Subgroups — C₁₃×#3562 #13112620

Order 1664.

1050 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#562	C₂	1	2	yes	maximal, complemented
2	C₁₃×#560	C₂	1	2	yes	maximal, complemented
3	C₁₃×#559	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₁₃×#551	C₂	1	2	yes	maximal, complemented
7	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#540	C₂	1	2	yes	maximal, complemented
16	C₁₃×#539	C₂	1	2	yes	maximal, complemented
17	C₁₃×#538	C₂	1	2	yes	maximal, complemented
18	C₁₃×#538	C₂	1	2	yes	maximal, complemented
19	C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
20	C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
21	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₁₃×#127	C₂²	1	1	yes	characteristic
34	C₁₃×#127	C₂²	1	2	yes	complemented
35	C₁₃×#126	C₂²	1	1	yes	characteristic
36	C₁₃×#126	C₂²	1	2	yes	—
37	C₁₃×#126	C₂²	1	2	yes	—
38	C₁₃×#126	C₂²	1	2	yes	complemented
39	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#126	C₂²	1	2	yes	complemented
41	C₁₃×#126	C₂²	1	2	yes	complemented
42	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#125	C₂²	1	2	yes	complemented
45	C₁₃×#125	C₂²	1	2	yes	complemented
46	C₁₃×#124	C₂²	1	1	yes	characteristic
47	C₁₃×#124	C₂²	1	1	yes	characteristic
48	C₁₃×#124	C₂²	1	1	yes	characteristic
49	C₁₃×#124	C₂²	1	1	yes	characteristic
50	C₁₃×#124	C₂²	1	1	yes	characteristic
51	C₁₃×#124	C₂²	1	2	yes	—
52	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×#124	C₂²	1	2	yes	complemented
54	C₁₃×#124	C₂²	1	2	yes	complemented
55	C₁₃×#123	C₂²	1	1	yes	characteristic
56	C₁₃×#123	C₂²	1	2	yes	—
57	C₁₃×#123	C₂²	1	2	yes	—
58	C₁₃×#123	C₂²	1	2	yes	—
59	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#123	C₂²	1	2	yes	complemented
61	C₁₃×#123	C₂²	1	2	yes	complemented
62	C₁₃×#123	C₂²	1	2	yes	complemented
63	C₁₃×#123	C₂²	1	2	yes	complemented
64	C₁₃×#123	C₂²	1	2	yes	complemented
65	C₁₃×#123	C₂²	1	2	yes	complemented
66	C₁₃×#123	C₂²	1	2	yes	complemented
67	C₁₃×#123	C₂²	1	2	yes	complemented
68	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
69	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
70	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
71	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
72	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₁₃×#121	C₂²	1	1	yes	characteristic
78	C₁₃×#121	C₂²	1	1	yes	characteristic
79	C₁₃×#121	C₂²	1	2	yes	—
80	C₁₃×#121	C₂²	1	2	yes	—
81	C₁₃×#121	C₂²	1	2	yes	—
82	C₁₃×#121	C₂²	1	2	yes	—
83	C₁₃×#121	C₂²	1	1	yes	characteristic
84	C₁₃×#121	C₂²	1	2	yes	—
85	C₁₃×#121	C₂²	1	2	yes	—
86	C₁₃×#121	C₂²	1	2	yes	complemented
87	C₁₃×#121	C₂²	1	2	yes	complemented
88	C₁₃×#121	C₂²	1	2	yes	complemented
89	C₁₃×#121	C₂²	1	2	yes	complemented
90	C₁₃×#121	C₂²	1	2	yes	complemented
91	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
92	C₁₃×#121	C₂²	1	2	yes	complemented
93	C₁₃×#121	C₂²	1	2	yes	complemented
94	C₁₃×#120	C₂²	1	2	yes	—
95	C₁₃×#120	C₂²	1	2	yes	—
96	C₁₃×#120	C₂²	1	2	yes	—
97	C₁₃×#120	C₂²	1	2	yes	—
98	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
100	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
101	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
103	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
107	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
109	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
110	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
