Subgroups — #16785719

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×#261	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718273	C₂	1	2	yes	maximal
4	#13130498	C₂	1	2	yes	maximal
5	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
7	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
8	C₂²×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	D₁₃⋊#108	—	2	2	no	—
12	D₁₃⋊#108	—	2	2	no	—
13	C₂×#88104	C₄	1	2	yes	complemented
14	C₂×#88103	C₄	1	2	yes	complemented
15	C₂×C₈×#261	—	2	2	no	—
16	C₂×C₈×#261	—	2	2	no	—
17	C₂×C₈×#261	C₄	1	2	yes	—
18	C₂×C₈×#261	C₄	1	2	yes	—
19	C₂×C₁₃×#108	C₄	1	1	yes	characteristic, complemented
20	C₂×#88062	C₄	1	2	yes	complemented
21	C₂×#88059	C₄	1	1	yes	characteristic, complemented
22	D₁₃×#108	—	2	2	no	—
23	D₁₃×#108	—	2	2	no	—
24	#11718273	—	2	4	no	—
25	(C₂×#261)⋊C₈	—	2	4	no	—
26	C₂³×#261	Q₈	1	2	yes	—
27	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
28	C₂×#6122	—	2	2	no	—
29	C₂²×#1057	—	2	1	no	—
30	C₂×C₄×#261	—	2	1	no	—
31	C₂×C₄×#261	—	2	1	no	—
32	C₂×C₄×#261	—	2	1	no	—
33	C₂×C₄×#261	—	2	1	no	—
34	C₂×C₄×#261	C₂×C₄	1	2	yes	—
35	C₂×C₄×#261	D₄	1	2	yes	—
36	D₁₃⋊M₁₆	—	2	2	no	—
37	D₁₃⋊M₁₆	—	2	2	no	—
38	D₁₃⋊M₁₆	—	2	2	no	—
39	D₁₃⋊M₁₆	—	2	2	no	—
40	C₂×#6118	C₂×C₄	1	4	yes	—
41	C₂×D₁₃⋊C₈	—	2	1	no	—
42	C₂×D₁₃⋊C₈	—	2	1	no	—
43	C₂×D₁₃⋊C₈	—	2	1	no	—
44	C₂×D₁₃⋊C₈	—	2	2	no	—
45	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
46	C₂×D₁₃⋊C₈	D₄	1	2	yes	—
47	C₂×D₁₃⋊C₈	Q₈	1	2	yes	—
48	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#6099	C₂×C₄	1	2	yes	—
51	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
52	M₁₆×D₁₃	—	2	2	no	—
53	M₁₆×D₁₃	—	2	2	no	—
54	M₁₆×D₁₃	—	2	2	no	—
55	M₁₆×D₁₃	—	2	2	no	—
56	C₂×#6094	—	2	2	no	—
57	C₂×C₈×D₁₃	—	2	2	no	—
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	D₄	1	2	yes	—
63	C₂×C₈×D₁₃	D₄	1	2	yes	—
64	C₂×C₈×D₁₃	D₄	1	2	yes	—
65	C₂×C₈×D₁₃	Q₈	1	2	yes	—
66	#88104	—	2	4	no	—
67	#88103	—	2	4	no	—
68	C₈×#261	—	2	4	no	—
69	C₈×#261	—	2	4	no	—
70	C₁₃×#108	—	2	2	no	—
71	#88062	—	2	4	no	—
72	#88059	—	2	2	no	—
73	#10864	—	13	1	no	maximal, Sylow
74	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
75	C₂²×#261	—	2	2	no	—
76	C₂²×#261	—	2	2	no	—
77	C₂²×#261	—	2	8	no	—
78	C₂²×#261	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×Dic₁₃	#41	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
91	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
92	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
93	#6122	—	4	2	no	—
94	#6122	—	4	2	no	—
95	C₂×#1057	—	2	2	no	—
96	C₂×#1057	—	2	2	no	—
97	C₂×#1057	—	2	2	no	—
98	C₂×#1057	—	2	4	no	—
99	C₄×#261	—	2	2	no	—
100	C₄×#261	—	2	2	no	—
101	C₄×#261	—	2	2	no	—
102	C₄×#261	—	2	2	no	—
103	#6118	—	2	4	no	—
104	#6118	—	2	4	no	—
105	D₁₃⋊C₈	—	2	2	no	—
106	D₁₃⋊C₈	—	2	2	no	—
107	D₁₃⋊C₈	—	2	2	no	—
108	D₁₃⋊C₈	—	4	2	no	—
109	D₁₃⋊C₈	—	4	2	no	—
