Subgroups — #13128325

Order 1664.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#6131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719539	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719381	C₂	1	3	yes	maximal, complemented
7	#11719373	C₂	1	3	yes	maximal, complemented
8	#11719336	C₂	1	3	yes	maximal, complemented
9	#11719332	C₂	1	3	yes	maximal, complemented
10	#11719314	C₂	1	3	yes	maximal, complemented
11	#11719311	C₂	1	3	yes	maximal, complemented
12	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#6131	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719255	C₂	1	3	yes	maximal, complemented
15	C₄×D₄×D₁₃	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	#41×D₁₃	—	2	8	no	—
19	C₂×#6131	—	2	8	no	—
20	C₂×#6131	C₂²	1	1	yes	characteristic
21	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
22	C₂×#6131	C₂²	1	3	yes	complemented
23	C₂×#6131	C₂²	1	3	yes	complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#6129	C₂²	1	3	yes	complemented
26	C₂×D₄×D₁₃	C₂²	1	3	yes	—
27	C₂×D₄×D₁₃	C₂²	1	3	yes	complemented
28	C₂×#6127	C₂²	1	3	yes	complemented
29	C₂²×D₅₂	C₂²	1	3	yes	complemented
30	C₂²×C₄×D₁₃	C₂²	1	3	yes	complemented
31	C₂²×C₄×D₁₃	C₂²	1	3	yes	complemented
32	C₁₃×#124	C₂²	1	3	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	complemented
34	C₁₃×#121	C₂²	1	3	yes	complemented
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
37	#88200	C₂²	1	3	yes	complemented
38	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
39	#88198	C₂²	1	3	yes	complemented
40	#88194	C₂²	1	3	yes	complemented
41	#88192	C₂²	1	3	yes	complemented
42	#88191	C₂²	1	6	yes	complemented
43	D₄×Dic₁₃	C₂²	1	3	yes	complemented
44	#88184	C₂²	1	3	yes	complemented
45	C₄×C₂²⋊D₁₃	C₂²	1	3	yes	—
46	C₄×C₂²⋊D₁₃	C₂²	1	3	yes	complemented
47	#88178	C₂²	1	3	yes	complemented
48	#88151	C₂²	1	3	yes	complemented
49	#88149	C₂²	1	3	yes	complemented
50	#88148	C₂²	1	6	yes	complemented
51	#88147	C₂²	1	3	yes	complemented
52	#88147	C₂²	1	3	yes	complemented
53	#88146	C₂²	1	3	yes	complemented
54	C₄⋊C₄×D₁₃	C₂²	1	3	yes	complemented
55	#88138	C₂²	1	6	yes	complemented
56	#88138	C₂²	1	6	yes	complemented
57	#88137	C₂²	1	6	yes	complemented
58	#88136	C₂²	1	6	yes	complemented
59	#88135	C₂²	1	1	yes	characteristic
60	#88135	C₂²	1	3	yes	complemented
61	#88135	C₂²	1	6	yes	complemented
62	C₂²⋊C₄×D₁₃	C₂²	1	3	yes	complemented
63	C₂²⋊C₄×D₁₃	C₂²	1	3	yes	complemented
64	#88129	C₂²	1	3	yes	complemented
65	C₄×D₅₂	C₂²	1	3	yes	complemented
