Subgroups — C₁₃×#3513 #13112571

Order 1664.

1152 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#553	C₂	1	2	yes	maximal, complemented
5	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#551	C₂	1	2	yes	maximal, complemented
7	C₁₃×#551	C₂	1	2	yes	maximal, complemented
8	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#546	C₂	1	2	yes	maximal, complemented
12	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#539	C₂	1	2	yes	maximal, complemented
16	C₁₃×#538	C₂	1	2	yes	maximal, complemented
17	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₃×#525	C₂	1	2	yes	maximal, complemented
20	C₂×C₁₃×#123	C₂	1	2	yes	maximal, complemented
21	C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
26	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂³×C₄×C₁₃	C₂²	1	2	yes	complemented
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#126	C₂²	1	2	yes	complemented
36	C₁₃×#126	C₂²	1	2	yes	complemented
37	C₁₃×#126	C₂²	1	2	yes	complemented
38	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#125	C₂²	1	2	yes	complemented
41	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#124	C₂²	1	2	yes	complemented
45	C₁₃×#124	C₂²	1	2	yes	complemented
46	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#123	C₂²	1	1	yes	characteristic
48	C₁₃×#123	C₂²	1	2	yes	—
49	C₁₃×#123	C₂²	1	2	yes	complemented
50	C₁₃×#123	C₂²	1	2	yes	complemented
51	C₁₃×#123	C₂²	1	2	yes	complemented
52	C₁₃×#123	C₂²	1	2	yes	complemented
53	C₁₃×#123	C₂²	1	2	yes	complemented
54	C₁₃×#123	C₂²	1	2	yes	complemented
55	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#123	C₂²	1	2	yes	complemented
57	C₁₃×#123	C₂²	1	2	yes	complemented
58	C₁₃×#123	C₂²	1	2	yes	complemented
59	C₁₃×#123	C₂²	1	2	yes	complemented
60	C₁₃×#123	C₂²	1	2	yes	complemented
61	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
69	C₁₃×#121	C₂²	1	1	yes	characteristic
70	C₁₃×#121	C₂²	1	1	yes	characteristic
71	C₁₃×#121	C₂²	1	2	yes	—
72	C₁₃×#121	C₂²	1	1	yes	characteristic
73	C₁₃×#121	C₂²	1	2	yes	complemented
74	C₁₃×#121	C₂²	1	2	yes	complemented
75	C₁₃×#121	C₂²	1	2	yes	complemented
76	C₁₃×#121	C₂²	1	2	yes	complemented
77	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
78	C₁₃×#121	C₂²	1	2	yes	complemented
79	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
80	C₁₃×#120	C₂²	1	2	yes	—
81	C₁₃×#120	C₂²	1	2	yes	—
82	C₁₃×#120	C₂²	1	2	yes	complemented
83	C₁₃×#120	C₂²	1	2	yes	complemented
84	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
86	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
90	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
93	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
95	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
97	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
99	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
100	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
101	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
102	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
103	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
104	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
106	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
107	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
108	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
110	C₁₃×#117	C₂²	1	2	yes	complemented
111	C₁₃×#117	C₂²	1	2	yes	complemented
112	C₁₃×#117	C₂²	1	2	yes	complemented
113	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
115	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
116	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
118	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
119	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₂⁴×C₁₃	C₂³	1	2	yes	—
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	4	4	no	—
