Subgroups — C₂×#13130641 #16797170

Order 3328.

1102 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719092	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719099	C₂	1	2	yes	maximal
3	C₂²×C₈×#261	C₂	1	1	yes	maximal, characteristic
4	#13130641	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718272	C₂	1	2	yes	maximal
6	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
7	C₂×#88237	C₂²	1	2	yes	—
8	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
9	C₂²×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11719099	—	2	4	no	—
13	#11719099	C₂²	1	8	yes	—
14	#11719092	C₄	1	4	yes	complemented
15	#11719092	C₂²	1	4	yes	—
16	C₂×#88102	C₄	1	2	yes	complemented
17	C₂×#88101	C₄	1	2	yes	complemented
18	C₂×#88100	—	2	2	no	—
19	C₂×C₈×#261	—	2	2	no	—
20	C₂×C₈×#261	C₄	1	4	yes	complemented
21	C₂×C₈×#261	C₄	1	2	yes	complemented
22	C₂×C₈×#261	C₄	1	2	yes	complemented
23	C₂×C₈×#261	C₂²	1	4	yes	—
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	#11718272	C₂²	1	8	yes	—
30	C₂³×#261	—	2	1	no	—
31	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₂²⋊#261	—	2	2	no	—
33	C₂²×#1057	Q₈	1	2	yes	—
34	#88237	—	2	2	no	—
35	#88237	—	2	2	no	—
36	#88237	C₂×C₄	1	4	yes	—
37	#88237	C₂³	1	4	yes	—
38	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
39	C₂×C₄×#261	—	2	2	no	—
40	C₂×C₄×#261	—	2	1	no	—
41	C₂×C₄×#261	—	2	1	no	—
42	C₂×C₄×#261	—	2	1	no	—
43	C₂×C₄×#261	C₂×C₄	1	2	yes	—
44	C₂×C₄×#261	C₂×C₄	1	2	yes	—
45	C₂×C₄×#261	C₂³	1	2	yes	—
46	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
49	C₂×D₁₃⋊C₈	D₄	1	1	yes	characteristic
50	C₂×D₁₃⋊C₈	D₄	1	2	yes	—
51	C₂×D₁₃⋊C₈	Q₈	1	2	yes	—
52	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
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	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
70	C₂×C₈×D₁₃	C₂³	1	2	yes	—
71	#88102	C₂×C₄	1	8	yes	complemented
72	#88101	C₂×C₄	1	8	yes	complemented
73	#88100	—	2	8	no	—
74	C₈×#261	—	2	8	no	—
75	C₈×#261	C₂×C₄	1	8	yes	complemented
76	C₈×#261	C₂×C₄	1	8	yes	complemented
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×#1772	—	13	1	no	maximal, Sylow
81	C₂³×D₁₃	#41	1	1	yes	characteristic
82	C₂²×#261	—	2	8	no	—
83	C₂²×#261	—	2	2	no	—
84	C₂²×#261	—	2	2	no	—
85	C₂²×#261	—	2	2	no	—
86	C₂²×#261	—	2	4	no	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
98	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
99	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²⋊#261	—	2	4	no	—
102	C₂²⋊#261	—	2	4	no	—
103	C₂×#1057	C₄⋊C₄	1	2	yes	—
104	C₂×#1057	C₄⋊C₄	1	2	yes	—
105	C₂×#1057	C₄⋊C₄	1	4	yes	—
106	C₂×#1057	C₂×Q₈	1	4	yes	—
107	C₄⋊#261	—	2	4	no	—
108	C₄⋊#261	C₂²×C₄	1	8	yes	—
109	C₄×#261	—	2	2	no	—
110	C₄×#261	—	2	2	no	—
111	C₄×#261	—	2	4	no	—
112	C₄×#261	—	2	4	no	—
113	C₄×#261	—	2	2	no	—
114	C₄×#261	C₂²×C₄	1	4	yes	—
115	D₁₃⋊C₈	C₄⋊C₄	1	2	yes	—
116	D₁₃⋊C₈	C₄⋊C₄	1	2	yes	—
117	D₁₃⋊C₈	C₄⋊C₄	1	4	yes	—
118	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
119	D₁₃⋊C₈	C₂×D₄	1	2	yes	—
120	D₁₃⋊C₈	C₂×D₄	1	2	yes	—
121	C₁₃×M₁₆	—	2	2	no	—
