Subgroups — #16807082

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131202	C₂	1	2	yes	maximal, complemented
2	#13131201	C₂	1	2	yes	maximal, complemented
3	#13131200	C₂	1	1	yes	maximal, characteristic, complemented
4	#13131199	C₂	1	1	yes	maximal, characteristic, complemented
5	#13131196	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131195	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131172	C₂	1	2	yes	maximal, complemented
8	#13131064	C₂	1	1	yes	maximal, characteristic
9	D₁₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
10	#13131046	C₂	1	2	yes	maximal, complemented
11	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×M₁₆×D₁₃	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	D₁₃×#117	C₄	1	1	yes	characteristic
15	C₂×#88098	C₂²	1	2	yes	—
16	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
17	C₁₃×#405	C₄	1	1	yes	characteristic
18	#11718783	C₂²	1	1	yes	characteristic
19	#11718762	C₄	1	1	yes	characteristic
20	#11718658	C₂²	1	1	yes	characteristic
21	#11718369	C₂²	1	1	yes	characteristic
22	#11718369	C₂²	1	1	yes	characteristic
23	D₁₃×#97	C₄	1	1	yes	characteristic
24	D₁₃×#97	C₄	1	1	yes	characteristic
25	#11718350	C₄	1	1	yes	characteristic
26	#11718350	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²⋊#6092	C₂²	1	2	yes	—
30	C₂²⋊#6092	C₂²	1	2	yes	—
31	#11718260	C₂²	1	2	yes	complemented
32	#11718260	C₂²	1	2	yes	complemented
33	#11718259	C₂²	1	1	yes	characteristic
34	#11718259	C₂²	1	1	yes	characteristic
35	#11718259	C₂²	1	1	yes	characteristic
36	#11718259	C₂²	1	1	yes	characteristic
37	#11718258	C₂²	1	2	yes	complemented
38	#11718257	C₂²	1	2	yes	complemented
39	#11718231	C₂²	1	2	yes	complemented
40	C₄⋊#6092	C₂²	1	2	yes	complemented
41	C₄⋊#6092	C₂²	1	2	yes	complemented
42	C₄×#6092	C₂²	1	2	yes	complemented
43	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
47	#88180	C₂×C₄	1	1	yes	characteristic
48	C₂×#6099	C₂×C₄	1	1	yes	characteristic
49	C₂²×#1055	C₂³	1	1	yes	characteristic
50	M₁₆×D₁₃	—	2	4	no	—
51	C₂×#6094	C₂×C₄	1	1	yes	characteristic
52	C₂×#6094	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	—	2	4	no	—
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
60	#88146	C₈	1	1	yes	characteristic
61	#88146	C₈	1	1	yes	characteristic
62	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
63	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
64	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
65	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
66	#88131	C₈	1	1	yes	characteristic
67	#88131	C₈	1	1	yes	characteristic
68	#88126	C₂×C₄	1	1	yes	characteristic
69	#88126	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×#6092	C₂³	1	2	yes	—
73	C₂×#6092	C₂³	1	2	yes	—
74	C₂×#6092	C₂³	1	2	yes	—
75	C₂×#6092	C₂³	1	2	yes	—
76	#88098	—	2	4	no	—
77	D₁₃⋊C₁₆	—	2	4	no	—
78	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	#88055	C₂×C₄	1	1	yes	characteristic
83	#88055	C₂×C₄	1	1	yes	characteristic
84	#88055	C₂×C₄	1	1	yes	characteristic
85	#88055	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
90	#88043	C₂×C₄	1	1	yes	characteristic
91	#88043	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂³	1	1	yes	characteristic
93	C₄×#1055	C₂³	1	1	yes	characteristic
94	#33422	—	13	1	no	maximal, Sylow
95	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	—	2	2	no	—
100	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₁₃×M₁₆	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
116	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
117	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
122	#6103	C₂×C₈	1	1	yes	characteristic
123	#6103	C₂×C₈	1	1	yes	characteristic
124	#6103	C₂×C₈	1	1	yes	characteristic
