Subgroups — C₂×#13130755 #16798163

Order 3328.

786 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	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719092	C₂	1	1	yes	maximal, characteristic
3	#13130755	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718266	C₂	1	2	yes	maximal
5	C₂×#11718235	C₂	1	2	yes	maximal
6	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₂²	1	2	yes	—
8	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂²×#6094	C₂²	1	1	yes	characteristic
10	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88126	C₂²	1	1	yes	characteristic
12	D₁₃⋊#108	—	2	2	no	—
13	D₁₃⋊#108	C₂²	1	4	yes	—
14	C₂×#88104	—	2	1	no	—
15	C₂×#88103	—	2	1	no	—
16	#11719092	—	2	2	no	—
17	#11719092	C₂²	1	4	yes	—
18	C₂×#88102	—	2	1	no	—
19	C₂×#88101	—	2	1	no	—
20	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
21	C₂×#88055	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
23	C₂×#88043	C₄	1	1	yes	characteristic, complemented
24	#11718350	C₄	1	4	yes	complemented
25	#11718350	C₂²	1	4	yes	—
26	#11718266	C₂²	1	8	yes	—
27	#11718235	C₂²	1	8	yes	—
28	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₂²⋊#261	—	2	2	no	—
30	C₂×#6122	—	2	2	no	—
31	#88237	—	2	2	no	—
32	#88237	—	2	2	no	—
33	#88237	—	2	2	no	—
34	#88237	C₂³	1	4	yes	—
35	C₂×C₄⋊#261	—	2	2	no	—
36	C₂×C₄×#261	—	2	2	no	—
37	D₁₃⋊M₁₆	—	2	2	no	—
38	D₁₃⋊M₁₆	—	2	2	no	—
39	D₁₃⋊M₁₆	—	2	2	no	—
40	D₁₃⋊M₁₆	C₂³	1	4	yes	—
41	C₂×#6118	—	2	2	no	—
42	C₂×D₁₃⋊C₈	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×#6103	—	2	1	no	—
47	C₂×#6101	—	2	1	no	—
48	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
50	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
51	C₂×#6094	—	2	1	no	—
52	C₂×#6094	—	2	1	no	—
53	C₂×#6094	—	2	1	no	—
54	C₂×#6094	—	2	1	no	—
55	C₂×#6094	C₂×C₄	1	2	yes	—
56	C₂×#6094	C₂³	1	2	yes	—
57	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	D₄	1	2	yes	—
61	C₂×C₈×D₁₃	Q₈	1	2	yes	—
62	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
63	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂³	1	2	yes	—
65	#88126	—	2	1	no	—
66	#88126	—	2	1	no	—
67	#88126	C₂×C₄	1	2	yes	—
68	#88126	C₂³	1	2	yes	—
69	#88104	—	2	4	no	—
70	#88103	—	2	4	no	—
71	#88102	—	2	4	no	—
72	#88101	—	2	4	no	—
73	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
74	#88055	C₂×C₄	1	4	yes	complemented
75	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
76	#88043	C₂×C₄	1	4	yes	complemented
77	C₂×#1833	—	13	1	no	maximal, Sylow
78	C₂³×D₁₃	#41	1	1	yes	characteristic
79	C₂²×#261	—	4	2	no	—
80	C₂²×C₄×C₁₃	—	2	1	no	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×Dic₁₃	—	2	1	no	—
83	C₂²×Dic₁₃	#41	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₂²×C₄	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×Q₈	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	#41	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	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
94	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
96	C₂²⋊#261	—	2	4	no	—
97	C₂²⋊#261	—	4	2	no	—
98	#6122	—	2	4	no	—
