Subgroups — #16799505

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131285	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊#261	C₂	1	1	yes	maximal, characteristic
3	#13130947	C₂	1	4	yes	maximal, complemented
4	#13130785	C₂	1	4	yes	maximal
5	C₄×#88102	C₂	1	4	yes	maximal, complemented
6	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	—	2	1	no	—
8	C₂²×C₄⋊#261	C₂²	1	2	yes	—
9	C₂²×C₄×#261	—	2	1	no	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719136	—	2	1	no	—
12	#11719136	C₂²	1	2	yes	—
13	C₂×(C₂×#261)⋊C₄	—	2	1	no	—
14	C₂×#88102	C₂²	1	8	yes	—
15	#11719060	—	2	1	no	—
16	#11719059	C₂²	1	2	yes	—
17	C₄×C₄⋊#261	—	2	1	no	—
18	C₄×C₄⋊#261	—	2	1	no	—
19	C₄×C₄⋊#261	—	2	1	no	—
20	C₄×C₄⋊#261	C₂²	1	2	yes	—
21	C₄×C₄⋊#261	C₂²	1	2	yes	—
22	C₄×C₄⋊#261	C₂²	1	2	yes	—
23	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
24	#11718586	C₄	1	1	yes	characteristic, complemented
25	#11718494	C₄	1	2	yes	complemented
26	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	#11718379	C₄	1	2	yes	complemented
29	#11718346	C₄	1	2	yes	complemented
30	C₄×C₈×D₁₃	C₂²	1	2	yes	—
31	#11718265	C₂²	1	8	yes	—
32	C₂³×#261	—	2	2	no	—
33	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₂²⋊#261	—	2	2	no	—
37	#88237	—	4	4	no	—
38	C₂×C₄⋊#261	—	2	2	no	—
39	C₂×C₄⋊#261	—	2	8	no	—
40	C₂×C₄⋊#261	—	2	2	no	—
41	C₂×C₄⋊#261	—	2	2	no	—
42	C₂×C₄⋊#261	C₂³	1	4	yes	—
43	C₂×C₄⋊#261	C₂³	1	4	yes	—
44	C₂×C₄×#261	—	2	2	no	—
45	C₂×C₄×#261	—	2	2	no	—
46	C₂×C₄×#261	—	2	2	no	—
47	C₂×C₄×#261	—	4	4	no	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂³	1	4	yes	—
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	D₄	1	1	yes	characteristic
56	C₄²×D₁₃	D₄	1	1	yes	characteristic
57	C₄²×D₁₃	Q₈	1	1	yes	characteristic
58	C₄²×D₁₃	Q₈	1	1	yes	characteristic
59	C₄²×D₁₃	C₂³	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	(C₂×#261)⋊C₄	—	2	2	no	—
62	(C₂×#261)⋊C₄	—	2	2	no	—
63	(C₂×#261)⋊C₄	—	2	2	no	—
64	(C₂×#261)⋊C₄	—	2	2	no	—
65	#88102	—	2	16	no	—
66	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
67	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
69	C₂²⋊#1055	C₂×C₄	1	2	yes	—
70	#88060	C₂×C₄	1	4	yes	—
71	#88054	C₂×C₄	1	4	yes	complemented
72	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
73	C₄⋊#1055	C₂×C₄	1	2	yes	complemented
74	C₄×#1055	C₂×C₄	1	2	yes	complemented
75	#21358	—	13	1	no	maximal, Sylow
76	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×#261	—	2	8	no	—
78	C₂²×#261	—	2	4	no	—
79	C₂²×#261	—	2	4	no	—
80	C₂²×#261	—	4	4	no	—
81	C₂²×#261	—	4	4	no	—
82	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₄×D₁₃	—	2	4	no	—
89	C₂×C₄×D₁₃	—	4	2	no	—
90	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	D₈	1	4	yes	—
95	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
