Subgroups — #15873540

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123468	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718346	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#423	C₂	1	1	yes	maximal, characteristic
4	#13115608	C₂	1	4	yes	maximal, complemented
5	#13115039	C₂	1	4	yes	maximal
6	#13115007	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114974	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114973	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#108	C₂²	1	4	yes	—
13	C₁₃×#423	C₂²	1	1	yes	characteristic
14	C₁₃×#423	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	#11718787	C₂²	1	2	yes	—
17	C₂×#88062	C₂²	1	4	yes	—
18	#11718779	C₂²	1	2	yes	—
19	M₁₆×Dic₁₃	C₂²	1	2	yes	—
20	C₂×#88060	C₂²	1	2	yes	—
21	C₂×#88054	C₂²	1	2	yes	—
22	#11718585	C₂²	1	1	yes	characteristic
23	#11718585	C₂²	1	1	yes	characteristic
24	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
25	#11718498	—	2	1	no	—
26	#11718498	—	2	1	no	—
27	#11718496	—	2	1	no	—
28	#11718496	—	2	1	no	—
29	#11718494	—	2	1	no	—
30	#11718494	—	2	1	no	—
31	D₁₃×C₄⋊C₈	—	2	1	no	—
32	D₁₃×C₄⋊C₈	—	2	1	no	—
33	#11718346	C₄	1	2	yes	—
34	#11718346	C₄	1	2	yes	—
35	#11718346	C₄	1	2	yes	—
36	#11718346	C₄	1	2	yes	—
37	#11718150	C₂²	1	4	yes	—
38	#11718144	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	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
43	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6099	C₂³	1	2	yes	—
50	C₂×#6099	C₂³	1	2	yes	—
51	C₂²×#1055	C₂³	1	2	yes	—
52	M₁₆×D₁₃	—	4	4	no	—
53	C₂×#6094	—	2	2	no	—
54	C₂×C₈×D₁₃	—	2	2	no	—
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	C₄²×D₁₃	D₄	1	1	yes	characteristic
61	C₄²×D₁₃	D₄	1	1	yes	characteristic
62	C₄²×D₁₃	D₄	1	1	yes	characteristic
63	C₁₃×#108	—	4	4	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	—	2	1	no	—
68	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
70	#88062	—	4	4	no	—
71	#88060	—	2	2	no	—
72	#88060	—	2	2	no	—
73	#88060	C₂×C₄	1	4	yes	—
74	#88060	C₂×C₄	1	4	yes	—
75	#88055	—	2	2	no	—
76	#88054	—	2	2	no	—
77	#88054	—	2	2	no	—
78	#88054	C₂×C₄	1	4	yes	—
79	#88054	C₂×C₄	1	4	yes	—
80	C₈×Dic₁₃	—	2	2	no	—
81	C₄⋊#1055	—	2	1	no	—
82	C₄⋊#1055	—	2	1	no	—
83	C₄⋊#1055	—	2	1	no	—
84	C₄⋊#1055	—	2	1	no	—
85	C₄×#1055	C₂×C₄	1	2	yes	—
86	C₄×#1055	C₂×C₄	1	2	yes	—
87	#21993	—	13	1	no	maximal, Sylow
88	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
95	C₂×C₄×D₁₃	—	2	2	no	—
96	C₂×C₄×D₁₃	—	2	2	no	—
97	C₂×C₄×D₁₃	—	2	4	no	—
98	C₂×C₄×D₁₃	—	4	2	no	—
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
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	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
111	C₁₃×M₁₆	—	2	4	no	—
112	C₁₃×M₁₆	—	2	4	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
134	#6099	—	2	4	no	—
135	#6099	—	2	4	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	2	no	—
138	C₂×#1055	—	2	2	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	C₂²×C₄	1	4	yes	—
141	#6094	—	4	4	no	—
142	C₈×D₁₃	—	4	4	no	—
143	#2920	—	13	1	no	—
144	C₂×#431	—	13	1	no	—
145	C₂×#423	—	13	1	no	—
146	#1950	—	13	4	no	—
147	#1855	—	13	4	no	—
148	#1848	—	13	1	no	—
149	#1848	D₁₃	1	1	yes	characteristic, complemented