99	#6122	—	4	2	no	—
100	C₂×#1057	—	4	2	no	—
101	C₄⋊#261	—	2	4	no	—
102	C₄⋊#261	—	4	2	no	—
103	C₄×#261	—	2	4	no	—
104	C₄×#261	—	4	2	no	—
105	#6118	—	2	4	no	—
106	#6118	—	4	2	no	—
107	D₁₃⋊C₈	—	2	4	no	—
108	D₁₃⋊C₈	—	4	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₄²×C₁₃	—	2	1	no	—
117	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
118	#6103	—	2	2	no	—
119	#6103	—	2	2	no	—
120	#6101	—	2	2	no	—
121	#6101	—	2	2	no	—
122	C₄×Dic₁₃	—	2	1	no	—
123	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
124	C₂×#1055	—	2	1	no	—
125	C₂×#1055	—	2	1	no	—
126	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
127	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
128	C₂×#1055	C₄⋊C₄	1	2	yes	—
129	C₂×#1055	C₂²×C₄	1	2	yes	—
130	C₂×#1055	C₂²×C₄	1	2	yes	—
131	#6094	—	2	2	no	—
132	#6094	—	2	2	no	—
133	#6094	—	2	2	no	—
134	#6094	—	2	2	no	—
135	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
136	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
137	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
138	C₈×D₁₃	C₄⋊C₄	1	2	yes	—
139	C₈×D₁₃	C₂×D₄	1	2	yes	—
140	C₈×D₁₃	C₂×D₄	1	2	yes	—
141	C₈×D₁₃	C₂×Q₈	1	2	yes	—
142	C₈×D₁₃	C₂×Q₈	1	2	yes	—
143	C₂²×#108	—	13	1	no	—
144	C₂×#427	—	13	1	no	—
145	C₂×#405	—	13	1	no	—
146	#1833	—	13	8	no	—
147	C₂×#344	—	13	2	no	—
148	C₂×H(3,ℤ/4)	—	13	2	no	—
149	C₂³×C₁₃	#117	1	1	yes	characteristic
150	C₂²×D₁₃	—	4	2	no	—
151	C₂²×D₁₃	#117	1	1	yes	characteristic
152	C₂²×D₁₃	#124	1	1	yes	characteristic
153	C₂²×D₁₃	#124	1	1	yes	characteristic
154	C₂²×D₁₃	#125	1	1	yes	characteristic
155	C₂²×D₁₃	#125	1	1	yes	characteristic
156	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
157	C₂×#261	—	4	4	no	—
158	C₂×#261	—	8	4	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
164	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	4	2	no	—
169	C₂×Dic₁₃	#117	1	1	yes	characteristic
170	C₂×Dic₁₃	#124	1	1	yes	characteristic
171	C₂×Dic₁₃	#124	1	1	yes	characteristic
172	C₂×Dic₁₃	#125	1	1	yes	characteristic
173	C₂×Dic₁₃	#125	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
175	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₄×D₁₃	#117	1	1	yes	characteristic
178	C₄×D₁₃	#117	1	1	yes	characteristic
179	C₄×D₁₃	#124	1	1	yes	characteristic
180	C₄×D₁₃	#124	1	1	yes	characteristic
181	C₄×D₁₃	#124	1	1	yes	characteristic
182	C₄×D₁₃	#124	1	1	yes	characteristic
183	C₄×D₁₃	#125	1	1	yes	characteristic
184	C₄×D₁₃	#125	1	1	yes	characteristic
185	C₄×D₁₃	#125	1	1	yes	characteristic
186	C₄×D₁₃	#125	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	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
191	#1057	—	4	4	no	—
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
194	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
195	#1055	—	2	2	no	—
196	#1055	C₂×C₄⋊C₄	1	2	yes	—
197	#1055	C₂×C₄⋊C₄	1	2	yes	—
198	C₂²×M₁₆	—	13	1	no	—
199	C₂²×M₁₆	—	13	2	no	—
200	C₂³×C₈	—	13	1	no	—
201	C₂×#117	—	13	1	no	—
202	C₂×#117	—	13	2	no	—
203	C₂×#108	—	13	4	no	—
204	C₂×#108	—	26	1	no	—
205	C₂×#108	—	26	1	no	—
206	C₂×#108	—	26	2	no	—
