Subgroups — C₂²×D₁₃×#124 #16769579

Order 3328.

14334 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#88201	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88190	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88139	C₂	1	4	yes	maximal, complemented
7	C₂×D₁₃×#124	C₂	1	48	yes	maximal, direct product factor
8	C₂²×C₂²⋊C₄×D₁₃	C₂	1	4	yes	maximal, complemented
9	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	2	yes	—
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
15	C₂²×Q₈×D₁₃	—	2	16	no	—
16	C₂²×Q₈×D₁₃	C₂²	1	24	yes	complemented
17	C₂²×D₄×D₁₃	—	2	16	no	—
18	C₂²×D₄×D₁₃	C₂²	1	24	yes	—
19	C₂³×D₅₂	C₂²	1	1	yes	characteristic
20	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
21	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
22	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×Dic₂₆	C₂²	1	2	yes	complemented
24	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₁₃×#124	C₂²	1	24	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
29	C₂×#88201	C₂²	1	24	yes	complemented
30	C₂×#88190	C₂²	1	24	yes	complemented
31	C₂²×#6103	C₂²	1	4	yes	complemented
32	C₂²×#6103	C₂²	1	4	yes	complemented
33	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
34	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
35	D₁₃×#124	C₂²	1	256	yes	direct product factor
36	C₂×#88139	C₂²	1	96	yes	complemented
37	C₂×C₂²⋊C₄×D₁₃	C₂²	1	96	yes	complemented
38	C₂×#88129	C₂²	1	24	yes	complemented
39	C₂×C₄²×D₁₃	C₂²	1	24	yes	complemented
40	C₂⁵×C₁₃	C₂³	1	2	yes	—
41	C₂⁴×D₁₃	—	2	16	no	—
42	C₂⁴×D₁₃	—	2	32	no	—
43	C₂⁴×D₁₃	C₂³	1	24	yes	—
44	C₂⁴×D₁₃	C₂³	1	2	yes	—
45	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	8	no	—
47	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
48	C₂²×D₄×C₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₂²⋊D₁₃	—	2	16	no	—
54	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
55	C₂³×Dic₁₃	C₂³	1	2	yes	—
56	C₂³×Dic₁₃	C₂³	1	2	yes	—
57	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂×Q₈×D₁₃	—	2	192	no	—
59	C₂×Q₈×D₁₃	C₂³	1	64	yes	complemented
60	C₂×D₄×D₁₃	—	2	192	no	—
61	C₂×D₄×D₁₃	C₂³	1	64	yes	—
62	C₂²×D₅₂	—	2	8	no	—
63	C₂²×D₅₂	C₂³	1	12	yes	—
64	C₂²×C₄×D₁₃	—	2	16	no	—
65	C₂²×C₄×D₁₃	—	2	16	no	—
66	C₂²×C₄×D₁₃	D₄	1	16	yes	—
67	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
68	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
69	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
70	C₂²×Dic₂₆	—	2	8	no	—
71	C₂²×Dic₂₆	—	2	16	no	—
72	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
73	C₂²×Dic₂₆	C₂³	1	24	yes	complemented
74	C₁₃×#124	C₂³	1	64	yes	complemented
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	complemented
