Subgroups — C₁₃×#34322 #15720661

Order 3328.

2228 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2373	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2367	C₂	1	2	yes	maximal
4	C₁₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2360	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2351	C₂	1	2	yes	maximal, complemented
8	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#2346	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2334	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2323	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₃×#124	C₂	1	2	yes	maximal
14	C₁₃×#2295	C₂	1	2	yes	maximal, complemented
15	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
16	C₁₃×#2274	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#556	C₄	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#126	C₂²	1	4	yes	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	C₂²	1	2	yes	—
32	C₂×C₁₃×#117	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#391	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	4	yes	—
46	C₁₃×#389	C₂²	1	4	yes	—
47	C₁₃×#388	C₂²	1	2	yes	—
48	C₁₃×#388	C₂²	1	2	yes	—
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#388	C₂²	1	4	yes	—
51	C₁₃×#388	C₂²	1	4	yes	—
52	C₁₃×#388	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	4	yes	—
54	C₁₃×#387	C₂²	1	4	yes	—
55	C₁₃×#387	C₂²	1	4	yes	—
56	C₁₃×#387	C₂²	1	4	yes	—
57	C₁₃×#385	C₂²	1	4	yes	—
58	C₁₃×#385	C₂²	1	4	yes	—
59	C₁₃×#384	C₂²	1	1	yes	characteristic
60	C₁₃×#382	C₂²	1	2	yes	—
61	C₁₃×#382	C₂²	1	4	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₁₃×#376	C₂²	1	4	yes	—
82	C₄³×C₁₃	C₂²	1	1	yes	characteristic
83	C₄³×C₁₃	C₂²	1	2	yes	—
84	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
89	C₁₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
90	C₁₃×#126	C₂×C₄	1	32	yes	complemented
91	C₁₃×#124	C₂×C₄	1	16	yes	—
92	C₁₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
93	C₄×Q₈×C₁₃	—	2	4	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	—	4	4	no	—
96	C₄×Q₈×C₁₃	—	4	4	no	—
97	C₄×Q₈×C₁₃	C₂×C₄	1	16	yes	complemented
98	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
99	C₄×D₄×C₁₃	—	4	4	no	—
100	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
101	C₁₃×#117	—	2	8	no	—
102	C₁₃×#117	C₂×C₄	1	16	yes	complemented
103	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	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	1	yes	characteristic
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
144	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
147	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
150	C₁₃×#95	C₂³	1	2	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	2	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	2	yes	—
158	C₁₃×#95	C₂³	1	2	yes	—
159	C₁₃×#95	C₂³	1	2	yes	—
160	C₁₃×#95	C₂³	1	4	yes	—
161	C₁₃×#95	C₂³	1	2	yes	—
162	C₁₃×#95	C₂³	1	4	yes	—
163	C₁₃×#95	C₂³	1	4	yes	—
164	#34322	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
166	C₂×Q₈×C₁₃	—	2	2	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	4	no	—
169	C₂×Q₈×C₁₃	—	2	4	no	—
170	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
171	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	—	2	2	no	—
174	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	8	no	—
178	C₂²×C₄×C₁₃	—	4	4	no	—
179	C₂²×C₄×C₁₃	—	4	4	no	—
180	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	—	2	8	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	2	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	4	2	no	—
208	C₁₃×C₄⋊C₄	—	4	4	no	—
209	C₁₃×C₄⋊C₄	—	4	4	no	—
210	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
211	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
212	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
213	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
214	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
215	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
216	C₁₃×C₄⋊C₄	#41	1	4	yes	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	4	no	—
222	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
223	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
