Subgroups — C₁₃×#60806 #15747145

Order 3328.

2222 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3220	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3005	C₂	1	2	yes	maximal, complemented
13	C₁₃×#3003	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₁₃×#542	C₂²	1	4	yes	complemented
22	C₁₃×#541	C₂²	1	2	yes	complemented
23	C₁₃×#540	C₂²	1	2	yes	complemented
24	C₁₃×#539	—	2	2	no	—
25	C₁₃×#538	—	2	2	no	—
26	C₁₃×#535	—	2	4	no	—
27	C₁₃×#535	C₂²	1	4	yes	—
28	C₁₃×#535	C₂²	1	4	yes	—
29	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₁₃×#529	—	2	4	no	—
34	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
36	C₁₃×#525	C₂²	1	2	yes	—
37	C₂×C₁₃×#121	—	2	2	no	—
38	C₂×C₁₃×#120	—	2	2	no	—
39	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
41	C₁₃×#497	C₂²	1	2	yes	complemented
42	C₁₃×#496	C₂²	1	2	yes	complemented
43	C₁₃×#496	C₂²	1	4	yes	complemented
44	C₁₃×#495	C₂²	1	4	yes	complemented
45	C₁₃×#493	C₂²	1	2	yes	complemented
46	C₁₃×#492	C₂²	1	2	yes	complemented
47	C₁₃×#490	C₂²	1	4	yes	complemented
48	C₁₃×#489	C₂²	1	4	yes	complemented
49	C₁₃×#488	C₂²	1	4	yes	complemented
50	C₁₃×#486	C₂²	1	4	yes	complemented
51	C₁₃×#464	C₂²	1	8	yes	complemented
52	C₁₃×#463	C₂²	1	8	yes	complemented
53	C₁₃×#460	C₂²	1	8	yes	complemented
54	C₁₃×#459	C₂²	1	8	yes	complemented
55	C₁₃×#452	C₂²	1	8	yes	complemented
56	C₁₃×#450	C₂²	1	8	yes	complemented
57	C₁₃×#449	C₂²	1	8	yes	complemented
58	C₁₃×#447	C₂²	1	8	yes	complemented
59	C₁₃×#433	C₂²	1	4	yes	complemented
60	C₁₃×#433	C₂²	1	4	yes	complemented
61	C₁₃×#423	C₂²	1	2	yes	complemented
62	C₁₃×#419	C₂²	1	2	yes	complemented
63	C₁₃×#418	C₂²	1	2	yes	—
64	C₁₃×#418	C₂²	1	2	yes	—
65	C₁₃×#418	C₂²	1	2	yes	complemented
66	C₁₃×#407	C₂²	1	2	yes	—
67	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₁₃	—	2	1	no	—
70	C₂×C₁₃×#41	—	2	2	no	—
71	C₂×C₁₃×#41	—	4	4	no	—
72	C₂×C₁₃×#41	C₂³	1	2	yes	—
73	C₂×C₁₃×#41	C₂³	1	4	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₁₃	—	2	1	no	—
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	2	no	—
78	C₂²×D₄×C₁₃	—	2	2	no	—
79	C₂²×D₄×C₁₃	—	2	2	no	—
80	C₂²×D₄×C₁₃	—	4	4	no	—
81	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	—	2	1	no	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#137	—	4	4	no	—
88	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
89	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
90	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
91	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
95	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	complemented
96	C₂×C₁₃×D₈	C₂³	1	4	yes	—
97	C₂×C₁₃×D₈	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	4	yes	complemented
99	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
100	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
102	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
103	C₁₃×#127	—	2	2	no	—
104	C₁₃×#127	—	2	2	no	—
105	C₁₃×#127	C₂³	1	4	yes	—
106	C₁₃×#127	C₂³	1	2	yes	—
107	C₁₃×#127	C₂³	1	2	yes	—
108	C₁₃×#127	C₂³	1	1	yes	characteristic, complemented
109	C₁₃×#126	—	2	4	no	—
110	C₁₃×#126	—	2	4	no	—
111	C₁₃×#125	—	2	4	no	—
112	C₁₃×#125	C₂³	1	2	yes	complemented
113	C₁₃×#124	—	2	4	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	—	2	2	no	—