207	#427	—	13	4	no	—
208	#427	—	26	2	no	—
209	C₂×#107	—	26	1	no	—
210	C₂×#106	—	26	1	no	—
211	#405	—	13	4	no	—
212	#405	—	13	4	no	—
213	C₂×#97	—	13	1	no	—
214	C₂×#97	—	13	1	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
217	#344	—	13	8	no	—
218	H(3,ℤ/4)	—	13	8	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	#382	1	1	yes	characteristic
221	C₂²×C₁₃	#382	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
223	C₂×D₁₃	—	2	2	no	—
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	—	4	1	no	—
226	C₂×D₁₃	—	4	1	no	—
227	C₂×D₁₃	—	4	1	no	—
228	C₂×D₁₃	—	4	1	no	—
229	C₂×D₁₃	#382	1	1	yes	characteristic
230	C₂×D₁₃	#382	1	1	yes	characteristic
231	C₂×D₁₃	C₂×#124	1	1	yes	characteristic
232	C₂×D₁₃	C₂×#125	1	1	yes	characteristic
233	#261	—	8	4	no	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	#382	1	1	yes	characteristic
236	C₄×C₁₃	#382	1	1	yes	characteristic
237	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
239	Dic₁₃	—	4	2	no	—
240	Dic₁₃	#382	1	1	yes	characteristic
241	Dic₁₃	#382	1	1	yes	characteristic
242	Dic₁₃	C₂×#124	1	1	yes	characteristic
243	Dic₁₃	C₂×#125	1	1	yes	characteristic
244	C₂³×C₄	—	13	1	no	—
245	C₂×M₁₆	—	13	2	no	—
246	C₂×M₁₆	—	13	2	no	—
247	C₂×M₁₆	—	13	4	no	—
248	C₂×M₁₆	—	26	1	no	—
249	C₂×M₁₆	—	26	1	no	—
250	C₂×M₁₆	—	26	1	no	—
251	C₂×M₁₆	—	26	1	no	—
252	C₂×M₁₆	—	26	2	no	—
253	C₂×M₁₆	—	26	2	no	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	26	2	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	26	2	no	—
268	C₂²×C₈	C₂×#261	1	1	yes	characteristic
269	C₂²×C₈	C₂×#261	1	1	yes	characteristic
270	#117	—	13	2	no	—
271	#117	—	13	2	no	—
272	#117	—	13	4	no	—
273	#117	—	26	1	no	—
274	#117	—	26	1	no	—
275	#117	—	26	2	no	—
276	#117	—	26	2	no	—
277	#117	—	26	2	no	—
278	C₂×C₄⋊C₄	—	26	1	no	—
279	C₂×C₄⋊C₄	—	26	2	no	—
280	C₂×C₂²⋊C₄	—	26	1	no	—
281	C₂×C₂²⋊C₄	—	26	2	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	26	2	no	—
284	C₂×C₄²	C₂×#261	1	1	yes	characteristic
285	#108	—	26	4	no	—
286	#108	—	26	4	no	—
287	#107	—	26	4	no	—
288	#106	—	26	4	no	—
289	#97	—	13	4	no	—
290	#97	—	13	4	no	—
291	C₄×C₈	—	13	4	no	—
292	C₄×C₈	C₂×#261	1	4	yes	complemented
293	C₂×C₁₃	—	2	1	no	—
294	C₂×C₁₃	—	2	1	no	—
295	C₂×C₁₃	#1833	1	2	yes	complemented
296	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
297	D₁₃	—	2	1	no	—
298	D₁₃	—	2	1	no	—
299	D₁₃	—	2	1	no	—
300	D₁₃	—	2	1	no	—
301	C₂⁴	—	13	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	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	—	26	1	no	—
317	C₂²×C₄	—	52	2	no	—
318	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
319	M₁₆	—	26	2	no	—
320	M₁₆	—	26	2	no	—
321	M₁₆	—	26	2	no	—
322	M₁₆	—	26	2	no	—
323	M₁₆	—	26	4	no	—
324	M₁₆	—	26	4	no	—
325	M₁₆	—	52	2	no	—
326	M₁₆	—	52	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	2	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	13	2	no	—
338	C₂×C₈	—	13	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	2	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	26	1	no	—
343	C₂×C₈	—	26	1	no	—
