Subgroups — #16807398

Order 3328.

536 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131253	C₂	1	2	yes	maximal, complemented
2	#13131219	C₂	1	2	yes	maximal, complemented
3	#13131218	C₂	1	2	yes	maximal, complemented
4	#13131214	C₂	1	2	yes	maximal, complemented
5	#13131200	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131197	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131196	C₂	1	1	yes	maximal, characteristic, complemented
8	#13131169	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊#6092	C₂	1	1	yes	maximal, characteristic, complemented
11	#13123792	C₂	1	1	yes	maximal, characteristic
12	C₄×#6127	C₄	1	1	yes	characteristic
13	C₂²×#6092	C₂²	1	2	yes	—
14	C₂×#88098	C₂²	1	2	yes	—
15	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
16	C₁₃×#431	C₄	1	1	yes	characteristic
17	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
18	#11718495	C₄	1	1	yes	characteristic
19	#11718495	C₂²	1	1	yes	characteristic
20	#11718491	C₄	1	1	yes	characteristic
21	#11718491	C₂²	1	1	yes	characteristic
22	#11718386	C₄	1	1	yes	characteristic
23	#11718386	C₄	1	1	yes	characteristic
24	#11718386	C₂²	1	1	yes	characteristic
25	#11718386	C₂²	1	1	yes	characteristic
26	#11718346	C₄	1	1	yes	characteristic
27	#11718346	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
30	C₂²⋊#6092	C₂²	1	2	yes	—
31	#11718260	C₂²	1	2	yes	—
32	#11718260	C₂²	1	2	yes	—
33	#11718259	C₂²	1	2	yes	—
34	#11718259	C₂²	1	2	yes	—
35	#11718258	C₂²	1	2	yes	—
36	#11718257	C₂²	1	2	yes	—
37	#11718231	C₂²	1	2	yes	—
38	C₄⋊#6092	C₂²	1	1	yes	characteristic
39	C₄⋊#6092	C₂²	1	1	yes	characteristic
40	C₄⋊#6092	C₂²	1	2	yes	—
41	C₄⋊#6092	C₂²	1	1	yes	characteristic
42	C₄⋊#6092	C₂²	1	1	yes	characteristic
43	C₂×#6127	C₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
49	#88180	C₈	1	1	yes	characteristic
50	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
51	C₂²×#1055	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	C₄×D₅₂	C₈	1	1	yes	characteristic
57	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
58	#88126	C₈	1	1	yes	characteristic
59	#88126	C₈	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₂₆	C₈	1	1	yes	characteristic
63	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
64	C₂×#6092	—	4	2	no	—
65	C₂×#6092	C₂³	1	2	yes	—
66	C₂×#6092	C₂³	1	2	yes	—
67	C₂×#6092	C₂³	1	2	yes	—
68	C₂×#6092	C₂³	1	2	yes	—
69	#88098	—	4	2	no	—
70	D₁₃⋊C₁₆	—	4	2	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
77	#88060	C₂×C₄	1	1	yes	characteristic
78	#88060	C₂×C₄	1	1	yes	characteristic
79	#88060	C₂×C₄	1	1	yes	characteristic
80	#88060	C₂×C₄	1	1	yes	characteristic
81	#88054	C₂×C₄	1	1	yes	characteristic
82	#88054	C₂×C₄	1	1	yes	characteristic
83	#88054	C₂×C₄	1	1	yes	characteristic
84	#88054	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
88	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₄×#1055	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	1	yes	characteristic
91	C₄×#1055	C₂³	1	1	yes	characteristic
92	C₄×#1055	C₂³	1	1	yes	characteristic
93	#33504	—	13	1	no	maximal, Sylow
94	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
99	#6127	—	2	4	no	—
100	C₂×D₅₂	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	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
117	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
118	#6103	C₂×C₈	1	1	yes	characteristic
119	#6103	C₂×C₈	1	1	yes	characteristic
120	#6103	C₂×C₈	1	1	yes	characteristic
121	#6103	C₂×C₈	1	1	yes	characteristic
122	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
124	#6101	C₂×C₈	1	1	yes	characteristic
125	#6101	C₂×C₈	1	1	yes	characteristic
126	#6101	C₂×C₈	1	1	yes	characteristic