116	C₁₃×#124	C₂³	1	4	yes	—
117	C₁₃×#124	C₂³	1	2	yes	—
118	C₁₃×#124	C₂³	1	2	yes	—
119	C₁₃×#124	C₂³	1	2	yes	complemented
120	C₁₃×#123	—	2	2	no	—
121	C₁₃×#123	—	2	4	no	—
122	C₁₃×#123	—	2	4	no	—
123	C₁₃×C₂²⋊Q₈	—	2	2	no	—
124	C₁₃×C₂²⋊Q₈	—	2	4	no	—
125	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₁₃×#121	—	2	2	no	—
127	C₁₃×#121	—	2	8	no	—
128	C₁₃×#121	—	2	8	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#121	C₂³	1	4	yes	—
131	C₁₃×#120	—	2	2	no	—
132	C₁₃×#120	—	2	8	no	—
133	C₁₃×#120	—	2	8	no	—
134	C₄×Q₈×C₁₃	—	2	2	no	—
135	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
136	C₄×D₄×C₁₃	—	2	4	no	—
137	C₄×D₄×C₁₃	—	2	4	no	—
138	C₄×D₄×C₁₃	—	2	2	no	—
139	C₄×D₄×C₁₃	C₂³	1	4	yes	complemented
140	C₁₃×#117	—	2	2	no	—
141	C₁₃×#117	D₄	1	4	yes	—
142	C₁₃×#117	C₂³	1	2	yes	—
143	C₁₃×#117	C₂³	1	2	yes	—
144	C₁₃×#117	C₂³	1	2	yes	—
145	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
146	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
149	C₂×C₄²×C₁₃	—	2	2	no	—
150	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
152	C₁₃×C₄⋊C₈	C₂³	1	8	yes	complemented
153	C₁₃×#103	C₂³	1	8	yes	complemented
154	C₁₃×#102	C₂³	1	8	yes	—
155	C₁₃×#102	C₂³	1	8	yes	—
156	C₁₃×#102	C₂³	1	8	yes	complemented
157	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
158	C₁₃×#97	C₂³	1	2	yes	complemented
159	C₁₃×#97	C₂³	1	2	yes	complemented
160	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
161	C₄×C₈×C₁₃	C₂³	1	2	yes	complemented
162	#60806	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	—	2	1	no	—
166	C₂⁴×C₁₃	—	2	4	no	—
167	C₂⁴×C₁₃	—	4	4	no	—
168	C₂⁴×C₁₃	—	8	4	no	—
169	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₁₃×#41	—	2	4	no	—
171	C₁₃×#41	—	2	4	no	—
172	C₁₃×#41	—	4	8	no	—
173	C₁₃×#41	—	4	8	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	2	no	—
176	C₂×Q₈×C₁₃	—	2	4	no	—
177	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	4	no	—
182	C₂×D₄×C₁₃	—	2	4	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	2	no	—
187	C₂×D₄×C₁₃	—	2	8	no	—
188	C₂×D₄×C₁₃	—	2	4	no	—
189	C₂×D₄×C₁₃	—	2	4	no	—
190	C₂×D₄×C₁₃	—	2	4	no	—
191	C₂×D₄×C₁₃	—	2	4	no	—
192	C₂×D₄×C₁₃	—	2	4	no	—
193	C₂×D₄×C₁₃	—	4	8	no	—
194	C₂×D₄×C₁₃	—	4	4	no	—
195	C₂×D₄×C₁₃	—	4	8	no	—
196	C₂×D₄×C₁₃	—	4	4	no	—
197	C₂×D₄×C₁₃	—	8	4	no	—
198	C₂×D₄×C₁₃	—	8	4	no	—
199	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
200	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
201	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	2	no	—
206	C₂²×C₄×C₁₃	—	2	4	no	—
207	C₂²×C₄×C₁₃	—	2	4	no	—
208	C₂²×C₄×C₁₃	—	4	4	no	—
209	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₁₃×Q₁₆	—	4	4	no	—
216	C₁₃×SD₁₆	—	4	4	no	—
217	C₁₃×SD₁₆	—	4	4	no	—
218	C₁₃×SD₁₆	—	4	4	no	—
219	C₁₃×SD₁₆	—	4	4	no	—
220	C₁₃×D₈	—	4	4	no	—
221	C₁₃×D₈	—	4	4	no	—
222	C₁₃×D₈	—	4	4	no	—
223	C₁₃×M₁₆	—	2	4	no	—
224	C₁₃×M₁₆	—	2	4	no	—
225	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
226	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
227	C₁₃×C₄⋊C₄	—	2	4	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	4	no	—
230	C₁₃×C₄⋊C₄	—	2	4	no	—
231	C₁₃×C₄⋊C₄	—	2	2	no	—
232	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