110	D₁₃⋊C₈	C₄⋊C₄	1	4	yes	—
111	C₁₃×M₁₆	—	2	2	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
118	#6099	—	2	2	no	—
119	#6099	—	2	2	no	—
120	C₂×#1055	—	2	2	no	—
121	C₂×#1055	C₄²	1	1	yes	characteristic
122	C₂×#1055	C₄²	1	1	yes	characteristic
123	C₂×#1055	C₂²⋊C₄	1	2	yes	—
124	C₂×#1055	C₄⋊C₄	1	2	yes	—
125	#6094	—	4	2	no	—
126	#6094	—	4	2	no	—
127	C₈×D₁₃	—	4	2	no	—
128	C₈×D₁₃	—	4	2	no	—
129	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
130	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
131	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
132	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
133	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
134	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
135	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
136	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
137	C₂²×#108	—	13	1	no	—
138	C₂²×#108	—	13	1	no	—
139	C₂²×C₄×C₈	—	13	1	no	—
140	C₂×#341	—	13	2	no	—
141	#1728	—	13	2	no	—
142	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
143	C₂²×D₁₃	—	2	4	no	—
144	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
146	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
149	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
150	C₂×#261	—	2	8	no	—
151	C₂×#261	—	2	8	no	—
152	C₂×#261	—	2	4	no	—
153	C₂×#261	—	2	4	no	—
154	C₂×#261	#108	1	8	yes	complemented
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
161	C₂×Dic₁₃	#117	1	1	yes	characteristic
162	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂×Dic₁₃	#121	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×Dic₁₃	#124	1	1	yes	characteristic
166	C₂×Dic₁₃	#125	1	1	yes	characteristic
167	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₄×D₁₃	#117	1	1	yes	characteristic
173	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
174	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
175	C₄×D₁₃	#121	1	1	yes	characteristic
176	C₄×D₁₃	#121	1	1	yes	characteristic
177	C₄×D₁₃	#121	1	1	yes	characteristic
178	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
179	C₄×D₁₃	#124	1	1	yes	characteristic
180	C₄×D₁₃	#125	1	1	yes	characteristic
181	C₄×D₁₃	#127	1	1	yes	characteristic
182	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
183	#1057	—	2	4	no	—
184	#1057	—	4	4	no	—
185	C₈×C₁₃	—	4	2	no	—
186	C₈×C₁₃	#95	1	2	yes	—
187	C₈×C₁₃	#95	1	2	yes	—
188	#1055	—	4	2	no	—
189	#1055	#95	1	2	yes	—
190	#1055	#95	1	2	yes	—
191	C₂²×M₁₆	—	13	2	no	—
192	C₂²×M₁₆	—	13	2	no	—
193	C₂³×C₈	—	13	1	no	—
194	C₂³×C₈	—	13	1	no	—
195	C₂²×C₄²	—	13	1	no	—
196	C₂×#108	—	13	2	no	—
197	C₂×#108	—	13	2	no	—
198	C₂×#108	—	13	2	no	—
199	C₂×#108	—	13	1	no	—
200	C₂×#108	—	26	2	no	—
201	C₂×#108	—	26	2	no	—
202	C₂×#108	—	26	2	no	—
203	C₂×#108	—	26	2	no	—
204	C₂×#108	#261	1	1	yes	characteristic, complemented
205	C₂×C₄×C₈	—	13	2	no	—
