Subgroups — C₁₃×#33606 #15719945

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3050	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2219	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2216	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#525	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
17	C₁₃×#510	—	2	4	no	—
18	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	complemented
19	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₁₃×M₃₂	—	2	4	no	—
21	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
23	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
25	C₁₃×#467	—	2	1	no	—
26	C₁₃×#467	—	2	1	no	—
27	C₁₃×#467	C₂²	1	2	yes	—
28	C₁₃×#467	C₂²	1	2	yes	—
29	C₁₃×#467	C₂²	1	1	yes	characteristic
30	C₁₃×#467	C₂²	1	1	yes	characteristic
31	C₁₃×#466	C₂²	1	1	yes	characteristic
32	C₁₃×#466	C₂²	1	1	yes	characteristic
33	C₁₃×#465	—	2	1	no	—
34	C₁₃×#465	—	2	1	no	—
35	C₁₃×#427	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₁₃×#416	—	2	1	no	—
38	C₂×C₁₃×#103	—	2	1	no	—
39	C₁₃×#367	C₂²	1	2	yes	complemented
40	C₁₃×#366	C₂²	1	2	yes	complemented
41	C₁₃×#358	C₂²	1	2	yes	complemented
42	C₁₃×#358	C₂²	1	2	yes	complemented
43	C₁₃×#358	C₂²	1	2	yes	complemented
44	C₁₃×#357	C₂²	1	2	yes	complemented
45	C₂×C₁₃×#41	—	2	1	no	—
46	C₂²×Q₈×C₁₃	—	2	1	no	—
47	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
48	C₁₃×#135	—	2	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
54	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	—	2	2	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#123	—	4	1	no	—
66	C₁₃×C₂²⋊Q₈	—	2	1	no	—
67	C₁₃×C₂²⋊Q₈	—	2	1	no	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	—	2	2	no	—
70	C₁₃×C₂²⋊Q₈	—	4	1	no	—
71	C₁₃×C₂²⋊Q₈	—	4	1	no	—
72	C₁₃×#121	—	2	1	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#120	—	4	1	no	—
75	C₄×D₄×C₁₃	—	4	1	no	—
76	C₄×D₄×C₁₃	—	4	1	no	—
77	C₁₃×#117	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
81	C₁₃×Q₃₂	—	2	4	no	—
82	C₁₃×SD₃₂	—	2	4	no	—
83	C₁₃×M₃₂	—	2	2	no	—
84	C₁₃×M₃₂	—	2	4	no	—
85	C₁₃×M₃₂	D₄	1	4	yes	complemented
86	C₂×C₁₃×C₁₆	—	2	4	no	—
87	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
88	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
89	C₁₃×#107	—	2	1	no	—
90	C₁₃×#107	C₂³	1	2	yes	—
91	C₁₃×#107	C₂³	1	1	yes	characteristic
92	C₁₃×#107	C₂³	1	1	yes	characteristic
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×#103	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	1	no	—
97	C₁₃×#103	—	2	1	no	—
98	C₁₃×#102	—	2	1	no	—
99	C₁₃×#102	—	2	1	no	—
100	#33606	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
102	C₁₃×#41	—	4	2	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	4	1	no	—
107	C₂×Q₈×C₁₃	—	4	2	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	4	1	no	—
111	C₂×D₄×C₁₃	—	4	1	no	—
112	C₂×D₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₁₃×Q₁₆	—	2	2	no	—
125	C₁₃×Q₁₆	—	2	1	no	—
126	C₁₃×Q₁₆	—	2	2	no	—
127	C₁₃×Q₁₆	—	2	1	no	—
128	C₁₃×Q₁₆	—	4	2	no	—
129	C₁₃×SD₁₆	—	4	2	no	—
130	C₁₃×D₈	—	2	1	no	—
131	C₁₃×D₈	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	#41	1	2	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	1	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	4	1	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	4	2	no	—
151	C₁₃×C₄⋊C₄	—	4	1	no	—
152	C₁₃×C₄⋊C₄	—	4	1	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	1	no	—
156	C₁₃×C₂²⋊C₄	—	4	1	no	—
157	C₁₃×C₂²⋊C₄	—	4	1	no	—
158	C₁₃×C₂²⋊C₄	—	4	1	no	—
159	C₁₃×C₂²⋊C₄	—	4	1	no	—
160	C₄²×C₁₃	—	4	1	no	—
161	C₁₃×C₁₆	—	2	2	no	—
162	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
163	C₂×#510	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#3050	C₂×C₁₃	1	1	yes	characteristic