233	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
234	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
235	C₁₃×C₂²⋊C₄	—	2	2	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	8	no	—
238	C₁₃×C₂²⋊C₄	—	2	4	no	—
239	C₁₃×C₂²⋊C₄	—	2	4	no	—
240	C₁₃×C₂²⋊C₄	—	2	4	no	—
241	C₁₃×C₂²⋊C₄	—	2	4	no	—
242	C₁₃×C₂²⋊C₄	—	2	4	no	—
243	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
244	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
245	C₄²×C₁₃	—	2	2	no	—
246	C₄²×C₁₃	—	2	4	no	—
247	C₄²×C₁₃	C₂×D₄	1	2	yes	—
248	C₄²×C₁₃	C₂×D₄	1	2	yes	—
249	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₁₃	C₂⁴	1	2	yes	—
252	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂×#535	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#3224	C₂×C₁₃	1	8	yes	complemented
255	#3222	C₂×C₁₃	1	4	yes	complemented
256	#3220	C₂×C₁₃	1	4	yes	complemented
257	#3153	C₂×C₁₃	1	1	yes	characteristic, complemented
258	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
259	#3140	C₂×C₁₃	1	1	yes	characteristic, complemented
260	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
261	#3040	C₂×C₁₃	1	2	yes	complemented
262	#3038	C₂×C₁₃	1	2	yes	complemented
263	#3005	C₂×C₁₃	1	2	yes	complemented
264	#3003	C₂×C₁₃	1	2	yes	complemented
265	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	2	no	—
269	C₂³×C₁₃	—	2	2	no	—
270	C₂³×C₁₃	—	2	2	no	—
271	C₂³×C₁₃	—	4	2	no	—
272	C₂³×C₁₃	—	4	8	no	—
273	C₂³×C₁₃	—	4	4	no	—
274	C₂³×C₁₃	—	4	4	no	—
275	C₂³×C₁₃	—	4	4	no	—
276	C₂³×C₁₃	—	4	2	no	—
277	C₂³×C₁₃	—	4	2	no	—
278	C₂³×C₁₃	—	4	2	no	—
279	C₂³×C₁₃	—	8	8	no	—
280	C₂³×C₁₃	—	8	16	no	—
281	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	Q₈×C₁₃	—	2	2	no	—
284	Q₈×C₁₃	—	2	2	no	—
285	Q₈×C₁₃	—	2	4	no	—
286	Q₈×C₁₃	—	4	2	no	—
287	Q₈×C₁₃	—	8	2	no	—
288	D₄×C₁₃	—	2	2	no	—
289	D₄×C₁₃	—	2	2	no	—
290	D₄×C₁₃	—	2	4	no	—
291	D₄×C₁₃	—	2	4	no	—
292	D₄×C₁₃	—	2	4	no	—
293	D₄×C₁₃	—	4	8	no	—
294	D₄×C₁₃	—	4	8	no	—
295	D₄×C₁₃	—	4	4	no	—
296	D₄×C₁₃	—	4	2	no	—
297	D₄×C₁₃	—	4	2	no	—
298	D₄×C₁₃	—	4	2	no	—
299	D₄×C₁₃	—	8	2	no	—
300	D₄×C₁₃	—	8	8	no	—
301	D₄×C₁₃	—	8	4	no	—
302	D₄×C₁₃	—	8	4	no	—
303	D₄×C₁₃	—	8	4	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	2	no	—
308	C₂×C₄×C₁₃	—	2	4	no	—
309	C₂×C₄×C₁₃	—	2	2	no	—
310	C₂×C₄×C₁₃	—	4	2	no	—
311	C₂×C₄×C₁₃	—	4	2	no	—
312	C₂×C₄×C₁₃	—	4	8	no	—
313	C₂×C₄×C₁₃	—	4	2	no	—
314	C₂×C₄×C₁₃	—	4	4	no	—
315	C₂×C₄×C₁₃	—	8	4	no	—
316	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
322	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
323	C₈×C₁₃	—	2	4	no	—
324	C₈×C₁₃	—	2	4	no	—
325	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
326	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
328	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
329	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
330	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	complemented
331	#542	C₂²×C₁₃	1	4	yes	complemented
332	#541	C₂²×C₁₃	1	2	yes	complemented
333	#540	C₂²×C₁₃	1	2	yes	complemented
334	#539	—	2	2	no	—
335	#538	—	2	2	no	—
336	#535	—	2	4	no	—
337	#535	C₂²×C₁₃	1	4	yes	—
338	#535	C₂²×C₁₃	1	4	yes	—
339	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
343	#529	—	2	4	no	—
