Subgroups — C₁₃×#33519 #15719858

Order 3328.

1144 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2189	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2186	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	—	2	1	no	—
11	C₂×C₁₃×#135	—	2	4	no	—
12	C₂×C₁₃×#135	—	2	4	no	—
13	C₂×C₁₃×#135	—	2	2	no	—
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#135	C₂²	1	4	yes	—
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	—	2	1	no	—
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#525	—	2	1	no	—
21	C₁₃×#510	—	2	4	no	—
22	C₁₃×#509	—	2	4	no	—
23	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
24	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
25	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
26	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
27	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
29	C₁₃×#467	C₂²	1	2	yes	complemented
30	C₁₃×#466	C₂²	1	2	yes	complemented
31	C₁₃×#465	—	2	2	no	—
32	C₁₃×#427	C₂²	1	1	yes	characteristic
33	C₁₃×#416	—	2	1	no	—
34	C₁₃×#358	C₂²	1	4	yes	complemented
35	C₁₃×#357	C₂²	1	4	yes	complemented
36	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	C₂×C₁₃×#41	—	2	8	no	—
38	C₂×C₁₃×#41	—	2	4	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	—	4	4	no	—
41	C₂×C₁₃×#41	—	4	2	no	—
42	C₂²×Q₈×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	4	1	no	—
45	C₂³×C₄×C₁₃	—	4	1	no	—
46	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
47	C₁₃×#135	—	2	16	no	—
48	C₁₃×#135	—	2	8	no	—
49	C₁₃×#135	—	2	8	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₁₃×#135	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	D₄	1	4	yes	complemented
55	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×SD₁₆	—	2	8	no	—
58	C₂×C₁₃×SD₁₆	—	2	4	no	—
59	C₂×C₁₃×SD₁₆	—	2	1	no	—
60	C₂×C₁₃×D₈	—	2	1	no	—
61	C₂×C₁₃×D₈	—	2	2	no	—
62	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
63	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×D₈	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃	—	2	2	no	—
66	C₂²×C₈×C₁₃	—	2	2	no	—
67	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	D₄	1	2	yes	—
69	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#123	—	4	1	no	—
72	C₁₃×C₂²⋊Q₈	—	2	2	no	—
73	C₁₃×#121	—	2	2	no	—
74	C₁₃×#120	—	4	1	no	—
75	C₄×D₄×C₁₃	—	4	2	no	—
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×Q₃₂	—	2	4	no	—
78	C₁₃×SD₃₂	—	2	4	no	—
79	C₁₃×SD₃₂	—	2	4	no	—
80	C₁₃×D₁₆	—	2	4	no	—
81	C₁₃×M₃₂	—	2	2	no	—
82	C₁₃×M₃₂	—	2	2	no	—
83	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
84	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
85	C₁₃×#107	C₂³	1	2	yes	—
86	C₁₃×#106	—	2	1	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#102	—	2	2	no	—
89	#33519	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
92	C₁₃×#41	—	2	16	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₁₃×#41	—	4	16	no	—
95	C₁₃×#41	—	4	2	no	—
96	C₁₃×#41	—	4	2	no	—
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	4	1	no	—
101	C₂×Q₈×C₁₃	—	4	2	no	—
102	C₂×D₄×C₁₃	—	2	4	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	4	8	no	—
106	C₂×D₄×C₁₃	—	4	4	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	4	1	no	—
109	C₂×D₄×C₁₃	—	4	1	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	4	8	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	4	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	D₈	1	2	yes	—
118	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₁₃×Q₁₆	—	2	4	no	—
122	C₁₃×Q₁₆	—	2	2	no	—
123	C₁₃×Q₁₆	—	2	1	no	—
124	C₁₃×Q₁₆	—	2	1	no	—
125	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
126	C₁₃×SD₁₆	—	2	16	no	—
127	C₁₃×SD₁₆	—	4	2	no	—
128	C₁₃×D₈	—	2	4	no	—
129	C₁₃×D₈	—	2	2	no	—
130	C₁₃×D₈	—	2	1	no	—
131	C₁₃×D₈	—	2	1	no	—
132	C₁₃×D₈	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	4	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	4	2	no	—
144	C₁₃×C₂²⋊C₄	—	4	1	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₄²×C₁₃	—	4	1	no	—
148	C₁₃×C₁₆	—	2	2	no	—
149	C₁₃×C₁₆	—	2	2	no	—
