Subgroups — C₂×#13129895 #16789102

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#13129895	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₃⋊M₁₆	—	2	1	no	—
6	C₂×M₁₆×D₁₃	—	2	1	no	—
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#6092	—	2	1	no	—
9	D₁₃⋊#108	—	2	1	no	—
10	D₁₃⋊#108	—	2	1	no	—
11	D₁₃⋊#108	C₄	1	2	yes	—
12	D₁₃⋊#108	C₂²	1	2	yes	—
13	C₂×#88104	C₄	1	2	yes	—
14	C₂×#88103	—	2	1	no	—
15	C₂×D₁₃⋊C₁₆	—	2	1	no	—
16	C₂×D₁₃⋊C₁₆	—	2	1	no	—
17	C₂×D₁₃⋊C₁₆	—	2	1	no	—
18	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	—
19	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	—
20	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
21	C₂×C₁₃×#108	C₄	1	1	yes	characteristic
22	C₂×#88062	—	2	1	no	—
23	C₂×#88059	C₄	1	1	yes	characteristic
24	D₁₃×#108	—	2	1	no	—
25	D₁₃×#108	—	2	1	no	—
26	D₁₃×#108	C₄	1	2	yes	—
27	D₁₃×#108	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂×#6122	—	4	1	no	—
30	D₁₃⋊M₁₆	—	2	2	no	—
31	D₁₃⋊M₁₆	—	2	2	no	—
32	D₁₃⋊M₁₆	—	4	1	no	—
33	D₁₃⋊M₁₆	—	4	1	no	—
34	C₂×#6118	—	2	2	no	—
35	C₂×D₁₃⋊C₈	—	4	1	no	—
36	C₂×C₁₃×M₁₆	—	2	1	no	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×#6099	—	2	1	no	—
39	C₂²×#1055	D₄	1	1	yes	characteristic
40	M₁₆×D₁₃	—	2	2	no	—
41	M₁₆×D₁₃	—	2	2	no	—
42	M₁₆×D₁₃	—	4	1	no	—
43	M₁₆×D₁₃	—	4	1	no	—
44	C₂×#6094	—	4	1	no	—
45	C₂×C₈×D₁₃	—	4	1	no	—
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	C₂×#6092	—	2	2	no	—
59	C₂×#6092	—	2	2	no	—
60	C₂×#6092	—	2	2	no	—
61	#88104	—	2	2	no	—
62	#88104	C₂×C₄	1	4	yes	—
63	#88103	—	2	2	no	—
64	#88103	—	2	2	no	—
65	D₁₃⋊C₁₆	—	2	2	no	—
66	D₁₃⋊C₁₆	—	2	2	no	—
67	D₁₃⋊C₁₆	—	2	2	no	—
68	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
69	C₁₃×#108	—	2	1	no	—
70	C₁₃×#108	C₂×C₄	1	2	yes	—
71	#88062	—	2	2	no	—
72	#88062	—	2	2	no	—
73	#88059	—	2	1	no	—
74	#88059	C₂×C₄	1	2	yes	—
75	C₂×#1381	—	13	1	no	maximal, Sylow
76	C₂³×D₁₃	Q₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₃	SD₁₆	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
85	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
86	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
89	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
91	#6122	—	4	2	no	—
92	#6122	—	4	2	no	—
93	C₂×#1057	—	4	2	no	—
94	#6118	—	2	4	no	—
95	#6118	—	4	2	no	—
96	D₁₃⋊C₈	—	4	2	no	—
97	D₁₃⋊C₈	—	4	2	no	—
98	C₁₃×M₁₆	—	2	2	no	—
99	C₁₃×M₁₆	—	4	1	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
103	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	#6099	—	2	2	no	—
108	#6099	—	4	1	no	—
109	C₂×#1055	—	4	1	no	—
110	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
113	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
114	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#1055	C₂×D₄	1	1	yes	characteristic
116	#6094	—	4	2	no	—
117	#6094	—	4	2	no	—
118	C₈×D₁₃	—	4	2	no	—
119	C₈×D₁₃	—	4	2	no	—
120	C₈×D₁₃	C₄²	1	1	yes	characteristic
121	C₈×D₁₃	C₄²	1	1	yes	characteristic
122	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
135	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
136	#6092	—	2	4	no	—
137	C₂³×C₁₆	—	13	1	no	—
138	C₂²×#108	—	13	1	no	—
139	C₂²×#108	—	13	1	no	—
140	#1381	—	13	4	no	—
141	C₂³×C₁₃	#103	1	1	yes	characteristic
142	C₂²×D₁₃	—	2	4	no	—
143	C₂²×D₁₃	#103	1	1	yes	characteristic
144	C₂²×D₁₃	#103	1	1	yes	characteristic
145	C₂²×D₁₃	#103	1	1	yes	characteristic
146	C₂²×D₁₃	#107	1	1	yes	characteristic
147	C₂²×D₁₃	#107	1	1	yes	characteristic
148	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
150	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	#102	1	1	yes	characteristic
