Subgroups — C₁₃×#60822 #15747161

Order 3328.

2194 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3224	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3210	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3208	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3207	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3205	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#3045	C₂	1	4	yes	maximal, complemented
13	C₁₃×#3012	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
18	C₁₃×#556	—	2	1	no	—
19	C₁₃×#555	—	2	1	no	—
20	C₁₃×#554	—	2	1	no	—
21	C₁₃×#553	—	2	2	no	—
22	C₁₃×#550	—	2	1	no	—
23	C₁₃×#550	—	2	1	no	—
24	C₁₃×#548	—	2	2	no	—
25	C₁₃×#547	—	2	1	no	—
26	D₄²×C₁₃	—	2	1	no	—
27	D₄²×C₁₃	—	2	2	no	—
28	D₄²×C₁₃	—	2	2	no	—
29	D₄²×C₁₃	—	2	1	no	—
30	C₁₃×#542	C₂²	1	4	yes	complemented
31	C₁₃×#537	C₂²	1	2	yes	—
32	C₁₃×#535	C₂²	1	2	yes	—
33	C₁₃×#535	C₂²	1	4	yes	—
34	C₁₃×#533	C₂²	1	2	yes	complemented
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₁₃×#532	C₂²	1	2	yes	—
37	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#532	C₂²	1	2	yes	complemented
39	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#127	C₂²	1	2	yes	—
42	C₁₃×#520	C₂²	1	2	yes	complemented
43	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
44	C₁₃×#496	C₂²	1	4	yes	complemented
45	C₁₃×#495	C₂²	1	4	yes	complemented
46	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#493	C₂²	1	2	yes	complemented
49	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
50	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
51	C₁₃×#492	C₂²	1	2	yes	complemented
52	C₁₃×#489	C₂²	1	4	yes	complemented
53	C₁₃×#487	C₂²	1	2	yes	complemented
54	C₁₃×#486	C₂²	1	2	yes	complemented
55	C₁₃×#486	C₂²	1	2	yes	complemented
56	C₁₃×#486	C₂²	1	4	yes	complemented
57	C₁₃×#486	C₂²	1	2	yes	complemented
58	C₁₃×#464	C₂²	1	8	yes	complemented
59	C₁₃×#463	C₂²	1	8	yes	complemented
60	C₁₃×#460	C₂²	1	8	yes	complemented
61	C₁₃×#459	C₂²	1	8	yes	complemented
62	C₁₃×#452	C₂²	1	8	yes	complemented
63	C₁₃×#450	C₂²	1	8	yes	complemented
64	C₁₃×#449	C₂²	1	8	yes	complemented
65	C₁₃×#447	C₂²	1	8	yes	complemented
66	C₁₃×#433	C₂²	1	4	yes	complemented
67	C₁₃×#431	C₂²	1	2	yes	complemented
68	C₁₃×#431	C₂²	1	2	yes	complemented
69	C₁₃×#424	C₂²	1	2	yes	complemented
70	C₁₃×#417	C₂²	1	4	yes	complemented
71	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
72	C₁₃×#408	C₂²	1	2	yes	—
73	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×H(5,𝔽₂)	—	4	8	no	—
76	C₂×C₁₃×#41	—	2	2	no	—
77	C₂×C₁₃×#41	—	2	2	no	—
78	C₂×C₁₃×#41	C₂³	1	2	yes	—
79	C₂×C₁₃×#41	C₂³	1	2	yes	—
80	C₂×C₁₃×#41	C₂³	1	4	yes	—
81	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₁₃	—	2	1	no	—
83	C₂²×D₄×C₁₃	—	2	4	no	—
84	C₂²×D₄×C₁₃	—	2	2	no	—
85	C₂²×D₄×C₁₃	—	2	1	no	—
86	C₂²×D₄×C₁₃	—	2	2	no	—
87	C₂²×D₄×C₁₃	—	2	1	no	—
88	C₂²×D₄×C₁₃	—	2	2	no	—
89	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
91	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
92	C₁₃×#135	—	4	8	no	—
93	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
96	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
97	C₂×C₁₃×D₈	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	8	yes	—
