Subgroups — #16799521

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131513	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#13130951	C₂	1	2	yes	maximal, complemented
4	#13130950	C₂	1	2	yes	maximal, complemented
5	#13130790	C₂	1	4	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	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719130	—	2	1	no	—
12	#11719127	C₂²	1	2	yes	—
13	C₄×#6122	—	2	1	no	—
14	C₄×#6122	—	2	1	no	—
15	#11719119	—	2	1	no	—
16	C₂×#88104	C₂²	1	4	yes	—
17	C₂×#88103	C₂²	1	4	yes	—
18	#11719054	—	2	1	no	—
19	#11719052	C₂²	1	2	yes	—
20	#11719051	—	2	1	no	—
21	C₄×#6118	C₂²	1	1	yes	characteristic
22	C₄×#6118	C₂²	1	1	yes	characteristic
23	C₄×#6118	C₂²	1	2	yes	—
24	C₄×#6118	C₂²	1	2	yes	—
25	#11719047	—	2	1	no	—
26	C₄×D₁₃⋊C₈	—	2	1	no	—
27	C₁₃×#431	C₄	1	1	yes	characteristic
28	#11718586	C₄	1	1	yes	characteristic
29	#11718494	C₄	1	1	yes	characteristic
30	#11718494	C₄	1	1	yes	characteristic
31	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	#11718379	C₄	1	2	yes	—
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	C₂×#6122	—	2	2	no	—
43	D₁₃⋊M₁₆	—	2	4	no	—
44	D₁₃⋊M₁₆	—	2	4	no	—
45	C₂×#6118	C₂³	1	4	yes	—
46	C₂×#6118	C₂³	1	2	yes	—
47	C₂×#6118	C₂³	1	2	yes	—
48	C₂×D₁₃⋊C₈	—	2	2	no	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂³	1	2	yes	—
54	C₂×C₈×D₁₃	C₂³	1	2	yes	—
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	D₄	1	1	yes	characteristic
58	C₄²×D₁₃	D₄	1	1	yes	characteristic
59	C₄²×D₁₃	Q₈	1	1	yes	characteristic
60	C₄²×D₁₃	Q₈	1	1	yes	characteristic
61	C₄²×D₁₃	C₂³	1	1	yes	characteristic
62	C₄²×D₁₃	C₂³	1	1	yes	characteristic
63	C₂²⋊#1057	—	2	2	no	—
64	#88111	—	2	2	no	—
65	#88110	—	2	2	no	—
66	#88110	—	2	1	no	—
67	#88110	—	2	1	no	—
68	#88110	—	2	2	no	—
69	C₄⋊#1057	—	2	2	no	—
70	C₄⋊#1057	—	2	2	no	—
71	C₄×#1057	—	2	1	no	—
72	C₄×#1057	—	2	1	no	—
73	C₄×#1057	—	2	2	no	—
74	C₄×#1057	—	2	2	no	—
75	#88104	—	2	8	no	—
76	#88103	—	2	8	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
81	C₂²⋊#1055	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
89	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	2	yes	—
91	#21370	—	13	1	no	maximal, Sylow
92	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	2	2	no	—
101	C₂×C₄×D₁₃	—	2	2	no	—
102	C₂×C₄×D₁₃	—	4	2	no	—
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	C₂×D₄	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	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
115	#6122	—	2	8	no	—
116	C₂×#1057	—	2	2	no	—
117	C₂×#1057	—	2	2	no	—
118	C₂×#1057	—	2	4	no	—
119	#6118	—	2	2	no	—
120	#6118	—	2	2	no	—
121	#6118	—	2	4	no	—
122	#6118	—	2	4	no	—
123	#6118	#41	1	4	yes	—
124	#6118	#41	1	4	yes	—
125	D₁₃⋊C₈	—	2	8	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×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	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	C₂×#1055	C₂²×C₄	1	2	yes	—
146	C₈×D₁₃	—	2	4	no	—
147	C₈×D₁₃	—	2	4	no	—
148	#2920	—	13	1	no	—
149	C₂×#431	—	13	1	no	—
150	C₂×C₄×M₁₆	—	13	1	no	—
151	#1950	—	13	2	no	—
152	#1950	—	13	2	no	—