156	C₂×Dic₁₃	#102	1	1	yes	characteristic
157	C₂×Dic₁₃	#103	1	1	yes	characteristic
158	C₂×Dic₁₃	#106	1	1	yes	characteristic
159	C₂×Dic₁₃	#106	1	1	yes	characteristic
160	C₂×Dic₁₃	C₂×SD₁₆	1	1	yes	characteristic
161	C₄×D₁₃	#95	1	1	yes	characteristic
162	C₄×D₁₃	#95	1	1	yes	characteristic
163	C₄×D₁₃	#102	1	1	yes	characteristic
164	C₄×D₁₃	#102	1	1	yes	characteristic
165	C₄×D₁₃	#102	1	1	yes	characteristic
166	C₄×D₁₃	#102	1	1	yes	characteristic
167	C₄×D₁₃	#103	1	1	yes	characteristic
168	C₄×D₁₃	#103	1	1	yes	characteristic
169	C₄×D₁₃	#106	1	1	yes	characteristic
170	C₄×D₁₃	#106	1	1	yes	characteristic
171	C₄×D₁₃	#107	1	1	yes	characteristic
172	C₄×D₁₃	#107	1	1	yes	characteristic
173	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
176	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
177	#1057	—	4	4	no	—
178	C₈×C₁₃	—	4	2	no	—
179	C₈×C₁₃	#95	1	1	yes	characteristic
180	C₈×C₁₃	#95	1	1	yes	characteristic
181	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#1055	—	4	2	no	—
184	#1055	#95	1	1	yes	characteristic
185	#1055	#95	1	1	yes	characteristic
186	#1055	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×M₁₆	—	26	1	no	—
189	C₂²×M₁₆	—	26	1	no	—
190	C₂³×C₈	—	13	1	no	—
191	C₂²×C₁₆	—	13	2	no	—
192	C₂²×C₁₆	—	13	2	no	—
193	C₂²×C₁₆	—	13	2	no	—
194	C₂²×C₁₆	—	26	1	no	—
195	C₂²×C₁₆	—	26	1	no	—
196	C₂²×C₁₆	—	26	1	no	—
197	C₂²×C₁₆	—	26	1	no	—
198	C₂×#108	—	13	2	no	—
199	C₂×#108	—	13	2	no	—
200	C₂×#108	—	13	2	no	—
201	C₂×#108	—	13	1	no	—
202	C₂×#108	—	13	2	no	—
203	C₂×#108	—	13	2	no	—
204	C₂×#108	—	26	1	no	—
205	C₂×#108	—	26	1	no	—
206	C₂×#108	—	26	1	no	—
207	C₂×#108	—	26	1	no	—
208	C₂×#108	—	26	1	no	—
209	C₂×#108	—	26	1	no	—
210	C₂×#108	#261	1	1	yes	characteristic
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	#340	1	1	yes	characteristic
213	C₂²×C₁₃	#340	1	1	yes	characteristic
214	C₂²×C₁₃	C₂×#103	1	1	yes	characteristic
215	C₂×D₁₃	—	2	2	no	—
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	#340	1	1	yes	characteristic
221	C₂×D₁₃	#340	1	1	yes	characteristic
222	C₂×D₁₃	#368	1	4	yes	—
223	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
224	C₂×D₁₃	C₂×#107	1	1	yes	characteristic
225	C₄×C₁₃	#340	1	1	yes	characteristic
226	C₄×C₁₃	#340	1	1	yes	characteristic
227	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
228	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
229	Dic₁₃	#340	1	1	yes	characteristic
230	Dic₁₃	#340	1	1	yes	characteristic
231	Dic₁₃	C₂×#102	1	1	yes	characteristic
232	Dic₁₃	C₂×#106	1	1	yes	characteristic
233	C₂³×C₄	—	13	1	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	26	2	no	—
236	C₂×M₁₆	—	26	2	no	—
237	C₂×M₁₆	—	26	2	no	—
238	C₂×M₁₆	—	26	2	no	—
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	—	26	1	no	—
241	C₂×M₁₆	—	52	1	no	—
242	C₂×M₁₆	—	52	1	no	—
243	C₂×M₁₆	—	52	1	no	—
244	C₂×M₁₆	—	52	1	no	—
245	C₂×M₁₆	—	52	1	no	—
246	C₂×M₁₆	—	52	1	no	—
247	C₂²×C₈	—	13	1	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	52	1	no	—
261	C₂²×C₈	—	52	1	no	—
262	C₂²×C₈	C₂×#261	1	1	yes	characteristic
263	C₂×C₁₆	—	13	4	no	—
264	C₂×C₁₆	—	26	2	no	—
265	C₂×C₁₆	—	26	2	no	—
266	C₂×C₁₆	—	26	2	no	—
267	C₂×C₁₆	—	26	2	no	—
268	C₂×C₁₆	—	26	2	no	—
269	C₂×C₁₆	—	26	2	no	—
270	#108	—	2	1	no	—
271	#108	—	13	4	no	—
272	#108	—	13	2	no	—
273	#108	—	26	2	no	—
274	#108	—	26	2	no	—
275	#108	—	26	2	no	—
276	#108	—	26	2	no	—
277	#108	—	26	2	no	—
278	#108	—	26	1	no	—
279	#108	C₂×#261	1	2	yes	—
280	C₂×C₁₃	—	2	1	no	—
281	C₂×C₁₃	—	2	1	no	—
282	C₂×C₁₃	#1381	1	2	yes	complemented
283	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
284	D₁₃	—	2	1	no	—
