Subgroups — C₁₃×#61572 #15747911

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3308	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3265	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3213	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3193	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3186	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3112	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3006	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	—	2	1	no	—
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
17	C₁₃×#548	—	2	4	no	—
18	C₁₃×#548	C₂²	1	8	yes	complemented
19	C₁₃×#547	C₂²	1	4	yes	complemented
20	C₁₃×#546	—	2	4	no	—
21	D₄²×C₁₃	C₂²	1	4	yes	complemented
22	C₁₃×#537	—	2	1	no	—
23	C₁₃×#534	—	2	1	no	—
24	C₁₃×#534	—	2	1	no	—
25	C₁₃×#532	C₂²	1	2	yes	—
26	C₂×C₁₃×#124	—	2	1	no	—
27	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#121	—	2	1	no	—
31	C₂×C₁₃×#121	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	C₂²	1	2	yes	—
33	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₁₃	—	2	1	no	—
36	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#496	C₂²	1	4	yes	complemented
38	C₁₃×#489	C₂²	1	4	yes	complemented
39	C₁₃×#484	C₂²	1	4	yes	complemented
40	C₁₃×#480	C₂²	1	4	yes	complemented
41	C₁₃×#480	C₂²	1	4	yes	complemented
42	C₁₃×#477	C₂²	1	4	yes	complemented
43	C₁₃×#468	C₂²	1	8	yes	complemented
44	C₁₃×#466	C₂²	1	8	yes	complemented
45	C₁₃×#463	C₂²	1	8	yes	complemented
46	C₁₃×#460	C₂²	1	4	yes	complemented
47	C₁₃×#450	C₂²	1	4	yes	complemented
48	C₁₃×#449	C₂²	1	8	yes	complemented
49	C₁₃×#448	C₂²	1	4	yes	complemented
50	C₁₃×#448	C₂²	1	8	yes	complemented
51	C₁₃×#448	C₂²	1	4	yes	complemented
52	C₁₃×#447	C₂²	1	4	yes	complemented
53	C₁₃×#447	C₂²	1	4	yes	complemented
54	C₁₃×#440	C₂²	1	8	yes	complemented
55	C₁₃×#435	C₂²	1	8	yes	complemented
56	C₁₃×#432	C₂²	1	2	yes	complemented
57	C₁₃×#417	C₂²	1	4	yes	complemented
58	C₂×C₁₃×#103	C₂²	1	4	yes	complemented
59	C₁₃×#407	C₂²	1	2	yes	complemented
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
61	C₁₃×H(5,𝔽₂)	—	4	8	no	—
62	C₂×C₁₃×#41	—	2	4	no	—
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	—	2	2	no	—
65	C₂×C₁₃×#41	—	4	4	no	—
66	C₂×C₁₃×#41	C₂³	1	4	yes	—
67	C₂²×Q₈×C₁₃	—	2	1	no	—
68	C₂²×Q₈×C₁₃	—	2	2	no	—
69	C₂²×Q₈×C₁₃	—	4	4	no	—
70	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
72	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₁₃	—	2	1	no	—
74	C₂²×D₄×C₁₃	—	2	1	no	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	2	no	—
77	C₂²×D₄×C₁₃	—	2	4	no	—
78	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	—	2	1	no	—
83	C₂³×C₄×C₁₃	—	2	1	no	—
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
87	C₂×C₁₃×SD₁₆	—	4	8	no	—
88	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
89	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
90	C₂×C₁₃×D₈	C₂³	1	8	yes	—
91	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
94	C₁₃×#127	C₂³	1	2	yes	—
95	C₁₃×#124	—	2	8	no	—
96	C₁₃×#124	—	2	2	no	—
97	C₁₃×#124	—	2	2	no	—
98	C₁₃×#124	C₂³	1	4	yes	—
99	C₁₃×#123	—	2	4	no	—
100	C₁₃×#123	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	—	2	2	no	—
102	C₁₃×C₂²⋊Q₈	—	2	8	no	—
103	C₁₃×C₂²⋊Q₈	—	2	4	no	—
