Subgroups — #15832948

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124918	C₂	1	1	yes	maximal, characteristic
2	#13123811	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113688	C₂	1	2	yes	maximal, complemented
5	#13113681	C₂	1	2	yes	maximal, complemented
6	#13113656	C₂	1	2	yes	maximal, complemented
7	#13113650	C₂	1	2	yes	maximal, complemented
8	#13113621	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113284	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113250	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719184	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	#11718772	—	2	1	no	—
18	C₈×C₂²⋊D₁₃	—	2	1	no	—
19	C₂×#88054	—	2	1	no	—
20	C₂×C₈×Dic₁₃	—	2	1	no	—
21	#11718587	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
23	#11718506	C₄	1	2	yes	—
24	#11718490	C₄	1	2	yes	—
25	#11718400	C₄	1	1	yes	characteristic
26	#11718399	C₄	1	1	yes	characteristic
27	#11718397	C₄	1	1	yes	characteristic
28	#11718382	C₄	1	1	yes	characteristic
29	C₄×Dic₅₂	C₂²	1	2	yes	—
30	C₄×#6095	C₂²	1	2	yes	—
31	#11718351	—	2	1	no	—
32	#11718350	—	2	1	no	—
33	#11718349	C₂²	1	1	yes	characteristic
34	C₈×D₅₂	C₂²	1	1	yes	characteristic
35	#11718340	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₆	—	2	1	no	—
37	C₈×Dic₂₆	—	2	1	no	—
38	C₈×Dic₂₆	C₂²	1	2	yes	—
39	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
40	C₈×Dic₂₆	C₂²	1	2	yes	—
41	C₁₃×#322	C₂²	1	2	yes	—
42	C₁₃×#322	C₂²	1	2	yes	—
43	#11718051	C₂²	1	2	yes	—
44	#11718050	C₂²	1	2	yes	—
45	#11718049	C₂²	1	2	yes	—
46	#11718048	C₂²	1	2	yes	—
47	#11718048	C₂²	1	2	yes	—
48	#11718048	C₂²	1	2	yes	—
49	C₂²×Dic₂₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	#88184	C₂×C₄	1	1	yes	characteristic
55	#88183	—	2	1	no	—
56	C₄×C₂²⋊D₁₃	—	2	1	no	—
57	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	#88178	C₂×C₄	1	1	yes	characteristic
59	C₂×#6101	—	2	1	no	—
60	C₂×C₄×Dic₁₃	—	2	1	no	—
61	C₂²×#1055	—	2	1	no	—
62	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
63	C₂×#6095	C₂×C₄	1	2	yes	—
64	C₂×#6094	—	2	1	no	—
65	C₂×C₈×D₁₃	—	2	1	no	—
66	#88130	—	2	1	no	—
67	#88129	C₂×C₄	1	1	yes	characteristic
68	C₄×D₅₂	C₂³	1	1	yes	characteristic
69	#88126	—	2	1	no	—
70	#88124	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₂₆	—	2	1	no	—
72	C₄×Dic₂₆	—	2	1	no	—
73	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
74	C₄×Dic₂₆	C₂³	1	2	yes	—
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×#97	—	2	1	no	—
80	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²⋊#1055	—	2	1	no	—
87	#88061	C₂×C₄	1	2	yes	—
88	#88060	—	2	1	no	—
89	#88060	—	2	1	no	—
90	#88058	C₂×C₄	1	2	yes	—
91	#88057	C₂×C₄	1	2	yes	—
92	#88056	C₂×C₄	1	2	yes	—
93	#88056	C₂×C₄	1	2	yes	—
94	#88056	C₂×C₄	1	2	yes	—
95	#88055	—	2	1	no	—
96	#88054	—	2	2	no	—
97	#88054	—	2	2	no	—
98	#88054	—	2	1	no	—
99	#88054	—	2	1	no	—
100	C₈×Dic₁₃	—	2	2	no	—
101	C₈×Dic₁₃	—	2	2	no	—
102	C₈×Dic₁₃	—	2	1	no	—
103	C₄⋊#1055	—	2	1	no	—
104	C₄⋊#1055	C₂³	1	1	yes	characteristic