150	#1837	—	13	1	no	—
151	#1837	—	13	1	no	—
152	C₂³×C₁₃	C₂²×Q₈	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	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
167	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	—	2	2	no	—
170	C₂×Dic₁₃	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	1	no	—
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	2	1	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	4	1	no	—
189	C₄×D₁₃	—	4	1	no	—
190	C₄×D₁₃	#108	1	4	yes	complemented
191	C₈×C₁₃	—	2	4	no	—
192	C₈×C₁₃	—	4	2	no	—
193	C₈×C₁₃	—	4	2	no	—
194	#1055	—	2	4	no	—
195	#1055	—	4	2	no	—
196	#1055	—	4	2	no	—
197	C₂²×M₁₆	—	13	2	no	—
198	C₂²×C₄²	—	13	1	no	—
199	#432	—	26	1	no	—
200	#432	—	26	1	no	—
201	#431	—	13	2	no	—
202	#431	—	13	2	no	—
203	#431	—	13	2	no	—
204	#431	—	13	2	no	—
205	#431	—	26	1	no	—
206	#431	—	26	1	no	—
207	C₂×#108	—	13	4	no	—
208	C₂×#108	C₂×D₁₃	1	4	yes	—
209	#423	—	13	2	no	—
210	#423	—	13	1	no	—
211	#423	—	13	1	no	—
212	#423	—	26	1	no	—
213	#423	—	26	1	no	—
214	#423	C₂×D₁₃	1	1	yes	characteristic
215	#423	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	13	2	no	—
217	C₂×C₄⋊C₈	—	26	1	no	—
218	C₂×C₄⋊C₈	—	26	1	no	—
219	#407	—	13	2	no	—
220	C₂×C₂²⋊C₈	—	13	2	no	—
221	C₄×M₁₆	—	13	2	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
224	#341	—	13	4	no	—
225	#341	—	13	4	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₁₃	#544	1	2	yes	—
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	—	2	1	no	—
235	C₂×D₁₃	—	4	4	no	—
236	C₂×D₁₃	C₂×#108	1	2	yes	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	1	no	—
239	C₄×C₁₃	C₂×#108	1	2	yes	—
240	C₄×C₁₃	#430	1	2	yes	—
241	C₄×C₁₃	#520	1	2	yes	—
242	C₄×C₁₃	#535	1	1	yes	characteristic
243	C₄×C₁₃	#536	1	1	yes	characteristic
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	1	no	—
247	Dic₁₃	—	2	1	no	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	C₂×#108	1	2	yes	—
250	C₂³×C₄	—	13	1	no	—
251	C₂³×C₄	—	13	1	no	—
252	C₂³×C₄	—	13	1	no	—
253	C₂×M₁₆	—	13	2	no	—
254	C₂×M₁₆	—	13	2	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	52	4	no	—
257	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
258	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
259	C₂²×C₈	—	13	2	no	—
260	C₂²×C₈	—	26	2	no	—
261	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
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	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
274	#108	—	4	4	no	—
275	#108	—	52	4	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	13	4	no	—
281	C₄⋊C₈	—	13	4	no	—
282	C₄⋊C₈	—	26	2	no	—
283	C₄⋊C₈	—	26	2	no	—
284	C₄⋊C₈	—	26	1	no	—
285	C₄⋊C₈	—	26	1	no	—
286	C₄⋊C₈	—	26	1	no	—
287	C₄⋊C₈	—	26	1	no	—
288	C₂²⋊C₈	—	13	4	no	—
289	C₂²⋊C₈	—	13	4	no	—
290	C₂²⋊C₈	—	26	2	no	—
291	C₂²⋊C₈	—	26	2	no	—
292	#97	—	26	2	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	—	13	2	no	—
295	C₄×C₈	—	26	2	no	—
296	C₄×C₈	C₄×D₁₃	1	2	yes	—
297	C₄×C₈	C₄×D₁₃	1	2	yes	—
298	C₂×C₁₃	—	2	2	no	—
299	C₂×C₁₃	#2317	1	1	yes	characteristic
300	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
301	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
302	D₁₃	—	2	2	no	—
303	D₁₃	—	4	1	no	—
304	C₂⁴	—	13	1	no	—