99	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	—	2	1	no	—
102	C₁₃×C₄⋊Q₈	—	2	1	no	—
103	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
106	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
107	C₁₃×#127	—	2	2	no	—
108	C₁₃×#127	—	2	1	no	—
109	C₁₃×#127	—	2	1	no	—
110	C₁₃×#127	—	2	2	no	—
111	C₁₃×#127	C₂³	1	4	yes	—
112	C₁₃×#127	C₂³	1	2	yes	—
113	C₁₃×#127	C₂³	1	1	yes	characteristic
114	C₁₃×#127	C₂³	1	2	yes	—
115	C₁₃×#127	C₂³	1	1	yes	characteristic
116	C₁₃×#126	—	2	4	no	—
117	C₁₃×#125	—	2	2	no	—
118	C₁₃×#124	—	2	4	no	—
119	C₁₃×#124	—	2	2	no	—
120	C₁₃×#124	C₂³	1	4	yes	—
121	C₁₃×#124	C₂³	1	2	yes	—
122	C₁₃×#124	C₂³	1	2	yes	—
123	C₁₃×#123	—	2	4	no	—
124	C₁₃×C₂²⋊Q₈	—	2	2	no	—
125	C₁₃×C₂²⋊Q₈	—	2	2	no	—
126	C₁₃×C₂²⋊Q₈	—	2	4	no	—
127	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₃×#121	—	2	2	no	—
129	C₁₃×#121	—	2	4	no	—
130	C₁₃×#121	—	2	1	no	—
131	C₁₃×#121	—	2	2	no	—
132	C₁₃×#121	—	2	1	no	—
133	C₁₃×#121	—	2	2	no	—
134	C₁₃×#121	—	2	1	no	—
135	C₁₃×#121	—	2	1	no	—
136	C₁₃×#121	—	2	2	no	—
137	C₁₃×#121	—	2	2	no	—
138	C₁₃×#121	—	2	2	no	—
139	C₁₃×#121	—	2	4	no	—
140	C₁₃×#121	—	2	4	no	—
141	C₁₃×#121	C₂³	1	4	yes	—
142	C₁₃×#120	—	2	4	no	—
143	C₁₃×#120	—	2	4	no	—
144	C₁₃×#120	—	2	4	no	—
145	C₄×Q₈×C₁₃	—	2	2	no	—
146	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
147	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
149	C₄×D₄×C₁₃	—	2	4	no	—
150	C₄×D₄×C₁₃	—	2	2	no	—
151	C₄×D₄×C₁₃	—	2	1	no	—
152	C₄×D₄×C₁₃	—	2	1	no	—
153	C₄×D₄×C₁₃	—	2	2	no	—
154	C₄×D₄×C₁₃	—	2	1	no	—
155	C₄×D₄×C₁₃	—	2	2	no	—
156	C₄×D₄×C₁₃	—	2	1	no	—
157	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
158	C₄×D₄×C₁₃	D₄	1	2	yes	—
159	C₄×D₄×C₁₃	D₄	1	2	yes	—
160	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
161	C₄×D₄×C₁₃	C₂³	1	4	yes	—
162	C₁₃×#117	—	2	2	no	—
163	C₁₃×#117	—	2	2	no	—
164	C₁₃×#117	C₂³	1	1	yes	characteristic
165	C₁₃×#117	C₂³	1	2	yes	—
166	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₁₃×#103	C₂³	1	8	yes	—
174	C₁₃×#102	C₂³	1	8	yes	—
175	C₁₃×#102	C₂³	1	8	yes	—
176	C₁₃×#102	C₂³	1	8	yes	—
177	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₁₃×#97	C₂³	1	2	yes	—
180	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₁₃	C₂³	1	2	yes	—
183	C₄×C₈×C₁₃	C₂³	1	2	yes	—
184	#60822	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂⁴×C₁₃	—	2	4	no	—
186	C₂⁴×C₁₃	—	2	2	no	—
187	C₁₃×#41	—	2	4	no	—
188	C₁₃×#41	—	2	8	no	—
189	C₁₃×#41	—	2	8	no	—
190	C₁₃×#41	—	4	8	no	—
191	C₁₃×#41	—	4	8	no	—
192	C₁₃×#41	—	8	4	no	—
193	C₂×Q₈×C₁₃	—	2	2	no	—
194	C₂×Q₈×C₁₃	—	2	2	no	—
195	C₂×Q₈×C₁₃	—	8	2	no	—
196	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
198	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
199	C₂×D₄×C₁₃	—	2	2	no	—
200	C₂×D₄×C₁₃	—	2	4	no	—
201	C₂×D₄×C₁₃	—	2	2	no	—
202	C₂×D₄×C₁₃	—	2	4	no	—
203	C₂×D₄×C₁₃	—	2	1	no	—
204	C₂×D₄×C₁₃	—	2	1	no	—
205	C₂×D₄×C₁₃	—	2	1	no	—
206	C₂×D₄×C₁₃	—	2	2	no	—
207	C₂×D₄×C₁₃	—	2	2	no	—
208	C₂×D₄×C₁₃	—	2	1	no	—
209	C₂×D₄×C₁₃	—	2	4	no	—
210	C₂×D₄×C₁₃	—	2	2	no	—
211	C₂×D₄×C₁₃	—	2	4	no	—
212	C₂×D₄×C₁₃	—	2	2	no	—
213	C₂×D₄×C₁₃	—	2	2	no	—
214	C₂×D₄×C₁₃	—	2	4	no	—