127	#6101	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	4	1	no	—
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂⁴	1	1	yes	characteristic
141	C₈×D₁₃	—	2	1	no	—
142	C₈×D₁₃	—	2	1	no	—
143	C₈×D₁₃	—	2	1	no	—
144	C₈×D₁₃	—	2	1	no	—
145	C₈×D₁₃	—	4	1	no	—
146	C₈×D₁₃	—	4	1	no	—
147	#6092	—	2	2	no	—
148	#6092	—	2	2	no	—
149	#6092	—	2	2	no	—
150	#6092	—	2	2	no	—
151	C₈×#41	—	13	1	no	—
152	#2183	—	13	2	no	—
153	#2168	—	13	2	no	—
154	#2168	—	13	2	no	—
155	D₄×C₁₆	—	13	2	no	—
156	#2163	—	13	1	no	—
157	#2163	—	13	1	no	—
158	#2162	—	13	1	no	—
159	#2150	—	13	1	no	—
160	C₂×C₄⋊C₁₆	—	13	1	no	—
161	C₂×C₄⋊C₁₆	—	13	1	no	—
162	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
163	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
164	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂²⋊D₁₃	—	2	2	no	—
176	C₂²⋊D₁₃	M₃₂	1	4	yes	complemented
177	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
183	D₅₂	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	1	no	—
186	C₄×D₁₃	—	2	1	no	—
187	C₄×D₁₃	—	2	1	no	—
188	C₄×D₁₃	—	2	1	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	Dic₂₆	—	2	2	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	—	2	1	no	—
196	C₈×C₁₃	—	2	1	no	—
197	#1055	—	2	1	no	—
198	#1055	—	2	1	no	—
199	#1055	—	2	1	no	—
200	#1055	H(5,𝔽₂)	1	1	yes	characteristic
201	#1055	2₋¹⁺⁴	1	1	yes	characteristic
202	C₄×#41	—	13	1	no	—
203	C₂×M₃₂	—	13	2	no	—
204	C₂²×C₁₆	—	13	2	no	—
205	C₂²×C₁₆	—	13	2	no	—
206	C₈×Q₈	—	13	1	no	—
207	C₈×Q₈	—	13	1	no	—
208	C₈×D₄	—	13	1	no	—
209	C₈×D₄	—	13	1	no	—
210	C₈×D₄	—	13	1	no	—
211	C₈×D₄	—	13	1	no	—
212	C₈×D₄	—	13	1	no	—
213	C₈×D₄	—	13	1	no	—
214	#431	—	13	1	no	—
215	#431	—	13	1	no	—
216	#431	#261	1	1	yes	characteristic
217	C₂×C₄×C₈	—	13	1	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₄⋊C₁₆	—	13	1	no	—
221	C₄⋊C₁₆	—	13	1	no	—
222	C₄⋊C₁₆	—	13	1	no	—
223	C₄⋊C₁₆	—	13	2	no	—
224	C₄⋊C₁₆	—	13	1	no	—
225	C₄⋊C₁₆	—	13	2	no	—
226	C₄⋊C₁₆	—	13	2	no	—
227	C₂²⋊C₁₆	—	13	2	no	—
228	C₂²⋊C₁₆	—	13	2	no	—
229	C₂²⋊C₁₆	—	13	2	no	—
230	#346	—	13	2	no	—
231	#346	—	13	2	no	—
232	C₄×C₁₆	—	13	2	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
236	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	2	1	no	—
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	C₂×M₃₂	1	2	yes	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	#504	1	2	yes	—
248	C₄×C₁₃	#520	1	1	yes	characteristic
249	C₄×C₁₃	#568	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	—	2	1	no	—
255	Dic₁₃	C₂×M₃₂	1	2	yes	—
256	C₂×#41	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₄×Q₈	—	13	1	no	—
264	C₄×Q₈	—	13	1	no	—
265	C₄×D₄	—	13	1	no	—
266	C₄×D₄	—	13	1	no	—
267	C₄×D₄	—	13	1	no	—
268	C₄×D₄	—	13	1	no	—
269	C₄×D₄	—	13	1	no	—
270	C₄×D₄	—	13	1	no	—
271	#117	—	13	1	no	—
272	#117	—	13	1	no	—
273	#117	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	C₂×#261	1	1	yes	characteristic
277	M₃₂	—	52	2	no	—
278	C₂×C₁₆	—	13	2	no	—
279	C₂×C₁₆	—	13	2	no	—
280	C₂×C₁₆	—	13	2	no	—
281	C₂×C₁₆	—	13	2	no	—
282	C₂×C₁₆	—	52	2	no	—
283	C₂×C₁₆	—	52	2	no	—
284	C₄⋊C₈	—	13	1	no	—
285	C₄⋊C₈	—	13	1	no	—
286	C₄⋊C₈	—	13	1	no	—
287	C₄⋊C₈	—	13	1	no	—
288	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
289	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
290	C₂²⋊C₈	—	13	1	no	—
291	C₂²⋊C₈	—	13	1	no	—
292	C₂²⋊C₈	—	13	1	no	—
293	C₂²⋊C₈	—	13	1	no	—
294	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
295	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	C₂×#261	1	1	yes	characteristic
305	C₄×C₈	C₂×#261	1	1	yes	characteristic
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	#2988	1	1	yes	characteristic