66	C₄×D₅₂	C₂²	1	3	yes	complemented
67	C₄²×D₁₃	C₂²	1	3	yes	complemented
68	C₂³×D₁₃	C₂³	1	3	yes	—
69	C₂³×D₁₃	C₂³	1	3	yes	—
70	C₁₃×#41	—	2	4	no	—
71	C₂×Q₈×C₁₃	—	2	4	no	—
72	C₂×Q₈×C₁₃	C₂³	1	3	yes	—
73	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₁₃	C₂³	1	3	yes	—
75	C₂×D₄×C₁₃	C₂³	1	3	yes	—
76	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
77	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
78	C₂×C₂²⋊D₁₃	C₂³	1	3	yes	—
79	C₂×C₂²⋊D₁₃	C₂³	1	6	yes	—
80	C₂×C₂²⋊D₁₃	C₂³	1	6	yes	—
81	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
83	C₂²×Dic₁₃	C₂³	1	3	yes	—
84	#6131	—	2	4	no	—
85	#6131	—	2	12	no	—
86	#6131	—	2	12	no	—
87	#6131	D₄	1	8	yes	complemented
88	Q₈×D₁₃	—	2	4	no	—
89	#6129	—	2	12	no	—
90	D₄×D₁₃	—	2	12	no	—
91	D₄×D₁₃	—	2	12	no	—
92	#6127	—	2	12	no	—
93	C₂×D₅₂	—	2	12	no	—
94	C₂×D₅₂	C₂³	1	3	yes	—
95	C₂×D₅₂	C₂³	1	3	yes	—
96	C₂×D₅₂	C₂³	1	6	yes	—
97	C₂×D₅₂	C₂³	1	3	yes	—
98	C₂×C₄×D₁₃	—	2	12	no	—
99	C₂×C₄×D₁₃	—	2	12	no	—
100	C₂×C₄×D₁₃	C₂³	1	3	yes	—
101	C₂×C₄×D₁₃	C₂³	1	3	yes	—
102	C₂×C₄×D₁₃	C₂³	1	3	yes	—
103	C₂×C₄×D₁₃	C₂³	1	3	yes	—
104	C₂×C₄×D₁₃	C₂³	1	3	yes	—
105	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂³	1	3	yes	—
107	C₂×C₄×D₁₃	C₂³	1	3	yes	—
108	C₂×C₄×D₁₃	C₂³	1	3	yes	—
109	C₂×Dic₂₆	C₂³	1	3	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
112	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
113	C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
114	C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
115	C₄²×C₁₃	C₂³	1	3	yes	—
116	C₂²⋊Dic₁₃	C₂³	1	3	yes	—
117	C₂²⋊Dic₁₃	C₂³	1	3	yes	—
118	#6103	C₂³	1	1	yes	characteristic
119	#6103	C₂³	1	3	yes	—
120	#6103	C₂³	1	6	yes	—
121	#6103	C₂³	1	6	yes	—
122	#6103	C₂³	1	3	yes	—
123	#6103	C₂³	1	3	yes	—
124	C₄⋊Dic₁₃	C₂³	1	3	yes	—
125	C₄⋊Dic₁₃	C₂³	1	3	yes	—
126	#6101	C₂³	1	1	yes	characteristic
127	#6101	C₂³	1	6	yes	—
128	#6101	C₂³	1	3	yes	—
129	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂³	1	3	yes	—
131	C₄×Dic₁₃	C₂³	1	3	yes	—
132	D₄×#41	—	13	1	no	maximal, Sylow
133	C₂³×C₁₃	C₂⁴	1	3	yes	—
134	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×D₁₃	—	2	6	no	—
136	C₂²×D₁₃	—	2	6	no	—
137	C₂²×D₁₃	—	2	6	no	—
138	C₂²×D₁₃	—	2	6	no	—
139	C₂²×D₁₃	—	4	3	no	—
140	C₂²×D₁₃	—	4	3	no	—
141	C₂²×D₁₃	C₂⁴	1	3	yes	—
142	C₂²×D₁₃	C₂⁴	1	3	yes	—
143	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
144	Q₈×C₁₃	—	2	6	no	—
145	Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
146	D₄×C₁₃	—	2	6	no	—