104	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
105	C₁₃×#121	—	2	8	no	—
106	C₁₃×#121	—	2	2	no	—
107	C₁₃×#121	—	2	2	no	—
108	C₁₃×#121	—	2	2	no	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	2	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	4	no	—
113	C₁₃×#121	C₂³	1	4	yes	—
114	C₁₃×#121	C₂³	1	4	yes	—
115	C₁₃×#121	C₂³	1	4	yes	—
116	C₁₃×#121	C₂³	1	4	yes	—
117	C₁₃×#120	—	2	4	no	—
118	C₁₃×#120	—	2	4	no	—
119	C₄×Q₈×C₁₃	—	2	2	no	—
120	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
121	C₄×D₄×C₁₃	—	2	8	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	D₄	1	4	yes	—
124	C₄×D₄×C₁₃	C₂³	1	4	yes	—
125	C₄×D₄×C₁₃	C₂³	1	4	yes	—
126	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
129	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
137	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
138	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
140	C₂×C₄²×C₁₃	—	2	1	no	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₁₃×#107	C₂³	1	8	yes	—
143	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
144	C₁₃×#103	C₂³	1	8	yes	—
145	C₁₃×#103	C₂³	1	8	yes	—
146	C₁₃×#102	C₂³	1	8	yes	—
147	C₁₃×#102	C₂³	1	8	yes	—
148	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
149	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
150	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
151	C₁₃×#97	C₂³	1	4	yes	—
152	#61572	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
153	C₂⁴×C₁₃	—	2	1	no	—
154	C₂⁴×C₁₃	—	2	2	no	—
155	C₂⁴×C₁₃	—	2	2	no	—
156	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₁₃×#41	—	2	8	no	—
159	C₁₃×#41	—	4	4	no	—
160	C₁₃×#41	—	4	8	no	—
161	C₁₃×#41	—	4	16	no	—
162	C₁₃×#41	—	4	8	no	—
163	C₂×Q₈×C₁₃	—	2	4	no	—
164	C₂×Q₈×C₁₃	—	2	1	no	—
165	C₂×Q₈×C₁₃	—	2	4	no	—
166	C₂×Q₈×C₁₃	—	2	1	no	—
167	C₂×Q₈×C₁₃	—	2	2	no	—
168	C₂×Q₈×C₁₃	—	2	8	no	—
169	C₂×Q₈×C₁₃	—	4	4	no	—
170	C₂×Q₈×C₁₃	—	4	2	no	—
171	C₂×Q₈×C₁₃	—	4	4	no	—
172	C₂×Q₈×C₁₃	—	4	8	no	—
173	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
174	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	4	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	4	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	2	no	—
183	C₂×D₄×C₁₃	—	2	2	no	—
184	C₂×D₄×C₁₃	—	2	2	no	—
185	C₂×D₄×C₁₃	—	2	2	no	—
186	C₂×D₄×C₁₃	—	4	2	no	—
187	C₂×D₄×C₁₃	—	4	4	no	—
188	C₂×D₄×C₁₃	—	4	4	no	—
189	C₂×D₄×C₁₃	—	4	4	no	—
190	C₂×D₄×C₁₃	—	4	16	no	—
191	C₂×D₄×C₁₃	—	4	8	no	—
192	C₂×D₄×C₁₃	—	4	4	no	—
193	C₂×D₄×C₁₃	—	4	8	no	—
194	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
195	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
196	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	—	2	1	no	—
198	C₂²×C₄×C₁₃	—	2	1	no	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	2	no	—
201	C₂²×C₄×C₁₃	—	2	2	no	—
202	C₂²×C₄×C₁₃	—	2	4	no	—
203	C₂²×C₄×C₁₃	—	2	4	no	—
204	C₂²×C₄×C₁₃	—	2	4	no	—
205	C₂²×C₄×C₁₃	—	4	2	no	—
206	C₂²×C₄×C₁₃	—	4	2	no	—
207	C₂²×C₄×C₁₃	—	4	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	1	yes	characteristic
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
213	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
218	C₁₃×SD₁₆	—	2	16	no	—
219	C₁₃×SD₁₆	—	4	8	no	—
220	C₁₃×D₈	—	4	8	no	—
221	C₁₃×M₁₆	—	4	4	no	—