215	C₂×D₄×C₁₃	—	2	8	no	—
216	C₂×D₄×C₁₃	—	4	8	no	—
217	C₂×D₄×C₁₃	—	4	16	no	—
218	C₂×D₄×C₁₃	—	4	8	no	—
219	C₂×D₄×C₁₃	—	8	2	no	—
220	C₂×D₄×C₁₃	—	8	4	no	—
221	C₂×D₄×C₁₃	—	8	2	no	—
222	C₂×D₄×C₁₃	—	8	4	no	—
223	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
226	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₁₃	—	2	2	no	—
229	C₂²×C₄×C₁₃	—	2	2	no	—
230	C₂²×C₄×C₁₃	—	2	4	no	—
231	C₂²×C₄×C₁₃	—	2	2	no	—
232	C₂²×C₄×C₁₃	—	2	4	no	—
233	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
235	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₁₃×Q₁₆	—	4	4	no	—
240	C₁₃×SD₁₆	—	4	4	no	—
241	C₁₃×SD₁₆	—	4	4	no	—
242	C₁₃×SD₁₆	—	4	8	no	—
243	C₁₃×D₈	—	4	4	no	—
244	C₁₃×D₈	—	4	8	no	—
245	C₁₃×M₁₆	—	2	4	no	—
246	C₂×C₈×C₁₃	—	2	4	no	—
247	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
250	C₁₃×C₄⋊C₄	—	2	2	no	—
251	C₁₃×C₄⋊C₄	—	2	2	no	—
252	C₁₃×C₄⋊C₄	—	2	4	no	—
253	C₁₃×C₄⋊C₄	—	2	2	no	—
254	C₁₃×C₄⋊C₄	—	2	1	no	—
255	C₁₃×C₄⋊C₄	—	2	1	no	—
256	C₁₃×C₄⋊C₄	—	2	1	no	—
257	C₁₃×C₄⋊C₄	—	2	1	no	—
258	C₁₃×C₄⋊C₄	—	2	4	no	—
259	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
263	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
264	C₁₃×C₂²⋊C₄	—	2	4	no	—
265	C₁₃×C₂²⋊C₄	—	2	4	no	—
266	C₁₃×C₂²⋊C₄	—	2	4	no	—
267	C₁₃×C₂²⋊C₄	—	2	2	no	—
268	C₁₃×C₂²⋊C₄	—	2	2	no	—
269	C₁₃×C₂²⋊C₄	—	2	4	no	—
270	C₁₃×C₂²⋊C₄	—	2	4	no	—
271	C₁₃×C₂²⋊C₄	—	2	2	no	—
272	C₁₃×C₂²⋊C₄	—	2	2	no	—
273	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
274	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
275	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
276	C₄²×C₁₃	—	2	4	no	—
277	C₄²×C₁₃	C₂×D₄	1	2	yes	—
278	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₁₃	C₂×D₄	1	2	yes	—
281	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
282	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
283	C₄²×C₁₃	C₂⁴	1	2	yes	—
284	#3511	C₂×C₁₃	1	1	yes	characteristic, complemented
285	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#3224	C₂×C₁₃	1	8	yes	complemented
287	#3210	C₂×C₁₃	1	2	yes	complemented
288	#3208	C₂×C₁₃	1	2	yes	complemented
289	#3207	C₂×C₁₃	1	2	yes	complemented
290	#3205	C₂×C₁₃	1	2	yes	complemented
291	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#3141	C₂×C₁₃	1	1	yes	characteristic, complemented
294	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
295	#3045	C₂×C₁₃	1	4	yes	complemented
296	#3012	C₂×C₁₃	1	4	yes	complemented
297	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
298	C₂³×C₁₃	—	2	2	no	—
299	C₂³×C₁₃	—	2	4	no	—
300	C₂³×C₁₃	—	2	2	no	—
301	C₂³×C₁₃	—	4	8	no	—
302	C₂³×C₁₃	—	4	4	no	—
303	C₂³×C₁₃	—	8	2	no	—
304	C₂³×C₁₃	—	8	2	no	—
305	C₂³×C₁₃	—	8	4	no	—
306	C₂³×C₁₃	—	8	4	no	—
307	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
308	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₁₃	—	2	2	no	—
310	Q₈×C₁₃	—	2	4	no	—
311	Q₈×C₁₃	—	2	4	no	—
312	Q₈×C₁₃	—	4	4	no	—
313	Q₈×C₁₃	—	8	2	no	—
314	D₄×C₁₃	—	2	4	no	—
315	D₄×C₁₃	—	2	2	no	—
316	D₄×C₁₃	—	2	4	no	—
317	D₄×C₁₃	—	2	8	no	—
318	D₄×C₁₃	—	2	4	no	—
319	D₄×C₁₃	—	4	8	no	—
320	D₄×C₁₃	—	4	8	no	—
321	D₄×C₁₃	—	4	4	no	—
322	D₄×C₁₃	—	4	4	no	—
323	D₄×C₁₃	—	4	4	no	—
324	D₄×C₁₃	—	4	4	no	—