206	C₂×C₄×C₈	—	13	2	no	—
207	C₂×C₄×C₈	—	26	2	no	—
208	C₂×C₄×C₈	—	26	2	no	—
209	#341	—	26	4	no	—
210	#336	—	26	4	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
213	C₂²×C₁₃	#389	1	1	yes	characteristic
214	C₂²×C₁₃	#391	1	1	yes	characteristic
215	C₂×D₁₃	—	2	2	no	—
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	#380	1	1	yes	characteristic
221	C₂×D₁₃	#384	1	1	yes	characteristic
222	C₂×D₁₃	#389	1	1	yes	characteristic
223	C₂×D₁₃	#391	1	1	yes	characteristic
224	C₂×D₁₃	C₂×#108	1	4	yes	—
225	#261	—	2	8	no	—
226	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
227	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₁₃	#389	1	1	yes	characteristic
229	C₄×C₁₃	#390	1	1	yes	characteristic
230	Dic₁₃	#380	1	1	yes	characteristic
231	Dic₁₃	#382	1	1	yes	characteristic
232	Dic₁₃	#389	1	1	yes	characteristic
233	Dic₁₃	#390	1	1	yes	characteristic
234	C₂³×C₄	—	13	1	no	—
235	C₂³×C₄	—	13	2	no	—
236	C₂×M₁₆	—	13	4	no	—
237	C₂×M₁₆	—	13	2	no	—
238	C₂×M₁₆	—	26	2	no	—
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	—	26	2	no	—
241	C₂×M₁₆	—	26	2	no	—
242	C₂×M₁₆	—	26	2	no	—
243	C₂×M₁₆	—	26	2	no	—
244	C₂×M₁₆	—	26	2	no	—
245	C₂×M₁₆	—	26	2	no	—
246	C₂×M₁₆	—	26	2	no	—
247	C₂×M₁₆	—	26	2	no	—
248	C₂×M₁₆	C₂×#261	1	2	yes	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	2	no	—
255	C₂²×C₈	—	13	2	no	—
256	C₂²×C₈	—	13	2	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	—	13	2	no	—
259	C₂²×C₈	—	13	2	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	26	2	no	—
262	C₂²×C₈	—	26	1	no	—
263	C₂²×C₈	—	26	1	no	—
264	C₂²×C₈	—	26	1	no	—
265	C₂²×C₈	—	26	1	no	—
266	C₂²×C₈	—	26	2	no	—
267	C₂²×C₈	C₂×#261	1	1	yes	characteristic
268	C₂×C₄²	—	13	2	no	—
269	C₂×C₄²	—	13	2	no	—
270	C₂×C₄²	—	26	1	no	—
271	C₂×C₄²	—	26	1	no	—
272	C₂×C₄²	—	26	1	no	—
273	C₂×C₄²	—	26	1	no	—
274	#108	—	2	2	no	—
275	#108	—	26	4	no	—
276	#108	—	26	4	no	—
277	#108	—	26	4	no	—
278	#108	—	26	2	no	—
279	C₄×C₈	—	26	4	no	—
280	C₄×C₈	—	26	4	no	—
281	C₂×C₁₃	—	2	1	no	—
282	C₂×C₁₃	—	2	1	no	—
283	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
284	C₂×C₁₃	C₄×#108	1	2	yes	—
285	D₁₃	—	2	1	no	—
286	D₁₃	—	2	1	no	—
287	D₁₃	#1810	1	2	yes	—
288	D₁₃	#1848	1	2	yes	—
289	C₂⁴	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	1	no	—
292	C₂²×C₄	—	13	1	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	4	no	—
304	C₂²×C₄	—	26	8	no	—
305	C₂²×C₄	—	26	2	no	—
306	C₂²×C₄	—	26	2	no	—
307	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
308	M₁₆	—	2	2	no	—
309	M₁₆	—	2	2	no	—
310	M₁₆	—	26	4	no	—
311	M₁₆	—	26	4	no	—
312	M₁₆	—	26	2	no	—
313	M₁₆	—	26	2	no	—
314	M₁₆	—	52	2	no	—
315	M₁₆	—	52	2	no	—
316	M₁₆	—	52	2	no	—
317	M₁₆	—	52	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	2	no	—
323	C₂×C₈	—	13	2	no	—
324	C₂×C₈	—	13	2	no	—
325	C₂×C₈	—	13	2	no	—
326	C₂×C₈	—	13	2	no	—
327	C₂×C₈	—	13	2	no	—