222	C₂×C₈×C₁₃	—	4	4	no	—
223	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
224	C₁₃×C₄⋊C₄	—	2	4	no	—
225	C₁₃×C₄⋊C₄	—	2	4	no	—
226	C₁₃×C₄⋊C₄	—	2	1	no	—
227	C₁₃×C₄⋊C₄	—	2	2	no	—
228	C₁₃×C₄⋊C₄	—	2	2	no	—
229	C₁₃×C₄⋊C₄	—	2	2	no	—
230	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
233	C₁₃×C₂²⋊C₄	—	2	4	no	—
234	C₁₃×C₂²⋊C₄	—	2	4	no	—
235	C₁₃×C₂²⋊C₄	—	2	4	no	—
236	C₁₃×C₂²⋊C₄	—	2	4	no	—
237	C₁₃×C₂²⋊C₄	—	2	4	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	C₂×D₄	1	4	yes	—
242	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
243	C₄²×C₁₃	—	2	4	no	—
244	C₄²×C₁₃	C₂×D₄	1	2	yes	—
245	C₄²×C₁₃	C₂⁴	1	2	yes	—
246	#3496	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂×#548	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#3308	C₂×C₁₃	1	8	yes	complemented
249	#3265	C₂×C₁₃	1	8	yes	complemented
250	#3213	C₂×C₁₃	1	2	yes	complemented
251	#3193	C₂×C₁₃	1	2	yes	complemented
252	#3186	C₂×C₁₃	1	2	yes	complemented
253	#3112	C₂×C₁₃	1	2	yes	complemented
254	#3006	C₂×C₁₃	1	2	yes	complemented
255	C₂×#448	C₂×C₁₃	1	2	yes	complemented
256	#2973	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₂³×C₁₃	—	2	2	no	—
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	4	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	2	no	—
265	C₂³×C₁₃	—	4	2	no	—
266	C₂³×C₁₃	—	4	4	no	—
267	C₂³×C₁₃	—	4	2	no	—
268	C₂³×C₁₃	—	4	4	no	—
269	C₂³×C₁₃	—	8	2	no	—
270	C₂³×C₁₃	—	8	2	no	—
271	C₂³×C₁₃	—	8	2	no	—
272	C₂³×C₁₃	—	8	2	no	—
273	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	complemented
274	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₁₃	—	2	4	no	—
278	Q₈×C₁₃	—	2	2	no	—
279	Q₈×C₁₃	—	2	4	no	—
280	Q₈×C₁₃	—	4	8	no	—
281	Q₈×C₁₃	—	4	2	no	—
282	Q₈×C₁₃	—	4	4	no	—
283	Q₈×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
284	D₄×C₁₃	—	2	8	no	—
285	D₄×C₁₃	—	2	4	no	—
286	D₄×C₁₃	—	2	8	no	—
287	D₄×C₁₃	—	4	8	no	—
288	D₄×C₁₃	—	4	4	no	—
289	D₄×C₁₃	—	4	2	no	—
290	D₄×C₁₃	—	4	8	no	—
291	D₄×C₁₃	—	4	8	no	—
292	D₄×C₁₃	—	4	8	no	—
293	D₄×C₁₃	—	4	8	no	—
294	D₄×C₁₃	—	8	2	no	—
295	D₄×C₁₃	—	8	2	no	—
296	D₄×C₁₃	—	8	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	4	no	—
301	C₂×C₄×C₁₃	—	2	4	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	2	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	4	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	2	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	2	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	8	no	—
312	C₂×C₄×C₁₃	—	4	8	no	—
313	C₂×C₄×C₁₃	—	4	8	no	—
314	C₂×C₄×C₁₃	—	4	2	no	—
315	C₂×C₄×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	4	2	no	—
317	C₂×C₄×C₁₃	—	4	4	no	—
318	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
324	C₈×C₁₃	—	2	8	no	—
325	C₂×H(5,𝔽₂)	—	2	1	no	—
326	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
328	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
329	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
330	#548	—	2	4	no	—
331	#548	C₂²×C₁₃	1	8	yes	complemented
332	#547	C₂²×C₁₃	1	4	yes	complemented
333	#546	—	2	4	no	—
334	D₄²	C₂²×C₁₃	1	4	yes	complemented
335	#537	—	2	1	no	—
336	#534	—	2	1	no	—
337	#534	—	2	1	no	—
338	#532	C₂²×C₁₃	1	2	yes	—
339	C₂×#124	—	2	1	no	—
340	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