96	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
104	C₂²⋊#261	—	4	4	no	—
105	C₄⋊#261	—	2	8	no	—
106	C₄⋊#261	—	2	4	no	—
107	C₄⋊#261	—	2	8	no	—
108	C₄⋊#261	—	4	4	no	—
109	C₄⋊#261	—	4	4	no	—
110	C₄⋊#261	#41	1	8	yes	—
111	C₄×#261	—	4	4	no	—
112	C₄×#261	—	4	4	no	—
113	C₄×#261	—	4	4	no	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
116	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₄⋊C₄	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	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
131	C₂×#1055	C₂²×C₄	1	4	yes	—
132	C₈×D₁₃	—	2	8	no	—
133	C₂×#431	—	13	1	no	—
134	#2285	—	13	1	no	—
135	C₂×C₄×C₄⋊C₄	—	13	1	no	—
136	#1947	—	13	4	no	—
137	#1852	—	13	4	no	—
138	C₄×#107	—	13	4	no	—
139	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂²×D₁₃	—	2	2	no	—
141	C₂²×D₁₃	—	2	2	no	—
142	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₁₃	C₂×D₈	1	2	yes	—
144	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
145	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×#261	—	2	8	no	—
147	C₂×#261	—	4	16	no	—
148	C₂×#261	—	4	4	no	—
149	C₂×#261	—	4	4	no	—
150	C₂×#261	—	4	4	no	—
151	C₂×#261	—	4	4	no	—
152	C₂×#261	—	4	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	#107	1	4	yes	complemented
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	—	4	1	no	—
164	C₂×Dic₁₃	#107	1	4	yes	complemented
165	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	4	1	no	—
177	C₄×D₁₃	—	4	1	no	—
178	C₄×D₁₃	#107	1	4	yes	complemented
179	C₄×D₁₃	#107	1	4	yes	complemented
180	C₄×D₁₃	C₂×D₈	1	2	yes	—
181	C₄×D₁₃	C₂×D₈	1	2	yes	—
182	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
183	C₄×D₁₃	C₂×Q₁₆	1	2	yes	—
184	C₄×D₁₃	C₂×#41	1	4	yes	—
185	C₈×C₁₃	—	2	4	no	—
186	#1055	—	2	4	no	—
187	C₂×#117	—	26	1	no	—
188	C₂²×C₄⋊C₄	—	13	2	no	—
189	C₂²×C₄²	—	13	1	no	—
190	C₂²×C₄²	—	26	1	no	—
191	#431	—	13	1	no	—
192	#431	—	13	2	no	—
193	#431	—	13	2	no	—
194	#431	—	13	2	no	—
195	#431	#261	1	1	yes	characteristic, complemented
196	C₂×#107	—	13	8	no	—
197	C₂×C₄⋊C₈	—	13	2	no	—
198	C₂×C₂²⋊C₈	—	13	2	no	—
199	C₂×C₄×C₈	—	13	2	no	—
200	#384	—	13	2	no	—
201	#382	—	26	1	no	—
202	#380	—	13	2	no	—
203	#380	—	26	1	no	—
204	C₄×C₄⋊C₄	—	13	2	no	—
205	C₄×C₄⋊C₄	—	13	2	no	—
206	C₄×C₄⋊C₄	—	13	2	no	—
207	C₄×C₄⋊C₄	—	26	1	no	—
208	C₄×C₄⋊C₄	—	26	1	no	—
209	C₄×C₄⋊C₄	—	26	1	no	—
210	C₂×#95	—	26	1	no	—
211	#340	—	13	8	no	—
212	C₂²×C₁₃	—	2	1	no	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	C₂×#107	1	2	yes	—
215	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂×D₁₃	—	2	1	no	—
217	C₂×D₁₃	—	2	1	no	—
218	C₂×D₁₃	—	2	4	no	—
219	C₂×D₁₃	—	2	4	no	—
220	C₂×D₁₃	C₂×#107	1	2	yes	—
221	C₂×D₁₃	#525	1	2	yes	—
222	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