76	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
77	C₂×C₂²⋊Dic₁₃	C₂³	1	48	yes	complemented
78	#88201	C₂³	1	64	yes	complemented
79	#88190	C₂³	1	64	yes	complemented
80	C₂×#6103	C₂³	1	48	yes	complemented
81	C₂×#6103	C₂³	1	48	yes	complemented
82	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
83	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
84	#88139	C₂³	1	256	yes	complemented
85	C₂²⋊C₄×D₁₃	C₂³	1	256	yes	complemented
86	#88129	C₂³	1	64	yes	complemented
87	C₄²×D₁₃	C₂³	1	64	yes	complemented
88	C₂³×#124	—	13	1	no	maximal, Sylow
89	C₂⁴×C₁₃	—	2	8	no	—
90	C₂⁴×C₁₃	—	2	16	no	—
91	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
92	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₂³×D₁₃	—	2	8	no	—
94	C₂³×D₁₃	—	2	16	no	—
95	C₂³×D₁₃	—	2	96	no	—
96	C₂³×D₁₃	—	2	192	no	—
97	C₂³×D₁₃	—	4	128	no	—
98	C₂³×D₁₃	C₂×D₄	1	8	yes	—
99	C₂³×D₁₃	#41	1	16	yes	—
100	C₂³×D₁₃	C₂⁴	1	32	yes	—
101	C₂³×D₁₃	C₂⁴	1	12	yes	—
102	C₂³×D₁₃	C₂⁴	1	6	yes	—
103	C₂×Q₈×C₁₃	—	2	48	no	—
104	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
105	C₂×D₄×C₁₃	—	2	48	no	—
106	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
113	C₂×C₂²⋊D₁₃	—	2	96	no	—
114	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
115	C₂²×Dic₁₃	—	2	8	no	—
116	C₂²×Dic₁₃	—	2	8	no	—
117	C₂²×Dic₁₃	C₂×D₄	1	8	yes	—
118	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
119	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
120	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
121	Q₈×D₁₃	—	2	256	no	—
122	D₄×D₁₃	—	2	256	no	—
123	C₂×D₅₂	—	2	48	no	—
124	C₂×D₅₂	C₂⁴	1	16	yes	—
125	C₂×C₄×D₁₃	—	2	96	no	—
126	C₂×C₄×D₁₃	—	2	96	no	—
127	C₂×C₄×D₁₃	C₂×D₄	1	96	yes	—
128	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
129	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
130	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
131	C₂×Dic₂₆	—	2	48	no	—
132	C₂×Dic₂₆	—	2	96	no	—
133	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
134	C₂×Dic₂₆	C₂⁴	1	32	yes	complemented
135	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
136	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
137	C₂²⋊Dic₁₃	C₂⁴	1	64	yes	complemented
138	#6103	C₂⁴	1	64	yes	complemented
139	#6103	C₂⁴	1	64	yes	complemented
140	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
141	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
142	C₂⁴×Q₈	—	13	1	no	—
143	C₂⁴×D₄	—	13	1	no	—
144	C₂²×#124	—	13	1	no	—
145	C₂²×#124	—	13	1	no	—
146	C₂²×#124	—	13	1	no	—
147	C₂²×#124	—	13	48	no	—
148	C₂²×#124	—	13	4	no	—
149	C₂²×#124	D₁₃	1	1	yes	characteristic, direct product factor
150	C₂³×C₂²⋊C₄	—	13	4	no	—
151	C₂³×C₄²	—	13	1	no	—