341	C₂×C₂²⋊Q₈	—	2	1	no	—
342	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	C₂×#121	—	2	1	no	—
344	C₂×#121	C₂²×C₁₃	1	2	yes	—
345	C₂×#121	C₂²×C₁₃	1	2	yes	—
346	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
347	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
348	C₂×C₄×D₄	—	2	1	no	—
349	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
350	#496	C₂²×C₁₃	1	4	yes	complemented
351	#489	C₂²×C₁₃	1	4	yes	complemented
352	#484	C₂²×C₁₃	1	4	yes	complemented
353	#480	C₂²×C₁₃	1	4	yes	complemented
354	#480	C₂²×C₁₃	1	4	yes	complemented
355	#477	C₂²×C₁₃	1	4	yes	complemented
356	#468	C₂²×C₁₃	1	8	yes	complemented
357	#466	C₂²×C₁₃	1	8	yes	complemented
358	#463	C₂²×C₁₃	1	8	yes	complemented
359	#460	C₂²×C₁₃	1	4	yes	complemented
360	#450	C₂²×C₁₃	1	4	yes	complemented
361	#449	C₂²×C₁₃	1	8	yes	complemented
362	#448	C₂²×C₁₃	1	4	yes	complemented
363	#448	C₂²×C₁₃	1	4	yes	complemented
364	#448	C₂²×C₁₃	1	8	yes	complemented
365	#447	C₂²×C₁₃	1	4	yes	complemented
366	#447	C₂²×C₁₃	1	4	yes	complemented
367	#440	C₂²×C₁₃	1	8	yes	complemented
368	#435	C₂²×C₁₃	1	8	yes	complemented
369	#432	C₂²×C₁₃	1	2	yes	complemented
370	#417	C₂²×C₁₃	1	4	yes	complemented
371	C₂×#103	C₂²×C₁₃	1	4	yes	complemented
372	#407	C₂²×C₁₃	1	2	yes	complemented
373	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
374	C₂²×C₁₃	—	2	1	no	—
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	2	1	no	—
377	C₂²×C₁₃	—	2	2	no	—
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	4	4	no	—
382	C₂²×C₁₃	—	4	4	no	—
383	C₂²×C₁₃	—	4	2	no	—
384	C₂²×C₁₃	—	4	2	no	—
385	C₂²×C₁₃	—	4	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	—	4	2	no	—
388	C₂²×C₁₃	—	8	2	no	—
389	C₂²×C₁₃	—	8	4	no	—
390	C₂²×C₁₃	—	16	4	no	—
391	C₂²×C₁₃	—	16	4	no	—
392	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
393	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
394	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	2	4	no	—
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	2	1	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	4	4	no	—
403	C₄×C₁₃	—	4	2	no	—
404	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
405	H(5,𝔽₂)	—	4	8	no	—
406	C₂×#41	—	2	4	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	2	2	no	—
409	C₂×#41	—	4	4	no	—
410	C₂×#41	C₂³×C₁₃	1	4	yes	—
411	C₂²×Q₈	—	2	1	no	—
412	C₂²×Q₈	—	2	2	no	—
413	C₂²×Q₈	—	4	4	no	—
414	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
416	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	—	2	2	no	—
420	C₂²×D₄	—	2	2	no	—
421	C₂²×D₄	—	2	4	no	—
422	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
423	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
424	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
425	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂³×C₄	—	2	1	no	—
427	C₂³×C₄	—	2	1	no	—
428	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	AGL(1,ℤ/8)	—	4	8	no	—
431	C₂×SD₁₆	—	4	8	no	—
432	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
433	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
434	C₂×D₈	C₂³×C₁₃	1	8	yes	—
435	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
436	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
