Subgroups — C₂×#13130956 #16799092

Order 3328.

858 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	C₂×#11719100	C₂	1	2	yes	maximal
2	C₂²×#88104	C₂	1	1	yes	maximal, characteristic
3	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
4	#13130956	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718274	C₂	1	2	yes	maximal
6	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₂²	1	1	yes	characteristic
8	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×#6118	C₂²	1	2	yes	—
10	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11719100	—	2	4	no	—
13	#11719100	C₂²	1	8	yes	—
14	C₂×#88104	—	2	2	no	—
15	C₂×#88104	—	2	1	no	—
16	C₂×#88104	—	2	1	no	—
17	C₂×#88104	—	2	2	no	—
18	C₂×#88104	C₂²	1	4	yes	—
19	C₂×#88103	—	2	2	no	—
20	#11719089	—	2	2	no	—
21	#11719089	C₂²	1	4	yes	—
22	C₂×#88100	—	2	1	no	—
23	C₂×C₈×#261	—	2	1	no	—
24	C₂×C₁₃×#108	C₄	1	1	yes	characteristic, complemented
25	C₂×#88062	C₄	1	2	yes	complemented
26	C₂×#88059	C₄	1	1	yes	characteristic, complemented
27	D₁₃×#108	C₄	1	4	yes	complemented
28	D₁₃×#108	C₂²	1	4	yes	—
29	#11718274	C₂²	1	8	yes	—
30	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊#261	Q₈	1	2	yes	—
32	C₂×#6122	—	2	1	no	—
33	C₂²×#1057	—	2	2	no	—
34	#88237	—	2	1	no	—
35	#88237	—	2	1	no	—
36	#88237	Q₈	1	2	yes	—
37	#88237	C₂³	1	2	yes	—
38	C₂×C₄⋊#261	—	2	1	no	—
39	C₂×C₄×#261	—	2	1	no	—
40	D₁₃⋊M₁₆	—	2	1	no	—
41	D₁₃⋊M₁₆	—	2	1	no	—
42	D₁₃⋊M₁₆	D₄	1	2	yes	—
43	D₁₃⋊M₁₆	C₂³	1	2	yes	—
44	C₂×#6118	—	2	2	no	—
45	C₂×#6118	—	2	2	no	—
46	C₂×#6118	—	2	2	no	—
47	C₂×#6118	—	2	2	no	—
48	C₂×#6118	—	2	2	no	—
49	C₂×#6118	D₄	1	1	yes	characteristic
50	C₂×#6118	D₄	1	1	yes	characteristic
51	C₂×#6118	C₂³	1	4	yes	—
52	C₂×D₁₃⋊C₈	—	2	1	no	—
53	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×#6099	C₂×C₄	1	2	yes	—
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	M₁₆×D₁₃	—	2	2	no	—
58	M₁₆×D₁₃	—	2	2	no	—
59	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
60	M₁₆×D₁₃	C₂³	1	4	yes	—
61	C₂×#6094	—	2	2	no	—
62	C₂×C₈×D₁₃	—	2	2	no	—
63	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	D₄	1	2	yes	—
67	C₂×C₈×D₁₃	Q₈	1	2	yes	—
68	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂³	1	2	yes	—
71	#88104	—	2	8	no	—
72	#88104	—	2	4	no	—
73	#88104	—	2	4	no	—
74	#88103	—	2	8	no	—
75	#88100	—	2	4	no	—
76	C₈×#261	—	2	4	no	—
77	C₁₃×#108	C₂×C₄	1	4	yes	complemented
78	#88062	C₂×C₄	1	8	yes	complemented
79	#88059	C₂×C₄	1	4	yes	complemented
80	C₂×#1953	—	13	1	no	maximal, Sylow
81	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
82	C₂²×#261	—	2	2	no	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×Dic₁₃	#41	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂²×C₄	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×D₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
93	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
94	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
95	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
97	C₂²⋊#261	—	2	2	no	—
98	C₂²⋊#261	C₂×Q₈	1	4	yes	—
99	#6122	—	2	2	no	—
100	#6122	—	2	2	no	—
101	C₂×#1057	—	2	1	no	—
102	C₂×#1057	—	2	1	no	—
103	C₂×#1057	—	2	4	no	—
104	C₂×#1057	—	4	2	no	—
