
407	C₂²×C₁₃	C₂²×#41	1	2	yes	—
408	C₂²×C₁₃	#585	1	2	yes	—
409	C₄×C₁₃	—	2	2	no	—
410	C₄×C₁₃	—	2	2	no	—
411	C₄×C₁₃	—	2	8	no	—
412	C₄×C₁₃	—	2	4	no	—
413	C₄×C₁₃	—	2	4	no	—
414	C₄×C₁₃	—	4	4	no	—
415	C₄×C₁₃	—	4	2	no	—
416	C₄×C₁₃	—	4	4	no	—
417	C₄×C₁₃	—	4	4	no	—
418	C₄×C₁₃	—	4	2	no	—
419	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
420	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
421	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
423	C₂³×C₄	—	2	4	no	—
424	C₂³×C₄	—	2	4	no	—
425	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
426	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
427	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
428	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₄⋊Q₈	—	2	8	no	—
436	#125	—	2	8	no	—
437	C₂²⋊Q₈	—	2	16	no	—
438	C₂²⋊Q₈	—	2	16	no	—
439	C₄×Q₈	—	2	16	no	—
440	#117	—	2	4	no	—
441	#117	—	2	4	no	—
442	#117	—	2	4	no	—
443	#117	—	2	8	no	—
444	#117	—	2	8	no	—
445	#117	—	2	8	no	—
446	#117	D₄×C₁₃	1	8	yes	—
447	C₂×C₄⋊C₄	—	2	8	no	—
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	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₂×C₂²⋊C₄	—	2	8	no	—
463	C₂×C₂²⋊C₄	—	2	8	no	—
464	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂×C₄²	—	2	4	no	—
476	C₂×C₄²	—	2	4	no	—
477	C₂×C₄²	—	2	8	no	—
478	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
479	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
480	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
481	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
483	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
485	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
486	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
489	#95	C₂³×C₁₃	1	2	yes	—
490	#95	C₂³×C₁₃	1	2	yes	—
491	#95	C₂³×C₁₃	1	2	yes	—
492	#95	C₂³×C₁₃	1	2	yes	—
493	#95	C₂³×C₁₃	1	4	yes	—
494	#95	C₂³×C₁₃	1	4	yes	—
495	#95	C₂³×C₁₃	1	4	yes	—
496	#95	C₂³×C₁₃	1	4	yes	—
497	#95	C₂³×C₁₃	1	4	yes	—
498	#95	C₂³×C₁₃	1	4	yes	—
499	#95	C₂³×C₁₃	1	4	yes	—
500	#95	C₂³×C₁₃	1	4	yes	—
501	C₂×C₁₃	—	2	4	no	—
502	C₂×C₁₃	—	2	4	no	—
503	C₂×C₁₃	—	4	2	no	—
504	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
505	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
506	C₂×C₁₃	#3458	1	1	yes	characteristic
507	C₂×C₁₃	D₄×#41	1	2	yes	—
508	C₂×C₁₃	#3475	1	2	yes	—
509	C₂⁴	—	2	2	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	2	2	no	—
512	C₂⁴	—	4	2	no	—
513	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
514	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
515	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
517	C₂×Q₈	—	2	8	no	—
518	C₂×Q₈	—	2	8	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂²×C₄	—	2	2	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	32	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	2	no	—
526	C₂²×C₄	—	2	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	8	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	2	4	no	—
537	C₂²×C₄	—	4	2	no	—
538	C₂²×C₄	—	4	4	no	—
539	C₂²×C₄	—	4	2	no	—
540	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
541	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
542	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
543	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
544	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
545	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
546	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
547	C₂²×C₄	C₁₃×#41	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
550	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
551	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
552	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
553	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
554	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
556	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
560	C₄⋊C₄	—	2	8	no	—
561	C₄⋊C₄	—	2	4	no	—
562	C₄⋊C₄	—	2	4	no	—
563	C₄⋊C₄	—	2	8	no	—
564	C₄⋊C₄	—	2	8	no	—
565	C₄⋊C₄	—	2	8	no	—
566	C₄⋊C₄	—	2	4	no	—
567	C₄⋊C₄	—	2	8	no	—
568	C₄⋊C₄	—	2	8	no	—
569	C₄⋊C₄	—	2	8	no	—
570	C₄⋊C₄	—	4	4	no	—
571	C₄⋊C₄	—	4	4	no	—
572	C₄⋊C₄	—	4	4	no	—
573	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
574	C₂²⋊C₄	—	2	4	no	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	2	8	no	—
579	C₂²⋊C₄	—	2	8	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	4	4	no	—
583	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
584	C₂²⋊C₄	C₁₃×#41	1	8	yes	—
585	C₄²	—	2	8	no	—
586	C₄²	—	2	4	no	—
587	C₄²	—	2	4	no	—
588	C₄²	—	2	2	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	2	2	no	—
592	C₄²	—	2	4	no	—
593	C₄²	—	2	2	no	—
594	C₄²	—	2	4	no	—
595	C₄²	C₂×D₄×C₁₃	1	8	yes	—
596	C₁₃	#34739	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	8	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	1	no	—
605	C₂³	—	2	2	no	—
606	C₂³	—	2	1	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	4	4	no	—
609	C₂³	—	4	8	no	—
610	C₂³	—	4	8	no	—