147	D₄×C₁₃	—	2	6	no	—
148	C₂×C₄×C₁₃	—	2	6	no	—
149	C₂×C₄×C₁₃	—	2	6	no	—
150	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
151	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂⁴	1	3	yes	—
155	C₂²⋊D₁₃	—	2	12	no	—
156	C₂²⋊D₁₃	—	2	6	no	—
157	C₂²⋊D₁₃	—	4	6	no	—
158	C₂²⋊D₁₃	#41	1	4	yes	complemented
159	C₂×Dic₁₃	—	2	2	no	—
160	C₂×Dic₁₃	—	2	6	no	—
161	C₂×Dic₁₃	C₂⁴	1	3	yes	—
162	C₂×Dic₁₃	C₂⁴	1	3	yes	—
163	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
166	D₅₂	—	2	12	no	—
167	D₅₂	—	2	6	no	—
168	D₅₂	—	2	6	no	—
169	D₅₂	C₂×D₄	1	12	yes	complemented
170	C₄×D₁₃	—	2	6	no	—
171	C₄×D₁₃	—	2	6	no	—
172	C₄×D₁₃	—	2	6	no	—
173	C₄×D₁₃	—	2	6	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	6	no	—
176	C₄×D₁₃	—	2	6	no	—
177	C₄×D₁₃	—	4	3	no	—
178	C₄×D₁₃	C₂×D₄	1	12	yes	complemented
179	Dic₂₆	—	2	6	no	—
180	C₂²×#41	—	13	1	no	—
181	C₂²×#41	—	13	1	no	—
182	#550	—	13	1	no	—
183	D₄×Q₈	—	13	1	no	—
184	#548	—	13	1	no	—
185	#548	D₁₃	1	1	yes	characteristic, complemented
186	#547	—	13	3	no	—
187	#546	—	13	3	no	—
188	#546	—	13	3	no	—
189	D₄²	—	13	3	no	—
190	#532	—	13	3	no	—
191	#525	—	13	3	no	—
192	#525	—	13	3	no	—
193	C₄×#41	—	13	1	no	—
194	C₂×C₄×D₄	—	13	3	no	—
195	C₂²×C₁₃	—	2	1	no	—
196	C₂²×C₁₃	—	2	1	no	—
197	C₂²×C₁₃	—	2	3	no	—
198	C₂²×C₁₃	—	2	3	no	—
199	C₂²×C₁₃	—	2	3	no	—
200	C₂²×C₁₃	C₂×#41	1	2	yes	complemented
201	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₃	—	2	1	no	—
203	C₂×D₁₃	—	2	3	no	—
204	C₂×D₁₃	—	2	3	no	—
205	C₂×D₁₃	—	2	1	no	—
206	C₂×D₁₃	—	2	3	no	—
207	C₂×D₁₃	—	2	3	no	—
208	C₂×D₁₃	—	2	3	no	—
209	C₂×D₁₃	—	4	12	no	—
210	C₂×D₁₃	—	4	12	no	—
211	C₂×D₁₃	C₂²×D₄	1	6	yes	—
212	C₂×D₁₃	C₂×#41	1	2	yes	complemented
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	3	no	—
215	C₄×C₁₃	—	2	3	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	C₂²×D₄	1	6	yes	—
218	Dic₁₃	—	2	3	no	—
219	Dic₁₃	—	2	1	no	—
220	Dic₁₃	—	2	3	no	—
221	Dic₁₃	C₂²×D₄	1	2	yes	—
222	Dic₁₃	C₂×#41	1	2	yes	complemented
223	C₂×#41	—	13	1	no	—
224	C₂×#41	—	13	3	no	—
225	C₂×#41	—	13	3	no	—
226	C₂×#41	—	13	1	no	—
227	C₂×#41	—	13	3	no	—
228	C₂×#41	—	13	3	no	—
229	C₂×#41	—	26	8	no	—
230	C₂×#41	—	26	8	no	—
231	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
232	C₂²×Q₈	—	13	1	no	—
233	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
234	C₂²×D₄	—	13	3	no	—
235	C₂²×D₄	—	13	3	no	—
236	C₂²×D₄	—	13	3	no	—
237	C₂³×C₄	—	13	3	no	—
238	C₂³×C₄	—	13	3	no	—
239	C₄⋊Q₈	—	13	3	no	—
240	#127	—	13	3	no	—
241	#124	—	13	3	no	—
