Subgroups — C₁₃×#33524 #15719863

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2186	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2185	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	—	2	1	no	—
11	C₁₃×#578	—	2	4	no	—
12	C₁₃×#578	—	2	4	no	—
13	C₂×C₁₃×#137	—	2	1	no	—
14	C₂×C₁₃×#137	—	2	2	no	—
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
21	C₁₃×#535	—	2	1	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₂×C₁₃×SD₃₂	—	2	4	no	—
24	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	—
25	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
26	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
27	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
29	C₁₃×#469	—	2	2	no	—
30	C₁₃×#466	C₂²	1	4	yes	—
31	C₁₃×#427	C₂²	1	1	yes	characteristic
32	C₁₃×#418	—	2	1	no	—
33	C₁₃×#358	C₂²	1	2	yes	complemented
34	C₁₃×#358	C₂²	1	4	yes	complemented
35	C₁₃×#357	C₂²	1	2	yes	complemented
36	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	C₁₃×2₋¹⁺⁴	—	2	8	no	—
38	C₁₃×2₋¹⁺⁴	—	4	4	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	4	2	no	—
42	C₂×C₁₃×#41	—	4	1	no	—
43	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	—	2	1	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	4	1	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₁₃×#137	—	2	8	no	—
49	C₁₃×#137	—	2	16	no	—
50	C₁₃×#135	—	2	4	no	—
51	C₁₃×#135	—	2	4	no	—
52	C₁₃×#135	—	2	2	no	—
53	C₁₃×#135	D₄	1	4	yes	complemented
54	C₂×C₁₃×Q₁₆	—	2	4	no	—
55	C₂×C₁₃×Q₁₆	—	2	4	no	—
56	C₂×C₁₃×Q₁₆	—	2	1	no	—
57	C₂×C₁₃×Q₁₆	—	2	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
60	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×SD₁₆	—	2	1	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×D₈	—	2	2	no	—
65	C₂×C₁₃×D₈	—	2	2	no	—
66	C₂×C₁₃×D₈	—	2	1	no	—
67	C₂×C₁₃×D₈	C₂³	1	2	yes	—
68	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
69	C₁₃×#131	—	2	2	no	—
70	C₁₃×#131	—	2	2	no	—
71	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
72	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#127	—	4	1	no	—
76	C₁₃×#124	—	4	1	no	—
77	C₁₃×#121	—	2	4	no	—
78	C₁₃×#120	—	4	2	no	—
79	C₁₃×#117	—	2	1	no	—
80	C₁₃×SD₃₂	—	2	8	no	—
81	C₁₃×SD₃₂	—	2	4	no	—
82	C₁₃×D₁₆	—	2	4	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₂×C₁₃×C₁₆	—	2	2	no	—
85	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
86	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
87	C₁₃×#107	C₂³	1	2	yes	—
88	C₁₃×#106	—	2	1	no	—
89	C₁₃×#102	—	2	4	no	—
90	#33524	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	4	1	no	—
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₁₃×#41	—	2	8	no	—
95	C₁₃×#41	—	2	4	no	—
96	C₁₃×#41	—	4	4	no	—
97	C₁₃×#41	—	4	16	no	—
98	C₁₃×#41	—	4	8	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	4	4	no	—
105	C₂×Q₈×C₁₃	—	4	8	no	—
106	C₂×Q₈×C₁₃	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	4	1	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	4	1	no	—
114	C₂×D₄×C₁₃	—	4	4	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	—	4	1	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	D₈	1	2	yes	—
119	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	—	4	1	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	4	1	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×Q₁₆	—	2	8	no	—
127	C₁₃×Q₁₆	—	2	4	no	—
128	C₁₃×Q₁₆	—	2	1	no	—
129	C₁₃×Q₁₆	—	2	2	no	—
130	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
131	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
132	C₁₃×SD₁₆	—	2	8	no	—
133	C₁₃×SD₁₆	—	2	4	no	—
134	C₁₃×D₈	—	2	1	no	—
135	C₁₃×D₈	—	2	2	no	—
136	C₁₃×D₈	—	2	2	no	—
137	C₁₃×D₈	—	4	2	no	—
138	C₁₃×D₈	C₂×D₄	1	2	yes	—
139	C₁₃×M₁₆	—	2	2	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₂²⋊C₄	—	4	1	no	—