150	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#509	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#3050	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2189	C₂×C₁₃	1	4	yes	complemented
155	#2186	C₂×C₁₃	1	4	yes	complemented
156	#2141	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2140	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	4	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	8	4	no	—
165	C₂³×C₁₃	C₂×D₈	1	2	yes	—
166	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
167	Q₈×C₁₃	—	2	4	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	4	4	no	—
170	Q₈×C₁₃	—	4	1	no	—
171	Q₈×C₁₃	—	4	1	no	—
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	—	4	16	no	—
174	D₄×C₁₃	—	4	1	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	1	no	—
177	D₄×C₁₃	—	4	4	no	—
178	D₄×C₁₃	—	8	4	no	—
179	D₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	4	16	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	4	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	#120	1	2	yes	—
191	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	#120	1	2	yes	—
197	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
199	C₂²×#41	—	2	1	no	—
200	C₂×#135	—	2	4	no	—
201	C₂×#135	—	2	4	no	—
202	C₂×#135	—	2	2	no	—
203	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#135	C₂²×C₁₃	1	4	yes	—
205	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×SD₁₆	—	2	1	no	—
207	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#525	—	2	1	no	—
210	#510	—	2	4	no	—
211	#509	—	2	4	no	—
212	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
213	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
214	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
215	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
216	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
218	#467	C₂²×C₁₃	1	2	yes	complemented
219	#466	C₂²×C₁₃	1	2	yes	complemented
220	#465	—	2	2	no	—
221	#427	C₂²×C₁₃	1	1	yes	characteristic
222	#416	—	2	1	no	—
223	#358	C₂²×C₁₃	1	4	yes	complemented
224	#357	C₂²×C₁₃	1	4	yes	complemented
225	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	—	4	4	no	—
231	C₂²×C₁₃	—	4	4	no	—
232	C₂²×C₁₃	—	8	8	no	—
233	C₂²×C₁₃	—	8	4	no	—
234	C₂²×C₁₃	—	8	2	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	#447	1	2	yes	—
237	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	4	4	no	—
240	C₄×C₁₃	—	8	2	no	—
241	C₄×C₁₃	—	8	1	no	—
242	C₄×C₁₃	#447	1	2	yes	—
243	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
244	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×#41	—	2	8	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	2	1	no	—
248	C₂×#41	—	4	4	no	—
249	C₂×#41	—	4	2	no	—
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	4	1	no	—
253	C₂³×C₄	—	4	1	no	—
254	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
255	#135	—	2	16	no	—
256	#135	—	2	8	no	—
257	#135	—	2	8	no	—
258	#135	—	2	2	no	—
259	#135	—	2	2	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	D₄×C₁₃	1	4	yes	complemented
263	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×SD₁₆	—	2	8	no	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	2	2	no	—
270	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
271	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×D₈	C₂³×C₁₃	1	2	yes	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	D₄×C₁₃	1	2	yes	—
277	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
278	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
279	#123	—	4	1	no	—
280	C₂²⋊Q₈	—	2	2	no	—
281	#121	—	2	2	no	—
282	#120	—	4	1	no	—
283	C₄×D₄	—	4	2	no	—
284	#117	—	2	1	no	—
285	Q₃₂	—	2	4	no	—
286	SD₃₂	—	2	4	no	—
287	SD₃₂	—	2	4	no	—
288	D₁₆	—	2	4	no	—
289	M₃₂	—	2	2	no	—
290	M₃₂	—	2	2	no	—
291	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
292	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
293	#107	C₂³×C₁₃	1	2	yes	—
294	#106	—	2	1	no	—
295	#103	—	2	2	no	—
296	#102	—	2	2	no	—
297	C₂×C₁₃	—	2	2	no	—
298	C₂×C₁₃	—	4	2	no	—
299	C₂×C₁₃	—	8	4	no	—
300	C₂×C₁₃	—	16	1	no	—
