Subgroups — #16799519

Order 3328.

780 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	#13131515	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
3	#13130952	C₂	1	4	yes	maximal, complemented
4	#13130789	C₂	1	2	yes	maximal
5	#13130788	C₂	1	2	yes	maximal
6	C₄×#88104	C₂	1	2	yes	maximal, complemented
7	C₄×#88103	C₂	1	2	yes	maximal, complemented
8	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂²×#6118	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719128	—	2	1	no	—
12	#11719127	C₂²	1	2	yes	—
13	#11719125	—	2	1	no	—
14	C₂×#88110	—	2	1	no	—
15	C₂×C₄×#1057	—	2	1	no	—
16	C₂×#88104	C₂²	1	4	yes	—
17	C₂×#88103	C₂²	1	4	yes	—
18	#11719055	—	2	1	no	—
19	#11719053	C₂²	1	2	yes	—
20	#11719049	—	2	1	no	—
21	C₄×#6118	—	2	1	no	—
22	C₄×#6118	—	2	1	no	—
23	C₄×#6118	C₂²	1	2	yes	—
24	C₄×#6118	C₂²	1	2	yes	—
25	C₄×#6118	C₂²	1	1	yes	characteristic
26	C₄×#6118	C₂²	1	1	yes	characteristic
27	C₁₃×#431	C₄	1	1	yes	characteristic
28	#11718586	C₄	1	1	yes	characteristic
29	#11718494	C₄	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	#11718379	C₄	1	1	yes	characteristic
34	#11718379	C₄	1	1	yes	characteristic
35	#11718346	C₄	1	2	yes	—
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	#11718268	C₂²	1	4	yes	—
38	#11718268	C₂²	1	4	yes	—
39	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
42	C₂²×#1057	—	2	2	no	—
43	C₂×#6118	—	2	2	no	—
44	C₂×#6118	—	2	8	no	—
45	C₂×#6118	C₂³	1	2	yes	—
46	C₂×#6118	C₂³	1	2	yes	—
47	C₂×#6118	C₂³	1	4	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	2	yes	—
53	C₂×C₈×D₁₃	C₂³	1	2	yes	—
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	D₄	1	1	yes	characteristic
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₄²×D₁₃	Q₈	1	1	yes	characteristic
59	C₄²×D₁₃	Q₈	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	C₂²⋊#1057	—	2	2	no	—
63	#88112	—	2	2	no	—
64	#88112	—	2	2	no	—
65	#88111	—	2	2	no	—
66	#88110	—	2	2	no	—
67	#88110	—	2	2	no	—
68	#88110	—	2	1	no	—
69	#88110	—	2	1	no	—
70	C₄×#1057	—	2	2	no	—
71	C₄×#1057	—	2	2	no	—
72	C₄×#1057	—	2	1	no	—
73	C₄×#1057	—	2	1	no	—
74	#88104	—	2	8	no	—
75	#88103	—	2	8	no	—
76	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
80	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
82	#88060	C₂×C₄	1	2	yes	—
83	#88060	C₂×C₄	1	2	yes	—
84	#88054	C₂×C₄	1	2	yes	—
85	#88054	C₂×C₄	1	2	yes	—
86	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
87	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
88	C₄⋊#1055	C₂×C₄	1	2	yes	—
89	C₄×#1055	C₂×C₄	1	2	yes	—
90	#21370	—	13	1	no	maximal, Sylow
91	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	—	2	4	no	—
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	4	2	no	—
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×#1057	—	2	8	no	—
114	C₂×#1057	—	2	4	no	—
115	C₂×#1057	—	2	2	no	—
116	C₂×#1057	—	2	2	no	—
117	#6118	—	2	8	no	—
118	#6118	—	2	4	no	—
119	#6118	—	2	4	no	—
120	#6118	—	2	4	no	—
121	#6118	#41	1	8	yes	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	2	yes	—
141	C₂×#1055	C₂²×C₄	1	2	yes	—
142	C₈×D₁₃	—	2	4	no	—