325	D₄×C₁₃	—	4	2	no	—
326	D₄×C₁₃	—	4	2	no	—
327	D₄×C₁₃	—	4	2	no	—
328	D₄×C₁₃	—	4	4	no	—
329	D₄×C₁₃	—	4	2	no	—
330	D₄×C₁₃	—	8	4	no	—
331	D₄×C₁₃	—	8	2	no	—
332	D₄×C₁₃	—	8	4	no	—
333	D₄×C₁₃	—	8	2	no	—
334	D₄×C₁₃	—	8	4	no	—
335	C₂×C₄×C₁₃	—	2	2	no	—
336	C₂×C₄×C₁₃	—	2	4	no	—
337	C₂×C₄×C₁₃	—	2	2	no	—
338	C₂×C₄×C₁₃	—	2	4	no	—
339	C₂×C₄×C₁₃	—	2	4	no	—
340	C₂×C₄×C₁₃	—	2	2	no	—
341	C₂×C₄×C₁₃	—	2	4	no	—
342	C₂×C₄×C₁₃	—	2	2	no	—
343	C₂×C₄×C₁₃	—	4	8	no	—
344	C₂×C₄×C₁₃	—	4	4	no	—
345	C₂×C₄×C₁₃	—	4	4	no	—
346	C₂×C₄×C₁₃	—	8	4	no	—
347	C₂×C₄×C₁₃	—	8	2	no	—
348	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
349	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
350	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
351	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
352	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
353	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
357	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
358	C₈×C₁₃	—	2	2	no	—
359	C₈×C₁₃	—	2	2	no	—
360	C₈×C₁₃	—	2	4	no	—
361	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
362	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
363	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
364	#556	—	2	1	no	—
365	#555	—	2	1	no	—
366	#554	—	2	1	no	—
367	#553	—	2	2	no	—
368	#550	—	2	1	no	—
369	#550	—	2	1	no	—
370	#548	—	2	2	no	—
371	#547	—	2	1	no	—
372	D₄²	—	2	1	no	—
373	D₄²	—	2	2	no	—
374	D₄²	—	2	2	no	—
375	D₄²	—	2	1	no	—
376	#542	C₂²×C₁₃	1	4	yes	complemented
377	#537	C₂²×C₁₃	1	2	yes	—
378	#535	C₂²×C₁₃	1	4	yes	—
379	#535	C₂²×C₁₃	1	2	yes	—
380	#533	C₂²×C₁₃	1	2	yes	complemented
381	#532	C₂²×C₁₃	1	1	yes	characteristic
382	#532	C₂²×C₁₃	1	2	yes	—
383	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
384	#532	C₂²×C₁₃	1	2	yes	complemented
385	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
387	C₂×#127	C₂²×C₁₃	1	2	yes	—
388	#520	C₂²×C₁₃	1	2	yes	complemented
389	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
390	#496	C₂²×C₁₃	1	4	yes	complemented
391	#495	C₂²×C₁₃	1	4	yes	complemented
392	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
393	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	#493	C₂²×C₁₃	1	2	yes	complemented
395	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	#492	C₂²×C₁₃	1	2	yes	complemented
398	#489	C₂²×C₁₃	1	4	yes	complemented
399	#487	C₂²×C₁₃	1	2	yes	complemented
400	#486	C₂²×C₁₃	1	2	yes	complemented
401	#486	C₂²×C₁₃	1	2	yes	complemented
402	#486	C₂²×C₁₃	1	4	yes	complemented
403	#486	C₂²×C₁₃	1	2	yes	complemented
404	#464	C₂²×C₁₃	1	8	yes	complemented
405	#463	C₂²×C₁₃	1	8	yes	complemented
406	#460	C₂²×C₁₃	1	8	yes	complemented
407	#459	C₂²×C₁₃	1	8	yes	complemented
408	#452	C₂²×C₁₃	1	8	yes	complemented
409	#450	C₂²×C₁₃	1	8	yes	complemented
410	#449	C₂²×C₁₃	1	8	yes	complemented
411	#447	C₂²×C₁₃	1	8	yes	complemented
412	#433	C₂²×C₁₃	1	4	yes	complemented
413	#431	C₂²×C₁₃	1	2	yes	complemented
414	#431	C₂²×C₁₃	1	2	yes	complemented
415	#424	C₂²×C₁₃	1	2	yes	complemented
416	#417	C₂²×C₁₃	1	4	yes	complemented
417	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
418	#408	C₂²×C₁₃	1	2	yes	—