224	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	4	no	—
227	C₄²×C₁₃	—	2	2	no	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	4	no	—
230	C₄²×C₁₃	—	2	2	no	—
231	C₄²×C₁₃	—	2	2	no	—
232	C₄²×C₁₃	—	2	2	no	—
233	C₄²×C₁₃	—	2	4	no	—
234	C₄²×C₁₃	—	4	2	no	—
235	C₄²×C₁₃	—	4	1	no	—
236	C₄²×C₁₃	—	4	4	no	—
237	C₄²×C₁₃	—	4	4	no	—
238	C₄²×C₁₃	—	4	4	no	—
239	C₄²×C₁₃	C₂²×C₄	1	16	yes	—
240	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
241	C₄²×C₁₃	C₂²×C₄	1	8	yes	—
242	C₄²×C₁₃	#41	1	4	yes	—
243	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
244	#2373	C₂×C₁₃	1	4	yes	complemented
245	#2367	C₂×C₁₃	1	2	yes	—
246	#2365	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#2360	C₂×C₁₃	1	2	yes	complemented
248	#2355	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#2351	C₂×C₁₃	1	2	yes	complemented
250	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
251	#2346	C₂×C₁₃	1	2	yes	complemented
252	#2334	C₂×C₁₃	1	4	yes	complemented
253	#2323	C₂×C₁₃	1	2	yes	complemented
254	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₄×#124	C₂×C₁₃	1	2	yes	—
256	#2295	C₂×C₁₃	1	2	yes	complemented
257	#2293	C₂×C₁₃	1	1	yes	characteristic
258	#2274	C₂×C₁₃	1	2	yes	complemented
259	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	2	no	—
265	C₂³×C₁₃	—	2	2	no	—
266	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
267	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
268	Q₈×C₁₃	—	2	8	no	—
269	Q₈×C₁₃	—	2	16	no	—
270	D₄×C₁₃	—	2	8	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	4	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	16	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	2	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	1	no	—
297	C₂×C₄×C₁₃	—	2	2	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	2	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	1	no	—
304	C₂×C₄×C₁₃	—	2	4	no	—
305	C₂×C₄×C₁₃	—	8	8	no	—
306	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
307	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
308	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
309	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
310	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
311	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
312	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
313	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
315	C₂×C₄×C₁₃	C₂×#41	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	H(5,𝔽₂)	1	2	yes	—
319	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
320	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
321	#556	C₄×C₁₃	1	16	yes	complemented
322	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#126	C₂²×C₁₃	1	4	yes	—
324	C₂×#124	C₂²×C₁₃	1	2	yes	—
325	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
326	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
329	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
330	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
331	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
333	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
334	C₂×#117	C₂²×C₁₃	1	2	yes	—
335	C₂×#117	C₂²×C₁₃	1	2	yes	—
336	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
337	#391	C₂²×C₁₃	1	2	yes	—
338	#391	C₂²×C₁₃	1	2	yes	—
339	#391	C₂²×C₁₃	1	2	yes	—
340	#390	C₂²×C₁₃	1	1	yes	characteristic
341	#390	C₂²×C₁₃	1	1	yes	characteristic
342	#389	C₂²×C₁₃	1	2	yes	—
343	#389	C₂²×C₁₃	1	2	yes	—
344	#389	C₂²×C₁₃	1	2	yes	—
345	#389	C₂²×C₁₃	1	4	yes	—
346	#389	C₂²×C₁₃	1	4	yes	—
347	#389	C₂²×C₁₃	1	2	yes	—
348	#389	C₂²×C₁₃	1	1	yes	characteristic
349	#389	C₂²×C₁₃	1	1	yes	characteristic
350	#388	C₂²×C₁₃	1	4	yes	—
351	#388	C₂²×C₁₃	1	4	yes	—
352	#388	C₂²×C₁₃	1	2	yes	—
353	#388	C₂²×C₁₃	1	4	yes	—
354	#388	C₂²×C₁₃	1	4	yes	—
355	#388	C₂²×C₁₃	1	2	yes	—
356	#387	C₂²×C₁₃	1	4	yes	—
357	#387	C₂²×C₁₃	1	4	yes	—
358	#387	C₂²×C₁₃	1	4	yes	—
359	#387	C₂²×C₁₃	1	4	yes	—
360	#385	C₂²×C₁₃	1	4	yes	—
361	#385	C₂²×C₁₃	1	4	yes	—
362	#384	C₂²×C₁₃	1	1	yes	characteristic
363	#382	C₂²×C₁₃	1	4	yes	—
364	#382	C₂²×C₁₃	1	2	yes	—
365	#380	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