122	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₄²	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	#6099	—	2	2	no	—
129	#6099	C₂²×C₄	1	4	yes	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	C₄²	1	1	yes	characteristic
132	C₂×#1055	C₄²	1	1	yes	characteristic
133	C₂×#1055	C₄²	1	2	yes	—
134	C₂×#1055	C₂²×C₄	1	2	yes	—
135	#6094	—	2	4	no	—
136	#6094	—	2	4	no	—
137	C₈×D₁₃	—	2	4	no	—
138	C₈×D₁₃	—	2	4	no	—
139	C₈×D₁₃	C₄²	1	2	yes	—
140	C₈×D₁₃	C₄²	1	2	yes	—
141	C₈×D₁₃	C₄²	1	2	yes	—
142	C₈×D₁₃	C₄²	1	2	yes	—
143	C₈×D₁₃	C₂²×C₄	1	2	yes	—
144	C₈×D₁₃	C₂²×C₄	1	2	yes	—
145	C₈×D₁₃	C₂²×C₄	1	2	yes	—
146	C₈×D₁₃	C₂²×C₄	1	2	yes	—
147	C₂²×#108	—	13	1	no	—
148	C₂×#427	—	13	1	no	—
149	C₂×#405	—	13	2	no	—
150	C₂²×C₄×C₈	—	13	1	no	—
151	#1772	—	13	8	no	—
152	C₂×#339	—	13	2	no	—
153	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
154	C₂²×D₁₃	—	2	4	no	—
155	C₂²×D₁₃	#117	1	1	yes	characteristic
156	C₂²×D₁₃	#117	1	1	yes	characteristic
157	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
160	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
161	C₂×#261	—	2	8	no	—
162	C₂×#261	—	2	8	no	—
163	C₂×#261	—	2	8	no	—
164	C₂×#261	—	2	4	no	—
165	C₂×#261	—	2	8	no	—
166	C₂×#261	—	4	8	no	—
167	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
176	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
177	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
179	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₄×D₁₃	#117	1	1	yes	characteristic
184	C₄×D₁₃	#117	1	1	yes	characteristic
185	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
186	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
187	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
188	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
189	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
190	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
191	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
192	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
193	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
195	#1057	C₂×C₄⋊C₄	1	4	yes	—
196	#1057	C₂×C₄⋊C₄	1	4	yes	—
197	C₈×C₁₃	—	2	4	no	—
198	C₈×C₁₃	C₂×C₄²	1	2	yes	—
199	C₈×C₁₃	C₂×C₄²	1	2	yes	—
200	#1055	—	2	4	no	—
201	#1055	C₂×C₄²	1	2	yes	—
202	#1055	C₂×C₄²	1	2	yes	—
203	C₂²×M₁₆	—	13	2	no	—
204	C₂³×C₈	—	13	1	no	—
205	C₂³×C₈	—	13	1	no	—
206	C₂×#117	—	13	2	no	—
207	C₂²×C₄²	—	13	1	no	—
208	C₂×#108	—	13	2	no	—
209	C₂×#108	—	13	1	no	—
210	C₂×#108	—	13	4	no	—
211	C₂×#108	—	13	4	no	—
212	C₂×#108	#261	1	1	yes	characteristic, complemented
213	#427	—	13	4	no	—
214	#427	—	13	4	no	—
215	C₂×#107	—	13	2	no	—
216	C₂×#106	—	13	2	no	—
217	#405	—	13	8	no	—
218	#405	—	26	4	no	—
219	C₂×#97	—	26	2	no	—
220	C₂×C₄×C₈	—	13	4	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	C₂×C₄×C₈	—	13	2	no	—
223	C₂×C₄×C₈	—	13	4	no	—
224	C₂×C₄×C₈	—	26	2	no	—
225	#339	—	13	8	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₂×D₁₃	—	2	2	no	—
231	C₂×D₁₃	—	2	2	no	—
232	C₂×D₁₃	—	2	2	no	—
233	C₂×D₁₃	—	2	2	no	—