419	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
420	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
421	C₂²×C₁₃	—	2	1	no	—
422	C₂²×C₁₃	—	2	1	no	—
423	C₂²×C₁₃	—	2	2	no	—
424	C₂²×C₁₃	—	2	2	no	—
425	C₂²×C₁₃	—	2	2	no	—
426	C₂²×C₁₃	—	4	4	no	—
427	C₂²×C₁₃	—	4	2	no	—
428	C₂²×C₁₃	—	4	2	no	—
429	C₂²×C₁₃	—	4	2	no	—
430	C₂²×C₁₃	—	4	4	no	—
431	C₂²×C₁₃	—	4	2	no	—
432	C₂²×C₁₃	—	4	4	no	—
433	C₂²×C₁₃	—	4	2	no	—
434	C₂²×C₁₃	—	4	2	no	—
435	C₂²×C₁₃	—	16	4	no	—
436	C₂²×C₁₃	—	16	8	no	—
437	C₂²×C₁₃	#535	1	2	yes	—
438	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₁₃	—	2	2	no	—
440	C₄×C₁₃	—	2	2	no	—
441	C₄×C₁₃	—	2	1	no	—
442	C₄×C₁₃	—	2	2	no	—
443	C₄×C₁₃	—	2	1	no	—
444	C₄×C₁₃	—	4	2	no	—
445	C₄×C₁₃	—	4	2	no	—
446	C₄×C₁₃	—	4	4	no	—
447	C₄×C₁₃	#535	1	2	yes	—
448	C₄×C₁₃	#576	1	2	yes	—
449	C₄×C₁₃	#577	1	2	yes	—
450	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
451	H(5,𝔽₂)	—	4	8	no	—
452	C₂×#41	—	2	2	no	—
453	C₂×#41	—	2	2	no	—
454	C₂×#41	C₂³×C₁₃	1	2	yes	—
455	C₂×#41	C₂³×C₁₃	1	2	yes	—
456	C₂×#41	C₂³×C₁₃	1	4	yes	—
457	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
458	C₂²×Q₈	—	2	1	no	—
459	C₂²×D₄	—	2	4	no	—
460	C₂²×D₄	—	2	2	no	—
461	C₂²×D₄	—	2	1	no	—
462	C₂²×D₄	—	2	2	no	—
463	C₂²×D₄	—	2	1	no	—
464	C₂²×D₄	—	2	2	no	—
465	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
466	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
467	AGL(1,ℤ/8)	—	4	8	no	—
468	#135	—	4	8	no	—
469	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
470	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
471	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
472	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
473	C₂×D₈	C₂³×C₁₃	1	4	yes	—
474	C₂×D₈	C₂³×C₁₃	1	8	yes	—
475	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
476	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
477	C₄⋊Q₈	—	2	1	no	—
478	C₄⋊Q₈	—	2	1	no	—
479	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
482	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
483	#127	—	2	2	no	—
484	#127	—	2	1	no	—
485	#127	—	2	1	no	—
486	#127	—	2	2	no	—
487	#127	C₂³×C₁₃	1	2	yes	—
488	#127	C₂³×C₁₃	1	1	yes	characteristic
489	#127	C₂³×C₁₃	1	4	yes	—
490	#127	C₂³×C₁₃	1	2	yes	—
491	#127	C₂³×C₁₃	1	1	yes	characteristic
492	#126	—	2	4	no	—
493	#125	—	2	2	no	—
494	#124	—	2	4	no	—
495	#124	—	2	2	no	—
496	#124	C₂³×C₁₃	1	4	yes	—
497	#124	C₂³×C₁₃	1	2	yes	—
498	#124	C₂³×C₁₃	1	2	yes	—
499	#123	—	2	4	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
504	#121	—	2	2	no	—
505	#121	—	2	4	no	—
506	#121	—	2	1	no	—
507	#121	—	2	2	no	—
508	#121	—	2	1	no	—
509	#121	—	2	2	no	—
510	#121	—	2	1	no	—
511	#121	—	2	1	no	—
512	#121	—	2	2	no	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	4	no	—
516	#121	—	2	4	no	—
517	#121	C₂³×C₁₃	1	4	yes	—
518	#120	—	2	4	no	—
519	#120	—	2	4	no	—
520	#120	—	2	4	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
523	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
524	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
525	C₄×D₄	—	2	4	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	2	1	no	—
528	C₄×D₄	—	2	1	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	1	no	—