372	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
376	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
379	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
380	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
384	#376	C₂²×C₁₃	1	4	yes	—
385	C₄³	C₂²×C₁₃	1	1	yes	characteristic
386	C₄³	C₂²×C₁₃	1	2	yes	—
387	C₂²×C₁₃	—	2	4	no	—
388	C₂²×C₁₃	—	2	4	no	—
389	C₂²×C₁₃	—	2	4	no	—
390	C₂²×C₁₃	—	4	2	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	2	no	—
394	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
395	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
399	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	C₂²×C₁₃	#585	1	1	yes	characteristic
401	C₄×C₁₃	—	2	4	no	—
402	C₄×C₁₃	—	2	4	no	—
403	C₄×C₁₃	—	2	8	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	4	no	—
409	C₄×C₁₃	—	2	2	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	1	no	—
414	C₄×C₁₃	—	4	4	no	—
415	C₄×C₁₃	C₄×#41	1	4	yes	—
416	C₄×C₁₃	#520	1	4	yes	—
417	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
419	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
421	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
422	C₄⋊Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
423	#126	C₂×C₄×C₁₃	1	32	yes	complemented
424	#124	C₂×C₄×C₁₃	1	16	yes	—
425	C₂²⋊Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
426	C₄×Q₈	—	2	4	no	—
427	C₄×Q₈	—	2	4	no	—
428	C₄×Q₈	—	4	4	no	—
429	C₄×Q₈	—	4	4	no	—
430	C₄×Q₈	C₂×C₄×C₁₃	1	16	yes	complemented
431	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
432	C₄×D₄	—	4	4	no	—
433	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
434	#117	—	2	8	no	—
435	#117	C₂×C₄×C₁₃	1	16	yes	complemented
436	C₂×C₄⋊C₄	—	2	8	no	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	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	4	yes	—
465	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
475	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
476	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
479	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
480	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
483	#95	C₂³×C₁₃	1	2	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	2	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	#95	C₂³×C₁₃	1	4	yes	—
491	#95	C₂³×C₁₃	1	2	yes	—
492	#95	C₂³×C₁₃	1	4	yes	—
493	#95	C₂³×C₁₃	1	2	yes	—
494	#95	C₂³×C₁₃	1	2	yes	—
495	#95	C₂³×C₁₃	1	4	yes	—
496	#95	C₂³×C₁₃	1	2	yes	—
497	C₂×C₁₃	—	4	4	no	—
498	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
499	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
500	C₂×C₁₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
501	C₂×C₁₃	#3507	1	1	yes	characteristic
502	C₂×C₁₃	#3511	1	1	yes	characteristic
503	C₂×C₁₃	#3514	1	1	yes	characteristic
504	C₂×C₁₃	#3523	1	1	yes	characteristic
505	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
506	C₂×Q₈	—	2	2	no	—
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
511	C₂×Q₈	C₂²×C₄×C₁₃	1	8	yes	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	—	2	2	no	—
514	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
537	C₄⋊C₄	—	2	8	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	4	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	—	4	4	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
552	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
554	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
555	C₄⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
556	C₄⋊C₄	C₁₃×#41	1	4	yes	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	2	no	—
562	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₁₃	1	8	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₁₃	1	16	yes	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	4	no	—
567	C₄²	—	2	2	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	2	2	no	—
572	C₄²	—	2	2	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	4	4	no	—
575	C₄²	—	4	4	no	—
576	C₄²	—	4	2	no	—
577	C₄²	—	4	1	no	—
578	C₄²	—	4	4	no	—
579	C₄²	C₂²×C₄×C₁₃	1	16	yes	—
580	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
581	C₄²	C₂²×C₄×C₁₃	1	8	yes	—
582	C₄²	C₁₃×#41	1	4	yes	—