111	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
112	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
113	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
115	C₁₃×#117	C₂²	1	1	yes	characteristic
116	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
117	C₁₃×#117	C₂²	1	2	yes	complemented
118	C₁₃×#117	C₂²	1	2	yes	complemented
119	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
120	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₁₃×#41	—	4	2	no	—
127	C₁₃×#41	—	4	2	no	—
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	—	4	2	no	—
135	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₁₃	C₂³	1	2	yes	—
141	C₂×D₄×C₁₃	C₂³	1	2	yes	—
142	C₂×D₄×C₁₃	C₂³	1	2	yes	—
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	C₂×D₄×C₁₃	C₂³	1	2	yes	—
149	C₂×D₄×C₁₃	C₂³	1	2	yes	—
150	C₂×D₄×C₁₃	C₂³	1	2	yes	—
151	C₂×D₄×C₁₃	C₂³	1	2	yes	—
152	C₂×D₄×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	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
189	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
191	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
192	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
199	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
203	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
205	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
208	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
217	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
224	C₄²×C₁₃	C₂³	1	2	yes	—
225	C₄²×C₁₃	C₂³	1	1	yes	characteristic
226	C₄²×C₁₃	C₂³	1	2	yes	—
227	C₄²×C₁₃	C₂³	1	2	yes	—
228	#3562	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂³×C₁₃	—	4	2	no	—
230	C₂³×C₁₃	—	4	2	no	—
231	C₂³×C₁₃	—	4	2	no	—
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	2	yes	—
234	C₂³×C₁₃	C₂⁴	1	2	yes	—
235	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂³×C₁₃	C₂⁴	1	2	yes	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	2	2	no	—
241	Q₈×C₁₃	—	4	2	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	D₄×C₁₃	—	2	2	no	—
246	D₄×C₁₃	—	4	2	no	—
247	D₄×C₁₃	—	4	1	no	—
248	D₄×C₁₃	—	4	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	D₄×C₁₃	—	4	2	no	—
251	D₄×C₁₃	—	4	2	no	—
252	D₄×C₁₃	—	4	2	no	—
253	D₄×C₁₃	—	4	1	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	—	4	2	no	—
259	D₄×C₁₃	—	4	2	no	—
260	D₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	2	no	—
270	C₂×C₄×C₁₃	—	4	2	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	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
281	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
285	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
286	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
291	#562	C₂×C₁₃	1	2	yes	complemented
292	#560	C₂×C₁₃	1	2	yes	complemented
293	#559	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#553	C₂×C₁₃	1	2	yes	complemented
296	#551	C₂×C₁₃	1	2	yes	complemented
297	#550	C₂×C₁₃	1	1	yes	characteristic, complemented
298	#548	C₂×C₁₃	1	1	yes	characteristic, complemented
299	#548	C₂×C₁₃	1	1	yes	characteristic, complemented
300	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
302	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
303	#541	C₂×C₁₃	1	1	yes	characteristic, complemented
304	#540	C₂×C₁₃	1	1	yes	characteristic, complemented
305	#540	C₂×C₁₃	1	2	yes	complemented
306	#539	C₂×C₁₃	1	2	yes	complemented
307	#538	C₂×C₁₃	1	2	yes	complemented
308	#538	C₂×C₁₃	1	2	yes	complemented