531	C₄×D₄	—	2	2	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
534	C₄×D₄	D₄×C₁₃	1	2	yes	—
535	C₄×D₄	D₄×C₁₃	1	2	yes	—
536	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
537	C₄×D₄	C₂³×C₁₃	1	4	yes	—
538	#117	—	2	2	no	—
539	#117	—	2	2	no	—
540	#117	C₂³×C₁₃	1	1	yes	characteristic
541	#117	C₂³×C₁₃	1	2	yes	—
542	C₂×C₄⋊C₄	—	2	1	no	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
545	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
547	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
548	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
549	#103	C₂³×C₁₃	1	8	yes	—
550	#102	C₂³×C₁₃	1	8	yes	—
551	#102	C₂³×C₁₃	1	8	yes	—
552	#102	C₂³×C₁₃	1	8	yes	—
553	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
555	#97	C₂³×C₁₃	1	2	yes	—
556	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₁₃	1	2	yes	—
559	C₄×C₈	C₂³×C₁₃	1	2	yes	—
560	C₂×C₁₃	—	2	2	no	—
561	C₂×C₁₃	—	4	2	no	—
562	C₂×C₁₃	—	8	2	no	—
563	C₂×C₁₃	—	8	4	no	—
564	C₂×C₁₃	—	8	2	no	—
565	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
566	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
567	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
568	C₂⁴	—	2	4	no	—
569	C₂⁴	—	2	2	no	—
570	#41	—	2	4	no	—
571	#41	—	2	8	no	—
572	#41	—	2	8	no	—
573	#41	—	4	8	no	—
574	#41	—	4	8	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	2	no	—
577	C₂×Q₈	—	2	2	no	—
578	C₂×Q₈	—	8	2	no	—
579	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
580	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
581	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	4	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	4	8	no	—
600	C₂×D₄	—	4	16	no	—
601	C₂×D₄	—	4	8	no	—
602	C₂×D₄	—	8	2	no	—
603	C₂×D₄	—	8	4	no	—
604	C₂×D₄	—	8	2	no	—
605	C₂×D₄	—	8	4	no	—
606	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
607	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
608	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
609	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
610	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
617	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
618	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
621	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
622	Q₁₆	—	4	4	no	—
623	SD₁₆	—	4	4	no	—
624	SD₁₆	—	4	4	no	—
625	SD₁₆	—	4	8	no	—
626	D₈	—	4	4	no	—
627	D₈	—	4	8	no	—
628	M₁₆	—	2	4	no	—
629	C₂×C₈	—	2	4	no	—
630	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
631	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
632	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	—	2	1	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
643	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
644	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
645	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	4	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
657	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
658	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
659	C₄²	—	2	4	no	—
660	C₄²	C₂×D₄×C₁₃	1	2	yes	—
661	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
662	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