583	C₁₃	#34322	1	1	yes	characteristic, direct product factor, Sylow
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	2	no	—
590	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
591	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
592	Q₈	—	2	8	no	—
593	Q₈	—	2	16	no	—
594	D₄	—	2	8	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	4	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	16	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	4	no	—
629	C₂×C₄	—	8	8	no	—
630	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
631	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
632	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
633	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
634	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
635	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
636	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
637	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
638	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
639	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
640	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
641	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
642	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
643	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
644	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	4	2	no	—
652	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
653	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
654	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
655	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²	C₁₃×#585	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	4	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	8	no	—
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	4	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	2	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	4	no	—
673	C₄	C₄×C₁₃×#41	1	4	yes	—
674	C₄	C₁₃×#520	1	4	yes	—
675	C₂	—	4	4	no	—
676	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
677	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
678	C₂	C₄×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
679	C₂	C₁₃×#3507	1	1	yes	characteristic
680	C₂	C₁₃×#3511	1	1	yes	characteristic
681	C₂	C₁₃×#3514	1	1	yes	characteristic
682	C₂	C₁₃×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2373	C₂	semidirect
4. C₁₃×#2365	C₂	semidirect
5. C₁₃×#2360	C₂	semidirect
6. C₁₃×#2355	C₂	semidirect
7. C₁₃×#2351	C₂	semidirect
9. C₁₃×#2346	C₂	semidirect
10. C₁₃×#2334	C₂	semidirect
11. C₁₃×#2323	C₂	semidirect
12. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
14. C₁₃×#2295	C₂	semidirect
16. C₁₃×#2274	C₂	semidirect
17. C₄²×Q₈×C₁₃	C₂	semidirect
18. C₁₃×#556	C₄	semidirect
89. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
90. C₁₃×#126	C₂×C₄	semidirect
92. C₁₃×C₂²⋊Q₈	C₂×C₄	semidirect
97. C₄×Q₈×C₁₃	C₂×C₄	semidirect
98. C₄×Q₈×C₁₃	C₂×C₄	semidirect
102. C₁₃×#117	C₂×C₄	semidirect
164. #34322	C₁₃	direct (N × H)
244. #2373	C₂×C₁₃	semidirect
246. #2365	C₂×C₁₃	semidirect
247. #2360	C₂×C₁₃	semidirect
248. #2355	C₂×C₁₃	semidirect
249. #2351	C₂×C₁₃	semidirect
251. #2346	C₂×C₁₃	semidirect
252. #2334	C₂×C₁₃	semidirect
253. #2323	C₂×C₁₃	semidirect
254. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
256. #2295	C₂×C₁₃	semidirect
258. #2274	C₂×C₁₃	semidirect
259. C₄²×Q₈	C₂×C₁₃	semidirect
321. #556	C₄×C₁₃	semidirect
422. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
423. #126	C₂×C₄×C₁₃	semidirect
425. C₂²⋊Q₈	C₂×C₄×C₁₃	semidirect
430. C₄×Q₈	C₂×C₄×C₁₃	semidirect
431. C₄×Q₈	C₂×C₄×C₁₃	semidirect
435. #117	C₂×C₄×C₁₃	semidirect
583. C₁₃	#34322	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#556	2
C₁₃×#2373	2
C₁₃×#2367	2
C₁₃×#2365	2
C₁₃×#2360	2
C₁₃×#2355	2
C₁₃×#2351	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2346	2
C₁₃×#2334	2
C₁₃×#2323	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#124	2
C₁₃×#2295	2
C₁₃×#2293	2
C₁₃×#2274	2
C₄²×Q₈×C₁₃	2
#34322	13

Subgroups — C13×#34322 #15720661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34322 #15720661