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂×D₁₃	#443	1	4	yes	—
238	C₂×D₁₃	C₂×#117	1	1	yes	characteristic
239	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	#261	—	2	8	no	—
241	#261	—	4	8	no	—
242	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
243	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
244	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
245	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
246	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
247	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
248	Dic₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
250	C₂³×C₄	—	13	1	no	—
251	C₂³×C₄	—	26	1	no	—
252	C₂×M₁₆	—	13	2	no	—
253	C₂×M₁₆	—	13	4	no	—
254	C₂×M₁₆	—	13	4	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	26	2	no	—
257	C₂×M₁₆	—	26	2	no	—
258	C₂×M₁₆	C₂×#261	1	2	yes	—
259	C₂²×C₈	—	13	2	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	—	13	2	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	1	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	—	13	2	no	—
276	C₂²×C₈	—	26	2	no	—
277	C₂²×C₈	C₂×#261	1	1	yes	characteristic
278	#117	—	13	4	no	—
279	#117	—	13	4	no	—
280	#117	—	26	2	no	—
281	#117	—	26	2	no	—
282	C₂×C₄⋊C₄	—	13	4	no	—
283	C₂×C₂²⋊C₄	—	26	2	no	—
284	C₂×C₄²	—	13	2	no	—
285	C₂×C₄²	—	13	2	no	—
286	C₂×C₄²	—	13	2	no	—
287	C₂×C₄²	—	26	2	no	—
288	C₂×C₄²	—	26	1	no	—
289	C₂×C₄²	—	26	1	no	—
290	C₂×C₄²	—	26	1	no	—
291	#108	—	13	8	no	—
292	#108	—	13	4	no	—
293	#108	C₂×#261	1	4	yes	complemented
294	#107	—	13	8	no	—
295	#106	—	13	8	no	—
296	#97	—	26	8	no	—
297	C₄×C₈	—	13	8	no	—
298	C₄×C₈	—	13	8	no	—
299	C₄×C₈	—	26	8	no	—
300	C₂×C₁₃	—	2	1	no	—
301	C₂×C₁₃	—	2	1	no	—
302	C₂×C₁₃	#1772	1	2	yes	complemented
303	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
304	D₁₃	—	2	1	no	—
305	D₁₃	—	2	1	no	—
306	D₁₃	#1772	1	2	yes	complemented
307	D₁₃	C₂×#443	1	2	yes	—
308	C₂⁴	—	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	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	26	2	no	—
323	C₂²×C₄	—	26	2	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	—	26	8	no	—
326	C₂²×C₄	—	26	4	no	—
327	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
328	M₁₆	—	2	2	no	—
329	M₁₆	—	13	4	no	—
330	M₁₆	—	26	4	no	—
331	M₁₆	—	26	4	no	—
332	M₁₆	—	26	2	no	—
333	M₁₆	C₂²×#261	1	4	yes	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	13	4	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	4	no	—
341	C₂×C₈	—	13	2	no	—
342	C₂×C₈	—	13	2	no	—
343	C₂×C₈	—	13	4	no	—
344	C₂×C₈	—	13	4	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	13	2	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	13	2	no	—
352	C₂×C₈	—	13	2	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	13	2	no	—
356	C₂×C₈	—	13	2	no	—
357	C₂×C₈	—	26	4	no	—
358	C₂×C₈	—	26	4	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	C₄×#261	1	1	yes	characteristic
361	C₂×C₈	C₄×#261	1	1	yes	characteristic
362	C₂×C₈	C₄×#261	1	2	yes	—
363	C₂×C₈	C₂²×#261	1	2	yes	—
364	C₄⋊C₄	—	13	8	no	—
365	C₄⋊C₄	—	26	4	no	—
366	C₂²⋊C₄	—	26	4	no	—
