Subgroups — C₂×#13112957 #15777874

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718901	C₂	1	2	yes	maximal
2	#13112957	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×#408	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	1	yes	characteristic, complemented
6	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂×#88180	—	2	2	no	—
8	C₁₃×#408	—	2	2	no	—
9	C₁₃×#408	C₄	1	2	yes	complemented
10	C₁₃×#408	C₂²	1	2	yes	—
11	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
12	#11718901	—	2	2	no	—
13	#11718901	—	2	2	no	—
14	#11718901	C₄	1	4	yes	complemented
15	#11718901	C₂²	1	4	yes	—
16	C₂×#88074	—	2	2	no	—
17	C₂×#88074	C₄	1	4	yes	complemented
18	C₂×C₁₃×#41	—	4	1	no	—
19	C₂×C₁₃×#41	—	4	1	no	—
20	C₂×C₁₃×#41	—	4	1	no	—
21	C₂×C₁₃×#41	—	4	1	no	—
22	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
23	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
25	C₂×C₁₃×#41	D₄	1	2	yes	—
26	C₂×C₁₃×#41	Q₈	1	1	yes	characteristic
27	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
28	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
29	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	D₄	1	2	yes	—
33	C₂×C₁₃×M₁₆	—	2	1	no	—
34	C₂×C₁₃×M₁₆	—	4	1	no	—
35	C₂×C₁₃×M₁₆	—	4	1	no	—
36	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	complemented
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₂²×C₈×C₁₃	—	2	1	no	—
40	C₂²×C₈×C₁₃	—	4	1	no	—
41	C₂²×C₈×C₁₃	—	4	1	no	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
43	C₂×C₂²⋊Dic₁₃	—	2	4	no	—
44	#88180	—	2	4	no	—
45	#88180	—	2	4	no	—
46	#88180	—	4	2	no	—
47	#88180	—	4	2	no	—
48	C₂×C₄⋊Dic₁₃	—	4	2	no	—
49	C₂×C₄×Dic₁₃	—	4	2	no	—
50	C₁₃×C₂²⋊C₈	—	2	4	no	—
51	C₁₃×C₂²⋊C₈	—	2	4	no	—
52	#88074	—	2	4	no	—
53	#88074	—	2	4	no	—
54	#88074	—	2	4	no	—
55	#88074	C₂×C₄	1	8	yes	complemented
56	C₂×#1391	—	13	1	no	maximal, Sylow
57	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
58	C₂⁴×C₁₃	C₂²⋊C₄	1	2	yes	—
59	C₁₃×#41	—	4	2	no	—
60	C₁₃×#41	—	4	2	no	—
61	C₁₃×#41	—	4	1	no	—
62	C₁₃×#41	—	4	1	no	—
63	C₁₃×#41	—	4	1	no	—
64	C₁₃×#41	—	4	1	no	—
65	C₁₃×#41	—	4	2	no	—
66	C₁₃×#41	—	4	2	no	—
67	C₁₃×#41	—	4	1	no	—
68	C₁₃×#41	—	4	1	no	—
69	C₁₃×#41	—	4	1	no	—
70	C₁₃×#41	—	4	1	no	—
71	C₂×Q₈×C₁₃	—	4	1	no	—
72	C₂×Q₈×C₁₃	—	4	1	no	—
73	C₂×Q₈×C₁₃	C₄⋊C₄	1	2	yes	—
74	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂×Q₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
76	C₂×D₄×C₁₃	—	4	2	no	—
77	C₂×D₄×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	—	4	1	no	—
79	C₂×D₄×C₁₃	—	4	1	no	—
80	C₂×D₄×C₁₃	C₄²	1	2	yes	—
81	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
82	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
83	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
84	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×Dic₁₃	—	4	4	no	—
107	C₁₃×M₁₆	—	4	2	no	—
108	C₁₃×M₁₆	—	4	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	4	2	no	—
112	C₂×C₈×C₁₃	—	4	1	no	—
113	C₂×C₈×C₁₃	—	4	1	no	—
114	C₂×C₈×C₁₃	—	4	1	no	—
115	C₂×C₈×C₁₃	—	4	1	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₂²⋊Dic₁₃	—	2	8	no	—
118	C₂²⋊Dic₁₃	—	4	4	no	—
119	C₄⋊Dic₁₃	—	4	4	no	—
120	C₄⋊Dic₁₃	—	4	4	no	—
121	C₄×Dic₁₃	—	4	4	no	—
122	C₄×Dic₁₃	—	4	4	no	—
123	C₂×#410	—	13	2	no	—
124	C₂×#408	D₁₃	1	1	yes	characteristic
125	#1391	—	13	4	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	1	no	—
128	C₂³×C₁₃	—	2	1	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	—	4	4	no	—
132	C₂³×C₁₃	#95	1	1	yes	characteristic