152	C₂³×C₁₃	—	2	24	no	—
153	C₂³×C₁₃	—	2	48	no	—
154	C₂³×C₁₃	—	4	32	no	—
155	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
156	C₂³×C₁₃	C₂×#41	1	8	yes	—
157	C₂³×C₁₃	C₂⁵	1	8	yes	—
158	C₂³×C₁₃	C₂⁵	1	3	yes	—
159	C₂²×D₁₃	—	2	24	no	—
160	C₂²×D₁₃	—	2	48	no	—
161	C₂²×D₁₃	—	2	64	no	—
162	C₂²×D₁₃	—	2	128	no	—
163	C₂²×D₁₃	—	4	32	no	—
164	C₂²×D₁₃	—	4	384	no	—
165	C₂²×D₁₃	#124	1	64	yes	direct product factor
166	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
167	C₂²×D₁₃	C₂×#41	1	48	yes	—
168	C₂²×D₁₃	C₂⁵	1	8	yes	—
169	C₂²×D₁₃	C₂⁵	1	4	yes	—
170	Q₈×C₁₃	—	2	32	no	—
171	D₄×C₁₃	—	2	32	no	—
172	C₂×C₄×C₁₃	—	2	24	no	—
173	C₂×C₄×C₁₃	—	2	24	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
175	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
176	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
177	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
178	C₂²⋊D₁₃	—	2	64	no	—
179	C₂×Dic₁₃	—	2	24	no	—
180	C₂×Dic₁₃	—	2	24	no	—
181	C₂×Dic₁₃	C₂²×D₄	1	24	yes	—
182	C₂×Dic₁₃	C₂⁵	1	8	yes	—
183	C₂×Dic₁₃	C₂⁵	1	8	yes	—
184	C₂×Dic₁₃	C₂⁵	1	4	yes	—
185	D₅₂	—	2	32	no	—
186	C₄×D₁₃	—	2	64	no	—
187	C₄×D₁₃	—	2	64	no	—
188	C₄×D₁₃	C₂²×D₄	1	64	yes	—
189	Dic₂₆	—	2	32	no	—
190	Dic₂₆	—	2	64	no	—
191	C₂⁶	—	13	2	no	—
192	C₂³×Q₈	—	13	24	no	—
193	C₂³×Q₈	—	13	2	no	—
194	C₂³×Q₈	—	13	1	no	—
195	C₂³×Q₈	—	26	16	no	—
196	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
197	C₂³×D₄	—	13	2	no	—
198	C₂³×D₄	—	13	24	no	—
199	C₂³×D₄	—	13	1	no	—
200	C₂³×D₄	—	26	16	no	—
201	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
202	C₂⁴×C₄	—	13	1	no	—
203	C₂⁴×C₄	—	13	2	no	—
204	C₂⁴×C₄	—	13	2	no	—
205	C₂×#124	—	13	24	no	—
206	C₂×#124	—	13	24	no	—
207	C₂×#124	—	13	256	no	—
208	C₂×#124	—	13	96	no	—
209	C₂×#124	—	13	24	no	—
210	C₂×#124	C₂×D₁₃	1	24	yes	direct product factor
211	C₂²×C₂²⋊C₄	—	13	4	no	—
212	C₂²×C₂²⋊C₄	—	13	4	no	—
213	C₂²×C₂²⋊C₄	—	13	4	no	—
214	C₂²×C₂²⋊C₄	—	13	96	no	—
215	C₂²×C₂²⋊C₄	C₂×D₁₃	1	4	yes	complemented
216	C₂²×C₄²	—	13	2	no	—
217	C₂²×C₄²	—	13	1	no	—
218	C₂²×C₄²	—	13	24	no	—
219	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
220	C₂²×C₁₃	—	2	8	no	—
221	C₂²×C₁₃	—	2	16	no	—
222	C₂²×C₁₃	—	4	48	no	—
223	C₂²×C₁₃	C₂×#124	1	16	yes	complemented
224	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
225	C₂²×C₁₃	C₂²×#41	1	12	yes	—
226	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
227	C₂×D₁₃	—	2	8	no	—
228	C₂×D₁₃	—	2	16	no	—
229	C₂×D₁₃	—	4	48	no	—
230	C₂×D₁₃	—	4	128	no	—
231	C₂×D₁₃	C₂×#124	1	96	yes	direct product factor
232	C₂×D₁₃	C₂³×D₄	1	8	yes	—
233	C₂×D₁₃	C₂²×#41	1	16	yes	—
234	C₄×C₁₃	—	2	8	no	—
235	C₄×C₁₃	—	2	8	no	—
236	C₄×C₁₃	C₂³×D₄	1	8	yes	—
237	Dic₁₃	—	2	8	no	—