242	#124	C₂×D₁₃	1	3	yes	complemented
243	#123	—	13	6	no	—
244	#123	—	13	6	no	—
245	C₂²⋊Q₈	—	13	3	no	—
246	C₂²⋊Q₈	—	13	3	no	—
247	C₂²⋊Q₈	—	13	3	no	—
248	C₂²⋊Q₈	C₂×D₁₃	1	3	yes	complemented
249	#121	—	13	3	no	—
250	#121	—	13	3	no	—
251	#121	—	13	3	no	—
252	#121	—	13	6	no	—
253	#121	—	13	6	no	—
254	#121	C₂×D₁₃	1	3	yes	complemented
255	#120	—	13	6	no	—
256	#120	—	13	6	no	—
257	C₄×Q₈	—	13	1	no	—
258	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
259	C₄×D₄	—	13	3	no	—
260	C₄×D₄	—	13	3	no	—
261	C₄×D₄	—	13	3	no	—
262	C₄×D₄	—	13	3	no	—
263	C₄×D₄	—	13	3	no	—
264	C₄×D₄	—	13	1	no	—
265	C₄×D₄	—	13	3	no	—
266	C₄×D₄	—	13	6	no	—
267	C₄×D₄	—	13	3	no	—
268	C₄×D₄	—	13	3	no	—
269	C₄×D₄	C₂×D₁₃	1	3	yes	complemented
270	#117	—	13	3	no	—
271	C₂×C₄⋊C₄	—	13	3	no	—
272	C₂×C₂²⋊C₄	—	13	3	no	—
273	C₂×C₂²⋊C₄	—	13	3	no	—
274	C₂×C₄²	—	13	3	no	—
275	C₂×C₁₃	—	2	2	no	—
276	C₂×C₁₃	—	4	3	no	—
277	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
278	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
279	C₂×C₁₃	#585	1	1	yes	characteristic
280	D₁₃	—	2	2	no	—
281	D₁₃	—	2	6	no	—
282	D₁₃	—	4	3	no	—
283	C₂⁴	—	13	3	no	—
284	C₂⁴	—	13	3	no	—
285	#41	—	2	4	no	—
286	#41	—	13	8	no	—
287	#41	—	26	12	no	—
288	#41	—	26	12	no	—
289	#41	—	26	12	no	—
290	#41	—	26	12	no	—
291	#41	—	26	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	13	3	no	—
294	C₂×Q₈	—	26	4	no	—
295	C₂×Q₈	C₂²×D₁₃	1	3	yes	—
296	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×D₄	—	13	1	no	—
298	C₂×D₄	—	13	3	no	—
299	C₂×D₄	—	13	6	no	—
300	C₂×D₄	—	13	6	no	—
301	C₂×D₄	—	13	3	no	—
302	C₂×D₄	—	13	3	no	—
303	C₂×D₄	—	13	6	no	—
304	C₂×D₄	—	13	3	no	—
305	C₂×D₄	—	26	12	no	—
306	C₂×D₄	—	26	12	no	—
307	C₂×D₄	—	26	12	no	—
308	C₂×D₄	C₂²×D₁₃	1	3	yes	—
309	C₂×D₄	C₂²×D₁₃	1	3	yes	—
310	C₂²×C₄	—	13	3	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	3	no	—
313	C₂²×C₄	—	13	3	no	—
314	C₂²×C₄	—	13	3	no	—
315	C₂²×C₄	—	13	3	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	3	no	—
318	C₂²×C₄	—	13	3	no	—
319	C₂²×C₄	—	13	3	no	—
320	C₂²×C₄	—	13	3	no	—
321	C₂²×C₄	—	26	12	no	—
322	C₂²×C₄	—	26	12	no	—
323	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
324	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
325	C₄⋊C₄	—	13	1	no	—
326	C₄⋊C₄	—	13	3	no	—
327	C₄⋊C₄	—	13	3	no	—
328	C₄⋊C₄	—	13	3	no	—
329	C₄⋊C₄	—	13	6	no	—
330	C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
331	C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
332	C₂²⋊C₄	—	13	3	no	—