105	C₂×#1057	—	4	2	no	—
106	C₄⋊#261	—	2	2	no	—
107	C₄⋊#261	—	2	2	no	—
108	C₄×#261	—	2	2	no	—
109	C₄×#261	—	2	2	no	—
110	#6118	—	2	1	no	—
111	#6118	—	2	1	no	—
112	#6118	—	2	4	no	—
113	#6118	—	2	4	no	—
114	#6118	—	4	2	no	—
115	#6118	—	4	2	no	—
116	#6118	C₂×D₄	1	2	yes	—
117	#6118	C₂×D₄	1	2	yes	—
118	D₁₃⋊C₈	—	2	2	no	—
119	D₁₃⋊C₈	—	2	2	no	—
120	C₁₃×M₁₆	—	2	2	no	—
121	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	#6099	—	2	2	no	—
128	#6099	C₂²×C₄	1	4	yes	—
129	C₂×#1055	—	2	2	no	—
130	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
131	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
132	C₂×#1055	C₄⋊C₄	1	2	yes	—
133	C₂×#1055	C₂²×C₄	1	2	yes	—
134	#6094	—	2	4	no	—
135	#6094	—	2	4	no	—
136	C₈×D₁₃	—	2	4	no	—
137	C₈×D₁₃	—	2	4	no	—
138	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
139	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
140	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
141	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
142	C₈×D₁₃	C₂×D₄	1	2	yes	—
143	C₈×D₁₃	C₂×D₄	1	2	yes	—
144	C₈×D₁₃	C₂×Q₈	1	2	yes	—
145	C₈×D₁₃	C₂×Q₈	1	2	yes	—
146	C₂×#430	—	13	2	no	—
147	C₂²×#108	—	13	1	no	—
148	C₂²×#108	—	13	1	no	—
149	C₂×#405	—	13	1	no	—
150	#1953	—	13	8	no	—
151	C₂×#344	—	13	2	no	—
152	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
153	C₂²×D₁₃	—	4	2	no	—
154	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
155	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
158	C₂²×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
159	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
160	C₂×#261	—	2	4	no	—
161	C₂×#261	—	4	4	no	—
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
169	C₂×Dic₁₃	#121	1	1	yes	characteristic
170	C₂×Dic₁₃	#121	1	1	yes	characteristic
171	C₂×Dic₁₃	#125	1	1	yes	characteristic
172	C₂×Dic₁₃	#125	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
174	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
177	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
178	C₄×D₁₃	#121	1	1	yes	characteristic
179	C₄×D₁₃	#121	1	1	yes	characteristic
180	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
181	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×D₁₃	#125	1	1	yes	characteristic
183	C₄×D₁₃	#125	1	1	yes	characteristic
184	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
185	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
186	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
189	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
190	#1057	—	2	2	no	—
191	#1057	—	2	2	no	—
192	#1057	—	4	4	no	—
193	C₈×C₁₃	—	2	4	no	—
194	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
195	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
196	#1055	—	2	4	no	—
197	#1055	C₂×C₄⋊C₄	1	2	yes	—
198	#1055	C₂×C₄⋊C₄	1	2	yes	—
199	C₂²×M₁₆	—	13	1	no	—
200	C₂²×M₁₆	—	13	2	no	—
201	C₂²×M₁₆	—	13	2	no	—
202	C₂³×C₈	—	13	1	no	—
203	C₂×#117	—	13	1	no	—
204	#430	—	13	8	no	—
205	#430	—	26	4	no	—
206	C₂×#108	—	13	2	no	—
207	C₂×#108	—	13	1	no	—
208	C₂×#108	—	13	4	no	—
209	C₂×#108	—	13	4	no	—
210	C₂×#108	—	13	4	no	—
211	C₂×#108	—	26	1	no	—
212	C₂×#108	—	26	1	no	—