437	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
438	#127	C₂³×C₁₃	1	2	yes	—
439	#124	—	2	8	no	—
440	#124	—	2	2	no	—
441	#124	—	2	2	no	—
442	#124	C₂³×C₁₃	1	4	yes	—
443	#123	—	2	4	no	—
444	#123	—	2	4	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	C₂²⋊Q₈	—	2	4	no	—
448	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
449	#121	—	2	8	no	—
450	#121	—	2	2	no	—
451	#121	—	2	2	no	—
452	#121	—	2	2	no	—
453	#121	—	2	2	no	—
454	#121	—	2	2	no	—
455	#121	—	2	2	no	—
456	#121	—	2	4	no	—
457	#121	C₂³×C₁₃	1	4	yes	—
458	#121	C₂³×C₁₃	1	4	yes	—
459	#121	C₂³×C₁₃	1	4	yes	—
460	#121	C₂³×C₁₃	1	4	yes	—
461	#120	—	2	4	no	—
462	#120	—	2	4	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
465	C₄×D₄	—	2	8	no	—
466	C₄×D₄	—	2	2	no	—
467	C₄×D₄	D₄×C₁₃	1	4	yes	—
468	C₄×D₄	C₂³×C₁₃	1	4	yes	—
469	C₄×D₄	C₂³×C₁₃	1	4	yes	—
470	C₂×C₄⋊C₄	—	2	1	no	—
471	C₂×C₄⋊C₄	—	2	1	no	—
472	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₂²⋊C₄	—	2	1	no	—
477	C₂×C₂²⋊C₄	—	2	1	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₂²⋊C₄	—	2	2	no	—
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	1	no	—
482	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄²	—	2	1	no	—
485	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
486	#107	C₂³×C₁₃	1	8	yes	—
487	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
488	#103	C₂³×C₁₃	1	8	yes	—
489	#103	C₂³×C₁₃	1	8	yes	—
490	#102	C₂³×C₁₃	1	8	yes	—
491	#102	C₂³×C₁₃	1	8	yes	—
492	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
493	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
494	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
495	#97	C₂³×C₁₃	1	4	yes	—
496	C₂×C₁₃	—	2	2	no	—
497	C₂×C₁₃	—	2	4	no	—
498	C₂×C₁₃	—	4	2	no	—
499	C₂×C₁₃	—	8	2	no	—
500	C₂×C₁₃	—	8	4	no	—
501	C₂×C₁₃	#3484	1	1	yes	characteristic
502	C₂×C₁₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
503	C₂×C₁₃	#3586	1	1	yes	characteristic
504	C₂⁴	—	2	1	no	—
505	C₂⁴	—	2	2	no	—
506	C₂⁴	—	2	2	no	—
507	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
509	#41	—	2	8	no	—
510	#41	—	4	4	no	—
511	#41	—	4	8	no	—
512	#41	—	4	16	no	—
513	#41	—	4	8	no	—
514	C₂×Q₈	—	2	4	no	—
515	C₂×Q₈	—	2	1	no	—
516	C₂×Q₈	—	2	4	no	—
517	C₂×Q₈	—	2	1	no	—
518	C₂×Q₈	—	2	2	no	—
519	C₂×Q₈	—	2	8	no	—
520	C₂×Q₈	—	4	4	no	—
521	C₂×Q₈	—	4	2	no	—
522	C₂×Q₈	—	4	4	no	—
523	C₂×Q₈	—	4	8	no	—
524	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
525	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	4	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	1	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	4	2	no	—
538	C₂×D₄	—	4	4	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	4	no	—
541	C₂×D₄	—	4	16	no	—
542	C₂×D₄	—	4	8	no	—
543	C₂×D₄	—	4	8	no	—
544	C₂×D₄	—	4	4	no	—
545	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
546	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
547	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	4	no	—
554	C₂²×C₄	—	2	4	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	2	no	—
558	C₂²×C₄	—	4	4	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
567	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
569	SD₁₆	—	2	16	no	—
570	SD₁₆	—	4	8	no	—
571	D₈	—	4	8	no	—