238	Dic₁₃	—	2	8	no	—
239	Dic₁₃	C₂³×D₄	1	8	yes	—
240	C₂⁵	—	13	1	no	—
241	C₂⁵	—	13	24	no	—
242	C₂⁵	—	13	2	no	—
243	C₂⁵	—	26	16	no	—
244	C₂⁵	—	26	32	no	—
245	C₂⁵	C₂²×D₁₃	1	2	yes	—
246	C₂²×Q₈	—	2	8	no	—
247	C₂²×Q₈	—	13	64	no	—
248	C₂²×Q₈	—	13	24	no	—
249	C₂²×Q₈	—	13	12	no	—
250	C₂²×Q₈	—	26	16	no	—
251	C₂²×Q₈	—	26	192	no	—
252	C₂²×Q₈	—	26	8	no	—
253	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
254	C₂²×D₄	—	2	8	no	—
255	C₂²×D₄	—	13	24	no	—
256	C₂²×D₄	—	13	64	no	—
257	C₂²×D₄	—	13	12	no	—
258	C₂²×D₄	—	26	192	no	—
259	C₂²×D₄	—	26	16	no	—
260	C₂²×D₄	—	26	8	no	—
261	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
262	C₂³×C₄	—	13	1	no	—
263	C₂³×C₄	—	13	16	no	—
264	C₂³×C₄	—	13	12	no	—
265	C₂³×C₄	—	13	2	no	—
266	C₂³×C₄	—	13	2	no	—
267	C₂³×C₄	—	13	24	no	—
268	C₂³×C₄	—	13	24	no	—
269	C₂³×C₄	—	26	16	no	—
270	C₂³×C₄	—	26	16	no	—
271	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
272	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
273	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
274	#124	—	13	64	no	—
275	#124	—	13	64	no	—
276	#124	—	13	256	no	—
277	#124	—	13	64	no	—
278	#124	C₂²×D₁₃	1	64	yes	direct product factor
279	C₂×C₂²⋊C₄	—	13	48	no	—
280	C₂×C₂²⋊C₄	—	13	48	no	—
281	C₂×C₂²⋊C₄	—	13	48	no	—
282	C₂×C₂²⋊C₄	—	13	256	no	—
283	C₂×C₂²⋊C₄	C₂²×D₁₃	1	48	yes	complemented
284	C₂×C₄²	—	13	24	no	—
285	C₂×C₄²	—	13	12	no	—
286	C₂×C₄²	—	13	64	no	—
287	C₂×C₄²	C₂²×D₁₃	1	12	yes	complemented
288	C₂×C₁₃	—	4	8	no	—
289	C₂×C₁₃	C₂²×#124	1	12	yes	complemented
290	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
291	C₂×C₁₃	C₂³×#41	1	2	yes	—
292	D₁₃	—	4	8	no	—
293	D₁₃	C₂²×#124	1	16	yes	direct product factor
294	C₂⁴	—	2	8	no	—
295	C₂⁴	—	2	16	no	—
296	C₂⁴	—	13	8	no	—
297	C₂⁴	—	13	16	no	—
298	C₂⁴	—	13	6	no	—
299	C₂⁴	—	13	32	no	—
300	C₂⁴	—	13	12	no	—
301	C₂⁴	—	26	96	no	—
302	C₂⁴	—	26	192	no	—
303	C₂⁴	—	26	8	no	—
304	C₂⁴	—	26	16	no	—
305	C₂⁴	—	52	128	no	—
306	C₂⁴	C₂³×D₁₃	1	12	yes	—
307	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
308	C₂×Q₈	—	2	48	no	—
309	C₂×Q₈	—	13	32	no	—
310	C₂×Q₈	—	13	16	no	—
311	C₂×Q₈	—	26	96	no	—
312	C₂×Q₈	—	26	256	no	—
313	C₂×Q₈	—	26	48	no	—
314	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
315	C₂×D₄	—	2	48	no	—
316	C₂×D₄	—	13	32	no	—
317	C₂×D₄	—	13	16	no	—
318	C₂×D₄	—	26	256	no	—
319	C₂×D₄	—	26	96	no	—
320	C₂×D₄	—	26	48	no	—
321	C₂×D₄	C₂³×D₁₃	1	16	yes	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	8	no	—
324	C₂²×C₄	—	13	8	no	—
325	C₂²×C₄	—	13	6	no	—
326	C₂²×C₄	—	13	96	no	—
327	C₂²×C₄	—	13	16	no	—
328	C₂²×C₄	—	13	12	no	—
329	C₂²×C₄	—	13	12	no	—
330	C₂²×C₄	—	13	32	no	—
331	C₂²×C₄	—	13	32	no	—