333	C₂²⋊C₄	—	13	3	no	—
334	C₂²⋊C₄	—	13	1	no	—
335	C₂²⋊C₄	—	13	3	no	—
336	C₂²⋊C₄	—	13	3	no	—
337	C₂²⋊C₄	—	13	3	no	—
338	C₂²⋊C₄	—	13	6	no	—
339	C₂²⋊C₄	—	13	6	no	—
340	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
341	C₂²⋊C₄	C₂²×D₁₃	1	3	yes	—
342	C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	3	no	—
345	C₄²	—	13	3	no	—
346	C₄²	C₂²×D₁₃	1	3	yes	—
347	C₁₃	D₄×#41	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	13	1	no	—
349	C₂³	—	13	3	no	—
350	C₂³	—	13	3	no	—
351	C₂³	—	26	6	no	—
352	C₂³	—	26	6	no	—
353	C₂³	—	26	6	no	—
354	C₂³	—	26	6	no	—
355	C₂³	—	52	3	no	—
356	C₂³	—	52	3	no	—
357	C₂³	C₂³×D₁₃	1	3	yes	—
358	C₂³	C₂³×D₁₃	1	1	yes	characteristic
359	Q₈	—	2	6	no	—
360	Q₈	—	26	6	no	—
361	Q₈	D₄×D₁₃	1	4	yes	complemented
362	D₄	—	2	6	no	—
363	D₄	—	2	6	no	—
364	D₄	—	13	4	no	—
365	D₄	—	13	12	no	—
366	D₄	—	26	6	no	—
367	D₄	—	26	12	no	—
368	D₄	—	26	6	no	—
369	D₄	—	26	12	no	—
370	D₄	—	26	6	no	—
371	D₄	—	52	6	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	12	no	—
377	C₂×C₄	—	13	3	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	3	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	6	no	—
382	C₂×C₄	—	26	6	no	—
383	C₂×C₄	—	26	6	no	—
384	C₂×C₄	—	26	6	no	—
385	C₂×C₄	—	26	2	no	—
386	C₂×C₄	—	26	6	no	—
387	C₂×C₄	—	26	6	no	—
388	C₂×C₄	—	26	6	no	—
389	C₂×C₄	—	52	3	no	—
390	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₁₃	1	3	yes	—
392	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂³×D₁₃	1	3	yes	—
394	C₂×C₄	C₂³×D₁₃	1	3	yes	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	3	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	13	6	no	—
401	C₂²	—	13	2	no	—
402	C₂²	—	26	1	no	—
403	C₂²	—	26	3	no	—
404	C₂²	—	26	3	no	—
405	C₂²	—	26	1	no	—
406	C₂²	—	26	3	no	—
407	C₂²	—	26	3	no	—
408	C₂²	—	26	3	no	—
409	C₂²	—	52	12	no	—
410	C₂²	—	52	12	no	—
411	C₂²	#41×D₁₃	1	2	yes	complemented
412	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	2	3	no	—
416	C₄	—	2	1	no	—
417	C₄	—	13	2	no	—
418	C₄	—	13	2	no	—
419	C₄	—	26	1	no	—
420	C₄	—	26	3	no	—
421	C₄	—	26	3	no	—
422	C₄	C₂×D₄×D₁₃	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	4	3	no	—
425	C₂	—	26	2	no	—
426	C₂	—	26	6	no	—
427	C₂	—	52	3	no	—
428	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
429	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
430	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#548	C₂
hypercenter	#548	D₁₃
hypocenter	C₁₃	D₄×#41
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₃	C₂	semidirect