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂×D₄×C₁₃	C₂³	1	2	yes	—
136	C₂×D₄×C₁₃	C₂³	1	2	yes	—
137	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₁₃	C₂³	1	2	yes	—
140	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂×D₄×C₁₃	C₂³	1	2	yes	—
144	C₂×D₄×C₁₃	C₂³	1	2	yes	—
145	C₂×D₄×C₁₃	C₂³	1	2	yes	—
146	C₂×D₄×C₁₃	C₂³	1	2	yes	—
147	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
190	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
194	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
195	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
196	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
212	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
219	C₄²×C₁₃	C₂³	1	1	yes	characteristic
220	C₄²×C₁₃	C₂³	1	1	yes	characteristic
221	C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₄²×C₁₃	C₂³	1	1	yes	characteristic
223	C₄²×C₁₃	C₂³	1	2	yes	—
224	C₄²×C₁₃	C₂³	1	2	yes	—
225	C₄²×C₁₃	C₂³	1	2	yes	—
226	C₄²×C₁₃	C₂³	1	1	yes	characteristic
227	C₄²×C₁₃	C₂³	1	1	yes	characteristic
228	#3513	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	4	2	no	—
233	C₂³×C₁₃	—	4	2	no	—
234	C₂³×C₁₃	—	4	2	no	—
235	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₃	C₂⁴	1	2	yes	—
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂³×C₁₃	C₂⁴	1	2	yes	—
240	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	2	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	4	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	4	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	2	2	no	—
251	D₄×C₁₃	—	2	2	no	—
252	D₄×C₁₃	—	4	2	no	—
253	D₄×C₁₃	—	4	2	no	—
254	D₄×C₁₃	—	4	2	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	4	2	no	—
257	D₄×C₁₃	—	4	2	no	—
258	D₄×C₁₃	#41	1	4	yes	complemented
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	2	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	2	no	—
274	C₂×C₄×C₁₃	—	4	2	no	—
275	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
284	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
288	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
291	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
292	#559	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#553	C₂×C₁₃	1	2	yes	complemented
296	#552	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#551	C₂×C₁₃	1	2	yes	complemented
298	#551	C₂×C₁₃	1	2	yes	complemented
299	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#546	C₂×C₁₃	1	2	yes	complemented
303	D₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#542	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#540	C₂×C₁₃	1	1	yes	characteristic, complemented
306	#539	C₂×C₁₃	1	2	yes	complemented
307	#538	C₂×C₁₃	1	2	yes	complemented
308	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
309	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#525	C₂×C₁₃	1	2	yes	complemented
311	C₂×#123	C₂×C₁₃	1	2	yes	complemented
312	#520	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#518	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	4	8	no	—
332	C₂²×C₁₃	—	8	4	no	—
333	C₂²×C₁₃	C₂×#41	1	4	yes	—
334	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
335	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	1	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	1	no	—
342	C₄×C₁₃	—	2	2	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	1	no	—
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	1	no	—
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	1	no	—
352	C₄×C₁₃	C₂×#41	1	2	yes	—
353	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#41	C₂²×C₁₃	1	2	yes	complemented
355	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×D₄	C₂²×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂²×C₁₃	1	2	yes	complemented
359	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