663	C₄²	C₂×D₄×C₁₃	1	2	yes	—
664	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
665	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
666	C₄²	C₂⁴×C₁₃	1	2	yes	—
667	C₁₃	#60822	1	1	yes	characteristic, direct product factor, Sylow
668	C₂³	—	2	2	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	4	8	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	8	2	no	—
674	C₂³	—	8	2	no	—
675	C₂³	—	8	4	no	—
676	C₂³	—	8	4	no	—
677	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
678	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
679	Q₈	—	2	2	no	—
680	Q₈	—	2	4	no	—
681	Q₈	—	2	4	no	—
682	Q₈	—	4	4	no	—
683	Q₈	—	8	2	no	—
684	D₄	—	2	4	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	4	no	—
687	D₄	—	2	8	no	—
688	D₄	—	2	4	no	—
689	D₄	—	4	8	no	—
690	D₄	—	4	8	no	—
691	D₄	—	4	4	no	—
692	D₄	—	4	4	no	—
693	D₄	—	4	4	no	—
694	D₄	—	4	4	no	—
695	D₄	—	4	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	4	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	2	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	2	no	—
704	D₄	—	8	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	4	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	4	8	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	8	4	no	—
717	C₂×C₄	—	8	2	no	—
718	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
719	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
720	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
721	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
722	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
723	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
724	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
725	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
726	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
727	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
728	C₈	—	2	2	no	—
729	C₈	—	2	2	no	—
730	C₈	—	2	4	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	4	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	4	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	8	no	—
747	C₂²	C₁₃×#535	1	2	yes	—
748	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
749	C₄	—	2	2	no	—
750	C₄	—	2	1	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	4	4	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₁₃×#535	1	2	yes	—
758	C₄	C₁₃×#576	1	2	yes	—
759	C₄	C₁₃×#577	1	2	yes	—
760	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
761	C₂	—	2	2	no	—
762	C₂	—	4	2	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	—	8	2	no	—
766	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
767	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
768	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3511	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3224	C₂	semidirect
4. C₁₃×#3210	C₂	semidirect
5. C₁₃×#3208	C₂	semidirect
6. C₁₃×#3207	C₂	semidirect
7. C₁₃×#3205	C₂	semidirect
8. C₁₃×#3151	C₂	semidirect
9. C₁₃×#3147	C₂	semidirect
10. C₁₃×#3141	C₂	semidirect
11. C₂×C₁₃×#486	C₂	semidirect
12. C₁₃×#3045	C₂	semidirect
13. C₁₃×#3012	C₂	semidirect