309	#536	C₂×C₁₃	1	1	yes	characteristic, complemented
310	#535	C₂×C₁₃	1	1	yes	characteristic, complemented
311	#532	C₂×C₁₃	1	1	yes	characteristic, complemented
312	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
313	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	2	2	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	8	4	no	—
333	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	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	1	no	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
351	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
355	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
356	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
357	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
358	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
359	#127	C₂²×C₁₃	1	1	yes	characteristic
360	#127	C₂²×C₁₃	1	1	yes	characteristic
361	#127	C₂²×C₁₃	1	2	yes	complemented
362	#126	C₂²×C₁₃	1	1	yes	characteristic
363	#126	C₂²×C₁₃	1	2	yes	—
364	#126	C₂²×C₁₃	1	2	yes	—
365	#126	C₂²×C₁₃	1	2	yes	complemented
366	#126	C₂²×C₁₃	1	1	yes	characteristic, complemented
367	#126	C₂²×C₁₃	1	2	yes	complemented
368	#126	C₂²×C₁₃	1	2	yes	complemented
369	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
370	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
371	#125	C₂²×C₁₃	1	2	yes	complemented
372	#125	C₂²×C₁₃	1	2	yes	complemented
373	#124	C₂²×C₁₃	1	1	yes	characteristic
374	#124	C₂²×C₁₃	1	1	yes	characteristic
375	#124	C₂²×C₁₃	1	1	yes	characteristic
376	#124	C₂²×C₁₃	1	1	yes	characteristic
377	#124	C₂²×C₁₃	1	1	yes	characteristic
378	#124	C₂²×C₁₃	1	2	yes	—
379	#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	#124	C₂²×C₁₃	1	2	yes	complemented
381	#124	C₂²×C₁₃	1	2	yes	complemented
382	#123	C₂²×C₁₃	1	1	yes	characteristic
383	#123	C₂²×C₁₃	1	2	yes	—
384	#123	C₂²×C₁₃	1	2	yes	—
385	#123	C₂²×C₁₃	1	2	yes	—
386	#123	C₂²×C₁₃	1	1	yes	characteristic, 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	#123	C₂²×C₁₃	1	2	yes	complemented
391	#123	C₂²×C₁₃	1	2	yes	complemented
392	#123	C₂²×C₁₃	1	2	yes	complemented
393	#123	C₂²×C₁₃	1	2	yes	complemented
394	#123	C₂²×C₁₃	1	2	yes	complemented
395	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
396	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
397	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
399	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
400	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
401	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
402	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
403	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
404	#121	C₂²×C₁₃	1	1	yes	characteristic
405	#121	C₂²×C₁₃	1	1	yes	characteristic
406	#121	C₂²×C₁₃	1	2	yes	—
407	#121	C₂²×C₁₃	1	2	yes	—
408	#121	C₂²×C₁₃	1	2	yes	—
409	#121	C₂²×C₁₃	1	2	yes	—
410	#121	C₂²×C₁₃	1	1	yes	characteristic
411	#121	C₂²×C₁₃	1	2	yes	—
412	#121	C₂²×C₁₃	1	2	yes	—
413	#121	C₂²×C₁₃	1	2	yes	complemented
414	#121	C₂²×C₁₃	1	2	yes	complemented
415	#121	C₂²×C₁₃	1	2	yes	complemented
416	#121	C₂²×C₁₃	1	2	yes	complemented
417	#121	C₂²×C₁₃	1	2	yes	complemented
418	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
419	#121	C₂²×C₁₃	1	2	yes	complemented
420	#121	C₂²×C₁₃	1	2	yes	complemented
421	#120	C₂²×C₁₃	1	2	yes	—
422	#120	C₂²×C₁₃	1	2	yes	—
423	#120	C₂²×C₁₃	1	2	yes	—
424	#120	C₂²×C₁₃	1	2	yes	—