360	#127	C₂²×C₁₃	1	1	yes	characteristic
361	#126	C₂²×C₁₃	1	2	yes	complemented
362	#126	C₂²×C₁₃	1	1	yes	characteristic, complemented
363	#126	C₂²×C₁₃	1	1	yes	characteristic, complemented
364	#126	C₂²×C₁₃	1	2	yes	complemented
365	#126	C₂²×C₁₃	1	2	yes	complemented
366	#126	C₂²×C₁₃	1	2	yes	complemented
367	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
368	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
369	#125	C₂²×C₁₃	1	2	yes	complemented
370	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
372	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	#124	C₂²×C₁₃	1	2	yes	complemented
374	#124	C₂²×C₁₃	1	2	yes	complemented
375	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
376	#123	C₂²×C₁₃	1	1	yes	characteristic
377	#123	C₂²×C₁₃	1	2	yes	—
378	#123	C₂²×C₁₃	1	2	yes	complemented
379	#123	C₂²×C₁₃	1	2	yes	complemented
380	#123	C₂²×C₁₃	1	2	yes	complemented
381	#123	C₂²×C₁₃	1	2	yes	complemented
382	#123	C₂²×C₁₃	1	2	yes	complemented
383	#123	C₂²×C₁₃	1	2	yes	complemented
384	#123	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	#123	C₂²×C₁₃	1	2	yes	complemented
386	#123	C₂²×C₁₃	1	2	yes	complemented
387	#123	C₂²×C₁₃	1	2	yes	complemented
388	#123	C₂²×C₁₃	1	2	yes	complemented
389	#123	C₂²×C₁₃	1	2	yes	complemented
390	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
391	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
392	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
395	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
396	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
397	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	#121	C₂²×C₁₃	1	1	yes	characteristic
399	#121	C₂²×C₁₃	1	1	yes	characteristic
400	#121	C₂²×C₁₃	1	2	yes	—
401	#121	C₂²×C₁₃	1	1	yes	characteristic
402	#121	C₂²×C₁₃	1	2	yes	complemented
403	#121	C₂²×C₁₃	1	2	yes	complemented
404	#121	C₂²×C₁₃	1	2	yes	complemented
405	#121	C₂²×C₁₃	1	2	yes	complemented
406	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
407	#121	C₂²×C₁₃	1	2	yes	complemented
408	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
409	#120	C₂²×C₁₃	1	2	yes	—
410	#120	C₂²×C₁₃	1	2	yes	—
411	#120	C₂²×C₁₃	1	2	yes	complemented
412	#120	C₂²×C₁₃	1	2	yes	complemented
413	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
414	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
415	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
417	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
418	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
419	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
420	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
421	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
422	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
424	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
425	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
426	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
429	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
430	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
431	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
432	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
433	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
434	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
435	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
436	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
438	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
439	#117	C₂²×C₁₃	1	2	yes	complemented
440	#117	C₂²×C₁₃	1	2	yes	complemented
441	#117	C₂²×C₁₃	1	2	yes	complemented
442	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
443	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
444	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