14. C₁₃×#2922	C₂	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₃×#135	C₂²	semidirect
30. C₁₃×#542	C₂²	semidirect
34. C₁₃×#533	C₂²	semidirect
37. C₁₃×#532	C₂²	semidirect
38. C₁₃×#532	C₂²	semidirect
39. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
42. C₁₃×#520	C₂²	semidirect
44. C₁₃×#496	C₂²	semidirect
45. C₁₃×#495	C₂²	semidirect
46. C₁₃×#494	C₂²	semidirect
47. C₁₃×#493	C₂²	semidirect
48. C₁₃×#493	C₂²	semidirect
49. C₁₃×#492	C₂²	semidirect
50. C₁₃×#492	C₂²	semidirect
51. C₁₃×#492	C₂²	semidirect
52. C₁₃×#489	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#486	C₂²	semidirect
55. C₁₃×#486	C₂²	semidirect
56. C₁₃×#486	C₂²	semidirect
57. C₁₃×#486	C₂²	semidirect
58. C₁₃×#464	C₂²	semidirect
59. C₁₃×#463	C₂²	semidirect
60. C₁₃×#460	C₂²	semidirect
61. C₁₃×#459	C₂²	semidirect
62. C₁₃×#452	C₂²	semidirect
63. C₁₃×#450	C₂²	semidirect
64. C₁₃×#449	C₂²	semidirect
65. C₁₃×#447	C₂²	semidirect
66. C₁₃×#433	C₂²	semidirect
67. C₁₃×#431	C₂²	semidirect
68. C₁₃×#431	C₂²	semidirect
69. C₁₃×#424	C₂²	semidirect
70. C₁₃×#417	C₂²	semidirect
71. C₂×C₁₃×#102	C₂²	semidirect
73. C₄×C₁₃×M₁₆	C₂²	semidirect
74. C₂×C₄×C₈×C₁₃	C₂²	semidirect
184. #60822	C₁₃	direct (N × H)
284. #3511	C₂×C₁₃	semidirect
285. #3498	C₂×C₁₃	semidirect
286. #3224	C₂×C₁₃	semidirect
287. #3210	C₂×C₁₃	semidirect
288. #3208	C₂×C₁₃	semidirect
289. #3207	C₂×C₁₃	semidirect
290. #3205	C₂×C₁₃	semidirect
291. #3151	C₂×C₁₃	semidirect
292. #3147	C₂×C₁₃	semidirect
293. #3141	C₂×C₁₃	semidirect
294. C₂×#486	C₂×C₁₃	semidirect
295. #3045	C₂×C₁₃	semidirect
296. #3012	C₂×C₁₃	semidirect
297. #2922	C₂×C₁₃	semidirect
362. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
363. C₂×#135	C₂²×C₁₃	semidirect
376. #542	C₂²×C₁₃	semidirect
380. #533	C₂²×C₁₃	semidirect
383. #532	C₂²×C₁₃	semidirect
384. #532	C₂²×C₁₃	semidirect
385. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
388. #520	C₂²×C₁₃	semidirect
390. #496	C₂²×C₁₃	semidirect
391. #495	C₂²×C₁₃	semidirect
392. #494	C₂²×C₁₃	semidirect
393. #493	C₂²×C₁₃	semidirect
394. #493	C₂²×C₁₃	semidirect
395. #492	C₂²×C₁₃	semidirect
396. #492	C₂²×C₁₃	semidirect
397. #492	C₂²×C₁₃	semidirect
398. #489	C₂²×C₁₃	semidirect
399. #487	C₂²×C₁₃	semidirect
400. #486	C₂²×C₁₃	semidirect
401. #486	C₂²×C₁₃	semidirect
402. #486	C₂²×C₁₃	semidirect
403. #486	C₂²×C₁₃	semidirect
404. #464	C₂²×C₁₃	semidirect
405. #463	C₂²×C₁₃	semidirect
406. #460	C₂²×C₁₃	semidirect
407. #459	C₂²×C₁₃	semidirect
408. #452	C₂²×C₁₃	semidirect
409. #450	C₂²×C₁₃	semidirect
410. #449	C₂²×C₁₃	semidirect
411. #447	C₂²×C₁₃	semidirect
412. #433	C₂²×C₁₃	semidirect
413. #431	C₂²×C₁₃	semidirect
414. #431	C₂²×C₁₃	semidirect
415. #424	C₂²×C₁₃	semidirect
416. #417	C₂²×C₁₃	semidirect
417. C₂×#102	C₂²×C₁₃	semidirect
419. C₄×M₁₆	C₂²×C₁₃	semidirect
420. C₂×C₄×C₈	C₂²×C₁₃	semidirect
667. C₁₃	#60822	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×#3511	2
C₁₃×#3498	2
C₁₃×#3224	2
C₁₃×#3210	2
C₁₃×#3208	2
C₁₃×#3207	2
C₁₃×#3205	2
C₁₃×#3151	2
C₁₃×#3147	2
C₁₃×#3141	2
C₂×C₁₃×#486	2
C₁₃×#3045	2
C₁₃×#3012	2
C₁₃×#2922	2
#60822	13

Subgroups — C13×#60822 #15747161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60822 #15747161