611	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
612	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
613	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
614	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
615	C₂³	C₂×C₁₃×#41	1	2	yes	—
616	C₂³	C₂×C₁₃×#41	1	4	yes	—
617	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
618	Q₈	—	4	16	no	—
619	C₂×C₄	—	2	8	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	8	no	—
631	C₂×C₄	—	2	8	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	8	no	—
634	C₂×C₄	—	2	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	4	16	no	—
650	C₂×C₄	—	4	8	no	—
651	C₂×C₄	—	4	8	no	—
652	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
653	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
654	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
656	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
657	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
658	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
659	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
660	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
661	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
662	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
663	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	4	no	—
669	C₂²	—	2	4	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	4	16	no	—
676	C₂²	—	4	2	no	—
677	C₂²	—	4	2	no	—
678	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
679	C₂²	C₁₃×#533	1	4	yes	complemented
680	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
681	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
682	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
683	C₂²	C₂²×C₁₃×#41	1	2	yes	—
684	C₂²	C₁₃×#585	1	2	yes	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	8	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	4	4	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
696	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
697	C₂	—	2	4	no	—
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
701	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
702	C₂	C₁₃×#3458	1	1	yes	characteristic
703	C₂	D₄×C₁₃×#41	1	2	yes	—
704	C₂	C₁₃×#3475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#2442	C₂	semidirect
4. C₁₃×#2441	C₂	semidirect
5. C₁₃×#2440	C₂	semidirect
6. C₁₃×#2439	C₂	semidirect
7. C₁₃×#2438	C₂	semidirect
9. C₁₃×#2396	C₂	semidirect
10. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
11. C₁₃×#2296	C₂	semidirect
12. C₁₃×#2296	C₂	semidirect
13. C₁₃×#2285	C₂	semidirect
18. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#400	C₂²	semidirect
39. C₁₃×#398	C₂²	semidirect
40. C₁₃×#398	C₂²	semidirect
43. C₁₃×#395	C₂²	semidirect
45. C₁₃×#391	C₂²	semidirect
46. C₁₃×#389	C₂²	semidirect
47. C₁₃×#389	C₂²	semidirect
48. C₁₃×#389	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#389	C₂²	semidirect
51. C₁₃×#387	C₂²	semidirect
52. C₁₃×#387	C₂²	semidirect
57. C₁₃×#384	C₂²	semidirect
58. C₁₃×#382	C₂²	semidirect
65. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
66. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
67. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
81. C₂³×C₄×C₁₃	Q₈	semidirect
157. #34739	C₁₃	direct (N × H)
245. C₂×#533	C₂×C₁₃	semidirect
247. #2442	C₂×C₁₃	semidirect
248. #2441	C₂×C₁₃	semidirect
249. #2440	C₂×C₁₃	semidirect
250. #2439	C₂×C₁₃	semidirect
251. #2438	C₂×C₁₃	semidirect
253. #2396	C₂×C₁₃	semidirect
254. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
255. #2296	C₂×C₁₃	semidirect
256. #2296	C₂×C₁₃	semidirect
257. #2285	C₂×C₁₃	semidirect
315. C₂×C₄×C₁₃	C₂²⋊Q₈	semidirect
329. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
330. C₂×#125	C₂²×C₁₃	semidirect
333. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
348. #400	C₂²×C₁₃	semidirect
350. #398	C₂²×C₁₃	semidirect
351. #398	C₂²×C₁₃	semidirect
354. #395	C₂²×C₁₃	semidirect
356. #391	C₂²×C₁₃	semidirect
357. #389	C₂²×C₁₃	semidirect
358. #389	C₂²×C₁₃	semidirect
359. #389	C₂²×C₁₃	semidirect
360. #389	C₂²×C₁₃	semidirect
361. #389	C₂²×C₁₃	semidirect
362. #387	C₂²×C₁₃	semidirect
363. #387	C₂²×C₁₃	semidirect
368. #384	C₂²×C₁₃	semidirect
369. #382	C₂²×C₁₃	semidirect
376. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
377. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
378. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
403. C₂²×C₁₃	#533	semidirect
425. C₂³×C₄	Q₈×C₁₃	semidirect
596. C₁₃	#34739	direct (N × H)
652. C₂×C₄	C₁₃×C₂²⋊Q₈	semidirect
679. C₂²	C₁₃×#533	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#533	2
C₂²×C₁₃×#117	2
C₁₃×#2442	2
C₁₃×#2441	2
C₁₃×#2440	2
C₁₃×#2439	2
C₁₃×#2438	2
C₁₃×#2437	2
C₁₃×#2396	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2296	2
C₁₃×#2285	2
C₁₃×#2280	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#34739	13

Subgroups — C13×#34739 #15721078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34739 #15721078