305	C₂²×C₄	—	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	—	26	4	no	—
321	C₂²×C₄	—	26	2	no	—
322	C₂²×C₄	—	26	2	no	—
323	C₂²×C₄	—	52	2	no	—
324	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
325	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
327	M₁₆	—	2	4	no	—
328	M₁₆	—	2	4	no	—
329	M₁₆	—	26	4	no	—
330	M₁₆	—	26	4	no	—
331	M₁₆	—	52	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	13	4	no	—
337	C₂×C₈	—	26	2	no	—
338	C₂×C₈	—	26	2	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	—	26	2	no	—
341	C₂×C₈	—	52	4	no	—
342	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
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	—	13	1	no	—
355	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
356	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
357	C₄²	D₄×D₁₃	1	1	yes	characteristic
358	C₄²	D₄×D₁₃	1	1	yes	characteristic
359	C₁₃	#21993	1	1	yes	characteristic, complemented, Sylow
360	C₂³	—	13	1	no	—
361	C₂³	—	13	1	no	—
362	C₂³	—	26	2	no	—
363	C₂³	—	26	2	no	—
364	C₂³	—	52	1	no	—
365	C₂³	C₂×Q₈×D₁₃	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	4	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	2	no	—
377	C₂×C₄	—	26	2	no	—
378	C₂×C₄	—	26	2	no	—
379	C₂×C₄	—	26	1	no	—
380	C₂×C₄	—	26	1	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	—	26	1	no	—
387	C₂×C₄	—	26	1	no	—
388	C₂×C₄	—	52	1	no	—
389	C₂×C₄	—	52	1	no	—
390	C₂×C₄	—	52	1	no	—
391	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
392	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
397	C₂×C₄	#88251	1	2	yes	—
398	C₂×C₄	#88254	1	2	yes	—
399	C₈	—	2	4	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	26	4	no	—
403	C₈	—	52	2	no	—
404	C₈	—	52	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	13	2	no	—
408	C₂²	—	26	1	no	—
409	C₂²	—	26	1	no	—
410	C₂²	—	26	1	no	—
411	C₂²	—	26	1	no	—
412	C₂²	—	26	1	no	—
413	C₂²	—	52	4	no	—
414	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
415	C₂²	#11719434	1	2	yes	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	13	2	no	—
419	C₄	—	26	1	no	—
420	C₄	—	26	1	no	—
421	C₄	—	26	1	no	—
422	C₄	—	26	1	no	—
423	C₄	—	26	1	no	—
424	C₄	D₁₃×#108	1	2	yes	—
425	C₄	#11718554	1	2	yes	—
426	C₄	#11719209	1	2	yes	—
427	C₄	#11719420	1	1	yes	characteristic
428	C₄	#11719429	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	26	2	no	—
431	C₂	—	52	1	no	—
432	C₂	#13117457	1	1	yes	characteristic
433	C₂	C₂×D₁₃×#108	1	1	yes	characteristic
434	C₂	C₂×#11718554	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1848	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1848	D₁₃
hypocenter	C₁₃	#21993
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

Complements

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

N	H ≅ G/N	type
4. #13115608	C₂	semidirect
6. #13115007	C₂	semidirect
7. #13114974	C₂	semidirect
8. #13114973	C₂	semidirect
9. C₁₃×#1848	C₂	semidirect
149. #1848	D₁₃	semidirect
190. C₄×D₁₃	#108	semidirect
359. C₁₃	#21993	semidirect

Maximal subgroups

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

subgroup	index
#13123468	2
C₂×#11718346	2
D₁₃×#423	2
#13115608	2
#13115039	2
#13115007	2
#13114974	2
#13114973	2
C₁₃×#1848	2
#21993	13