425	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
426	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
427	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
428	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
430	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
431	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
432	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
433	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
434	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
435	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
436	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
437	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
438	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
439	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
440	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
441	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
442	#117	C₂²×C₁₃	1	1	yes	characteristic
443	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
444	#117	C₂²×C₁₃	1	2	yes	complemented
445	#117	C₂²×C₁₃	1	2	yes	complemented
446	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
447	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
449	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
450	C₂×C₁₃	—	4	1	no	—
451	C₂×C₁₃	—	4	1	no	—
452	C₂×C₁₃	—	4	2	no	—
453	C₂×C₁₃	—	4	2	no	—
454	C₂×C₁₃	—	4	2	no	—
455	C₂×C₁₃	—	4	1	no	—
456	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₁₃	#585	1	1	yes	characteristic
458	C₂×C₁₃	#585	1	1	yes	characteristic
459	C₂⁴	C₂³×C₁₃	1	2	yes	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	#41	—	4	2	no	—
464	C₂×Q₈	—	4	2	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	1	yes	characteristic
468	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
475	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×D₄	C₂³×C₁₃	1	2	yes	—
477	C₂×D₄	C₂³×C₁₃	1	2	yes	—
478	C₂×D₄	C₂³×C₁₃	1	2	yes	—
479	C₂×D₄	C₂³×C₁₃	1	2	yes	—
480	C₂×D₄	C₂³×C₁₃	1	2	yes	—
481	C₂×D₄	C₂³×C₁₃	1	2	yes	—
482	C₂×D₄	C₂³×C₁₃	1	2	yes	—
483	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
484	C₂×D₄	C₂³×C₁₃	1	2	yes	—
485	C₂×D₄	C₂³×C₁₃	1	2	yes	—
486	C₂×D₄	C₂³×C₁₃	1	2	yes	—
487	C₂×D₄	C₂³×C₁₃	1	2	yes	—
488	C₂×D₄	C₂³×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
504	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
510	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
523	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
526	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
527	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
533	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
537	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
538	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
539	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
540	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
541	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
544	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
545	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
546	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
547	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
548	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
549	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
550	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
551	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