572	M₁₆	—	4	4	no	—
573	C₂×C₈	—	4	4	no	—
574	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
582	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
583	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	4	no	—
589	C₂²⋊C₄	—	2	4	no	—
590	C₂²⋊C₄	—	2	4	no	—
591	C₂²⋊C₄	—	2	4	no	—
592	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
593	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
594	C₄²	—	2	4	no	—
595	C₄²	C₂×D₄×C₁₃	1	2	yes	—
596	C₄²	C₂⁴×C₁₃	1	2	yes	—
597	C₁₃	#61572	1	1	yes	characteristic, direct product factor, Sylow
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	4	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	2	no	—
606	C₂³	—	4	2	no	—
607	C₂³	—	4	4	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	4	no	—
610	C₂³	—	8	2	no	—
611	C₂³	—	8	2	no	—
612	C₂³	—	8	2	no	—
613	C₂³	—	8	2	no	—
614	C₂³	C₁₃×AGL(1,ℤ/8)	1	4	yes	complemented
615	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
616	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
617	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
618	Q₈	—	2	4	no	—
619	Q₈	—	2	2	no	—
620	Q₈	—	2	4	no	—
621	Q₈	—	4	8	no	—
622	Q₈	—	4	2	no	—
623	Q₈	—	4	4	no	—
624	Q₈	C₁₃×H(5,𝔽₂)	1	4	yes	complemented
625	D₄	—	2	8	no	—
626	D₄	—	2	4	no	—
627	D₄	—	2	8	no	—
628	D₄	—	4	8	no	—
629	D₄	—	4	4	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	8	no	—
632	D₄	—	4	8	no	—
633	D₄	—	4	8	no	—
634	D₄	—	4	8	no	—
635	D₄	—	8	2	no	—
636	D₄	—	8	2	no	—
637	D₄	—	8	2	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	2	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	8	no	—
653	C₂×C₄	—	4	8	no	—
654	C₂×C₄	—	4	8	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	4	no	—
659	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
660	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
661	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
662	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
663	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
664	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
665	C₈	—	2	8	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	2	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	4	4	no	—
674	C₂²	—	4	4	no	—
675	C₂²	—	4	2	no	—
676	C₂²	—	4	4	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	4	no	—
680	C₂²	—	8	2	no	—
681	C₂²	—	8	4	no	—
682	C₂²	—	16	4	no	—
683	C₂²	—	16	4	no	—
684	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
685	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	4	yes	—
686	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	4	no	—
690	C₄	—	2	2	no	—
691	C₄	—	2	1	no	—
692	C₄	—	2	2	no	—
693	C₄	—	4	4	no	—
694	C₄	—	4	2	no	—
695	C₄	—	4	2	no	—
696	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
697	C₂	—	2	2	no	—
698	C₂	—	2	4	no	—
699	C₂	—	4	2	no	—
700	C₂	—	8	2	no	—
701	C₂	—	8	4	no	—
702	C₂	C₁₃×#3484	1	1	yes	characteristic
703	C₂	C₂²×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
704	C₂	C₁₃×#3586	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 ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3496	C₂	semidirect
2. C₂×C₁₃×#548	C₂	semidirect
3. C₁₃×#3308	C₂	semidirect
4. C₁₃×#3265	C₂	semidirect
5. C₁₃×#3213	C₂	semidirect