105	C₄⋊#1055	C₂³	1	1	yes	characteristic
106	C₄⋊#1055	C₂³	1	2	yes	—
107	#88043	—	2	1	no	—
108	#17915	—	13	1	no	maximal, Sylow
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₁₃	—	2	1	no	—
113	C₂²×Dic₁₃	—	2	1	no	—
114	C₂²×Dic₁₃	—	2	1	no	—
115	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	—	2	1	no	—
117	C₂×Dic₂₆	—	2	1	no	—
118	C₂×Dic₂₆	—	2	4	no	—
119	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
120	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
121	C₁₃×M₁₆	—	4	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	4	1	no	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₁₃	—	2	1	no	—
136	#6103	—	2	1	no	—
137	#6103	—	2	1	no	—
138	#6103	—	2	1	no	—
139	#6103	—	2	1	no	—
140	C₄⋊Dic₁₃	—	2	1	no	—
141	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
142	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	#6101	—	2	2	no	—
145	#6101	—	2	1	no	—
146	#6101	—	2	1	no	—
147	#6101	—	2	1	no	—
148	#6101	—	2	2	no	—
149	#6101	—	2	1	no	—
150	C₄×Dic₁₃	—	2	2	no	—
151	C₄×Dic₁₃	—	2	2	no	—
152	C₄×Dic₁₃	—	2	1	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	4	2	no	—
157	Dic₅₂	—	2	4	no	—
158	#6095	—	2	4	no	—
159	#6094	—	4	2	no	—
160	C₈×D₁₃	—	4	2	no	—
161	#3108	—	13	1	no	—
162	#2966	—	13	1	no	—
163	C₂×C₈×Q₈	—	13	1	no	—
164	#1584	—	13	2	no	—
165	#1583	—	13	2	no	—
166	#1579	—	13	2	no	—
167	SD₁₆⋊C₈	—	13	2	no	—
168	#1573	—	13	1	no	—
169	#1491	—	13	1	no	—
170	#1483	—	13	1	no	—
171	#1451	D₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
173	C₂²×D₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
184	C₂²⋊D₁₃	—	4	2	no	—
185	C₂×Dic₁₃	—	2	4	no	—
186	C₂×Dic₁₃	—	2	2	no	—
187	C₂×Dic₁₃	—	2	2	no	—
188	C₂×Dic₁₃	—	2	1	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	4	2	no	—
192	D₅₂	—	2	2	no	—
193	C₄×D₁₃	—	4	1	no	—
194	C₄×D₁₃	—	4	1	no	—
195	Dic₂₆	—	2	4	no	—
196	Dic₂₆	—	2	2	no	—
197	Dic₂₆	—	2	2	no	—
198	Dic₂₆	#131	1	4	yes	—
199	C₈×C₁₃	—	2	2	no	—
200	C₈×C₁₃	—	2	2	no	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	—	4	2	no	—
205	C₈×C₁₃	#137	1	2	yes	—
206	#1055	—	4	1	no	—
207	#1055	—	4	1	no	—
208	#1055	—	4	2	no	—
209	#529	—	13	1	no	—
210	C₂×C₄×Q₈	—	13	1	no	—
211	#483	—	13	1	no	—
212	#480	—	13	1	no	—
213	#479	—	13	2	no	—
214	#464	—	13	2	no	—
215	#451	—	13	1	no	—
216	#448	—	13	1	no	—
217	#446	—	13	1	no	—
218	C₈×Q₈	—	13	2	no	—
219	C₈×Q₈	—	13	1	no	—
220	C₈×Q₈	—	13	2	no	—
221	C₈×Q₈	—	26	1	no	—
222	C₈×Q₈	—	26	1	no	—
223	C₄×Q₁₆	—	13	2	no	—
224	C₄×SD₁₆	—	13	2	no	—
225	#436	—	13	1	no	—
226	#435	—	26	1	no	—
227	C₈×D₄	—	13	1	no	—
228	C₈×D₄	—	26	1	no	—
229	#433	—	26	1	no	—
230	#432	—	13	1	no	—
231	#431	C₂×D₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	—	13	1	no	—
233	C₂×C₄⋊C₈	—	26	1	no	—
234	#405	—	26	1	no	—
235	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
236	C₂×C₄×C₈	—	26	1	no	—
237	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
238	#335	—	13	2	no	—
239	#334	—	13	2	no	—
240	Q₈⋊C₈	—	13	2	no	—
241	Q₈⋊C₈	—	13	2	no	—
242	Q₈⋊C₈	—	13	2	no	—