223	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
224	C₂×D₁₃	#575	1	2	yes	—
225	#261	—	4	8	no	—
226	#261	—	8	4	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	C₂×#107	1	2	yes	—
231	C₄×C₁₃	C₂×#107	1	2	yes	—
232	C₄×C₁₃	C₄×#41	1	2	yes	—
233	Dic₁₃	—	2	1	no	—
234	Dic₁₃	—	2	1	no	—
235	Dic₁₃	—	2	1	no	—
236	Dic₁₃	C₂×#107	1	2	yes	—
237	Dic₁₃	C₂×#107	1	2	yes	—
238	Dic₁₃	#533	1	2	yes	—
239	C₂³×C₄	—	13	1	no	—
240	C₂³×C₄	—	13	1	no	—
241	C₂³×C₄	—	13	1	no	—
242	C₂³×C₄	—	26	2	no	—
243	C₂²×C₈	—	13	4	no	—
244	#117	—	52	4	no	—
245	C₂×C₄⋊C₄	—	13	4	no	—
246	C₂×C₄⋊C₄	—	13	4	no	—
247	C₂×C₄⋊C₄	—	26	8	no	—
248	C₂×C₄⋊C₄	—	26	2	no	—
249	C₂×C₄⋊C₄	—	26	2	no	—
250	C₂×C₄⋊C₄	—	26	2	no	—
251	C₂×C₂²⋊C₄	—	26	2	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	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	—	26	2	no	—
264	C₂×C₄²	—	26	2	no	—
265	C₂×C₄²	—	26	2	no	—
266	C₂×C₄²	—	52	4	no	—
267	C₂×C₄²	C₂×#261	1	1	yes	characteristic
268	#107	—	26	16	no	—
269	C₄⋊C₈	—	13	4	no	—
270	C₄⋊C₈	—	13	2	no	—
271	C₄⋊C₈	C₂×#261	1	2	yes	complemented
272	C₂²⋊C₈	—	13	2	no	—
273	C₂²⋊C₈	—	13	4	no	—
274	C₂²⋊C₈	C₂×#261	1	2	yes	—
275	C₄×C₈	—	13	4	no	—
276	C₄×C₈	—	13	2	no	—
277	C₄×C₈	C₂×#261	1	2	yes	complemented
278	#95	—	26	2	no	—
279	#95	—	26	2	no	—
280	#95	—	26	2	no	—
281	#95	—	26	2	no	—
282	C₂×C₁₃	—	2	2	no	—
283	C₂×C₁₃	#2296	1	1	yes	characteristic
284	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
285	C₂×C₁₃	#2911	1	1	yes	characteristic
286	D₁₃	—	2	2	no	—
287	D₁₃	#3100	1	2	yes	—
288	D₁₃	#3104	1	2	yes	—
289	C₂⁴	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	4	no	—
292	C₂²×C₄	—	13	4	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	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	26	4	no	—
308	C₂²×C₄	—	26	4	no	—
309	C₂²×C₄	—	26	8	no	—
310	C₂²×C₄	—	26	4	no	—
311	C₂²×C₄	—	52	2	no	—
312	C₂²×C₄	—	52	4	no	—
313	C₂²×C₄	—	52	4	no	—
314	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
315	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
316	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
317	C₂×C₈	—	13	4	no	—
318	C₂×C₈	—	26	8	no	—
319	C₂×C₈	C₂²×#261	1	4	yes	—
320	C₄⋊C₄	—	13	8	no	—
321	C₄⋊C₄	—	26	4	no	—
322	C₄⋊C₄	—	26	8	no	—
323	C₄⋊C₄	—	26	8	no	—
324	C₄⋊C₄	—	52	4	no	—
325	C₄⋊C₄	—	52	4	no	—
326	C₂²⋊C₄	—	52	4	no	—
327	C₄²	—	13	1	no	—
328	C₄²	—	13	1	no	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	52	4	no	—
340	C₄²	—	52	4	no	—
341	C₄²	—	52	4	no	—
342	C₄²	C₄⋊#261	1	1	yes	characteristic
343	C₄²	C₄⋊#261	1	1	yes	characteristic
344	C₄²	C₂²×#261	1	1	yes	characteristic
345	C₄²	C₂²×#261	1	1	yes	characteristic
346	C₁₃	#21358	1	1	yes	characteristic, complemented, Sylow
347	C₂³	—	13	1	no	—
348	C₂³	—	13	2	no	—
349	C₂³	—	13	2	no	—
350	C₂³	—	13	1	no	—