344	C₂×C₈	—	26	4	no	—
345	C₂×C₈	—	52	2	no	—
346	C₂×C₈	—	52	2	no	—
347	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
348	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
349	C₂×C₈	C₄⋊#261	1	2	yes	—
350	C₂×C₈	C₂²×#261	1	2	yes	—
351	C₂×C₈	C₂²×#261	1	2	yes	—
352	C₄⋊C₄	—	26	2	no	—
353	C₄⋊C₄	—	26	2	no	—
354	C₄⋊C₄	—	26	4	no	—
355	C₄⋊C₄	—	52	2	no	—
356	C₂²⋊C₄	—	26	2	no	—
357	C₂²⋊C₄	—	26	2	no	—
358	C₂²⋊C₄	—	26	4	no	—
359	C₂²⋊C₄	—	52	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	13	2	no	—
362	C₄²	—	26	4	no	—
363	C₄²	—	26	1	no	—
364	C₄²	—	52	2	no	—
365	C₄²	C₂²×#261	1	2	yes	—
366	C₁₃	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
367	C₂³	—	13	1	no	—
368	C₂³	—	13	1	no	—
369	C₂³	—	13	1	no	—
370	C₂³	—	13	1	no	—
371	C₂³	—	13	1	no	—
372	C₂³	—	13	1	no	—
373	C₂³	—	52	2	no	—
374	C₂³	#88237	1	1	yes	characteristic
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	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	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	2	no	—
400	C₂×C₄	—	52	2	no	—
401	C₂×C₄	—	52	4	no	—
402	C₂×C₄	—	104	4	no	—
403	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
404	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
405	C₂×C₄	#88237	1	1	yes	characteristic
406	C₂×C₄	#88237	1	1	yes	characteristic
407	C₂×C₄	#88237	1	1	yes	characteristic
408	C₂×C₄	C₂³×#261	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	13	2	no	—
411	C₈	—	13	2	no	—
412	C₈	—	26	2	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	#11719060	1	1	yes	characteristic
428	C₂²	#11719060	1	1	yes	characteristic
429	C₂²	C₂×#88237	1	1	yes	characteristic
430	C₄	—	4	2	no	—
431	C₄	—	13	1	no	—
432	C₄	—	13	1	no	—
433	C₄	—	13	1	no	—
434	C₄	—	13	1	no	—
435	C₄	—	52	2	no	—
436	C₄	—	104	4	no	—
437	C₄	#11719060	1	1	yes	characteristic
438	C₄	#11719060	1	1	yes	characteristic
439	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
440	C₄	C₂×#88237	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	26	1	no	—
444	C₂	—	26	1	no	—
445	C₂	—	26	1	no	—
446	C₂	—	26	1	no	—
447	C₂	#13130755	1	2	yes	direct product factor
448	C₂	C₂×#11719060	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88237
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	#382
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1833
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. #13130755	C₂	direct (N × H)
20. C₂×C₄×C₈×C₁₃	C₄	semidirect
21. C₂×#88055	C₄	semidirect
22. C₂×C₈×Dic₁₃	C₄	semidirect
23. C₂×#88043	C₄	semidirect
24. #11718350	C₄	semidirect
73. C₄×C₈×C₁₃	C₂×C₄	semidirect
74. #88055	C₂×C₄	semidirect
75. C₈×Dic₁₃	C₂×C₄	semidirect
76. #88043	C₂×C₄	semidirect
216. C₂×C₄×C₈	#261	semidirect
292. C₄×C₈	C₂×#261	semidirect
295. C₂×C₁₃	#1833	semidirect
366. C₁₃	C₂×#1833	semidirect
447. C₂	#13130755	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×D₁₃⋊#108	2
C₂×#11719092	2
#13130755	2
C₂×#11718266	2
C₂×#11718235	2
C₂×#11718350	2
C₂×#1833	13

Subgroups — C2×#13130755 #16798163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130755 #16798163