2. C₂²×#6131	C₂	semidirect
3. C₁₃×#548	C₂	semidirect
4. #11719539	C₂	semidirect
5. Q₈×C₂²⋊D₁₃	C₂	semidirect
6. #11719381	C₂	semidirect
7. #11719373	C₂	semidirect
8. #11719336	C₂	semidirect
9. #11719332	C₂	semidirect
10. #11719314	C₂	semidirect
11. #11719311	C₂	semidirect
12. #11719281	C₂	semidirect
13. C₄×#6131	C₂	semidirect
14. #11719255	C₂	semidirect
15. C₄×D₄×D₁₃	C₂	semidirect
16. C₂×C₁₃×#41	C₂²	semidirect
17. C₂²×Q₈×C₁₃	C₂²	semidirect
21. C₂×#6131	C₂²	semidirect
22. C₂×#6131	C₂²	semidirect
23. C₂×#6131	C₂²	semidirect
24. C₂×Q₈×D₁₃	C₂²	semidirect
25. C₂×#6129	C₂²	semidirect
27. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
29. C₂²×D₅₂	C₂²	semidirect
30. C₂²×C₄×D₁₃	C₂²	semidirect
31. C₂²×C₄×D₁₃	C₂²	semidirect
32. C₁₃×#124	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
34. C₁₃×#121	C₂²	semidirect
35. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. #88200	C₂²	semidirect
38. Q₈×Dic₁₃	C₂²	semidirect
39. #88198	C₂²	semidirect
40. #88194	C₂²	semidirect
41. #88192	C₂²	semidirect
42. #88191	C₂²	semidirect
43. D₄×Dic₁₃	C₂²	semidirect
44. #88184	C₂²	semidirect
46. C₄×C₂²⋊D₁₃	C₂²	semidirect
47. #88178	C₂²	semidirect
48. #88151	C₂²	semidirect
49. #88149	C₂²	semidirect
50. #88148	C₂²	semidirect
51. #88147	C₂²	semidirect
52. #88147	C₂²	semidirect
53. #88146	C₂²	semidirect
54. C₄⋊C₄×D₁₃	C₂²	semidirect
55. #88138	C₂²	semidirect
56. #88138	C₂²	semidirect
57. #88137	C₂²	semidirect
58. #88136	C₂²	semidirect
60. #88135	C₂²	semidirect
61. #88135	C₂²	semidirect
62. C₂²⋊C₄×D₁₃	C₂²	semidirect
63. C₂²⋊C₄×D₁₃	C₂²	semidirect
64. #88129	C₂²	semidirect
65. C₄×D₅₂	C₂²	semidirect
66. C₄×D₅₂	C₂²	semidirect
67. C₄²×D₁₃	C₂²	semidirect
87. #6131	D₄	semidirect
145. Q₈×C₁₃	C₂×D₄	semidirect
158. C₂²⋊D₁₃	#41	semidirect
169. D₅₂	C₂×D₄	semidirect
178. C₄×D₁₃	C₂×D₄	semidirect
185. #548	D₁₃	semidirect
200. C₂²×C₁₃	C₂×#41	semidirect
212. C₂×D₁₃	C₂×#41	semidirect
222. Dic₁₃	C₂×#41	semidirect
231. C₂×#41	C₂×D₁₃	semidirect
233. C₂²×Q₈	C₂×D₁₃	semidirect
242. #124	C₂×D₁₃	semidirect
248. C₂²⋊Q₈	C₂×D₁₃	semidirect
254. #121	C₂×D₁₃	semidirect
258. C₄×Q₈	C₂×D₁₃	semidirect
269. C₄×D₄	C₂×D₁₃	semidirect
347. C₁₃	D₄×#41	semidirect
361. Q₈	D₄×D₁₃	semidirect
411. C₂²	#41×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₃	2
C₂²×#6131	2
C₁₃×#548	2
#11719539	2
Q₈×C₂²⋊D₁₃	2
#11719381	2
#11719373	2
#11719336	2
#11719332	2
#11719314	2
#11719311	2
#11719281	2
C₄×#6131	2
#11719255	2
C₄×D₄×D₁₃	2
D₄×#41	13