153	#1855	—	13	4	no	—
154	C₄×#108	—	13	2	no	—
155	C₄×#108	—	13	2	no	—
156	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	—	2	2	no	—
159	C₂²×D₁₃	—	4	1	no	—
160	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	4	1	no	—
175	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₄×D₁₃	—	2	2	no	—
182	C₄×D₁₃	—	2	2	no	—
183	C₄×D₁₃	—	2	1	no	—
184	C₄×D₁₃	—	2	1	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	4	1	no	—
191	C₄×D₁₃	—	4	1	no	—
192	C₄×D₁₃	#108	1	4	yes	complemented
193	C₄×D₁₃	C₂×#41	1	2	yes	—
194	C₄×D₁₃	C₂×#41	1	2	yes	—
195	#1057	—	2	4	no	—
196	#1057	—	2	4	no	—
197	#1057	—	4	4	no	—
198	C₈×C₁₃	—	2	2	no	—
199	C₈×C₁₃	—	2	2	no	—
200	#1055	—	2	2	no	—
201	#1055	—	2	2	no	—
202	C₂²×M₁₆	—	13	2	no	—
203	C₂²×C₄²	—	13	1	no	—
204	#432	—	26	1	no	—
205	#432	—	26	1	no	—
206	#431	—	13	1	no	—
207	#431	—	13	1	no	—
208	#431	—	13	1	no	—
209	#431	—	13	2	no	—
210	#431	—	13	2	no	—
211	#431	—	26	1	no	—
212	#431	—	26	1	no	—
213	#431	#261	1	1	yes	characteristic
214	C₂×#108	—	13	4	no	—
215	C₂×#108	—	13	4	no	—
216	#423	—	13	2	no	—
217	C₂×C₄⋊C₈	—	13	1	no	—
218	C₂×C₄⋊C₈	—	13	1	no	—
219	#407	—	13	2	no	—
220	C₂×C₂²⋊C₈	—	13	2	no	—
221	C₄×M₁₆	—	13	2	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₄×M₁₆	—	13	1	no	—
224	C₄×M₁₆	—	13	2	no	—
225	C₄×M₁₆	—	26	1	no	—
226	C₄×M₁₆	—	26	1	no	—
227	C₂×#97	—	26	1	no	—
228	C₂×C₄×C₈	—	13	2	no	—
229	C₂×C₄×C₈	—	26	1	no	—
230	#341	—	13	4	no	—
231	#341	—	13	4	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	2	1	no	—
240	C₂×D₁₃	—	4	4	no	—
241	C₂×D₁₃	C₂×#108	1	2	yes	—
242	C₂×D₁₃	#533	1	2	yes	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	C₂×#108	1	2	yes	—
247	C₄×C₁₃	#430	1	2	yes	—
248	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
249	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	C₂×#108	1	2	yes	—
255	Dic₁₃	#525	1	2	yes	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	—	13	1	no	—
258	C₂³×C₄	—	13	1	no	—
259	C₂×M₁₆	—	13	2	no	—
260	C₂×M₁₆	—	13	2	no	—
261	C₂×M₁₆	—	13	4	no	—
262	C₂×M₁₆	—	26	4	no	—
263	C₂×M₁₆	—	26	4	no	—
264	C₂×M₁₆	—	26	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	—	13	2	no	—
267	C₂²×C₈	—	26	2	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	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	C₂×#261	1	1	yes	characteristic
280	#108	—	26	8	no	—
281	#108	—	26	8	no	—
282	C₄⋊C₈	—	13	2	no	—
283	C₄⋊C₈	—	13	2	no	—
284	C₄⋊C₈	—	13	1	no	—
285	C₄⋊C₈	—	13	1	no	—
286	C₄⋊C₈	—	26	2	no	—
287	C₄⋊C₈	—	26	2	no	—
288	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
289	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
290	C₂²⋊C₈	—	13	2	no	—
291	C₂²⋊C₈	—	13	2	no	—
292	C₂²⋊C₈	—	13	2	no	—
293	C₂²⋊C₈	—	26	2	no	—
294	C₂²⋊C₈	—	26	2	no	—
295	C₂²⋊C₈	C₂×#261	1	2	yes	—
296	#97	—	26	1	no	—
297	#97	—	26	1	no	—
298	#97	—	26	2	no	—
299	#97	—	26	2	no	—
300	C₄×C₈	—	13	2	no	—
301	C₄×C₈	—	13	2	no	—
302	C₄×C₈	—	13	2	no	—
303	C₄×C₈	—	26	2	no	—
304	C₄×C₈	—	26	1	no	—
305	C₄×C₈	—	26	1	no	—
306	C₄×C₈	—	26	2	no	—
307	C₄×C₈	C₂×#261	1	2	yes	—
308	C₂×C₁₃	—	4	1	no	—
309	C₂×C₁₃	#2296	1	1	yes	characteristic