143	C₈×D₁₃	—	2	4	no	—
144	#2920	—	13	1	no	—
145	C₂×#431	—	13	1	no	—
146	C₂×C₄×M₁₆	—	13	1	no	—
147	#1950	—	13	4	no	—
148	#1855	—	13	2	no	—
149	#1855	—	13	2	no	—
150	C₄×#108	—	13	2	no	—
151	C₄×#108	—	13	2	no	—
152	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂²×D₁₃	—	2	2	no	—
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	4	1	no	—
156	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	4	1	no	—
169	C₂×Dic₁₃	#108	1	4	yes	complemented
170	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	4	1	no	—
186	C₄×D₁₃	—	4	1	no	—
187	C₄×D₁₃	C₂×#41	1	4	yes	—
188	#1057	—	2	8	no	—
189	#1057	—	4	2	no	—
190	#1057	—	4	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	2	2	no	—
193	#1055	—	2	2	no	—
194	#1055	—	2	2	no	—
195	C₂²×M₁₆	—	13	2	no	—
196	C₂²×C₄²	—	13	1	no	—
197	#432	—	26	1	no	—
198	#432	—	26	1	no	—
199	#431	—	13	1	no	—
200	#431	—	13	2	no	—
201	#431	—	13	1	no	—
202	#431	—	13	1	no	—
203	#431	—	13	2	no	—
204	#431	—	26	1	no	—
205	#431	—	26	1	no	—
206	#431	#261	1	1	yes	characteristic
207	C₂×#108	—	13	4	no	—
208	C₂×#108	—	13	4	no	—
209	#423	—	13	2	no	—
210	C₂×C₄⋊C₈	—	13	2	no	—
211	#407	—	13	2	no	—
212	C₂×C₂²⋊C₈	—	13	1	no	—
213	C₂×C₂²⋊C₈	—	13	1	no	—
214	C₄×M₁₆	—	13	2	no	—
215	C₄×M₁₆	—	13	2	no	—
216	C₄×M₁₆	—	13	1	no	—
217	C₄×M₁₆	—	13	1	no	—
218	C₄×M₁₆	—	26	1	no	—
219	C₄×M₁₆	—	26	1	no	—
220	C₂×#97	—	26	1	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	C₂×C₄×C₈	—	26	1	no	—
223	#341	—	13	4	no	—
224	#341	—	13	4	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	C₂×#108	1	2	yes	—
228	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	—	2	1	no	—
233	C₂×D₁₃	—	2	1	no	—
234	C₂×D₁₃	—	4	4	no	—
235	C₂×D₁₃	#533	1	2	yes	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	#430	1	2	yes	—
241	C₄×C₁₃	C₄×#41	1	2	yes	—
242	Dic₁₃	—	2	1	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	C₂×#108	1	2	yes	—
246	Dic₁₃	C₂×#108	1	2	yes	—
247	Dic₁₃	#525	1	2	yes	—
248	C₂³×C₄	—	13	1	no	—
249	C₂³×C₄	—	13	1	no	—
250	C₂³×C₄	—	13	1	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	13	2	no	—
253	C₂×M₁₆	—	13	2	no	—
254	C₂×M₁₆	—	26	8	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂²×C₈	—	13	2	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	—	26	2	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	1	no	—
266	C₂×C₄²	—	13	1	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	C₂×#261	1	1	yes	characteristic
271	#108	—	26	8	no	—
272	#108	—	26	8	no	—
273	C₄⋊C₈	—	13	2	no	—
274	C₄⋊C₈	—	13	2	no	—
275	C₄⋊C₈	—	13	2	no	—
276	C₄⋊C₈	—	26	2	no	—
277	C₄⋊C₈	—	26	2	no	—
278	C₄⋊C₈	C₂×#261	1	2	yes	—
279	C₂²⋊C₈	—	13	1	no	—
280	C₂²⋊C₈	—	13	1	no	—
281	C₂²⋊C₈	—	13	2	no	—
282	C₂²⋊C₈	—	13	2	no	—
283	C₂²⋊C₈	—	26	2	no	—
284	C₂²⋊C₈	—	26	2	no	—
285	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
286	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
287	#97	—	26	2	no	—
288	#97	—	26	2	no	—
289	#97	—	26	1	no	—
290	#97	—	26	1	no	—
291	C₄×C₈	—	13	2	no	—
292	C₄×C₈	—	13	2	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	—	26	2	no	—
295	C₄×C₈	—	26	2	no	—
296	C₄×C₈	—	26	1	no	—