301	C₂×C₁₃	C₂×#447	1	1	yes	characteristic
302	C₂×C₁₃	#3414	1	2	yes	—
303	C₂⁴	—	4	1	no	—
304	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
305	#41	—	2	16	no	—
306	#41	—	4	16	no	—
307	#41	—	4	8	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	4	8	no	—
319	C₂×D₄	—	4	4	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₁₃×D₈	1	2	yes	—
331	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	Q₁₆	—	2	4	no	—
335	Q₁₆	—	2	2	no	—
336	Q₁₆	—	2	1	no	—
337	Q₁₆	—	2	1	no	—
338	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
339	SD₁₆	—	2	16	no	—
340	SD₁₆	—	4	2	no	—
341	D₈	—	2	4	no	—
342	D₈	—	2	2	no	—
343	D₈	—	2	1	no	—
344	D₈	—	2	1	no	—
345	D₈	C₂×D₄×C₁₃	1	4	yes	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
351	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
354	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₄²	—	4	1	no	—
361	C₁₆	—	2	2	no	—
362	C₁₆	—	2	2	no	—
363	C₁₃	#33519	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	2	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	8	4	no	—
370	C₂³	C₂×C₁₃×D₈	1	2	yes	—
371	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
372	Q₈	—	2	4	no	—
373	Q₈	—	4	4	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	1	no	—
376	Q₈	—	4	1	no	—
377	D₄	—	2	4	no	—
378	D₄	—	4	16	no	—
379	D₄	—	4	4	no	—
380	D₄	—	4	1	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	8	4	no	—
384	D₄	—	8	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	C₁₃×#120	1	2	yes	—
396	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
397	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
398	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
399	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	C₁₃×#120	1	2	yes	—
402	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
403	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	8	no	—
411	C₂²	—	8	4	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	C₁₃×#447	1	2	yes	—
415	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	4	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	1	no	—
420	C₄	C₁₃×#447	1	2	yes	—
421	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
422	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂	—	2	2	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	4	no	—
426	C₂	—	16	1	no	—
427	C₂	C₂×C₁₃×#447	1	1	yes	characteristic
428	C₂	C₁₃×#3414	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 ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂×C₁₃×#510	C₂	semidirect
3. C₂×C₁₃×#509	C₂	semidirect
4. C₁₃×#3050	C₂	semidirect
5. C₁₃×#2189	C₂	semidirect
6. C₁₃×#2186	C₂	semidirect
7. C₁₃×#2141	C₂	semidirect
8. C₁₃×#2140	C₂	semidirect
9. C₁₃×#2112	C₂	semidirect
23. C₂×C₁₃×Q₃₂	C₂²	semidirect
24. C₂×C₁₃×SD₃₂	C₂²	semidirect
25. C₂×C₁₃×SD₃₂	C₂²	semidirect
26. C₂×C₁₃×D₁₆	C₂²	semidirect
29. C₁₃×#467	C₂²	semidirect
30. C₁₃×#466	C₂²	semidirect
34. C₁₃×#358	C₂²	semidirect
35. C₁₃×#357	C₂²	semidirect
36. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
54. C₂×C₁₃×Q₁₆	D₄	semidirect
62. C₂×C₁₃×D₈	D₄	semidirect
89. #33519	C₁₃	direct (N × H)
150. C₂²×#135	C₂×C₁₃	semidirect
151. C₂×#510	C₂×C₁₃	semidirect
152. C₂×#509	C₂×C₁₃	semidirect
153. #3050	C₂×C₁₃	semidirect
154. #2189	C₂×C₁₃	semidirect
155. #2186	C₂×C₁₃	semidirect
156. #2141	C₂×C₁₃	semidirect
157. #2140	C₂×C₁₃	semidirect
158. #2112	C₂×C₁₃	semidirect
212. C₂×Q₃₂	C₂²×C₁₃	semidirect
213. C₂×SD₃₂	C₂²×C₁₃	semidirect
214. C₂×SD₃₂	C₂²×C₁₃	semidirect
215. C₂×D₁₆	C₂²×C₁₃	semidirect
218. #467	C₂²×C₁₃	semidirect
219. #466	C₂²×C₁₃	semidirect
223. #358	C₂²×C₁₃	semidirect
224. #357	C₂²×C₁₃	semidirect
225. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
262. C₂×Q₁₆	D₄×C₁₃	semidirect
270. C₂×D₈	D₄×C₁₃	semidirect
363. C₁₃	#33519	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₁₃×#510	2
C₂×C₁₃×#509	2
C₁₃×#3050	2
C₁₃×#2189	2
C₁₃×#2186	2
C₁₃×#2141	2
C₁₃×#2140	2
C₁₃×#2112	2
#33519	13

Subgroups — C13×#33519 #15719858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33519 #15719858