150	C₁₃×C₂²⋊C₄	—	4	4	no	—
151	C₄²×C₁₃	—	4	1	no	—
152	C₁₃×C₁₆	—	2	2	no	—
153	C₁₃×C₁₆	—	2	2	no	—
154	C₂×#578	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2186	C₂×C₁₃	1	4	yes	complemented
159	#2185	C₂×C₁₃	1	4	yes	complemented
160	#2141	C₂×C₁₃	1	1	yes	characteristic, complemented
161	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	8	2	no	—
166	C₂³×C₁₃	—	16	2	no	—
167	C₂³×C₁₃	C₂×D₈	1	2	yes	—
168	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	2	4	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	4	8	no	—
173	Q₈×C₁₃	—	4	1	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	Q₈×C₁₃	—	4	4	no	—
176	D₄×C₁₃	—	2	4	no	—
177	D₄×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	4	8	no	—
180	D₄×C₁₃	—	4	4	no	—
181	D₄×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	4	1	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	8	2	no	—
185	D₄×C₁₃	—	16	4	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	4	8	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	#120	1	2	yes	—
196	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	#120	1	2	yes	—
202	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×2₋¹⁺⁴	—	2	1	no	—
205	#578	—	2	4	no	—
206	#578	—	2	4	no	—
207	C₂×#137	—	2	1	no	—
208	C₂×#137	—	2	2	no	—
209	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
211	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
213	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
215	#535	—	2	1	no	—
216	#509	—	2	4	no	—
217	C₂×SD₃₂	—	2	4	no	—
218	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	—
219	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
220	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
221	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
223	#469	—	2	2	no	—
224	#466	C₂²×C₁₃	1	4	yes	—
225	#427	C₂²×C₁₃	1	1	yes	characteristic
226	#418	—	2	1	no	—
227	#358	C₂²×C₁₃	1	2	yes	complemented
228	#358	C₂²×C₁₃	1	4	yes	complemented
229	#357	C₂²×C₁₃	1	2	yes	complemented
230	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	4	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	—	8	4	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	16	4	no	—
239	C₂²×C₁₃	#447	1	2	yes	—
240	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	—	4	4	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	8	2	no	—
245	C₄×C₁₃	#447	1	2	yes	—
246	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
247	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
248	2₋¹⁺⁴	—	2	8	no	—
249	2₋¹⁺⁴	—	4	4	no	—
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	4	2	no	—
253	C₂×#41	—	4	1	no	—
254	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	—	2	2	no	—
257	C₂²×Q₈	—	4	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	#137	—	2	8	no	—
260	#137	—	2	16	no	—
261	#135	—	2	4	no	—
262	#135	—	2	4	no	—
263	#135	—	2	2	no	—
264	#135	D₄×C₁₃	1	4	yes	complemented
265	C₂×Q₁₆	—	2	4	no	—
266	C₂×Q₁₆	—	2	4	no	—
267	C₂×Q₁₆	—	2	1	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
271	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
272	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
273	C₂×SD₁₆	—	2	1	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	1	no	—
278	C₂×D₈	C₂³×C₁₃	1	2	yes	—
279	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
280	#131	—	2	2	no	—
281	#131	—	2	2	no	—
282	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
283	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	#127	—	4	1	no	—
287	#124	—	4	1	no	—
288	#121	—	2	4	no	—
289	#120	—	4	2	no	—
290	#117	—	2	1	no	—
291	SD₃₂	—	2	8	no	—
292	SD₃₂	—	2	4	no	—
293	D₁₆	—	2	4	no	—
294	M₃₂	—	2	2	no	—
295	C₂×C₁₆	—	2	2	no	—
296	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