213	C₂×#108	—	26	2	no	—
214	C₂×#108	—	26	2	no	—
215	C₂×#108	—	26	2	no	—
216	C₂×#108	#261	1	1	yes	characteristic, complemented
217	#405	—	13	4	no	—
218	#405	—	26	2	no	—
219	C₂×#97	—	26	1	no	—
220	C₂×C₄×C₈	—	26	1	no	—
221	#344	—	13	8	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	#389	1	1	yes	characteristic
224	C₂²×C₁₃	#389	1	1	yes	characteristic
225	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂×D₁₃	—	2	2	no	—
227	C₂×D₁₃	—	2	2	no	—
228	C₂×D₁₃	—	4	1	no	—
229	C₂×D₁₃	—	4	1	no	—
230	C₂×D₁₃	—	4	1	no	—
231	C₂×D₁₃	—	4	1	no	—
232	C₂×D₁₃	#389	1	1	yes	characteristic
233	C₂×D₁₃	#389	1	1	yes	characteristic
234	C₂×D₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×D₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
236	#261	—	4	4	no	—
237	C₄×C₁₃	#389	1	1	yes	characteristic
238	C₄×C₁₃	#389	1	1	yes	characteristic
239	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	Dic₁₃	#389	1	1	yes	characteristic
242	Dic₁₃	#389	1	1	yes	characteristic
243	Dic₁₃	C₂×#121	1	1	yes	characteristic
244	Dic₁₃	C₂×#125	1	1	yes	characteristic
245	C₂³×C₄	—	13	1	no	—
246	C₂×M₁₆	—	13	2	no	—
247	C₂×M₁₆	—	13	1	no	—
248	C₂×M₁₆	—	13	1	no	—
249	C₂×M₁₆	—	13	2	no	—
250	C₂×M₁₆	—	13	2	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	13	4	no	—
253	C₂×M₁₆	—	13	4	no	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	26	2	no	—
257	C₂×M₁₆	—	26	1	no	—
258	C₂×M₁₆	—	26	1	no	—
259	C₂×M₁₆	—	26	1	no	—
260	C₂×M₁₆	—	26	2	no	—
261	C₂×M₁₆	—	26	2	no	—
262	C₂×M₁₆	—	26	2	no	—
263	C₂×M₁₆	—	26	2	no	—
264	C₂×M₁₆	—	26	2	no	—
265	C₂×M₁₆	C₂×#261	1	2	yes	—
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	2	no	—
270	C₂²×C₈	—	13	2	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	2	no	—
274	C₂²×C₈	—	13	2	no	—
275	C₂²×C₈	—	26	2	no	—
276	C₂²×C₈	—	26	1	no	—
277	C₂²×C₈	—	26	2	no	—
278	C₂²×C₈	C₂×#261	1	1	yes	characteristic
279	#117	—	13	2	no	—
280	#117	—	13	2	no	—
281	#117	—	26	1	no	—
282	#117	—	26	1	no	—
283	C₂×C₄⋊C₄	—	26	1	no	—
284	C₂×C₂²⋊C₄	—	13	2	no	—
285	C₂×C₄²	—	26	1	no	—
286	#108	—	13	8	no	—
287	#108	—	13	4	no	—
288	#108	—	26	4	no	—
289	#108	—	26	4	no	—
290	#108	—	26	8	no	—
291	#108	—	26	8	no	—
292	#108	C₂×#261	1	4	yes	complemented
293	#97	—	26	4	no	—
294	C₄×C₈	—	26	4	no	—
295	C₂×C₁₃	—	2	1	no	—
296	C₂×C₁₃	—	2	1	no	—
297	C₂×C₁₃	#1953	1	2	yes	complemented
298	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
299	D₁₃	—	2	1	no	—
300	D₁₃	—	2	1	no	—
301	D₁₃	—	2	1	no	—
302	D₁₃	—	2	1	no	—
303	C₂⁴	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	26	2	no	—
318	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
319	M₁₆	—	2	2	no	—
320	M₁₆	—	13	2	no	—
321	M₁₆	—	13	2	no	—
322	M₁₆	—	13	4	no	—
323	M₁₆	—	26	4	no	—
324	M₁₆	—	26	4	no	—
325	M₁₆	—	26	1	no	—
326	M₁₆	—	26	1	no	—
327	M₁₆	—	26	2	no	—
328	M₁₆	—	26	2	no	—
329	M₁₆	—	26	2	no	—
330	M₁₆	—	26	4	no	—
331	M₁₆	—	26	4	no	—
332	M₁₆	—	52	2	no	—
333	M₁₆	—	52	2	no	—
334	M₁₆	C₂²×#261	1	4	yes	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	13	2	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	26	4	no	—
349	C₂×C₈	—	26	4	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	1	no	—