310	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
312	D₁₃	—	2	2	no	—
313	D₁₃	—	2	2	no	—
314	C₂⁴	—	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	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	26	2	no	—
331	C₂²×C₄	—	26	2	no	—
332	C₂²×C₄	—	26	4	no	—
333	C₂²×C₄	—	52	2	no	—
334	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
335	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
336	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
337	M₁₆	—	13	4	no	—
338	M₁₆	—	13	4	no	—
339	M₁₆	—	26	2	no	—
340	M₁₆	—	26	2	no	—
341	M₁₆	—	26	8	no	—
342	M₁₆	—	26	4	no	—
343	M₁₆	—	26	4	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	13	2	no	—
346	C₂×C₈	—	26	4	no	—
347	C₂×C₈	—	26	4	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	8	no	—
351	C₂×C₈	—	26	4	no	—
352	C₂×C₈	C₂²×#261	1	2	yes	—
353	C₂×C₈	C₂²×#261	1	2	yes	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	C₄⋊#261	1	1	yes	characteristic
367	C₄²	C₄⋊#261	1	1	yes	characteristic
368	C₄²	C₂²×#261	1	1	yes	characteristic
369	C₄²	C₂²×#261	1	1	yes	characteristic
370	C₁₃	#21370	1	1	yes	characteristic, complemented, Sylow
371	C₂³	—	13	1	no	—
372	C₂³	—	13	1	no	—
373	C₂³	—	26	2	no	—
374	C₂³	—	26	2	no	—
375	C₂³	—	52	1	no	—
376	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	4	no	—
384	C₂×C₄	—	13	2	no	—
385	C₂×C₄	—	13	2	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	26	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	1	no	—
400	C₂×C₄	—	26	1	no	—
401	C₂×C₄	—	52	1	no	—
402	C₂×C₄	—	52	1	no	—
403	C₂×C₄	—	52	1	no	—
404	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
405	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
406	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
407	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
409	C₂×C₄	C₂³×#261	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	26	4	no	—
413	C₈	—	26	4	no	—
414	C₈	—	26	2	no	—
415	C₈	—	26	2	no	—
416	C₈	—	52	4	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	13	2	no	—
421	C₂²	—	13	2	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	26	1	no	—
424	C₂²	—	26	1	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	52	4	no	—
427	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	13	2	no	—
432	C₄	—	13	2	no	—
433	C₄	—	26	1	no	—
434	C₄	—	26	1	no	—
435	C₄	—	26	1	no	—
436	C₄	—	26	1	no	—
437	C₄	D₁₃⋊#108	1	2	yes	—
438	C₄	#11719100	1	2	yes	—
439	C₄	#41×#261	1	1	yes	characteristic
440	C₄	#41×#261	1	1	yes	characteristic
441	C₂	—	4	1	no	—
442	C₂	—	26	2	no	—
443	C₂	—	26	2	no	—
444	C₂	#13131296	1	1	yes	characteristic
445	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic
446	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. #13130951	C₂	semidirect
4. #13130950	C₂	semidirect
6. C₄×#88104	C₂	semidirect
7. C₄×#88103	C₂	semidirect
192. C₄×D₁₃	#108	semidirect
370. C₁₃	#21370	semidirect

Maximal subgroups

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

subgroup	index
#13131513	2
C₄×D₁₃⋊M₁₆	2
#13130951	2
#13130950	2
#13130790	2
C₄×#88104	2
C₄×#88103	2
D₁₃×#431	2
#21370	13