446	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
447	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
448	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
449	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
450	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
451	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
452	C₂×C₁₃	—	2	2	no	—
453	C₂×C₁₃	—	2	4	no	—
454	C₂×C₁₃	—	4	1	no	—
455	C₂×C₁₃	—	4	2	no	—
456	C₂×C₁₃	—	4	2	no	—
457	C₂×C₁₃	—	4	1	no	—
458	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
459	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₁₃	#585	1	1	yes	characteristic
461	C₂⁴	C₂³×C₁₃	1	2	yes	—
462	C₂⁴	C₂³×C₁₃	1	2	yes	—
463	#41	—	2	4	no	—
464	#41	—	4	4	no	—
465	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
466	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×D₄	C₂³×C₁₃	1	2	yes	—
473	C₂×D₄	C₂³×C₁₃	1	2	yes	—
474	C₂×D₄	C₂³×C₁₃	1	2	yes	—
475	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₁₃	1	2	yes	—
478	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
479	C₂×D₄	C₂³×C₁₃	1	2	yes	—
480	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₂×D₄	C₂³×C₁₃	1	2	yes	—
482	C₂×D₄	C₂³×C₁₃	1	2	yes	—
483	C₂×D₄	C₂³×C₁₃	1	2	yes	—
484	C₂×D₄	C₂³×C₁₃	1	2	yes	—
485	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	—	4	4	no	—
487	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
498	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
501	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
502	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
503	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
508	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
511	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
512	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
530	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
535	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
536	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
539	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
540	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
541	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
547	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
549	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
550	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
552	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
553	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
556	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
557	C₄²	C₂³×C₁₃	1	1	yes	characteristic
558	C₄²	C₂³×C₁₃	1	1	yes	characteristic
559	C₄²	C₂³×C₁₃	1	1	yes	characteristic
560	C₄²	C₂³×C₁₃	1	1	yes	characteristic
561	C₄²	C₂³×C₁₃	1	2	yes	—
562	C₄²	C₂³×C₁₃	1	2	yes	—
563	C₄²	C₂³×C₁₃	1	2	yes	—
564	C₄²	C₂³×C₁₃	1	1	yes	characteristic
565	C₄²	C₂³×C₁₃	1	1	yes	characteristic
566	C₁₃	#3513	1	1	yes	characteristic, direct product factor, Sylow
567	C₂³	—	2	4	no	—
568	C₂³	—	2	4	no	—
569	C₂³	—	2	4	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₂³	C₂⁴×C₁₃	1	2	yes	—
575	C₂³	C₂⁴×C₁₃	1	2	yes	—
576	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
577	C₂³	C₂⁴×C₁₃	1	2	yes	—
578	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
579	Q₈	—	2	2	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	4	1	no	—
582	D₄	—	2	4	no	—
583	D₄	—	2	4	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	4	no	—
587	D₄	—	2	2	no	—
588	D₄	—	2	2	no	—
589	D₄	—	2	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	C₁₃×#41	1	4	yes	complemented
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
616	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
618	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
619	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
626	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