332	C₂²×C₄	—	26	96	no	—
333	C₂²×C₄	—	26	96	no	—
334	C₂²×C₄	—	26	8	no	—
335	C₂²×C₄	—	26	8	no	—
336	C₂²×C₄	D₄×D₁₃	1	8	yes	—
337	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
338	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
339	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
340	C₂²⋊C₄	—	13	64	no	—
341	C₂²⋊C₄	—	13	64	no	—
342	C₂²⋊C₄	—	13	64	no	—
343	C₂²⋊C₄	C₂³×D₁₃	1	64	yes	complemented
344	C₄²	—	13	32	no	—
345	C₄²	—	13	16	no	—
346	C₄²	C₂³×D₁₃	1	16	yes	complemented
347	C₁₃	C₂³×#124	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	2	24	no	—
349	C₂³	—	2	48	no	—
350	C₂³	—	4	32	no	—
351	C₂³	—	13	64	no	—
352	C₂³	—	13	24	no	—
353	C₂³	—	13	48	no	—
354	C₂³	—	13	4	no	—
355	C₂³	—	13	8	no	—
356	C₂³	—	26	64	no	—
357	C₂³	—	26	128	no	—
358	C₂³	—	26	24	no	—
359	C₂³	—	26	48	no	—
360	C₂³	—	52	384	no	—
361	C₂³	—	52	32	no	—
362	C₂³	C₂×D₄×D₁₃	1	4	yes	—
363	C₂³	#41×D₁₃	1	8	yes	—
364	C₂³	C₂⁴×D₁₃	1	8	yes	—
365	C₂³	C₂⁴×D₁₃	1	3	yes	—
366	Q₈	—	2	32	no	—
367	Q₈	—	26	64	no	—
368	Q₈	—	26	32	no	—
369	D₄	—	2	32	no	—
370	D₄	—	26	64	no	—
371	D₄	—	26	32	no	—
372	C₂×C₄	—	2	24	no	—
373	C₂×C₄	—	2	24	no	—
374	C₂×C₄	—	13	24	no	—
375	C₂×C₄	—	13	4	no	—
376	C₂×C₄	—	13	64	no	—
377	C₂×C₄	—	13	8	no	—
378	C₂×C₄	—	13	8	no	—
379	C₂×C₄	—	26	64	no	—
380	C₂×C₄	—	26	64	no	—
381	C₂×C₄	—	26	24	no	—
382	C₂×C₄	—	26	24	no	—
383	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
384	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
385	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
386	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	16	no	—
389	C₂²	—	4	48	no	—
390	C₂²	—	13	96	no	—
391	C₂²	—	13	8	no	—
392	C₂²	—	13	16	no	—
393	C₂²	—	26	8	no	—
394	C₂²	—	26	16	no	—
395	C₂²	—	52	128	no	—
396	C₂²	—	52	48	no	—
397	C₂²	D₁₃×#124	1	16	yes	direct product factor
398	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
399	C₂²	C₂×#41×D₁₃	1	12	yes	—
400	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	8	no	—
403	C₄	—	13	8	no	—
404	C₄	—	26	8	no	—
405	C₄	—	26	8	no	—
406	C₄	C₂²×D₄×D₁₃	1	8	yes	—
407	C₂	—	4	8	no	—
408	C₂	—	13	16	no	—
409	C₂	—	52	8	no	—
410	C₂	C₂×D₁₃×#124	1	12	yes	direct product factor
411	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
412	C₂	C₂²×#41×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#124	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₄×D₁₃	C₂
hypercenter	C₂²×#124	D₁₃
hypocenter	C₁₃	C₂³×#124
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₁₃	C₂	semidirect
3. C₂²×#88201	C₂	semidirect
4. C₂²×#88129	C₂	semidirect
5. C₂²×#88190	C₂	semidirect
6. C₂²×#88139	C₂	semidirect
7. C₂×D₁₃×#124	C₂	direct (N × H)
8. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