133	C₂³×C₁₃	#95	1	2	yes	—
134	C₂³×C₁₃	#95	1	1	yes	characteristic
135	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
136	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
137	Q₈×C₁₃	—	4	2	no	—
138	Q₈×C₁₃	—	4	1	no	—
139	Q₈×C₁₃	—	4	1	no	—
140	D₄×C₁₃	—	4	2	no	—
141	D₄×C₁₃	—	4	2	no	—
142	D₄×C₁₃	—	4	2	no	—
143	D₄×C₁₃	—	4	2	no	—
144	D₄×C₁₃	—	4	1	no	—
145	D₄×C₁₃	—	4	2	no	—
146	D₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
168	C₂×C₄×C₁₃	#95	1	2	yes	—
169	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
170	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
171	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
172	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
173	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	—	4	8	no	—
178	C₂×Dic₁₃	—	8	8	no	—
179	C₈×C₁₃	—	4	2	no	—
180	C₈×C₁₃	—	4	2	no	—
181	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
182	C₂²×M₁₆	Dic₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₈	Dic₁₃	1	1	yes	characteristic, complemented
184	C₂×#117	—	26	2	no	—
185	#410	—	13	4	no	—
186	#410	—	13	4	no	—
187	#410	—	26	2	no	—
188	#410	—	26	2	no	—
189	C₂×#99	—	13	4	no	—
190	C₂×#99	—	26	2	no	—
191	#408	—	2	2	no	—
192	#408	Dic₁₃	1	2	yes	complemented
193	#408	C₂×D₁₃	1	2	yes	—
194	C₂×C₂²⋊C₈	—	2	2	no	—
195	C₂²×C₁₃	—	2	2	no	—
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	2	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	4	1	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	4	1	no	—
203	C₂²×C₁₃	—	4	2	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	4	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	—	8	2	no	—
208	C₂²×C₁₃	#342	1	1	yes	characteristic
209	C₂²×C₁₃	#342	1	1	yes	characteristic
210	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
211	C₄×C₁₃	—	2	2	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	2	no	—
214	C₄×C₁₃	—	2	1	no	—
215	C₄×C₁₃	#342	1	1	yes	characteristic
216	C₄×C₁₃	#342	1	1	yes	characteristic
217	C₄×C₁₃	C₂×#99	1	1	yes	characteristic
218	C₄×C₁₃	C₂×#99	1	1	yes	characteristic
219	Dic₁₃	—	8	8	no	—
220	C₂×#41	—	4	1	no	—
221	C₂×#41	—	4	1	no	—
222	C₂×#41	—	4	1	no	—
223	C₂×#41	—	4	1	no	—
224	C₂×#41	Dic₂₆	1	1	yes	characteristic
225	C₂×#41	C₄×D₁₃	1	2	yes	—
226	C₂×#41	D₅₂	1	1	yes	characteristic
227	C₂×#41	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂×#41	C₂²⋊D₁₃	1	2	yes	—
229	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
230	C₂²×Q₈	Dic₂₆	1	1	yes	characteristic
231	C₂²×D₄	C₄×D₁₃	1	2	yes	—
232	C₂²×D₄	D₅₂	1	1	yes	characteristic
233	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
234	C₂³×C₄	C₂²⋊D₁₃	1	2	yes	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	4	1	no	—
237	C₂×M₁₆	—	4	1	no	—
238	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	complemented
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	4	1	no	—
243	C₂²×C₈	—	4	1	no	—
244	C₂²×C₈	C₂×Dic₁₃	1	2	yes	complemented
245	#117	—	26	4	no	—
246	#117	—	26	4	no	—
247	#117	—	52	2	no	—
248	#117	—	52	2	no	—
249	C₂×C₄⋊C₄	—	52	2	no	—
250	C₂×C₂²⋊C₄	—	26	4	no	—
251	C₂×C₄²	—	52	2	no	—
252	#99	—	13	8	no	—
253	#99	—	26	4	no	—
254	#99	—	26	4	no	—
255	#99	—	26	4	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	2	4	no	—
258	C₂×C₁₃	—	2	1	no	—
259	C₂×C₁₃	—	2	1	no	—
260	C₂×C₁₃	—	4	2	no	—
261	C₂×C₁₃	—	4	1	no	—
262	C₂×C₁₃	—	4	1	no	—
263	C₂×C₁₃	—	4	2	no	—
264	C₂×C₁₃	#1391	1	2	yes	complemented
265	C₂×C₁₃	C₂×#342	1	1	yes	characteristic
266	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