344	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
346	#525	C₂²×C₁₃	1	2	yes	—
347	C₂×#121	—	2	2	no	—
348	C₂×#120	—	2	2	no	—
349	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
350	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
351	#497	C₂²×C₁₃	1	2	yes	complemented
352	#496	C₂²×C₁₃	1	2	yes	complemented
353	#496	C₂²×C₁₃	1	4	yes	complemented
354	#495	C₂²×C₁₃	1	4	yes	complemented
355	#493	C₂²×C₁₃	1	2	yes	complemented
356	#492	C₂²×C₁₃	1	2	yes	complemented
357	#490	C₂²×C₁₃	1	4	yes	complemented
358	#489	C₂²×C₁₃	1	4	yes	complemented
359	#488	C₂²×C₁₃	1	4	yes	complemented
360	#486	C₂²×C₁₃	1	4	yes	complemented
361	#464	C₂²×C₁₃	1	8	yes	complemented
362	#463	C₂²×C₁₃	1	8	yes	complemented
363	#460	C₂²×C₁₃	1	8	yes	complemented
364	#459	C₂²×C₁₃	1	8	yes	complemented
365	#452	C₂²×C₁₃	1	8	yes	complemented
366	#450	C₂²×C₁₃	1	8	yes	complemented
367	#449	C₂²×C₁₃	1	8	yes	complemented
368	#447	C₂²×C₁₃	1	8	yes	complemented
369	#433	C₂²×C₁₃	1	4	yes	complemented
370	#433	C₂²×C₁₃	1	4	yes	complemented
371	#423	C₂²×C₁₃	1	2	yes	complemented
372	#419	C₂²×C₁₃	1	2	yes	complemented
373	#418	C₂²×C₁₃	1	2	yes	—
374	#418	C₂²×C₁₃	1	2	yes	—
375	#418	C₂²×C₁₃	1	2	yes	complemented
376	#407	C₂²×C₁₃	1	2	yes	—
377	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
378	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	4	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	4	4	no	—
383	C₂²×C₁₃	—	4	4	no	—
384	C₂²×C₁₃	—	4	4	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	2	no	—
391	C₂²×C₁₃	—	8	4	no	—
392	C₂²×C₁₃	—	8	4	no	—
393	C₂²×C₁₃	—	8	4	no	—
394	C₂²×C₁₃	—	8	16	no	—
395	C₂²×C₁₃	#535	1	2	yes	—
396	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₁₃	—	2	4	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	4	4	no	—
402	C₄×C₁₃	—	4	2	no	—
403	C₄×C₁₃	—	4	2	no	—
404	C₄×C₁₃	#535	1	2	yes	—
405	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂⁵	—	2	1	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	4	4	no	—
409	C₂×#41	C₂³×C₁₃	1	2	yes	—
410	C₂×#41	C₂³×C₁₃	1	4	yes	—
411	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	—	2	1	no	—
414	C₂²×D₄	—	2	2	no	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	2	no	—
417	C₂²×D₄	—	4	4	no	—
418	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
422	C₂³×C₄	—	2	1	no	—
423	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
424	#137	—	4	4	no	—
425	AGL(1,ℤ/8)	—	4	4	no	—
426	AGL(1,ℤ/8)	—	4	4	no	—
427	AGL(1,ℤ/8)	—	4	4	no	—
428	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
429	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
430	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
431	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
432	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	complemented
433	C₂×D₈	C₂³×C₁₃	1	4	yes	—
434	C₂×D₈	C₂³×C₁₃	1	4	yes	—
435	C₂×D₈	C₂³×C₁₃	1	4	yes	complemented
436	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
437	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
438	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic, complemented
439	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	complemented
440	#127	—	2	2	no	—
441	#127	—	2	2	no	—
442	#127	C₂³×C₁₃	1	4	yes	—