243	D₄⋊C₈	—	13	2	no	—
244	#322	C₂×D₁₃	1	2	yes	—
245	#322	C₂×D₁₃	1	2	yes	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	#444	1	2	yes	—
249	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₁₃	—	4	1	no	—
251	C₂×D₁₃	—	4	1	no	—
252	C₂×D₁₃	—	4	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	C₂×#131	1	2	yes	—
258	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
259	C₄×C₁₃	#575	1	1	yes	characteristic
260	Dic₁₃	—	2	4	no	—
261	Dic₁₃	—	4	1	no	—
262	Dic₁₃	—	4	1	no	—
263	Dic₁₃	—	4	2	no	—
264	Dic₁₃	—	4	1	no	—
265	C₂²×Q₈	—	13	1	no	—
266	C₂×Q₁₆	—	13	2	no	—
267	C₂×SD₁₆	—	13	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	26	1	no	—
270	C₂²×C₈	—	26	1	no	—
271	C₂²×C₈	—	26	1	no	—
272	C₂²×C₈	D₅₂	1	1	yes	characteristic
273	C₂²×C₈	D₅₂	1	1	yes	characteristic
274	#126	—	26	1	no	—
275	#125	—	13	1	no	—
276	#124	—	13	1	no	—
277	#123	—	26	1	no	—
278	C₂²⋊Q₈	—	13	1	no	—
279	#121	—	13	1	no	—
280	C₄×Q₈	—	13	2	no	—
281	C₄×Q₈	—	13	2	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×Q₈	—	26	1	no	—
284	C₄×Q₈	—	26	1	no	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	—	26	1	no	—
287	#117	—	26	1	no	—
288	C₂×C₄⋊C₄	—	13	1	no	—
289	C₂×C₄⋊C₄	—	26	1	no	—
290	C₂×C₄²	—	26	1	no	—
291	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
292	#107	—	13	2	no	—
293	#106	—	13	2	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	13	1	no	—
296	C₄⋊C₈	—	13	1	no	—
297	C₄⋊C₈	—	26	2	no	—
298	C₄⋊C₈	—	26	2	no	—
299	C₄⋊C₈	—	26	1	no	—
300	C₄⋊C₈	—	26	1	no	—
301	C₄⋊C₈	—	26	1	no	—
302	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
303	#103	—	13	2	no	—
304	#103	—	13	2	no	—
305	#103	—	13	2	no	—
306	#102	—	13	2	no	—
307	C₂²⋊C₈	—	26	1	no	—
308	C₂²⋊C₈	—	26	1	no	—
309	C₂²⋊C₈	—	26	1	no	—
310	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
311	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
312	#97	—	2	1	no	—
313	#97	—	26	1	no	—
314	#97	—	26	1	no	—
315	C₄×C₈	—	26	2	no	—
316	C₄×C₈	—	26	2	no	—
317	C₄×C₈	—	26	1	no	—
318	C₄×C₈	D₅₂	1	1	yes	characteristic
319	C₄×C₈	D₅₂	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₃	1	2	yes	—
321	C₄×C₈	C₂²×D₁₃	1	2	yes	—
322	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×C₁₃	—	2	2	no	—
325	C₂×C₁₃	#2929	1	1	yes	characteristic
326	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
327	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
328	D₁₃	—	8	1	no	—
329	C₂×Q₈	—	13	2	no	—
330	C₂×Q₈	—	13	1	no	—
331	C₂×Q₈	—	26	4	no	—
332	C₂×Q₈	—	26	1	no	—
333	C₂×D₄	—	13	1	no	—
334	C₂×D₄	—	26	1	no	—
335	C₂²×C₄	—	26	1	no	—
336	C₂²×C₄	—	26	1	no	—
337	C₂²×C₄	—	26	1	no	—
338	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
340	C₂²×C₄	#6127	1	1	yes	characteristic
341	Q₁₆	—	26	4	no	—
342	SD₁₆	—	26	4	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	52	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	1	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	52	2	no	—
352	C₂×C₈	—	52	2	no	—
353	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