367	C₂²⋊C₄	—	26	4	no	—
368	C₄²	—	13	4	no	—
369	C₄²	—	26	4	no	—
370	C₄²	—	26	2	no	—
371	C₄²	—	26	2	no	—
372	C₄²	—	26	2	no	—
373	C₄²	—	26	4	no	—
374	C₁₃	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
375	C₂³	—	13	1	no	—
376	C₂³	—	13	1	no	—
377	C₂³	—	13	1	no	—
378	C₂³	—	13	1	no	—
379	C₂³	—	13	1	no	—
380	C₂³	—	13	1	no	—
381	C₂³	—	26	4	no	—
382	C₂³	Q₈×#261	1	1	yes	characteristic
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	—	13	1	no	—
400	C₂×C₄	—	13	1	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	26	8	no	—
407	C₂×C₄	—	26	8	no	—
408	C₂×C₄	—	26	8	no	—
409	C₂×C₄	—	26	8	no	—
410	C₂×C₄	—	52	8	no	—
411	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
413	C₂×C₄	D₄×#261	1	1	yes	characteristic
414	C₂×C₄	D₄×#261	1	1	yes	characteristic
415	C₂×C₄	Q₈×#261	1	1	yes	characteristic
416	C₂×C₄	C₂³×#261	1	1	yes	characteristic
417	C₈	—	2	4	no	—
418	C₈	—	13	4	no	—
419	C₈	—	13	4	no	—
420	C₈	—	13	2	no	—
421	C₈	—	13	2	no	—
422	C₈	—	26	4	no	—
423	C₈	C₂×C₄×#261	1	2	yes	—
424	C₈	C₂×C₄×#261	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	13	1	no	—
427	C₂²	—	13	1	no	—
428	C₂²	—	13	4	no	—
429	C₂²	—	13	1	no	—
430	C₂²	—	13	1	no	—
431	C₂²	—	26	2	no	—
432	C₂²	—	26	2	no	—
433	C₂²	—	26	2	no	—
434	C₂²	—	26	2	no	—
435	C₂²	—	26	2	no	—
436	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
437	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
438	C₂²	C₂×Q₈×#261	1	1	yes	characteristic
439	C₄	—	13	1	no	—
440	C₄	—	13	1	no	—
441	C₄	—	13	1	no	—
442	C₄	—	13	1	no	—
443	C₄	—	26	8	no	—
444	C₄	—	52	8	no	—
445	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
446	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
447	C₄	C₂²×C₄×#261	1	1	yes	characteristic
448	C₄	C₂×D₄×#261	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	13	2	no	—
452	C₂	—	13	2	no	—
453	C₂	—	26	1	no	—
454	C₂	—	26	1	no	—
455	C₂	#13130641	1	2	yes	direct product factor
456	C₂	C₂×C₄⋊C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×#108	#261
hypocenter	C₁₃	C₂×#1772
LCS	G ▷ 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
4. #13130641	C₂	direct (N × H)
14. #11719092	C₄	semidirect
16. C₂×#88102	C₄	semidirect
17. C₂×#88101	C₄	semidirect
20. C₂×C₈×#261	C₄	semidirect
21. C₂×C₈×#261	C₄	semidirect
22. C₂×C₈×#261	C₄	semidirect
24. C₂×C₁₃×#108	C₄	semidirect
25. C₂×#88062	C₄	semidirect
26. C₂×#88059	C₄	semidirect
27. D₁₃×#108	C₄	semidirect
71. #88102	C₂×C₄	semidirect
72. #88101	C₂×C₄	semidirect
75. C₈×#261	C₂×C₄	semidirect
76. C₈×#261	C₂×C₄	semidirect
77. C₁₃×#108	C₂×C₄	semidirect
78. #88062	C₂×C₄	semidirect
79. #88059	C₂×C₄	semidirect
212. C₂×#108	#261	semidirect
293. #108	C₂×#261	semidirect
302. C₂×C₁₃	#1772	semidirect
306. D₁₃	#1772	semidirect
374. C₁₃	C₂×#1772	semidirect
455. C₂	#13130641	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×#11719092	2
C₂×#11719099	2
C₂²×C₈×#261	2
#13130641	2
C₂×#11718272	2
C₂×D₁₃×#108	2
C₂×#1772	13

Subgroups — C2×#13130641 #16797170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130641 #16797170