6. C₁₃×#3193	C₂	semidirect
7. C₁₃×#3186	C₂	semidirect
8. C₁₃×#3112	C₂	semidirect
9. C₁₃×#3006	C₂	semidirect
10. C₂×C₁₃×#448	C₂	semidirect
11. C₁₃×#2973	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
15. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂²×C₁₃×SD₁₆	C₂²	semidirect
18. C₁₃×#548	C₂²	semidirect
19. C₁₃×#547	C₂²	semidirect
21. D₄²×C₁₃	C₂²	semidirect
27. C₂×C₁₃×#124	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
34. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#496	C₂²	semidirect
38. C₁₃×#489	C₂²	semidirect
39. C₁₃×#484	C₂²	semidirect
40. C₁₃×#480	C₂²	semidirect
41. C₁₃×#480	C₂²	semidirect
42. C₁₃×#477	C₂²	semidirect
43. C₁₃×#468	C₂²	semidirect
44. C₁₃×#466	C₂²	semidirect
45. C₁₃×#463	C₂²	semidirect
46. C₁₃×#460	C₂²	semidirect
47. C₁₃×#450	C₂²	semidirect
48. C₁₃×#449	C₂²	semidirect
49. C₁₃×#448	C₂²	semidirect
50. C₁₃×#448	C₂²	semidirect
51. C₁₃×#448	C₂²	semidirect
52. C₁₃×#447	C₂²	semidirect
53. C₁₃×#447	C₂²	semidirect
54. C₁₃×#440	C₂²	semidirect
55. C₁₃×#435	C₂²	semidirect
56. C₁₃×#432	C₂²	semidirect
57. C₁₃×#417	C₂²	semidirect
58. C₂×C₁₃×#103	C₂²	semidirect
59. C₁₃×#407	C₂²	semidirect
60. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
152. #61572	C₁₃	direct (N × H)
246. #3496	C₂×C₁₃	semidirect
247. C₂×#548	C₂×C₁₃	semidirect
248. #3308	C₂×C₁₃	semidirect
249. #3265	C₂×C₁₃	semidirect
250. #3213	C₂×C₁₃	semidirect
251. #3193	C₂×C₁₃	semidirect
252. #3186	C₂×C₁₃	semidirect
253. #3112	C₂×C₁₃	semidirect
254. #3006	C₂×C₁₃	semidirect
255. C₂×#448	C₂×C₁₃	semidirect
256. #2973	C₂×C₁₃	semidirect
273. C₂³×C₁₃	AGL(1,ℤ/8)	semidirect
283. Q₈×C₁₃	H(5,𝔽₂)	semidirect
326. C₂²×#41	C₂²×C₁₃	semidirect
327. C₂³×Q₈	C₂²×C₁₃	semidirect
328. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
329. C₂²×SD₁₆	C₂²×C₁₃	semidirect
331. #548	C₂²×C₁₃	semidirect
332. #547	C₂²×C₁₃	semidirect
334. D₄²	C₂²×C₁₃	semidirect
340. C₂×#124	C₂²×C₁₃	semidirect
342. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
346. C₂×#121	C₂²×C₁₃	semidirect
347. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
350. #496	C₂²×C₁₃	semidirect
351. #489	C₂²×C₁₃	semidirect
352. #484	C₂²×C₁₃	semidirect
353. #480	C₂²×C₁₃	semidirect
354. #480	C₂²×C₁₃	semidirect
355. #477	C₂²×C₁₃	semidirect
356. #468	C₂²×C₁₃	semidirect
357. #466	C₂²×C₁₃	semidirect
358. #463	C₂²×C₁₃	semidirect
359. #460	C₂²×C₁₃	semidirect
360. #450	C₂²×C₁₃	semidirect
361. #449	C₂²×C₁₃	semidirect
362. #448	C₂²×C₁₃	semidirect
363. #448	C₂²×C₁₃	semidirect
364. #448	C₂²×C₁₃	semidirect
365. #447	C₂²×C₁₃	semidirect
366. #447	C₂²×C₁₃	semidirect
367. #440	C₂²×C₁₃	semidirect
368. #435	C₂²×C₁₃	semidirect
369. #432	C₂²×C₁₃	semidirect
370. #417	C₂²×C₁₃	semidirect
371. C₂×#103	C₂²×C₁₃	semidirect
372. #407	C₂²×C₁₃	semidirect
373. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
597. C₁₃	#61572	direct (N × H)
614. C₂³	C₁₃×AGL(1,ℤ/8)	semidirect
624. Q₈	C₁₃×H(5,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3496	2
C₂×C₁₃×#548	2
C₁₃×#3308	2
C₁₃×#3265	2
C₁₃×#3213	2
C₁₃×#3193	2
C₁₃×#3186	2
C₁₃×#3112	2
C₁₃×#3006	2
C₂×C₁₃×#448	2
C₁₃×#2973	2
#61572	13

Subgroups — C13×#61572 #15747911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61572 #15747911