629	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	4	8	no	—
647	C₂²	—	8	4	no	—
648	C₂²	C₂×C₁₃×#41	1	4	yes	—
649	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
650	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	C₂×C₁₃×#41	1	2	yes	—
668	C₂	—	2	2	no	—
669	C₂	—	2	4	no	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	4	1	no	—
674	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
675	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	C₁₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#559	C₂	semidirect
2. C₁₃×#554	C₂	semidirect
3. C₁₃×#553	C₂	semidirect
4. C₁₃×#553	C₂	semidirect
5. C₁₃×#552	C₂	semidirect
6. C₁₃×#551	C₂	semidirect
7. C₁₃×#551	C₂	semidirect
8. C₁₃×#547	C₂	semidirect
9. C₁₃×#546	C₂	semidirect
10. C₁₃×#546	C₂	semidirect
11. C₁₃×#546	C₂	semidirect
12. D₄²×C₁₃	C₂	semidirect
13. C₁₃×#542	C₂	semidirect
14. C₁₃×#540	C₂	semidirect
15. C₁₃×#539	C₂	semidirect
16. C₁₃×#538	C₂	semidirect
17. C₁₃×#529	C₂	semidirect
18. C₁₃×#529	C₂	semidirect
19. C₁₃×#525	C₂	semidirect
20. C₂×C₁₃×#123	C₂	semidirect
21. C₁₃×#520	C₂	semidirect
22. C₁₃×#518	C₂	semidirect
23. C₂×C₄×D₄×C₁₃	C₂	semidirect
25. C₂×C₁₃×#41	C₂²	semidirect
29. C₂³×C₄×C₁₃	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#126	C₂²	semidirect
34. C₁₃×#126	C₂²	semidirect
35. C₁₃×#126	C₂²	semidirect
36. C₁₃×#126	C₂²	semidirect
37. C₁₃×#126	C₂²	semidirect
38. C₁₃×#125	C₂²	semidirect
39. C₁₃×#125	C₂²	semidirect
40. C₁₃×#125	C₂²	semidirect
41. C₁₃×#125	C₂²	semidirect
42. C₁₃×#124	C₂²	semidirect
43. C₁₃×#124	C₂²	semidirect
44. C₁₃×#124	C₂²	semidirect
45. C₁₃×#124	C₂²	semidirect
46. C₁₃×#124	C₂²	semidirect
49. C₁₃×#123	C₂²	semidirect
50. C₁₃×#123	C₂²	semidirect
51. C₁₃×#123	C₂²	semidirect
52. C₁₃×#123	C₂²	semidirect
53. C₁₃×#123	C₂²	semidirect
54. C₁₃×#123	C₂²	semidirect
55. C₁₃×#123	C₂²	semidirect
56. C₁₃×#123	C₂²	semidirect
57. C₁₃×#123	C₂²	semidirect
58. C₁₃×#123	C₂²	semidirect
59. C₁₃×#123	C₂²	semidirect
60. C₁₃×#123	C₂²	semidirect
61. C₁₃×C₂²⋊Q₈	C₂²	semidirect
62. C₁₃×C₂²⋊Q₈	C₂²	semidirect
63. C₁₃×C₂²⋊Q₈	C₂²	semidirect
64. C₁₃×C₂²⋊Q₈	C₂²	semidirect
65. C₁₃×C₂²⋊Q₈	C₂²	semidirect
66. C₁₃×C₂²⋊Q₈	C₂²	semidirect
67. C₁₃×C₂²⋊Q₈	C₂²	semidirect
68. C₁₃×C₂²⋊Q₈	C₂²	semidirect
73. C₁₃×#121	C₂²	semidirect
74. C₁₃×#121	C₂²	semidirect
75. C₁₃×#121	C₂²	semidirect
76. C₁₃×#121	C₂²	semidirect
77. C₁₃×#121	C₂²	semidirect
78. C₁₃×#121	C₂²	semidirect
79. C₁₃×#121	C₂²	semidirect
82. C₁₃×#120	C₂²	semidirect
83. C₁₃×#120	C₂²	semidirect
84. C₄×Q₈×C₁₃	C₂²	semidirect
85. C₄×Q₈×C₁₃	C₂²	semidirect
86. C₄×Q₈×C₁₃	C₂²	semidirect
92. C₄×D₄×C₁₃	C₂²	semidirect
93. C₄×D₄×C₁₃	C₂²	semidirect
94. C₄×D₄×C₁₃	C₂²	semidirect
95. C₄×D₄×C₁₃	C₂²	semidirect
96. C₄×D₄×C₁₃	C₂²	semidirect
97. C₄×D₄×C₁₃	C₂²	semidirect
98. C₄×D₄×C₁₃	C₂²	semidirect
99. C₄×D₄×C₁₃	C₂²	semidirect
100. C₄×D₄×C₁₃	C₂²	semidirect
101. C₄×D₄×C₁₃	C₂²	semidirect
102. C₄×D₄×C₁₃	C₂²	semidirect
103. C₄×D₄×C₁₃	C₂²	semidirect
104. C₄×D₄×C₁₃	C₂²	semidirect
105. C₄×D₄×C₁₃	C₂²	semidirect
106. C₄×D₄×C₁₃	C₂²	semidirect
107. C₁₃×#117	C₂²	semidirect
108. C₁₃×#117	C₂²	semidirect
109. C₁₃×#117	C₂²	semidirect
110. C₁₃×#117	C₂²	semidirect
111. C₁₃×#117	C₂²	semidirect
112. C₁₃×#117	C₂²	semidirect
113. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
114. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
115. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
116. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
117. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
118. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
119. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
120. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
121. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₄²×C₁₃	C₂²	semidirect
228. #3513	C₁₃	direct (N × H)
258. D₄×C₁₃	#41	semidirect