297	C₄×C₈	—	26	1	no	—
298	C₄×C₈	C₂×#261	1	2	yes	—
299	C₂×C₁₃	—	2	2	no	—
300	C₂×C₁₃	#2296	1	1	yes	characteristic
301	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
302	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
303	D₁₃	—	2	2	no	—
304	D₁₃	—	4	1	no	—
305	C₂⁴	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	26	4	no	—
322	C₂²×C₄	—	26	4	no	—
323	C₂²×C₄	—	52	2	no	—
324	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
325	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
326	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
327	M₁₆	—	13	8	no	—
328	M₁₆	—	26	4	no	—
329	M₁₆	—	26	8	no	—
330	M₁₆	—	26	4	no	—
331	M₁₆	—	26	4	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	26	4	no	—
335	C₂×C₈	—	26	4	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	8	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	C₂²×#261	1	2	yes	—
341	C₂×C₈	C₂²×#261	1	2	yes	—
342	C₄²	—	13	1	no	—
343	C₄²	—	13	1	no	—
344	C₄²	—	13	1	no	—
345	C₄²	—	13	1	no	—
346	C₄²	—	13	1	no	—
347	C₄²	—	13	1	no	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	C₄⋊#261	1	1	yes	characteristic
355	C₄²	C₄⋊#261	1	1	yes	characteristic
356	C₄²	C₂²×#261	1	1	yes	characteristic
357	C₄²	C₂²×#261	1	1	yes	characteristic
358	C₁₃	#21370	1	1	yes	characteristic, complemented, Sylow
359	C₂³	—	13	1	no	—
360	C₂³	—	13	1	no	—
361	C₂³	—	26	2	no	—
362	C₂³	—	26	2	no	—
363	C₂³	—	52	1	no	—
364	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	13	4	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	4	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	2	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	2	no	—
386	C₂×C₄	—	52	1	no	—
387	C₂×C₄	—	52	1	no	—
388	C₂×C₄	—	52	1	no	—
389	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
393	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
394	C₂×C₄	C₂³×#261	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	26	8	no	—
398	C₈	—	26	2	no	—
399	C₈	—	26	2	no	—
400	C₈	—	52	2	no	—
401	C₈	—	52	2	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	13	2	no	—
405	C₂²	—	26	1	no	—
406	C₂²	—	26	1	no	—
407	C₂²	—	26	1	no	—
408	C₂²	—	26	1	no	—
409	C₂²	—	26	1	no	—
410	C₂²	—	52	4	no	—
411	C₂²	D₁₃⋊#108	1	2	yes	—
412	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	13	2	no	—
418	C₄	—	13	2	no	—
419	C₄	—	13	2	no	—
420	C₄	—	26	1	no	—
421	C₄	—	26	1	no	—
422	C₄	—	26	1	no	—
423	C₄	#11719100	1	2	yes	—
424	C₄	#41×#261	1	2	yes	—
425	C₂	—	2	2	no	—
426	C₂	—	26	2	no	—
427	C₂	—	52	1	no	—
428	C₂	#13131296	1	1	yes	characteristic
429	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic
430	C₂	C₂×#11719100	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#21370
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130952	C₂	semidirect
6. C₄×#88104	C₂	semidirect
7. C₄×#88103	C₂	semidirect
169. C₂×Dic₁₃	#108	semidirect
358. C₁₃	#21370	semidirect

Maximal subgroups

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

subgroup	index
#13131515	2
C₂×C₄×#6118	2
#13130952	2
#13130789	2
#13130788	2
C₄×#88104	2
C₄×#88103	2
D₁₃×#431	2
#21370	13