285	D₁₃	—	2	1	no	—
286	D₁₃	#1381	1	2	yes	complemented
287	D₁₃	C₂×#368	1	2	yes	—
288	C₂⁴	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
303	M₁₆	—	2	2	no	—
304	M₁₆	—	4	1	no	—
305	M₁₆	—	26	4	no	—
306	M₁₆	—	26	2	no	—
307	M₁₆	—	52	2	no	—
308	M₁₆	—	52	2	no	—
309	M₁₆	—	52	2	no	—
310	M₁₆	—	52	2	no	—
311	M₁₆	—	52	2	no	—
312	M₁₆	—	52	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	13	1	no	—
315	C₂×C₈	—	13	1	no	—
316	C₂×C₈	—	13	1	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	13	1	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	1	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	1	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	13	1	no	—
335	C₂×C₈	—	13	1	no	—
336	C₂×C₈	—	52	2	no	—
337	C₂×C₈	—	52	2	no	—
338	C₂×C₈	—	52	2	no	—
339	C₂×C₈	—	52	2	no	—
340	C₂×C₈	—	52	2	no	—
341	C₂×C₈	—	52	1	no	—
342	C₂×C₈	C₄×#261	1	1	yes	characteristic
343	C₂×C₈	C₄×#261	1	1	yes	characteristic
344	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
345	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
346	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
347	C₂×C₈	C₂²×#261	1	1	yes	characteristic
348	C₁₆	—	26	4	no	—
349	C₁₃	C₂×#1381	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	13	1	no	—
351	C₂³	—	13	1	no	—
352	C₂³	—	13	1	no	—
353	C₂³	—	13	1	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	13	1	no	—
356	C₂³	—	26	4	no	—
357	C₂³	#88117	1	1	yes	characteristic
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	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	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
381	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
382	C₂×C₄	#88115	1	1	yes	characteristic
383	C₂×C₄	#88115	1	1	yes	characteristic
384	C₂×C₄	#88117	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	13	1	no	—
388	C₈	—	13	1	no	—
389	C₈	—	13	1	no	—
390	C₈	—	13	1	no	—
391	C₈	—	52	4	no	—
392	C₈	—	52	2	no	—
393	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
394	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
395	C₈	C₂×C₄×#261	1	1	yes	characteristic
396	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
397	C₂²	—	2	2	no	—
398	C₂²	—	13	1	no	—
399	C₂²	—	13	1	no	—
400	C₂²	—	13	4	no	—
401	C₂²	—	13	1	no	—
402	C₂²	—	13	1	no	—
403	C₂²	—	26	2	no	—
404	C₂²	—	26	2	no	—
405	C₂²	—	26	2	no	—
406	C₂²	—	26	2	no	—
407	C₂²	—	26	2	no	—
408	C₂²	#11718246	1	1	yes	characteristic
409	C₂²	#11718246	1	1	yes	characteristic
410	C₂²	C₂×#88117	1	1	yes	characteristic
411	C₄	—	13	1	no	—
412	C₄	—	13	1	no	—
413	C₄	—	13	1	no	—
414	C₄	—	13	1	no	—
415	C₄	#11718246	1	1	yes	characteristic
416	C₄	#11718246	1	1	yes	characteristic
417	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
418	C₄	C₂×#88115	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	13	2	no	—
422	C₂	—	13	2	no	—
423	C₂	—	26	1	no	—
424	C₂	—	26	1	no	—
425	C₂	#13129895	1	2	yes	direct product factor
426	C₂	C₂×#11718246	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88115
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂²×C₁₃	#340
prime radical	C₂³×D₁₃	Q₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₂×#108	#261
hypocenter	C₁₃	C₂×#1381
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
3. #13129895	C₂	direct (N × H)
282. C₂×C₁₃	#1381	semidirect
286. D₁₃	#1381	semidirect
349. C₁₃	C₂×#1381	semidirect
425. C₂	#13129895	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₃⋊C₁₆	2
C₂×D₁₃⋊#108	2
#13129895	2
C₂×D₁₃×#108	2
C₂×#1381	13

Subgroups — C2×#13129895 #16789102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129895 #16789102