351	C₂³	—	26	2	no	—
352	C₂³	—	26	2	no	—
353	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	13	4	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	13	1	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	13	2	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	13	4	no	—
363	C₂×C₄	—	13	4	no	—
364	C₂×C₄	—	13	2	no	—
365	C₂×C₄	—	13	2	no	—
366	C₂×C₄	—	13	4	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	26	2	no	—
374	C₂×C₄	—	26	2	no	—
375	C₂×C₄	—	26	2	no	—
376	C₂×C₄	—	26	8	no	—
377	C₂×C₄	—	52	1	no	—
378	C₂×C₄	—	52	1	no	—
379	C₂×C₄	—	52	1	no	—
380	C₂×C₄	—	52	4	no	—
381	C₂×C₄	—	52	4	no	—
382	C₂×C₄	—	52	16	no	—
383	C₂×C₄	—	52	4	no	—
384	C₂×C₄	—	52	4	no	—
385	C₂×C₄	—	52	4	no	—
386	C₂×C₄	#88102	1	4	yes	complemented
387	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
388	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
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	C₂³×#261	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	26	4	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	13	2	no	—
398	C₂²	—	13	1	no	—
399	C₂²	—	13	1	no	—
400	C₂²	—	13	2	no	—
401	C₂²	—	13	2	no	—
402	C₂²	—	26	4	no	—
403	C₂²	—	26	4	no	—
404	C₂²	—	26	1	no	—
405	C₂²	—	26	1	no	—
406	C₂²	C₂×#88102	1	2	yes	—
407	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	13	2	no	—
412	C₄	—	13	2	no	—
413	C₄	—	13	2	no	—
414	C₄	—	26	1	no	—
415	C₄	—	26	1	no	—
416	C₄	—	26	1	no	—
417	C₄	—	52	8	no	—
418	C₄	—	104	4	no	—
419	C₄	C₂×#88102	1	2	yes	—
420	C₄	C₂×#88102	1	2	yes	—
421	C₄	#41×#261	1	2	yes	—
422	C₂	—	2	2	no	—
423	C₂	—	13	2	no	—
424	C₂	—	13	2	no	—
425	C₂	—	26	2	no	—
426	C₂	#13131296	1	1	yes	characteristic
427	C₂	C₂²×#88102	1	1	yes	characteristic
428	C₂	#13131489	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×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#21358
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. #13130947	C₂	semidirect
5. C₄×#88102	C₂	semidirect
23. C₁₃×#431	C₄	semidirect
24. #11718586	C₄	semidirect
25. #11718494	C₄	semidirect
28. #11718379	C₄	semidirect
29. #11718346	C₄	semidirect
66. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
68. C₄×C₈×C₁₃	C₂×C₄	semidirect
71. #88054	C₂×C₄	semidirect
72. C₈×Dic₁₃	C₂×C₄	semidirect
73. C₄⋊#1055	C₂×C₄	semidirect
74. C₄×#1055	C₂×C₄	semidirect
155. C₂×C₄×C₁₃	#107	semidirect
164. C₂×Dic₁₃	#107	semidirect
178. C₄×D₁₃	#107	semidirect
179. C₄×D₁₃	#107	semidirect
195. #431	#261	semidirect
271. C₄⋊C₈	C₂×#261	semidirect
277. C₄×C₈	C₂×#261	semidirect
346. C₁₃	#21358	semidirect
386. C₂×C₄	#88102	semidirect

Maximal subgroups

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

subgroup	index
#13131285	2
C₂×C₄×C₄⋊#261	2
#13130947	2
#13130785	2
C₄×#88102	2
D₁₃×#431	2
#21358	13