Subgroups — #23774994

Order 10112.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14579185	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099212	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098934	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098809	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098806	C₂	1	1	yes	maximal, characteristic, complemented
7	#19098766	C₂	1	1	yes	maximal, characteristic, complemented
8	#19098756	C₂	1	1	yes	maximal, characteristic, complemented
9	#19098714	C₂	1	1	yes	maximal, characteristic, complemented
10	#19098712	C₂	1	1	yes	maximal, characteristic, complemented
11	#19098708	C₂	1	1	yes	maximal, characteristic, complemented
12	#19098705	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#19098639	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×AGL(1,ℤ/8)×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11929623	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₇₉	—	2	1	no	—
18	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic
19	#14579185	—	2	4	no	—
20	C₂×#11929613	C₂²	1	1	yes	characteristic, complemented
21	C₂×#11929612	C₂²	1	1	yes	characteristic
22	C₂×#11929612	C₂²	1	1	yes	characteristic, complemented
23	C₂×#11929611	C₂²	1	1	yes	characteristic, complemented
24	C₂×#11929609	C₂²	1	1	yes	characteristic, complemented
25	C₂×#11929607	C₂²	1	1	yes	characteristic, complemented
26	#14579159	C₂²	1	1	yes	characteristic, complemented
27	#14579157	C₂²	1	1	yes	characteristic
28	#14579144	—	2	1	no	—
29	#14579142	—	2	1	no	—
30	#14579140	C₂²	1	1	yes	characteristic, complemented
31	#14579137	C₂²	1	1	yes	characteristic, complemented
32	#14579135	C₂²	1	1	yes	characteristic
33	#14579133	—	2	1	no	—
34	#14579133	—	2	1	no	—
35	#14579132	C₂²	1	1	yes	characteristic
36	#14579130	—	2	1	no	—
37	#14579129	—	2	1	no	—
38	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
39	D₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
41	C₂×Dic₇₉⋊C₄	—	2	1	no	—
42	#14579095	C₂²	1	1	yes	characteristic, complemented
43	Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#14579086	C₂²	1	1	yes	characteristic, complemented
45	#14579085	C₂²	1	1	yes	characteristic, complemented
46	#14579083	C₂²	1	1	yes	characteristic, complemented
47	#14579082	C₂²	1	1	yes	characteristic
48	#14579082	C₂²	1	1	yes	characteristic, complemented
49	#14579082	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₇₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×#41×C₇₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₇₉	C₂²	1	1	yes	characteristic
55	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
56	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×M₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₇₉	—	2	1	no	—
62	#11929623	—	2	2	no	—
63	#11929623	—	4	1	no	—
64	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
65	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₇₉	—	2	1	no	—
67	C₂×C₂²⋊D₇₉	—	2	1	no	—
68	C₂×C₂²⋊D₇₉	—	2	1	no	—
69	C₂×C₂²⋊D₇₉	—	2	1	no	—
70	C₂×C₂²⋊D₇₉	—	2	1	no	—
71	C₂×C₂²⋊D₇₉	—	2	1	no	—
72	C₂×C₂²⋊D₇₉	—	4	4	no	—
73	C₂×C₂²⋊D₇₉	D₄	1	1	yes	characteristic
74	D₄×D₇₉	—	2	2	no	—
75	D₄×D₇₉	—	4	1	no	—
76	C₂²×Dic₇₉	—	2	1	no	—
77	C₂²×Dic₇₉	—	2	1	no	—
78	C₂²×Dic₇₉	—	2	1	no	—
79	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
80	#11929613	—	2	2	no	—
81	#11929612	—	2	2	no	—
82	#11929612	—	4	1	no	—
83	#11929611	—	4	1	no	—
84	#11929609	—	2	2	no	—
85	#11929607	—	2	2	no	—
86	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
90	Dic₇₉⋊C₄	—	2	1	no	—
91	Dic₇₉⋊C₄	—	2	1	no	—
92	Dic₇₉⋊C₄	—	2	1	no	—
93	Dic₇₉⋊C₄	—	2	1	no	—
94	Dic₇₉⋊C₄	D₄	1	1	yes	characteristic