297	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
298	#107	C₂³×C₁₃	1	2	yes	—
299	#106	—	2	1	no	—
300	#102	—	2	4	no	—
301	C₂×C₁₃	—	2	2	no	—
302	C₂×C₁₃	—	4	2	no	—
303	C₂×C₁₃	—	8	2	no	—
304	C₂×C₁₃	—	16	2	no	—
305	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
306	C₂×C₁₃	#3416	1	2	yes	—
307	C₂⁴	—	4	1	no	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	2	8	no	—
311	#41	—	2	4	no	—
312	#41	—	4	4	no	—
313	#41	—	4	16	no	—
314	#41	—	4	8	no	—
315	#41	—	4	2	no	—
316	C₂×Q₈	—	2	8	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	8	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	C₁₃×D₈	1	2	yes	—
335	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	1	no	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	Q₁₆	—	2	4	no	—
344	Q₁₆	—	2	1	no	—
345	Q₁₆	—	2	2	no	—
346	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
347	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
348	SD₁₆	—	2	8	no	—
349	SD₁₆	—	2	4	no	—
350	D₈	—	2	1	no	—
351	D₈	—	2	2	no	—
352	D₈	—	2	2	no	—
353	D₈	—	4	2	no	—
354	D₈	C₂×D₄×C₁₃	1	2	yes	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
363	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	4	no	—
367	C₄²	—	4	1	no	—
368	C₁₆	—	2	2	no	—
369	C₁₆	—	2	2	no	—
370	C₁₃	#33524	1	1	yes	characteristic, direct product factor, Sylow
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	16	2	no	—
375	C₂³	C₂×C₁₃×D₈	1	2	yes	—
376	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	4	8	no	—
381	Q₈	—	4	4	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	16	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₁₃×#120	1	2	yes	—
404	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
405	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
406	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	C₁₃×#120	1	2	yes	—
410	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
411	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	16	4	no	—
420	C₂²	C₁₃×#447	1	2	yes	—
421	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	C₁₃×#447	1	2	yes	—
427	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
428	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	2	no	—
432	C₂	—	16	2	no	—
433	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
434	C₂	C₁₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₂×C₁₃×#509	C₂	semidirect
3. C₂²×C₁₃×SD₃₂	C₂	semidirect
4. C₁₃×#3058	C₂	semidirect
5. C₁₃×#2186	C₂	semidirect
6. C₁₃×#2185	C₂	semidirect
7. C₁₃×#2141	C₂	semidirect
8. C₁₃×#2138	C₂	semidirect
9. C₁₃×#2113	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
18. C₂²×C₁₃×Q₁₆	C₂²	semidirect
33. C₁₃×#358	C₂²	semidirect
34. C₁₃×#358	C₂²	semidirect
35. C₁₃×#357	C₂²	semidirect
36. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
53. C₁₃×#135	D₄	semidirect
59. C₂×C₁₃×Q₁₆	D₄	semidirect
90. #33524	C₁₃	direct (N × H)
154. C₂×#578	C₂×C₁₃	semidirect
155. C₂×#509	C₂×C₁₃	semidirect
156. C₂²×SD₃₂	C₂×C₁₃	semidirect
157. #3058	C₂×C₁₃	semidirect
158. #2186	C₂×C₁₃	semidirect
159. #2185	C₂×C₁₃	semidirect
160. #2141	C₂×C₁₃	semidirect
161. #2138	C₂×C₁₃	semidirect
162. #2113	C₂×C₁₃	semidirect
210. C₂×#135	C₂²×C₁₃	semidirect
212. C₂²×Q₁₆	C₂²×C₁₃	semidirect
227. #358	C₂²×C₁₃	semidirect
228. #358	C₂²×C₁₃	semidirect
229. #357	C₂²×C₁₃	semidirect
230. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
264. #135	D₄×C₁₃	semidirect
270. C₂×Q₁₆	D₄×C₁₃	semidirect
370. C₁₃	#33524	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#578	2
C₂×C₁₃×#509	2
C₂²×C₁₃×SD₃₂	2
C₁₃×#3058	2
C₁₃×#2186	2
C₁₃×#2185	2
C₁₃×#2141	2
C₁₃×#2138	2
C₁₃×#2113	2
#33524	13

Subgroups — C13×#33524 #15719863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33524 #15719863