443	#127	C₂³×C₁₃	1	2	yes	—
444	#127	C₂³×C₁₃	1	2	yes	—
445	#127	C₂³×C₁₃	1	1	yes	characteristic, complemented
446	#126	—	2	4	no	—
447	#126	—	2	4	no	—
448	#125	—	2	4	no	—
449	#125	C₂³×C₁₃	1	2	yes	complemented
450	#124	—	2	4	no	—
451	#124	—	2	2	no	—
452	#124	—	2	2	no	—
453	#124	C₂³×C₁₃	1	4	yes	—
454	#124	C₂³×C₁₃	1	2	yes	—
455	#124	C₂³×C₁₃	1	2	yes	—
456	#124	C₂³×C₁₃	1	2	yes	complemented
457	#123	—	2	2	no	—
458	#123	—	2	4	no	—
459	#123	—	2	4	no	—
460	C₂²⋊Q₈	—	2	2	no	—
461	C₂²⋊Q₈	—	2	4	no	—
462	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
463	#121	—	2	2	no	—
464	#121	—	2	8	no	—
465	#121	—	2	8	no	—
466	#121	—	2	4	no	—
467	#121	C₂³×C₁₃	1	4	yes	—
468	#120	—	2	2	no	—
469	#120	—	2	8	no	—
470	#120	—	2	8	no	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
473	C₄×D₄	—	2	4	no	—
474	C₄×D₄	—	2	4	no	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	C₂³×C₁₃	1	4	yes	complemented
477	#117	—	2	2	no	—
478	#117	D₄×C₁₃	1	4	yes	—
479	#117	C₂³×C₁₃	1	2	yes	—
480	#117	C₂³×C₁₃	1	2	yes	—
481	#117	C₂³×C₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
483	C₂×C₂²⋊C₄	—	2	2	no	—
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
486	C₂×C₄²	—	2	2	no	—
487	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
488	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
489	C₄⋊C₈	C₂³×C₁₃	1	8	yes	complemented
490	#103	C₂³×C₁₃	1	8	yes	complemented
491	#102	C₂³×C₁₃	1	8	yes	—
492	#102	C₂³×C₁₃	1	8	yes	—
493	#102	C₂³×C₁₃	1	8	yes	complemented
494	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
495	#97	C₂³×C₁₃	1	2	yes	complemented
496	#97	C₂³×C₁₃	1	2	yes	complemented
497	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
498	C₄×C₈	C₂³×C₁₃	1	2	yes	complemented
499	C₂×C₁₃	—	2	2	no	—
500	C₂×C₁₃	—	4	2	no	—
501	C₂×C₁₃	—	8	2	no	—
502	C₂×C₁₃	—	8	2	no	—
503	C₂×C₁₃	—	8	2	no	—
504	C₂×C₁₃	—	8	2	no	—
505	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
506	C₂×C₁₃	#3585	1	2	yes	—
507	C₂⁴	—	2	1	no	—
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	4	no	—
511	C₂⁴	—	4	4	no	—
512	C₂⁴	—	8	4	no	—
513	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
514	#41	—	2	4	no	—
515	#41	—	2	4	no	—
516	#41	—	4	8	no	—
517	#41	—	4	8	no	—
518	C₂×Q₈	—	2	1	no	—
519	C₂×Q₈	—	2	2	no	—
520	C₂×Q₈	—	2	4	no	—
521	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
522	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
523	C₂×D₄	—	2	2	no	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	8	no	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	4	8	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	8	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	8	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
544	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
546	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂²×C₄	—	2	4	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	4	4	no	—
553	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
554	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
555	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
559	Q₁₆	—	4	4	no	—
560	SD₁₆	—	4	4	no	—
561	SD₁₆	—	4	4	no	—
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	D₈	—	4	4	no	—