267	C₂⁴	#6103	1	2	yes	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	4	1	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	1	no	—
276	#41	—	4	2	no	—
277	#41	—	4	2	no	—
278	#41	—	4	1	no	—
279	#41	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	#6101	1	2	yes	—
283	C₂×Q₈	C₄⋊Dic₁₃	1	1	yes	characteristic
284	C₂×Q₈	C₂×Dic₂₆	1	1	yes	characteristic
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	C₄×Dic₁₃	1	2	yes	—
290	C₂×D₄	#6101	1	2	yes	—
291	C₂×D₄	C₄⋊Dic₁₃	1	1	yes	characteristic
292	C₂×D₄	#6103	1	2	yes	—
293	C₂×D₄	#6103	1	2	yes	—
294	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
295	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	52	4	no	—
305	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
306	C₂²×C₄	#6101	1	2	yes	—
307	C₂²×C₄	#6101	1	2	yes	—
308	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
310	C₂²×C₄	#6103	1	2	yes	—
311	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
312	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	2	no	—
326	C₄⋊C₄	—	52	4	no	—
327	C₄⋊C₄	—	52	4	no	—
328	C₂²⋊C₄	—	26	8	no	—
329	C₂²⋊C₄	—	52	4	no	—
330	C₄²	—	52	4	no	—
331	C₄²	—	52	4	no	—
332	C₁₃	C₂×#1391	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	2	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	#88071	1	1	yes	characteristic
340	C₂³	#88071	1	2	yes	—
341	C₂³	#88071	1	1	yes	characteristic
342	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
343	C₂³	C₂×#6103	1	2	yes	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	52	8	no	—
375	C₂×C₄	—	104	8	no	—
376	C₂×C₄	#88071	1	1	yes	characteristic
377	C₂×C₄	#88071	1	2	yes	—
378	C₂×C₄	#88071	1	1	yes	characteristic
379	C₂×C₄	#88074	1	1	yes	characteristic
380	C₂×C₄	#88074	1	1	yes	characteristic
381	C₂×C₄	#88074	1	1	yes	characteristic
382	C₂×C₄	#88074	1	1	yes	characteristic
383	C₂×C₄	C₂×#6101	1	2	yes	—
384	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	#11718118	1	1	yes	characteristic
402	C₂²	#11718118	1	1	yes	characteristic
403	C₂²	C₂×#88071	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	104	8	no	—
409	C₄	#11718118	1	1	yes	characteristic
410	C₄	#11718118	1	1	yes	characteristic
411	C₄	C₂×#88074	1	1	yes	characteristic
412	C₄	C₂×#88074	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	4	2	no	—
416	C₂	—	4	1	no	—
417	C₂	—	4	1	no	—
418	C₂	—	4	2	no	—
419	C₂	#13112957	1	2	yes	direct product factor
420	C₂	C₂×#11718118	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88074
commutator	C₂³×C₁₃	C₂×C₄²
Frattini	C₂×#41	C₂²×D₁₃
Fitting	C₂×C₁₃×#408	C₂
socle	C₂²×C₁₃	#342
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂×C₁₃×#41	C₂³
hypercenter	C₂×#408	D₁₃
hypocenter	C₁₃	C₂×#1391
LCS	G ▷ C₂³×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
2. #13112957	C₂	direct (N × H)
5. C₂²×C₁₃×M₁₆	C₄	semidirect
6. C₂³×C₈×C₁₃	C₄	semidirect
9. C₁₃×#408	C₄	semidirect
14. #11718901	C₄	semidirect
17. C₂×#88074	C₄	semidirect
36. C₂×C₁₃×M₁₆	C₂×C₄	semidirect
42. C₂²×C₈×C₁₃	C₂×C₄	semidirect
55. #88074	C₂×C₄	semidirect
182. C₂²×M₁₆	Dic₁₃	semidirect
183. C₂³×C₈	Dic₁₃	semidirect
192. #408	Dic₁₃	semidirect
238. C₂×M₁₆	C₂×Dic₁₃	semidirect
244. C₂²×C₈	C₂×Dic₁₃	semidirect
264. C₂×C₁₃	#1391	semidirect
332. C₁₃	C₂×#1391	semidirect
419. C₂	#13112957	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×#11718901	2
#13112957	2
C₂×C₁₃×#408	2
C₂×#1391	13

Subgroups — C2×#13112957 #15777874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112957 #15777874