354	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
355	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
356	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
357	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
358	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
359	C₄⋊C₄	—	13	2	no	—
360	C₄⋊C₄	—	13	1	no	—
361	C₄⋊C₄	—	13	1	no	—
362	C₄⋊C₄	—	26	1	no	—
363	C₄⋊C₄	—	26	2	no	—
364	C₄⋊C₄	—	26	1	no	—
365	C₄⋊C₄	—	26	1	no	—
366	C₄⋊C₄	—	26	1	no	—
367	C₄⋊C₄	—	26	2	no	—
368	C₄⋊C₄	—	26	1	no	—
369	C₂²⋊C₄	—	26	1	no	—
370	C₂²⋊C₄	—	26	1	no	—
371	C₂²⋊C₄	—	26	1	no	—
372	C₂²⋊C₄	—	26	1	no	—
373	C₂²⋊C₄	—	26	1	no	—
374	C₄²	—	26	2	no	—
375	C₄²	—	26	2	no	—
376	C₄²	—	26	1	no	—
377	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
378	C₄²	C₂×D₅₂	1	1	yes	characteristic
379	C₄²	#6127	1	1	yes	characteristic
380	C₄²	C₂³×D₁₃	1	1	yes	characteristic
381	C₁₃	#17915	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	26	1	no	—
383	C₂³	C₄×D₅₂	1	1	yes	characteristic
384	Q₈	—	13	4	no	—
385	Q₈	—	26	4	no	—
386	Q₈	—	26	2	no	—
387	Q₈	—	26	2	no	—
388	D₄	—	26	2	no	—
389	D₄	—	52	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	26	4	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	26	2	no	—
397	C₂×C₄	—	26	1	no	—
398	C₂×C₄	—	26	1	no	—
399	C₂×C₄	—	26	1	no	—
400	C₂×C₄	—	52	2	no	—
401	C₂×C₄	—	52	1	no	—
402	C₂×C₄	—	52	1	no	—
403	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
404	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
405	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
408	C₂×C₄	C₂×#6127	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	52	1	no	—
416	C₈	—	52	1	no	—
417	C₈	—	52	2	no	—
418	C₈	#88163	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	52	1	no	—
422	C₂²	—	52	1	no	—
423	C₂²	—	52	1	no	—
424	C₂²	#11718378	1	2	yes	—
425	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	26	4	no	—
431	C₄	—	52	1	no	—
432	C₄	—	52	2	no	—
433	C₄	—	52	1	no	—
434	C₄	—	52	1	no	—
435	C₄	C₂×#88163	1	1	yes	characteristic
436	C₄	#11719453	1	1	yes	characteristic
437	C₄	D₁₃×#131	1	2	yes	—
438	C₂	—	2	2	no	—
439	C₂	—	104	1	no	—
440	C₂	#13123532	1	1	yes	characteristic
441	C₂	C₄×#88163	1	1	yes	characteristic
442	C₂	C₂×#11718378	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1451	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#88184	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1451	D₁₃
hypocenter	C₁₃	#17915
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
3. C₂×C₈×Dic₂₆	C₂	semidirect
4. #13113688	C₂	semidirect
5. #13113681	C₂	semidirect
6. #13113656	C₂	semidirect
7. #13113650	C₂	semidirect
8. #13113621	C₂	semidirect
9. #13113284	C₂	semidirect
11. C₁₃×#1451	C₂	semidirect
171. #1451	D₁₃	semidirect
381. C₁₃	#17915	semidirect

Maximal subgroups

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

subgroup	index
#13124918	2
#13123811	2
C₂×C₈×Dic₂₆	2
#13113688	2
#13113681	2
#13113656	2
#13113650	2
#13113621	2
#13113284	2
#13113250	2
C₁₃×#1451	2
#17915	13