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	C₄²	C₂³×C₁₃	1	1	yes	characteristic
556	C₄²	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	2	yes	—
561	C₄²	C₂³×C₁₃	1	1	yes	characteristic
562	C₄²	C₂³×C₁₃	1	2	yes	—
563	C₄²	C₂³×C₁₃	1	2	yes	—
564	C₁₃	#3562	1	1	yes	characteristic, direct product factor, Sylow
565	C₂³	—	4	2	no	—
566	C₂³	—	4	2	no	—
567	C₂³	—	4	2	no	—
568	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
569	C₂³	C₂⁴×C₁₃	1	2	yes	—
570	C₂³	C₂⁴×C₁₃	1	2	yes	—
571	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂³	C₂⁴×C₁₃	1	2	yes	—
574	Q₈	—	2	2	no	—
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	4	2	no	—
578	Q₈	—	4	1	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	2	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	1	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	2	no	—
610	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
613	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
615	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
616	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
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	2	yes	—
621	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
622	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
623	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
624	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
626	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	8	4	no	—
646	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	1	no	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
671	C₂	C₁₃×#585	1	1	yes	characteristic
672	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×#562	C₂	semidirect
2. C₁₃×#560	C₂	semidirect
3. C₁₃×#559	C₂	semidirect
4. C₁₃×#556	C₂	semidirect
5. C₁₃×#553	C₂	semidirect
6. C₁₃×#551	C₂	semidirect
7. C₁₃×#550	C₂	semidirect
8. C₁₃×#548	C₂	semidirect
9. C₁₃×#548	C₂	semidirect
10. C₁₃×#547	C₂	semidirect
11. C₁₃×#546	C₂	semidirect
12. C₁₃×#546	C₂	semidirect
13. C₁₃×#541	C₂	semidirect
14. C₁₃×#540	C₂	semidirect
15. C₁₃×#540	C₂	semidirect
16. C₁₃×#539	C₂	semidirect
17. C₁₃×#538	C₂	semidirect
18. C₁₃×#538	C₂	semidirect
19. C₁₃×#536	C₂	semidirect
20. C₁₃×#535	C₂	semidirect
21. C₁₃×#532	C₂	semidirect
22. C₁₃×#529	C₂	semidirect
23. C₁₃×#529	C₂	semidirect
27. C₂×C₁₃×#41	C₂²	semidirect
28. C₂²×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#127	C₂²	semidirect
38. C₁₃×#126	C₂²	semidirect
39. C₁₃×#126	C₂²	semidirect
40. C₁₃×#126	C₂²	semidirect
41. C₁₃×#126	C₂²	semidirect
42. C₁₃×#125	C₂²	semidirect
43. C₁₃×#125	C₂²	semidirect
44. C₁₃×#125	C₂²	semidirect
45. C₁₃×#125	C₂²	semidirect
52. C₁₃×#124	C₂²	semidirect
53. C₁₃×#124	C₂²	semidirect
54. C₁₃×#124	C₂²	semidirect
59. C₁₃×#123	C₂²	semidirect
60. C₁₃×#123	C₂²	semidirect
61. C₁₃×#123	C₂²	semidirect
62. C₁₃×#123	C₂²	semidirect
63. C₁₃×#123	C₂²	semidirect
64. C₁₃×#123	C₂²	semidirect
65. C₁₃×#123	C₂²	semidirect
66. C₁₃×#123	C₂²	semidirect
67. C₁₃×#123	C₂²	semidirect
70. C₁₃×C₂²⋊Q₈	C₂²	semidirect
71. C₁₃×C₂²⋊Q₈	C₂²	semidirect
72. C₁₃×C₂²⋊Q₈	C₂²	semidirect
73. C₁₃×C₂²⋊Q₈	C₂²	semidirect
74. C₁₃×C₂²⋊Q₈	C₂²	semidirect
75. C₁₃×C₂²⋊Q₈	C₂²	semidirect
76. C₁₃×C₂²⋊Q₈	C₂²	semidirect
86. C₁₃×#121	C₂²	semidirect
87. C₁₃×#121	C₂²	semidirect
88. C₁₃×#121	C₂²	semidirect
89. C₁₃×#121	C₂²	semidirect
90. C₁₃×#121	C₂²	semidirect
91. C₁₃×#121	C₂²	semidirect
92. C₁₃×#121	C₂²	semidirect
93. C₁₃×#121	C₂²	semidirect