328	C₂×C₈	—	13	2	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	13	4	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	2	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	26	2	no	—
336	C₂×C₈	—	26	2	no	—
337	C₂×C₈	—	26	2	no	—
338	C₂×C₈	—	26	4	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	—	52	2	no	—
341	C₂×C₈	—	52	2	no	—
342	C₂×C₈	—	52	2	no	—
343	C₂×C₈	—	52	2	no	—
344	C₂×C₈	C₄×#261	1	1	yes	characteristic
345	C₂×C₈	C₄×#261	1	1	yes	characteristic
346	C₂×C₈	C₄⋊#261	1	2	yes	—
347	C₂×C₈	C₂²⋊#261	1	2	yes	—
348	C₄²	—	26	2	no	—
349	C₄²	—	26	2	no	—
350	C₄²	—	26	2	no	—
351	C₄²	—	26	2	no	—
352	C₁₃	#10864	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	1	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	13	1	no	—
356	C₂³	—	13	1	no	—
357	C₂³	—	13	1	no	—
358	C₂³	—	13	1	no	—
359	C₂³	—	26	4	no	—
360	C₂³	Q₈×#261	1	1	yes	characteristic
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	8	no	—
384	C₂×C₄	—	26	4	no	—
385	C₂×C₄	—	26	4	no	—
386	C₂×C₄	—	26	8	no	—
387	C₂×C₄	—	26	8	no	—
388	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
389	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
390	C₂×C₄	D₄×#261	1	1	yes	characteristic
391	C₂×C₄	D₄×#261	1	1	yes	characteristic
392	C₂×C₄	Q₈×#261	1	1	yes	characteristic
393	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	13	2	no	—
396	C₈	—	13	2	no	—
397	C₈	—	26	4	no	—
398	C₈	—	52	4	no	—
399	C₈	—	52	2	no	—
400	C₈	(C₂×#261)⋊C₄	1	2	yes	—
401	C₈	(C₂×#261)⋊C₄	1	2	yes	—
402	C₂²	—	2	2	no	—
403	C₂²	—	13	1	no	—
404	C₂²	—	13	1	no	—
405	C₂²	—	13	4	no	—
406	C₂²	—	13	1	no	—
407	C₂²	—	13	1	no	—
408	C₂²	—	26	2	no	—
409	C₂²	—	26	2	no	—
410	C₂²	—	26	2	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	26	2	no	—
413	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
414	C₂²	#11719083	1	1	yes	characteristic
415	C₂²	(C₂×#261)⋊Q₈	1	1	yes	characteristic
416	C₄	—	13	1	no	—
417	C₄	—	13	1	no	—
418	C₄	—	13	1	no	—
419	C₄	—	13	1	no	—
420	C₄	—	26	8	no	—
421	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
422	C₄	#11719083	1	1	yes	characteristic
423	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
424	C₄	#11719151	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	13	2	no	—
428	C₂	—	13	2	no	—
429	C₂	—	26	1	no	—
430	C₂	—	26	1	no	—
431	C₂	#13130013	1	1	yes	characteristic
432	C₂	#108×#261	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂²×C₄×D₁₃	C₂³
hypercenter	C₂×#108	#261
hypocenter	C₁₃	#10864
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
13. C₂×#88104	C₄	semidirect
14. C₂×#88103	C₄	semidirect
19. C₂×C₁₃×#108	C₄	semidirect
20. C₂×#88062	C₄	semidirect
21. C₂×#88059	C₄	semidirect
154. C₂×#261	#108	semidirect
204. C₂×#108	#261	semidirect
352. C₁₃	#10864	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊#108	2
C₂²×C₈×#261	2
C₂×#11718273	2
#13130498	2
C₂×D₁₃×#108	2
#10864	13