9. C₂²×C₄²×D₁₃	C₂	semidirect
10. C₂²×C₁₃×#124	C₂	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
16. C₂²×Q₈×D₁₃	C₂²	semidirect
23. C₂³×Dic₂₆	C₂²	semidirect
24. C₂³×Dic₂₆	C₂²	semidirect
25. C₂×C₁₃×#124	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₁₃	C₂²	semidirect
28. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
29. C₂×#88201	C₂²	semidirect
30. C₂×#88190	C₂²	semidirect
31. C₂²×#6103	C₂²	semidirect
32. C₂²×#6103	C₂²	semidirect
33. C₂²×C₄×Dic₁₃	C₂²	semidirect
34. C₂²×C₄×Dic₁₃	C₂²	semidirect
35. D₁₃×#124	C₂²	direct (N × H)
36. C₂×#88139	C₂²	semidirect
37. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
38. C₂×#88129	C₂²	semidirect
39. C₂×C₄²×D₁₃	C₂²	semidirect
47. C₂²×Q₈×C₁₃	C₂³	semidirect
59. C₂×Q₈×D₁₃	C₂³	semidirect
72. C₂²×Dic₂₆	C₂³	semidirect
73. C₂²×Dic₂₆	C₂³	semidirect
74. C₁₃×#124	C₂³	semidirect
75. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
76. C₂×C₄²×C₁₃	C₂³	semidirect
77. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
78. #88201	C₂³	semidirect
79. #88190	C₂³	semidirect
80. C₂×#6103	C₂³	semidirect
81. C₂×#6103	C₂³	semidirect
82. C₂×C₄×Dic₁₃	C₂³	semidirect
83. C₂×C₄×Dic₁₃	C₂³	semidirect
84. #88139	C₂³	semidirect
85. C₂²⋊C₄×D₁₃	C₂³	semidirect
86. #88129	C₂³	semidirect
87. C₄²×D₁₃	C₂³	semidirect
104. C₂×Q₈×C₁₃	C₂⁴	semidirect
133. C₂×Dic₂₆	C₂⁴	semidirect
134. C₂×Dic₂₆	C₂⁴	semidirect
135. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
136. C₄²×C₁₃	C₂⁴	semidirect
137. C₂²⋊Dic₁₃	C₂⁴	semidirect
138. #6103	C₂⁴	semidirect
139. #6103	C₂⁴	semidirect
140. C₄×Dic₁₃	C₂⁴	semidirect
141. C₄×Dic₁₃	C₂⁴	semidirect
149. C₂²×#124	D₁₃	direct (N × H)
165. C₂²×D₁₃	#124	direct (N × H)
196. C₂³×Q₈	C₂×D₁₃	semidirect
210. C₂×#124	C₂×D₁₃	direct (N × H)
215. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
219. C₂²×C₄²	C₂×D₁₃	semidirect
223. C₂²×C₁₃	C₂×#124	semidirect
231. C₂×D₁₃	C₂×#124	direct (N × H)
253. C₂²×Q₈	C₂²×D₁₃	semidirect
278. #124	C₂²×D₁₃	direct (N × H)
283. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
287. C₂×C₄²	C₂²×D₁₃	semidirect
289. C₂×C₁₃	C₂²×#124	semidirect
293. D₁₃	C₂²×#124	direct (N × H)
314. C₂×Q₈	C₂³×D₁₃	semidirect
343. C₂²⋊C₄	C₂³×D₁₃	semidirect
346. C₄²	C₂³×D₁₃	semidirect
347. C₁₃	C₂³×#124	semidirect
397. C₂²	D₁₃×#124	direct (N × H)
410. C₂	C₂×D₁₃×#124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₁₃	2
C₂³×D₄×D₁₃	2
C₂²×#88201	2
C₂²×#88129	2
C₂²×#88190	2
C₂²×#88139	2
C₂×D₁₃×#124	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₄²×D₁₃	2
C₂²×C₁₃×#124	2
C₂³×#124	13

Subgroups — C22×D13×#124 #16769579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃×#124 #16769579