Subgroups — C₁₃×#34634 #15720973

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2629	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2628	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2627	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	4	yes	maximal
7	C₁₃×#2396	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2296	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#533	—	2	8	no	—
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#117	—	2	8	no	—
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₂×C₁₃×#117	C₂²	1	2	yes	—
20	C₂×C₁₃×#117	C₂²	1	2	yes	—
21	C₂×C₁₃×#117	C₂²	1	2	yes	—
22	C₂×C₁₃×#117	C₂²	1	4	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#400	C₂²	1	8	yes	complemented
28	C₁₃×#399	C₂²	1	8	yes	—
29	C₁₃×#398	C₂²	1	16	yes	complemented
30	C₁₃×#396	C₂²	1	16	yes	—
31	C₁₃×#395	C₂²	1	8	yes	complemented
32	C₁₃×#393	C₂²	1	8	yes	—
33	C₁₃×#389	C₂²	1	8	yes	complemented
34	C₁₃×#385	C₂²	1	8	yes	—
35	C₁₃×#384	C₂²	1	2	yes	complemented
36	C₁₃×#382	C₂²	1	2	yes	complemented
37	C₁₃×#381	C₂²	1	4	yes	—
38	C₁₃×#380	C₂²	1	8	yes	—
39	C₁₃×#380	C₂²	1	4	yes	—
40	C₁₃×#379	C₂²	1	4	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
43	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	2	4	no	—
47	C₂³×C₄×C₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×C₄⋊Q₈	—	2	8	no	—
56	C₁₃×#125	—	2	8	no	—
57	C₁₃×C₂²⋊Q₈	—	2	16	no	—
58	C₄×Q₈×C₁₃	—	2	16	no	—
59	C₁₃×#117	—	2	8	no	—
60	C₁₃×#117	—	2	8	no	—
61	C₁₃×#117	—	2	16	no	—
62	C₁₃×#117	—	2	8	no	—
63	C₁₃×#117	—	2	8	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
79	C₂×C₄²×C₁₃	—	2	4	no	—
80	C₂×C₄²×C₁₃	D₄	1	8	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
88	C₁₃×#95	C₂³	1	16	yes	—
89	C₁₃×#95	C₂³	1	8	yes	—
90	C₁₃×#95	C₂³	1	16	yes	—
91	#34634	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₂⁴×C₁₃	—	4	4	no	—
95	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×Q₈×C₁₃	—	2	8	no	—
99	C₂×Q₈×C₁₃	—	4	8	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	32	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	4	4	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
114	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
115	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₁₃	#41	1	4	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×C₄⋊C₄	—	2	8	no	—
126	C₁₃×C₄⋊C₄	—	2	8	no	—
127	C₁₃×C₄⋊C₄	—	2	8	no	—
128	C₁₃×C₄⋊C₄	—	2	16	no	—
129	C₁₃×C₄⋊C₄	—	2	8	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	4	8	no	—
132	C₁₃×C₄⋊C₄	—	4	16	no	—
133	C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₁₃×C₂²⋊C₄	—	2	8	no	—
135	C₁₃×C₂²⋊C₄	—	2	8	no	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	—	4	16	no	—
138	C₄²×C₁₃	—	2	4	no	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	—	2	8	no	—
142	C₄²×C₁₃	C₂×D₄	1	8	yes	—
143	C₄²×C₁₃	C₂×D₄	1	4	yes	—
144	C₄²×C₁₃	C₂×D₄	1	4	yes	—
145	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
146	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
147	#2629	C₂×C₁₃	1	4	yes	complemented
148	#2628	C₂×C₁₃	1	4	yes	complemented
149	#2627	C₂×C₁₃	1	4	yes	complemented
150	#2626	C₂×C₁₃	1	4	yes	—
151	#2396	C₂×C₁₃	1	8	yes	complemented
152	#2296	C₂×C₁₃	1	2	yes	complemented
153	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2280	C₂×C₁₃	1	2	yes	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	—	2	8	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	8	no	—
160	C₂³×C₁₃	—	4	8	no	—
161	C₂³×C₁₃	—	4	8	no	—
162	C₂³×C₁₃	—	4	8	no	—
163	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
164	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
165	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
166	C₂³×C₁₃	C₂×#41	1	2	yes	—
167	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
168	Q₈×C₁₃	—	4	16	no	—
169	C₂×C₄×C₁₃	—	2	8	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	16	no	—
175	C₂×C₄×C₁₃	—	2	16	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	16	no	—
180	C₂×C₄×C₁₃	—	2	16	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	4	8	no	—
183	C₂×C₄×C₁₃	—	4	8	no	—
184	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
190	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
194	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
195	#533	—	2	8	no	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
197	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
198	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
199	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
200	C₂×#117	—	2	8	no	—
201	C₂×#117	C₂²×C₁₃	1	2	yes	—
202	C₂×#117	C₂²×C₁₃	1	2	yes	—
203	C₂×#117	C₂²×C₁₃	1	4	yes	—
204	C₂×#117	C₂²×C₁₃	1	2	yes	—
205	C₂×#117	C₂²×C₁₃	1	2	yes	—
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
207	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
209	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
210	#400	C₂²×C₁₃	1	8	yes	complemented
211	#399	C₂²×C₁₃	1	8	yes	—
212	#398	C₂²×C₁₃	1	16	yes	complemented
213	#396	C₂²×C₁₃	1	16	yes	—
214	#395	C₂²×C₁₃	1	8	yes	complemented
215	#393	C₂²×C₁₃	1	8	yes	—
216	#389	C₂²×C₁₃	1	8	yes	complemented
217	#385	C₂²×C₁₃	1	8	yes	—
218	#384	C₂²×C₁₃	1	2	yes	complemented
219	#382	C₂²×C₁₃	1	2	yes	complemented
220	#381	C₂²×C₁₃	1	4	yes	—
221	#380	C₂²×C₁₃	1	4	yes	—
222	#380	C₂²×C₁₃	1	8	yes	—
223	#379	C₂²×C₁₃	1	4	yes	—
224	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
225	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
226	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	2	4	no	—
229	C₂²×C₁₃	—	2	4	no	—
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	8	no	—
232	C₂²×C₁₃	—	4	16	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	—	4	4	no	—
235	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
236	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