565	D₈	—	4	4	no	—
566	D₈	—	4	4	no	—
567	M₁₆	—	2	4	no	—
568	M₁₆	—	2	4	no	—
569	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
570	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
571	C₄⋊C₄	—	2	4	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	4	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
577	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
578	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
579	C₂²⋊C₄	—	2	2	no	—
580	C₂²⋊C₄	—	2	4	no	—
581	C₂²⋊C₄	—	2	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
588	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	C₂×D₄×C₁₃	1	2	yes	—
592	C₄²	C₂×D₄×C₁₃	1	2	yes	—
593	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
594	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₄²	C₂⁴×C₁₃	1	2	yes	—
596	C₁₃	#60806	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	16	no	—
612	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
613	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	8	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	8	8	no	—
631	D₄	—	8	4	no	—
632	D₄	—	8	4	no	—
633	D₄	—	8	2	no	—
634	D₄	—	8	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
652	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
653	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
654	C₈	—	2	4	no	—
655	C₈	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	4	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	4	no	—
661	C₂²	—	4	4	no	—
662	C₂²	—	4	4	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	2	no	—
665	C₂²	—	4	2	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	8	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	16	no	—
672	C₂²	C₁₃×#535	1	2	yes	—
673	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
674	C₄	—	2	4	no	—
675	C₄	—	2	2	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	4	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	2	no	—
681	C₄	C₁₃×#535	1	2	yes	—
682	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	2	no	—
688	C₂	—	8	2	no	—
689	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
690	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₂×C₁₃×#535	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3222	C₂	semidirect
5. C₁₃×#3220	C₂	semidirect
6. C₁₃×#3153	C₂	semidirect
7. C₁₃×#3151	C₂	semidirect
8. C₁₃×#3140	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3040	C₂	semidirect
11. C₁₃×#3038	C₂	semidirect
12. C₁₃×#3005	C₂	semidirect
13. C₁₃×#3003	C₂	semidirect
14. C₁₃×#2921	C₂	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₁₃×#542	C₂²	semidirect
22. C₁₃×#541	C₂²	semidirect
23. C₁₃×#540	C₂²	semidirect
29. C₁₃×#533	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
39. C₄×C₁₃×#41	C₂²	semidirect
41. C₁₃×#497	C₂²	semidirect
42. C₁₃×#496	C₂²	semidirect
43. C₁₃×#496	C₂²	semidirect
44. C₁₃×#495	C₂²	semidirect
45. C₁₃×#493	C₂²	semidirect
46. C₁₃×#492	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#489	C₂²	semidirect
49. C₁₃×#488	C₂²	semidirect
50. C₁₃×#486	C₂²	semidirect
51. C₁₃×#464	C₂²	semidirect
52. C₁₃×#463	C₂²	semidirect
53. C₁₃×#460	C₂²	semidirect
54. C₁₃×#459	C₂²	semidirect
55. C₁₃×#452	C₂²	semidirect