353	C₂×C₈	—	26	1	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	—	26	4	no	—
356	C₂×C₈	—	52	2	no	—
357	C₂×C₈	—	52	2	no	—
358	C₂×C₈	C₄⋊#261	1	2	yes	—
359	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
360	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
361	C₂×C₈	C₂²×#261	1	2	yes	—
362	C₄⋊C₄	—	26	2	no	—
363	C₄⋊C₄	—	26	2	no	—
364	C₂²⋊C₄	—	13	4	no	—
365	C₂²⋊C₄	—	26	2	no	—
366	C₄²	—	26	2	no	—
367	C₄²	—	26	2	no	—
368	C₁₃	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
369	C₂³	—	13	1	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	—	13	1	no	—
373	C₂³	—	13	1	no	—
374	C₂³	—	13	1	no	—
375	C₂³	—	52	2	no	—
376	C₂³	Q₈×#261	1	1	yes	characteristic
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	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	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	—	13	1	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	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	26	4	no	—
400	C₂×C₄	—	52	4	no	—
401	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
402	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
403	C₂×C₄	D₄×#261	1	1	yes	characteristic
404	C₂×C₄	D₄×#261	1	1	yes	characteristic
405	C₂×C₄	Q₈×#261	1	1	yes	characteristic
406	C₂×C₄	C₂³×#261	1	1	yes	characteristic
407	C₈	—	2	4	no	—
408	C₈	—	13	2	no	—
409	C₈	—	13	2	no	—
410	C₈	—	26	2	no	—
411	C₈	—	26	2	no	—
412	C₈	—	26	4	no	—
413	C₈	—	52	4	no	—
414	C₈	C₂×C₄⋊#261	1	2	yes	—
415	C₈	C₂×C₄⋊#261	1	2	yes	—
416	C₂²	—	2	2	no	—
417	C₂²	—	13	1	no	—
418	C₂²	—	13	1	no	—
419	C₂²	—	13	1	no	—
420	C₂²	—	13	1	no	—
421	C₂²	—	26	2	no	—
422	C₂²	—	26	2	no	—
423	C₂²	—	52	1	no	—
424	C₂²	—	52	1	no	—
425	C₂²	—	52	1	no	—
426	C₂²	—	52	1	no	—
427	C₂²	#11719083	1	1	yes	characteristic
428	C₂²	#11719083	1	1	yes	characteristic
429	C₂²	C₂×Q₈×#261	1	1	yes	characteristic
430	C₄	—	13	1	no	—
431	C₄	—	13	1	no	—
432	C₄	—	13	1	no	—
433	C₄	—	13	1	no	—
434	C₄	—	52	4	no	—
435	C₄	#11719083	1	1	yes	characteristic
436	C₄	#11719083	1	1	yes	characteristic
437	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
438	C₄	C₂×D₄×#261	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	26	1	no	—
442	C₂	—	26	1	no	—
443	C₂	—	26	1	no	—
444	C₂	—	26	1	no	—
445	C₂	#13130956	1	2	yes	direct product factor
446	C₂	C₂×#11719083	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11719083
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂²×C₁₃	#389
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×#108	#261
hypocenter	C₁₃	C₂×#1953
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #13130956	C₂	direct (N × H)
24. C₂×C₁₃×#108	C₄	semidirect
25. C₂×#88062	C₄	semidirect
26. C₂×#88059	C₄	semidirect
27. D₁₃×#108	C₄	semidirect
77. C₁₃×#108	C₂×C₄	semidirect
78. #88062	C₂×C₄	semidirect
79. #88059	C₂×C₄	semidirect
216. C₂×#108	#261	semidirect
292. #108	C₂×#261	semidirect
297. C₂×C₁₃	#1953	semidirect
368. C₁₃	C₂×#1953	semidirect
445. C₂	#13130956	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11719100	2
C₂²×#88104	2
C₂×#11719089	2
#13130956	2
C₂×#11718274	2
C₂×D₁₃×#108	2
C₂×#1953	13

Subgroups — C2×#13130956 #16799092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130956 #16799092