308	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
310	D₁₃	—	2	2	no	—
311	D₁₃	—	4	1	no	—
312	#41	—	26	4	no	—
313	C₂×Q₈	—	13	1	no	—
314	C₂×D₄	—	13	1	no	—
315	C₂×D₄	—	13	1	no	—
316	C₂×D₄	—	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	D₁₃⋊C₈	1	1	yes	characteristic
324	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
325	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
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	—	26	1	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	1	no	—
333	C₂×C₈	—	26	1	no	—
334	C₂×C₈	—	26	1	no	—
335	C₂×C₈	—	26	1	no	—
336	C₂×C₈	—	52	1	no	—
337	C₂×C₈	—	52	1	no	—
338	C₂×C₈	—	52	1	no	—
339	C₂×C₈	C₂²×#261	1	1	yes	characteristic
340	C₂×C₈	C₂²×#261	1	1	yes	characteristic
341	C₂×C₈	C₂²×#261	1	1	yes	characteristic
342	C₂×C₈	C₂²×#261	1	1	yes	characteristic
343	C₄⋊C₄	—	13	1	no	—
344	C₄⋊C₄	—	13	1	no	—
345	C₄⋊C₄	—	13	1	no	—
346	C₄⋊C₄	—	13	1	no	—
347	C₄⋊C₄	—	13	1	no	—
348	C₄⋊C₄	—	13	1	no	—
349	C₂²⋊C₄	—	13	1	no	—
350	C₂²⋊C₄	—	13	1	no	—
351	C₂²⋊C₄	—	13	1	no	—
352	C₂²⋊C₄	—	13	1	no	—
353	C₂²⋊C₄	—	13	1	no	—
354	C₂²⋊C₄	—	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	D₁₃⋊C₈	1	1	yes	characteristic
362	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
363	C₄²	C₂²×#261	1	1	yes	characteristic
364	C₄²	C₂²×#261	1	1	yes	characteristic
365	C₁₆	—	26	2	no	—
366	C₁₆	—	26	2	no	—
367	C₁₆	—	26	2	no	—
368	C₁₆	—	26	2	no	—
369	C₁₃	#33504	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
373	Q₈	—	26	2	no	—
374	D₄	—	13	4	no	—
375	D₄	—	26	2	no	—
376	D₄	—	26	2	no	—
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	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	1	no	—
392	C₂×C₄	—	26	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	1	no	—
395	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
396	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
397	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
398	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
399	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
400	C₂×C₄	C₂³×#261	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	13	1	no	—
406	C₈	—	13	1	no	—
407	C₈	—	26	1	no	—
408	C₈	—	26	1	no	—
409	C₈	—	26	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	13	2	no	—
413	C₂²	—	26	1	no	—
414	C₂²	—	26	1	no	—
415	C₂²	—	26	1	no	—
416	C₂²	—	26	1	no	—
417	C₂²	—	26	1	no	—
418	C₂²	D₁₃⋊M₃₂	1	2	yes	—
419	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	13	2	no	—
425	C₄	—	26	1	no	—
426	C₄	—	26	1	no	—
427	C₄	—	26	1	no	—
428	C₄	—	26	1	no	—
429	C₄	—	26	1	no	—
430	C₄	#11719096	1	2	yes	—
431	C₄	#11719629	1	1	yes	characteristic
432	C₄	#11719631	1	1	yes	characteristic
433	C₂	—	2	2	no	—
434	C₂	—	26	2	no	—
435	C₂	—	52	1	no	—
436	C₂	#13131753	1	1	yes	characteristic
437	C₂	C₂×D₁₃⋊M₃₂	1	1	yes	characteristic
438	C₂	C₂×#11719096	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#431	C₄
prime radical	C₂×#6127	C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#33504
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
1. #13131253	C₂	semidirect
2. #13131219	C₂	semidirect
3. #13131218	C₂	semidirect
4. #13131214	C₂	semidirect
5. #13131200	C₂	semidirect
6. #13131197	C₂	semidirect
7. #13131196	C₂	semidirect
8. #13131169	C₂	semidirect
9. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
10. C₂×C₄⋊#6092	C₂	semidirect
176. C₂²⋊D₁₃	M₃₂	semidirect
369. C₁₃	#33504	semidirect

Maximal subgroups

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

subgroup	index
#13131253	2
#13131219	2
#13131218	2
#13131214	2
#13131200	2
#13131197	2
#13131196	2
#13131169	2
D₁₃⋊(C₄⋊C₁₆)	2
C₂×C₄⋊#6092	2
#13123792	2
#33504	13