98. C₄×Q₈×C₁₃	C₂²	semidirect
99. C₄×Q₈×C₁₃	C₂²	semidirect
100. C₄×Q₈×C₁₃	C₂²	semidirect
101. C₄×Q₈×C₁₃	C₂²	semidirect
106. C₄×D₄×C₁₃	C₂²	semidirect
107. C₄×D₄×C₁₃	C₂²	semidirect
108. C₄×D₄×C₁₃	C₂²	semidirect
109. C₄×D₄×C₁₃	C₂²	semidirect
110. C₄×D₄×C₁₃	C₂²	semidirect
111. C₄×D₄×C₁₃	C₂²	semidirect
112. C₄×D₄×C₁₃	C₂²	semidirect
113. C₄×D₄×C₁₃	C₂²	semidirect
114. C₄×D₄×C₁₃	C₂²	semidirect
116. C₁₃×#117	C₂²	semidirect
117. C₁₃×#117	C₂²	semidirect
118. C₁₃×#117	C₂²	semidirect
119. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
122. C₂×C₄²×C₁₃	C₂²	semidirect
228. #3562	C₁₃	direct (N × H)
291. #562	C₂×C₁₃	semidirect
292. #560	C₂×C₁₃	semidirect
293. #559	C₂×C₁₃	semidirect
294. #556	C₂×C₁₃	semidirect
295. #553	C₂×C₁₃	semidirect
296. #551	C₂×C₁₃	semidirect
297. #550	C₂×C₁₃	semidirect
298. #548	C₂×C₁₃	semidirect
299. #548	C₂×C₁₃	semidirect
300. #547	C₂×C₁₃	semidirect
301. #546	C₂×C₁₃	semidirect
302. #546	C₂×C₁₃	semidirect
303. #541	C₂×C₁₃	semidirect
304. #540	C₂×C₁₃	semidirect
305. #540	C₂×C₁₃	semidirect
306. #539	C₂×C₁₃	semidirect
307. #538	C₂×C₁₃	semidirect
308. #538	C₂×C₁₃	semidirect
309. #536	C₂×C₁₃	semidirect
310. #535	C₂×C₁₃	semidirect
311. #532	C₂×C₁₃	semidirect
312. #529	C₂×C₁₃	semidirect
313. #529	C₂×C₁₃	semidirect
354. C₂×#41	C₂²×C₁₃	semidirect
355. C₂²×Q₈	C₂²×C₁₃	semidirect
357. C₄⋊Q₈	C₂²×C₁₃	semidirect
358. C₄⋊Q₈	C₂²×C₁₃	semidirect
361. #127	C₂²×C₁₃	semidirect
365. #126	C₂²×C₁₃	semidirect
366. #126	C₂²×C₁₃	semidirect
367. #126	C₂²×C₁₃	semidirect
368. #126	C₂²×C₁₃	semidirect
369. #125	C₂²×C₁₃	semidirect
370. #125	C₂²×C₁₃	semidirect
371. #125	C₂²×C₁₃	semidirect
372. #125	C₂²×C₁₃	semidirect
379. #124	C₂²×C₁₃	semidirect
380. #124	C₂²×C₁₃	semidirect
381. #124	C₂²×C₁₃	semidirect
386. #123	C₂²×C₁₃	semidirect
387. #123	C₂²×C₁₃	semidirect
388. #123	C₂²×C₁₃	semidirect
389. #123	C₂²×C₁₃	semidirect
390. #123	C₂²×C₁₃	semidirect
391. #123	C₂²×C₁₃	semidirect
392. #123	C₂²×C₁₃	semidirect
393. #123	C₂²×C₁₃	semidirect
394. #123	C₂²×C₁₃	semidirect
397. C₂²⋊Q₈	C₂²×C₁₃	semidirect
398. C₂²⋊Q₈	C₂²×C₁₃	semidirect
399. C₂²⋊Q₈	C₂²×C₁₃	semidirect
400. C₂²⋊Q₈	C₂²×C₁₃	semidirect
401. C₂²⋊Q₈	C₂²×C₁₃	semidirect
402. C₂²⋊Q₈	C₂²×C₁₃	semidirect
403. C₂²⋊Q₈	C₂²×C₁₃	semidirect
413. #121	C₂²×C₁₃	semidirect
414. #121	C₂²×C₁₃	semidirect
415. #121	C₂²×C₁₃	semidirect
416. #121	C₂²×C₁₃	semidirect
417. #121	C₂²×C₁₃	semidirect
418. #121	C₂²×C₁₃	semidirect
419. #121	C₂²×C₁₃	semidirect
420. #121	C₂²×C₁₃	semidirect
425. C₄×Q₈	C₂²×C₁₃	semidirect
426. C₄×Q₈	C₂²×C₁₃	semidirect
427. C₄×Q₈	C₂²×C₁₃	semidirect
428. C₄×Q₈	C₂²×C₁₃	semidirect
433. C₄×D₄	C₂²×C₁₃	semidirect
434. C₄×D₄	C₂²×C₁₃	semidirect
435. C₄×D₄	C₂²×C₁₃	semidirect
436. C₄×D₄	C₂²×C₁₃	semidirect
437. C₄×D₄	C₂²×C₁₃	semidirect
438. C₄×D₄	C₂²×C₁₃	semidirect
439. C₄×D₄	C₂²×C₁₃	semidirect
440. C₄×D₄	C₂²×C₁₃	semidirect
441. C₄×D₄	C₂²×C₁₃	semidirect
443. #117	C₂²×C₁₃	semidirect
444. #117	C₂²×C₁₃	semidirect
445. #117	C₂²×C₁₃	semidirect
446. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
449. C₂×C₄²	C₂²×C₁₃	semidirect
564. C₁₃	#3562	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×#562	2
C₁₃×#560	2
C₁₃×#559	2
C₁₃×#556	2
C₁₃×#553	2
C₁₃×#551	2
C₁₃×#550	2
C₁₃×#548	2
C₁₃×#547	2
C₁₃×#546	2
C₁₃×#541	2
C₁₃×#540	2
C₁₃×#539	2
C₁₃×#538	2
C₁₃×#536	2
C₁₃×#535	2
C₁₃×#532	2
C₁₃×#529	2
#3562	13

Subgroups — C13×#3562 #13112620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3562 #13112620