56. C₁₃×#450	C₂²	semidirect
57. C₁₃×#449	C₂²	semidirect
58. C₁₃×#447	C₂²	semidirect
59. C₁₃×#433	C₂²	semidirect
60. C₁₃×#433	C₂²	semidirect
61. C₁₃×#423	C₂²	semidirect
62. C₁₃×#419	C₂²	semidirect
65. C₁₃×#418	C₂²	semidirect
67. C₄×C₁₃×M₁₆	C₂²	semidirect
68. C₄×C₁₃×M₁₆	C₂²	semidirect
91. C₂×C₁₃×Q₁₆	C₂³	semidirect
94. C₂×C₁₃×SD₁₆	C₂³	semidirect
95. C₂×C₁₃×SD₁₆	C₂³	semidirect
98. C₂×C₁₃×D₈	C₂³	semidirect
101. C₁₃×C₄⋊Q₈	C₂³	semidirect
102. C₁₃×C₄⋊Q₈	C₂³	semidirect
108. C₁₃×#127	C₂³	semidirect
112. C₁₃×#125	C₂³	semidirect
119. C₁₃×#124	C₂³	semidirect
135. C₄×Q₈×C₁₃	C₂³	semidirect
139. C₄×D₄×C₁₃	C₂³	semidirect
152. C₁₃×C₄⋊C₈	C₂³	semidirect
153. C₁₃×#103	C₂³	semidirect
156. C₁₃×#102	C₂³	semidirect
158. C₁₃×#97	C₂³	semidirect
159. C₁₃×#97	C₂³	semidirect
160. C₄×C₈×C₁₃	C₂³	semidirect
161. C₄×C₈×C₁₃	C₂³	semidirect
162. #60806	C₁₃	direct (N × H)
252. #3455	C₂×C₁₃	semidirect
253. C₂×#535	C₂×C₁₃	semidirect
254. #3224	C₂×C₁₃	semidirect
255. #3222	C₂×C₁₃	semidirect
256. #3220	C₂×C₁₃	semidirect
257. #3153	C₂×C₁₃	semidirect
258. #3151	C₂×C₁₃	semidirect
259. #3140	C₂×C₁₃	semidirect
260. #3138	C₂×C₁₃	semidirect
261. #3040	C₂×C₁₃	semidirect
262. #3038	C₂×C₁₃	semidirect
263. #3005	C₂×C₁₃	semidirect
264. #3003	C₂×C₁₃	semidirect
265. #2921	C₂×C₁₃	semidirect
327. C₂×#137	C₂²×C₁₃	semidirect
330. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
331. #542	C₂²×C₁₃	semidirect
332. #541	C₂²×C₁₃	semidirect
333. #540	C₂²×C₁₃	semidirect
339. #533	C₂²×C₁₃	semidirect
340. #532	C₂²×C₁₃	semidirect
349. C₄×#41	C₂²×C₁₃	semidirect
351. #497	C₂²×C₁₃	semidirect
352. #496	C₂²×C₁₃	semidirect
353. #496	C₂²×C₁₃	semidirect
354. #495	C₂²×C₁₃	semidirect
355. #493	C₂²×C₁₃	semidirect
356. #492	C₂²×C₁₃	semidirect
357. #490	C₂²×C₁₃	semidirect
358. #489	C₂²×C₁₃	semidirect
359. #488	C₂²×C₁₃	semidirect
360. #486	C₂²×C₁₃	semidirect
361. #464	C₂²×C₁₃	semidirect
362. #463	C₂²×C₁₃	semidirect
363. #460	C₂²×C₁₃	semidirect
364. #459	C₂²×C₁₃	semidirect
365. #452	C₂²×C₁₃	semidirect
366. #450	C₂²×C₁₃	semidirect
367. #449	C₂²×C₁₃	semidirect
368. #447	C₂²×C₁₃	semidirect
369. #433	C₂²×C₁₃	semidirect
370. #433	C₂²×C₁₃	semidirect
371. #423	C₂²×C₁₃	semidirect
372. #419	C₂²×C₁₃	semidirect
375. #418	C₂²×C₁₃	semidirect
377. C₄×M₁₆	C₂²×C₁₃	semidirect
378. C₄×M₁₆	C₂²×C₁₃	semidirect
428. C₂×Q₁₆	C₂³×C₁₃	semidirect
431. C₂×SD₁₆	C₂³×C₁₃	semidirect
432. C₂×SD₁₆	C₂³×C₁₃	semidirect
435. C₂×D₈	C₂³×C₁₃	semidirect
438. C₄⋊Q₈	C₂³×C₁₃	semidirect
439. C₄⋊Q₈	C₂³×C₁₃	semidirect
445. #127	C₂³×C₁₃	semidirect
449. #125	C₂³×C₁₃	semidirect
456. #124	C₂³×C₁₃	semidirect
472. C₄×Q₈	C₂³×C₁₃	semidirect
476. C₄×D₄	C₂³×C₁₃	semidirect
489. C₄⋊C₈	C₂³×C₁₃	semidirect
490. #103	C₂³×C₁₃	semidirect
493. #102	C₂³×C₁₃	semidirect
495. #97	C₂³×C₁₃	semidirect
496. #97	C₂³×C₁₃	semidirect
497. C₄×C₈	C₂³×C₁₃	semidirect
498. C₄×C₈	C₂³×C₁₃	semidirect
596. C₁₃	#60806	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×#3455	2
C₂×C₁₃×#535	2
C₁₃×#3224	2
C₁₃×#3222	2
C₁₃×#3220	2
C₁₃×#3153	2
C₁₃×#3151	2
C₁₃×#3140	2
C₁₃×#3138	2
C₁₃×#3040	2
C₁₃×#3038	2
C₁₃×#3005	2
C₁₃×#3003	2
C₁₃×#2921	2
#60806	13

Subgroups — C13×#60806 #15747145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60806 #15747145