166	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#2220	C₂×C₁₃	1	2	yes	complemented
168	#2219	C₂×C₁₃	1	2	yes	complemented
169	#2217	C₂×C₁₃	1	2	yes	complemented
170	#2216	C₂×C₁₃	1	2	yes	complemented
171	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#2141	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	1	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	2	no	—
184	Q₈×C₁₃	—	4	1	no	—
185	Q₈×C₁₃	—	8	2	no	—
186	D₄×C₁₃	—	4	1	no	—
187	D₄×C₁₃	—	4	1	no	—
188	D₄×C₁₃	—	8	2	no	—
189	D₄×C₁₃	—	8	2	no	—
190	D₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	2	no	—
204	C₂×C₄×C₁₃	—	8	2	no	—
205	C₂×C₄×C₁₃	—	8	2	no	—
206	C₂×C₄×C₁₃	#121	1	2	yes	—
207	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#135	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	#121	1	2	yes	—
215	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
218	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
220	#525	—	2	1	no	—
221	C₂×C₂²⋊Q₈	—	2	1	no	—
222	#510	—	2	4	no	—
223	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	complemented
224	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
225	C₂×M₃₂	—	2	4	no	—
226	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
228	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
229	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
230	#467	—	2	1	no	—
231	#467	—	2	1	no	—
232	#467	C₂²×C₁₃	1	1	yes	characteristic
233	#467	C₂²×C₁₃	1	2	yes	—
234	#467	C₂²×C₁₃	1	1	yes	characteristic
235	#467	C₂²×C₁₃	1	2	yes	—
236	#466	C₂²×C₁₃	1	1	yes	characteristic
237	#466	C₂²×C₁₃	1	1	yes	characteristic
238	#465	—	2	1	no	—
239	#465	—	2	1	no	—
240	#427	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
242	#416	—	2	1	no	—
243	C₂×#103	—	2	1	no	—
244	#367	C₂²×C₁₃	1	2	yes	complemented
245	#366	C₂²×C₁₃	1	2	yes	complemented
246	#358	C₂²×C₁₃	1	2	yes	complemented
247	#358	C₂²×C₁₃	1	2	yes	complemented
248	#358	C₂²×C₁₃	1	2	yes	complemented
249	#357	C₂²×C₁₃	1	2	yes	complemented
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	8	1	no	—
259	C₂²×C₁₃	—	8	1	no	—
260	C₂²×C₁₃	—	8	1	no	—
261	C₂²×C₁₃	#466	1	2	yes	—
262	C₂²×C₁₃	#510	1	2	yes	complemented
263	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	—	8	1	no	—
269	C₄×C₁₃	—	8	1	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	#466	1	2	yes	—
272	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
273	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
274	C₂×#41	—	2	1	no	—
275	C₂²×Q₈	—	2	1	no	—
276	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
277	#135	—	2	2	no	—
278	#135	—	2	2	no	—
279	C₂×Q₁₆	—	2	2	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
283	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×SD₁₆	—	2	1	no	—
285	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	#123	—	4	1	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	—	4	1	no	—
300	C₂²⋊Q₈	—	4	1	no	—
301	#121	—	2	1	no	—
302	#121	—	2	1	no	—
303	#120	—	4	1	no	—
304	C₄×D₄	—	4	1	no	—
305	C₄×D₄	—	4	1	no	—
306	#117	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	4	1	no	—
309	C₂×C₂²⋊C₄	—	4	1	no	—
310	Q₃₂	—	2	4	no	—
311	SD₃₂	—	2	4	no	—
312	M₃₂	—	2	2	no	—
313	M₃₂	—	2	4	no	—
314	M₃₂	D₄×C₁₃	1	4	yes	complemented
315	C₂×C₁₆	—	2	4	no	—
316	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
317	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
318	#107	—	2	1	no	—
319	#107	C₂³×C₁₃	1	2	yes	—
320	#107	C₂³×C₁₃	1	1	yes	characteristic
321	#107	C₂³×C₁₃	1	1	yes	characteristic
322	#106	—	2	1	no	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	1	no	—
326	#103	—	2	1	no	—
327	#102	—	2	1	no	—
328	#102	—	2	1	no	—