292. #559	C₂×C₁₃	semidirect
293. #554	C₂×C₁₃	semidirect
294. #553	C₂×C₁₃	semidirect
295. #553	C₂×C₁₃	semidirect
296. #552	C₂×C₁₃	semidirect
297. #551	C₂×C₁₃	semidirect
298. #551	C₂×C₁₃	semidirect
299. #547	C₂×C₁₃	semidirect
300. #546	C₂×C₁₃	semidirect
301. #546	C₂×C₁₃	semidirect
302. #546	C₂×C₁₃	semidirect
303. D₄²	C₂×C₁₃	semidirect
304. #542	C₂×C₁₃	semidirect
305. #540	C₂×C₁₃	semidirect
306. #539	C₂×C₁₃	semidirect
307. #538	C₂×C₁₃	semidirect
308. #529	C₂×C₁₃	semidirect
309. #529	C₂×C₁₃	semidirect
310. #525	C₂×C₁₃	semidirect
311. C₂×#123	C₂×C₁₃	semidirect
312. #520	C₂×C₁₃	semidirect
313. #518	C₂×C₁₃	semidirect
314. C₂×C₄×D₄	C₂×C₁₃	semidirect
354. C₂×#41	C₂²×C₁₃	semidirect
358. C₂³×C₄	C₂²×C₁₃	semidirect
359. C₄⋊Q₈	C₂²×C₁₃	semidirect
361. #126	C₂²×C₁₃	semidirect
362. #126	C₂²×C₁₃	semidirect
363. #126	C₂²×C₁₃	semidirect
364. #126	C₂²×C₁₃	semidirect
365. #126	C₂²×C₁₃	semidirect
366. #126	C₂²×C₁₃	semidirect
367. #125	C₂²×C₁₃	semidirect
368. #125	C₂²×C₁₃	semidirect
369. #125	C₂²×C₁₃	semidirect
370. #125	C₂²×C₁₃	semidirect
371. #124	C₂²×C₁₃	semidirect
372. #124	C₂²×C₁₃	semidirect
373. #124	C₂²×C₁₃	semidirect
374. #124	C₂²×C₁₃	semidirect
375. #124	C₂²×C₁₃	semidirect
378. #123	C₂²×C₁₃	semidirect
379. #123	C₂²×C₁₃	semidirect
380. #123	C₂²×C₁₃	semidirect
381. #123	C₂²×C₁₃	semidirect
382. #123	C₂²×C₁₃	semidirect
383. #123	C₂²×C₁₃	semidirect
384. #123	C₂²×C₁₃	semidirect
385. #123	C₂²×C₁₃	semidirect
386. #123	C₂²×C₁₃	semidirect
387. #123	C₂²×C₁₃	semidirect
388. #123	C₂²×C₁₃	semidirect
389. #123	C₂²×C₁₃	semidirect
390. C₂²⋊Q₈	C₂²×C₁₃	semidirect
391. C₂²⋊Q₈	C₂²×C₁₃	semidirect
392. C₂²⋊Q₈	C₂²×C₁₃	semidirect
393. C₂²⋊Q₈	C₂²×C₁₃	semidirect
394. C₂²⋊Q₈	C₂²×C₁₃	semidirect
395. C₂²⋊Q₈	C₂²×C₁₃	semidirect
396. C₂²⋊Q₈	C₂²×C₁₃	semidirect
397. C₂²⋊Q₈	C₂²×C₁₃	semidirect
402. #121	C₂²×C₁₃	semidirect
403. #121	C₂²×C₁₃	semidirect
404. #121	C₂²×C₁₃	semidirect
405. #121	C₂²×C₁₃	semidirect
406. #121	C₂²×C₁₃	semidirect
407. #121	C₂²×C₁₃	semidirect
408. #121	C₂²×C₁₃	semidirect
411. #120	C₂²×C₁₃	semidirect
412. #120	C₂²×C₁₃	semidirect
413. C₄×Q₈	C₂²×C₁₃	semidirect
414. C₄×Q₈	C₂²×C₁₃	semidirect
415. C₄×Q₈	C₂²×C₁₃	semidirect
421. C₄×D₄	C₂²×C₁₃	semidirect
422. C₄×D₄	C₂²×C₁₃	semidirect
423. C₄×D₄	C₂²×C₁₃	semidirect
424. C₄×D₄	C₂²×C₁₃	semidirect
425. C₄×D₄	C₂²×C₁₃	semidirect
426. C₄×D₄	C₂²×C₁₃	semidirect
427. C₄×D₄	C₂²×C₁₃	semidirect
428. C₄×D₄	C₂²×C₁₃	semidirect
429. C₄×D₄	C₂²×C₁₃	semidirect
430. C₄×D₄	C₂²×C₁₃	semidirect
431. C₄×D₄	C₂²×C₁₃	semidirect
432. C₄×D₄	C₂²×C₁₃	semidirect
433. C₄×D₄	C₂²×C₁₃	semidirect
434. C₄×D₄	C₂²×C₁₃	semidirect
435. C₄×D₄	C₂²×C₁₃	semidirect
436. #117	C₂²×C₁₃	semidirect
437. #117	C₂²×C₁₃	semidirect
438. #117	C₂²×C₁₃	semidirect
439. #117	C₂²×C₁₃	semidirect
440. #117	C₂²×C₁₃	semidirect
441. #117	C₂²×C₁₃	semidirect
442. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
443. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
444. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
445. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
446. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
447. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
448. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
449. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
450. C₂×C₂²⋊C₄	C₂²×C₁₃	semidirect
451. C₂×C₄²	C₂²×C₁₃	semidirect
566. C₁₃	#3513	direct (N × H)
596. D₄	C₁₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#559	2
C₁₃×#554	2
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#551	2
C₁₃×#547	2
C₁₃×#546	2
D₄²×C₁₃	2
C₁₃×#542	2
C₁₃×#540	2
C₁₃×#539	2
C₁₃×#538	2
C₁₃×#529	2
C₁₃×#525	2
C₂×C₁₃×#123	2
C₁₃×#520	2
C₁₃×#518	2
C₂×C₄×D₄×C₁₃	2
#3513	13

Subgroups — C13×#3513 #13112571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3513 #13112571