125	#6103	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
128	#6101	C₂×C₈	1	1	yes	characteristic
129	#6101	C₂×C₈	1	1	yes	characteristic
130	#6101	C₂×C₈	1	1	yes	characteristic
131	#6101	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	#6099	—	2	2	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂⁴	1	1	yes	characteristic
144	#6094	—	2	2	no	—
145	#6094	M₁₆	1	4	yes	—
146	C₈×D₁₃	—	2	2	no	—
147	C₈×D₁₃	—	2	2	no	—
148	C₈×D₁₃	—	2	2	no	—
149	C₈×D₁₃	—	2	2	no	—
150	C₈×D₁₃	—	2	2	no	—
151	C₈×D₁₃	#41	1	4	yes	—
152	#6092	—	2	2	no	—
153	#6092	—	2	2	no	—
154	#6092	—	2	2	no	—
155	#6092	—	2	2	no	—
156	C₂×#405	—	13	1	no	—
157	#2164	—	13	2	no	—
158	#2164	—	13	2	no	—
159	#2163	—	13	1	no	—
160	#2163	—	13	1	no	—
161	#2162	—	13	1	no	—
162	#2162	—	13	1	no	—
163	#2151	—	13	2	no	—
164	#2112	—	13	1	no	—
165	C₂×C₂²⋊C₁₆	—	13	1	no	—
166	#2108	—	13	2	no	—
167	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	—	4	1	no	—
171	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
172	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	1	no	—
192	C₄×D₁₃	—	2	1	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	4	1	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	#117	1	2	yes	—
197	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	#117	1	2	yes	—
201	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
202	#1055	—	2	1	no	—
203	#1055	—	2	1	no	—
204	#1055	C₂×M₁₆	1	2	yes	—
205	#1055	C₂×#41	1	2	yes	—
206	C₂²×M₁₆	—	13	1	no	—
207	C₂³×C₈	—	13	1	no	—
208	C₂×#117	—	13	1	no	—
209	C₂×M₃₂	—	13	2	no	—
210	C₂²×C₁₆	—	13	2	no	—
211	#405	—	13	1	no	—
212	#405	—	13	1	no	—
213	#405	—	13	1	no	—
214	#405	—	13	1	no	—
215	#405	—	13	1	no	—
216	#405	—	13	1	no	—
217	#405	—	13	1	no	—
218	#405	#261	1	1	yes	characteristic
219	C₂×#97	—	13	1	no	—
220	C₂×#97	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₄⋊C₁₆	—	13	2	no	—
224	C₄⋊C₁₆	—	13	2	no	—
225	C₄⋊C₁₆	—	13	2	no	—
226	C₄⋊C₁₆	—	13	2	no	—
227	C₂²⋊C₁₆	—	13	1	no	—
228	C₂²⋊C₁₆	—	13	1	no	—
229	C₂²⋊C₁₆	—	13	2	no	—
230	C₂²⋊C₁₆	—	13	1	no	—
231	C₂²⋊C₁₆	—	13	1	no	—
232	C₂²⋊C₁₆	—	13	2	no	—
233	#346	—	13	2	no	—
234	#346	—	13	2	no	—
235	C₄×C₁₆	—	13	2	no	—
236	C₄×C₁₆	—	13	2	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	1	no	—
245	C₂×D₁₃	—	4	4	no	—
246	C₂×D₁₃	#431	1	2	yes	—
247	C₂×D₁₃	#504	1	2	yes	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
254	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	#431	1	2	yes	—
261	C₂³×C₄	—	13	1	no	—
262	C₂×M₁₆	—	13	1	no	—
263	C₂×M₁₆	—	13	1	no	—
264	C₂×M₁₆	—	13	1	no	—
265	C₂×M₁₆	—	26	4	no	—
266	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	26	4	no	—
275	C₂²×C₈	C₂×#261	1	1	yes	characteristic
276	#117	—	13	1	no	—
277	#117	—	13	1	no	—
278	#117	—	13	1	no	—
279	#117	—	13	1	no	—
280	#117	—	13	1	no	—
281	#117	—	13	1	no	—
282	#117	—	13	1	no	—
283	#117	C₂×#261	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	13	1	no	—
285	C₂×C₄⋊C₄	—	13	1	no	—
286	C₂×C₂²⋊C₄	—	13	1	no	—
287	C₂×C₂²⋊C₄	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	M₃₂	—	26	4	no	—
291	C₂×C₁₆	—	13	2	no	—
292	C₂×C₁₆	—	13	2	no	—
293	C₂×C₁₆	—	13	2	no	—
294	C₂×C₁₆	—	13	2	no	—
295	C₂×C₁₆	—	26	4	no	—
296	#97	—	13	1	no	—
297	#97	—	13	1	no	—
298	#97	—	13	1	no	—
299	#97	—	13	1	no	—
300	#97	—	13	1	no	—
301	#97	—	13	1	no	—
302	#97	C₂×#261	1	1	yes	characteristic
303	#97	C₂×#261	1	1	yes	characteristic
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	—	13	1	no	—
310	C₄×C₈	C₂×#261	1	1	yes	characteristic
311	C₄×C₈	C₂×#261	1	1	yes	characteristic
312	C₂×C₁₃	—	4	1	no	—
313	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
315	C₂×C₁₃	#3407	1	1	yes	characteristic
316	D₁₃	—	2	2	no	—
317	D₁₃	—	2	2	no	—