329	C₂×C₁₃	—	2	2	no	—
330	C₂×C₁₃	—	2	2	no	—
331	C₂×C₁₃	—	4	1	no	—
332	C₂×C₁₃	—	16	1	no	—
333	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
334	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
335	C₂×C₁₃	#3414	1	1	yes	characteristic
336	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
337	#41	—	4	2	no	—
338	#41	—	4	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	4	1	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
354	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
355	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
359	Q₁₆	—	2	2	no	—
360	Q₁₆	—	2	1	no	—
361	Q₁₆	—	2	2	no	—
362	Q₁₆	—	2	1	no	—
363	Q₁₆	—	4	2	no	—
364	SD₁₆	—	4	2	no	—
365	D₈	—	2	1	no	—
366	D₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
378	C₂×C₈	C₁₃×#41	1	2	yes	—
379	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₂²⋊C₄	—	4	1	no	—
395	C₄²	—	4	1	no	—
396	C₁₆	—	2	2	no	—
397	C₁₆	C₂×D₄×C₁₃	1	4	yes	—
398	C₁₃	#33606	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
404	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
405	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
406	Q₈	—	4	1	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	8	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	C₁₃×#121	1	2	yes	—
432	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
434	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
435	C₂×C₄	C₁₃×#135	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	C₁₃×#121	1	2	yes	—
440	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
441	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	C₁₃×#466	1	2	yes	—
454	C₂²	C₁₃×#510	1	2	yes	complemented
455	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	C₁₃×#466	1	2	yes	—
464	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
465	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	1	no	—
469	C₂	—	16	1	no	—
470	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
471	C₂	C₂×C₁₃×#510	1	1	yes	characteristic
472	C₂	C₁₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3050	C₂
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. C₂×C₁₃×#510	C₂	semidirect
2. C₂²×C₁₃×M₃₂	C₂	semidirect
4. C₂×C₁₃×#467	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2219	C₂	semidirect
7. C₁₃×#2217	C₂	semidirect
8. C₁₃×#2216	C₂	semidirect
9. C₁₃×#2159	C₂	semidirect
10. C₁₃×#2141	C₂	semidirect
11. C₁₃×#2139	C₂	semidirect
18. C₂×C₁₃×Q₃₂	C₂²	semidirect
19. C₂×C₁₃×SD₃₂	C₂²	semidirect
39. C₁₃×#367	C₂²	semidirect
40. C₁₃×#366	C₂²	semidirect
41. C₁₃×#358	C₂²	semidirect
42. C₁₃×#358	C₂²	semidirect
43. C₁₃×#358	C₂²	semidirect
44. C₁₃×#357	C₂²	semidirect
85. C₁₃×M₃₂	D₄	semidirect
100. #33606	C₁₃	direct (N × H)
163. C₂×#510	C₂×C₁₃	semidirect
164. C₂²×M₃₂	C₂×C₁₃	semidirect
166. C₂×#467	C₂×C₁₃	semidirect
167. #2220	C₂×C₁₃	semidirect
168. #2219	C₂×C₁₃	semidirect
169. #2217	C₂×C₁₃	semidirect
170. #2216	C₂×C₁₃	semidirect
171. #2159	C₂×C₁₃	semidirect
172. #2141	C₂×C₁₃	semidirect
173. #2139	C₂×C₁₃	semidirect
223. C₂×Q₃₂	C₂²×C₁₃	semidirect
224. C₂×SD₃₂	C₂²×C₁₃	semidirect
244. #367	C₂²×C₁₃	semidirect
245. #366	C₂²×C₁₃	semidirect
246. #358	C₂²×C₁₃	semidirect
247. #358	C₂²×C₁₃	semidirect
248. #358	C₂²×C₁₃	semidirect
249. #357	C₂²×C₁₃	semidirect
262. C₂²×C₁₃	#510	semidirect
314. M₃₂	D₄×C₁₃	semidirect
398. C₁₃	#33606	direct (N × H)
454. C₂²	C₁₃×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#510	2
C₂²×C₁₃×M₃₂	2
C₁₃×#3050	2
C₂×C₁₃×#467	2
C₁₃×#2220	2
C₁₃×#2219	2
C₁₃×#2217	2
C₁₃×#2216	2
C₁₃×#2159	2
C₁₃×#2141	2
C₁₃×#2139	2
#33606	13

Subgroups — C13×#33606 #15719945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33606 #15719945