237	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
238	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
239	C₂²×C₁₃	#585	1	4	yes	—
240	C₄×C₁₃	—	2	4	no	—
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	2	4	no	—
243	C₄×C₁₃	—	4	4	no	—
244	C₄×C₁₃	—	4	8	no	—
245	C₄×C₁₃	—	4	8	no	—
246	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
247	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
248	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
250	C₂³×C₄	—	2	4	no	—
251	C₂³×C₄	—	2	4	no	—
252	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
253	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
255	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
258	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
259	C₄⋊Q₈	—	2	8	no	—
260	#125	—	2	8	no	—
261	C₂²⋊Q₈	—	2	16	no	—
262	C₄×Q₈	—	2	16	no	—
263	#117	—	2	8	no	—
264	#117	—	2	8	no	—
265	#117	—	2	16	no	—
266	#117	—	2	8	no	—
267	#117	—	2	8	no	—
268	C₂×C₄⋊C₄	—	2	8	no	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
277	C₂×C₂²⋊C₄	—	2	8	no	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
283	C₂×C₄²	—	2	4	no	—
284	C₂×C₄²	D₄×C₁₃	1	8	yes	—
285	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
288	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	#95	C₂³×C₁₃	1	16	yes	—
293	#95	C₂³×C₁₃	1	8	yes	—
294	#95	C₂³×C₁₃	1	16	yes	—
295	C₂×C₁₃	—	2	4	no	—
296	C₂×C₁₃	—	4	4	no	—
297	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
298	C₂×C₁₃	#3449	1	2	yes	—
299	C₂×C₁₃	#3455	1	2	yes	—
300	C₂×C₁₃	#3458	1	2	yes	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
305	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
306	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
307	C₂×Q₈	—	2	8	no	—
308	C₂×Q₈	—	4	8	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	32	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
320	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
321	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
322	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
323	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
324	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
325	C₂²×C₄	C₁₃×#41	1	4	yes	—
326	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
329	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	16	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	4	8	no	—
341	C₄⋊C₄	—	4	16	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	4	16	no	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	8	no	—
350	C₄²	—	2	8	no	—
351	C₄²	C₂×D₄×C₁₃	1	8	yes	—
352	C₄²	C₂×D₄×C₁₃	1	4	yes	—
353	C₄²	C₂×D₄×C₁₃	1	4	yes	—
354	C₁₃	#34634	1	1	yes	characteristic, direct product factor, Sylow
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
364	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
365	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
366	C₂³	C₂×C₁₃×#41	1	2	yes	—
367	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
368	Q₈	—	4	16	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	16	no	—
380	C₂×C₄	—	2	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
385	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
389	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
390	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
391	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
392	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
393	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	16	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
403	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
404	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
405	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
406	C₂²	C₁₃×#585	1	4	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	4	8	no	—
413	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
414	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
415	C₂	—	2	4	no	—
416	C₂	—	4	4	no	—
417	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
418	C₂	C₁₃×#3449	1	2	yes	—
419	C₂	C₁₃×#3455	1	2	yes	—
420	C₂	C₁₃×#3458	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#2629	C₂	semidirect
4. C₁₃×#2628	C₂	semidirect
5. C₁₃×#2627	C₂	semidirect
7. C₁₃×#2396	C₂	semidirect
8. C₁₃×#2296	C₂	semidirect
9. C₁₃×#2285	C₂	semidirect
13. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
14. C₂×C₁₃×#125	C₂²	semidirect
16. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
27. C₁₃×#400	C₂²	semidirect
29. C₁₃×#398	C₂²	semidirect
31. C₁₃×#395	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
35. C₁₃×#384	C₂²	semidirect
36. C₁₃×#382	C₂²	semidirect
41. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
48. C₂³×C₄×C₁₃	Q₈	semidirect
91. #34634	C₁₃	direct (N × H)
145. C₂×#533	C₂×C₁₃	semidirect
147. #2629	C₂×C₁₃	semidirect
148. #2628	C₂×C₁₃	semidirect
149. #2627	C₂×C₁₃	semidirect
151. #2396	C₂×C₁₃	semidirect
152. #2296	C₂×C₁₃	semidirect
153. #2285	C₂×C₁₃	semidirect
196. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
197. C₂×#125	C₂²×C₁₃	semidirect
199. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
210. #400	C₂²×C₁₃	semidirect
212. #398	C₂²×C₁₃	semidirect
214. #395	C₂²×C₁₃	semidirect
216. #389	C₂²×C₁₃	semidirect
218. #384	C₂²×C₁₃	semidirect
219. #382	C₂²×C₁₃	semidirect
224. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
225. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
252. C₂³×C₄	Q₈×C₁₃	semidirect
354. C₁₃	#34634	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×#533	2
C₂²×C₁₃×#117	2
C₁₃×#2629	2
C₁₃×#2628	2
C₁₃×#2627	2
C₁₃×#2626	2
C₁₃×#2396	2
C₁₃×#2296	2
C₁₃×#2285	2
C₁₃×#2280	2
#34634	13

Subgroups — C13×#34634 #15720973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34634 #15720973