318	C₂⁴	—	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	—	26	2	no	—
329	C₂²×C₄	—	26	2	no	—
330	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	13	4	no	—
333	M₁₆	—	26	2	no	—
334	M₁₆	—	26	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	4	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	26	2	no	—
343	C₂×C₈	—	26	2	no	—
344	C₂×C₈	—	26	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	2	no	—
347	C₂×C₈	C₂²×#261	1	1	yes	characteristic
348	C₂×C₈	C₂²×#261	1	1	yes	characteristic
349	C₂×C₈	C₂²×#261	1	1	yes	characteristic
350	C₂×C₈	C₂²×#261	1	1	yes	characteristic
351	C₄⋊C₄	—	13	1	no	—
352	C₄⋊C₄	—	13	1	no	—
353	C₄⋊C₄	—	13	1	no	—
354	C₄⋊C₄	—	13	1	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	1	no	—
357	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
358	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
359	C₂²⋊C₄	—	13	1	no	—
360	C₂²⋊C₄	—	13	1	no	—
361	C₂²⋊C₄	—	13	1	no	—
362	C₂²⋊C₄	—	13	1	no	—
363	C₂²⋊C₄	—	13	1	no	—
364	C₂²⋊C₄	—	13	1	no	—
365	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
366	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	C₂²×#261	1	1	yes	characteristic
374	C₄²	C₂²×#261	1	1	yes	characteristic
375	C₁₆	—	26	2	no	—
376	C₁₆	—	26	2	no	—
377	C₁₆	—	26	2	no	—
378	C₁₆	—	26	2	no	—
379	C₁₃	#33422	1	1	yes	characteristic, complemented, Sylow
380	C₂³	—	13	1	no	—
381	C₂³	—	13	1	no	—
382	C₂³	—	26	2	no	—
383	C₂³	—	26	2	no	—
384	C₂³	—	52	1	no	—
385	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	2	no	—
390	C₂×C₄	—	13	2	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	1	no	—
402	C₂×C₄	—	26	1	no	—
403	C₂×C₄	—	52	1	no	—
404	C₂×C₄	—	52	1	no	—
405	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
406	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
407	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
408	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
409	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
410	C₂×C₄	C₂³×#261	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	13	2	no	—
414	C₈	—	13	2	no	—
415	C₈	—	26	1	no	—
416	C₈	—	26	1	no	—
417	C₈	D₁₃⋊M₁₆	1	2	yes	—
418	C₈	#88237	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	13	2	no	—
423	C₂²	—	13	2	no	—
424	C₂²	—	26	1	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	26	1	no	—
427	C₂²	—	26	1	no	—
428	C₂²	—	52	4	no	—
429	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	13	2	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	1	no	—
439	C₄	—	26	1	no	—
440	C₄	—	26	1	no	—
441	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
442	C₄	C₂×#88237	1	1	yes	characteristic
443	C₂	—	4	1	no	—
444	C₂	—	26	2	no	—
445	C₂	—	26	2	no	—
446	C₂	D₁₃⋊#431	1	1	yes	characteristic
447	C₂	D₁₃⋊#504	1	1	yes	characteristic
448	C₂	#13131804	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#405	C₄
prime radical	C₂³×D₁₃	C₂×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#33422
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
1. #13131202	C₂	semidirect
2. #13131201	C₂	semidirect
3. #13131200	C₂	semidirect
4. #13131199	C₂	semidirect
5. #13131196	C₂	semidirect
6. #13131195	C₂	semidirect
7. #13131172	C₂	semidirect
10. #13131046	C₂	semidirect
31. #11718260	C₂²	semidirect
32. #11718260	C₂²	semidirect
37. #11718258	C₂²	semidirect
38. #11718257	C₂²	semidirect
39. #11718231	C₂²	semidirect
40. C₄⋊#6092	C₂²	semidirect
41. C₄⋊#6092	C₂²	semidirect
42. C₄×#6092	C₂²	semidirect
379. C₁₃	#33422	semidirect

Maximal subgroups

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

subgroup	index
#13131202	2
#13131201	2
#13131200	2
#13131199	2
#13131196	2
#13131195	2
#13131172	2
#13131064	2
D₁₃⋊(C₂²⋊C₁₆)	2
#13131046	2
D₁₃×#405	2
#33422	13