95	C₂²⋊Dic₇₉	—	2	1	no	—
96	C₂²⋊Dic₇₉	—	2	1	no	—
97	C₂²⋊Dic₇₉	—	2	1	no	—
98	C₂²⋊Dic₇₉	—	2	1	no	—
99	C₂²⋊Dic₇₉	D₄	1	1	yes	characteristic
100	(C₂×D₇₉)⋊C₄	—	2	1	no	—
101	(C₂×D₇₉)⋊C₄	—	2	1	no	—
102	(C₂×D₇₉)⋊C₄	D₄	1	1	yes	characteristic
103	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₇₉	—	2	1	no	—
105	#41×C₇₉	—	2	2	no	—
106	#41×C₇₉	—	4	1	no	—
107	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₇₉	—	2	2	no	—
109	C₂×D₄×C₇₉	—	2	1	no	—
110	C₂×D₄×C₇₉	—	2	1	no	—
111	C₂×D₄×C₇₉	—	4	1	no	—
112	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
113	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	—	2	1	no	—
116	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₇₉	—	2	2	no	—
118	SD₁₆×C₇₉	—	2	2	no	—
119	D₈×C₇₉	—	2	2	no	—
120	D₈×C₇₉	D₄	1	4	yes	complemented
121	M₁₆×C₇₉	—	2	2	no	—
122	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
124	C₂³×C₇₉	—	2	1	no	—
125	C₂³×C₇₉	—	2	1	no	—
126	C₂³×C₇₉	—	2	1	no	—
127	C₂³×C₇₉	—	4	2	no	—
128	C₂³×C₇₉	—	4	2	no	—
129	C₂³×C₇₉	—	8	1	no	—
130	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₇₉	—	2	1	no	—
132	C₂²×D₇₉	—	4	2	no	—
133	C₂²×D₇₉	—	4	2	no	—
134	C₂²×D₇₉	—	8	1	no	—
135	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₇₉	—	2	1	no	—
137	Q₈×C₇₉	—	2	1	no	—
138	D₄×C₇₉	—	2	1	no	—
139	D₄×C₇₉	—	2	1	no	—
140	D₄×C₇₉	—	2	1	no	—
141	D₄×C₇₉	—	2	1	no	—
142	D₄×C₇₉	—	4	2	no	—
143	D₄×C₇₉	—	4	2	no	—
144	D₄×C₇₉	C₂×D₄	1	2	yes	—
145	D₄×C₇₉	C₂×D₄	1	2	yes	complemented
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
152	C₂²⋊D₇₉	—	2	2	no	—
153	C₂²⋊D₇₉	—	4	2	no	—
154	C₂²⋊D₇₉	—	4	2	no	—
155	C₂²⋊D₇₉	—	4	2	no	—
156	C₂²⋊D₇₉	—	4	2	no	—
157	C₂²⋊D₇₉	—	4	2	no	—
158	C₂²⋊D₇₉	—	8	1	no	—
159	C₂×Dic₇₉	—	2	1	no	—
160	C₂×Dic₇₉	—	2	1	no	—
161	C₂×Dic₇₉	—	2	1	no	—
162	C₂×Dic₇₉	—	4	2	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	2	no	—
165	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
167	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
168	D₃₁₆	—	2	1	no	—
169	D₃₁₆	—	2	1	no	—
170	C₄×D₇₉	—	2	1	no	—
171	C₄×D₇₉	—	2	1	no	—
172	Dic₁₅₈	—	2	1	no	—
173	Dic₁₅₈	—	2	1	no	—
174	C₈×C₇₉	—	2	1	no	—
175	C₈×C₇₉	C₂×D₄	1	2	yes	complemented
176	C₇₉⋊C₈	—	2	1	no	—
177	C₇₉⋊C₈	—	2	1	no	—
178	C₂²×C₇₉	—	2	2	no	—
179	C₂²×C₇₉	—	2	2	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	1	no	—
182	C₂²×C₇₉	—	2	1	no	—
183	C₂²×C₇₉	—	4	1	no	—
184	C₂²×C₇₉	—	4	1	no	—
185	C₂²×C₇₉	—	4	1	no	—
186	C₂²×C₇₉	—	4	1	no	—
187	C₂²×C₇₉	—	4	1	no	—
188	C₂²×C₇₉	—	4	1	no	—
189	C₂²×C₇₉	—	4	1	no	—
190	C₂²×C₇₉	—	8	4	no	—
191	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₇₉	—	2	1	no	—
193	C₂×D₇₉	—	2	1	no	—
194	C₂×D₇₉	—	2	1	no	—
195	C₂×D₇₉	—	4	1	no	—
196	C₂×D₇₉	—	4	1	no	—
197	C₂×D₇₉	—	4	1	no	—
198	C₂×D₇₉	—	8	4	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	4	1	no	—
201	C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₇₉	—	2	1	no	—
204	Dic₇₉	—	2	1	no	—
205	Dic₇₉	—	4	1	no	—
206	Dic₇₉	—	4	1	no	—
207	Dic₇₉	—	4	1	no	—
208	Dic₇₉	AGL(1,ℤ/8)	1	2	yes	complemented
209	C₂×C₇₉	—	4	2	no	—
210	C₂×C₇₉	—	4	1	no	—
211	C₂×C₇₉	—	4	2	no	—
212	C₂×C₇₉	—	8	1	no	—
213	C₂×C₇₉	D₄²	1	1	yes	characteristic
214	C₂×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₇₉	#577	1	1	yes	characteristic
216	D₇₉	—	4	1	no	—
217	D₇₉	—	8	1	no	—
218	#3272	—	79	1	no	maximal, Sylow
219	C₇₉	#3272	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	79	1	no	—
221	C₂×AGL(1,ℤ/8)	D₇₉	1	1	yes	characteristic, complemented
222	#547	—	79	1	no	—
223	D₄²	—	79	1	no	—
224	#492	—	79	1	no	—
225	#468	—	79	1	no	—
226	#468	—	79	1	no	—
227	#461	—	79	1	no	—
228	#459	—	79	1	no	—
229	#450	—	79	1	no	—
230	#450	—	79	1	no	—
231	#449	—	79	1	no	—
232	#449	—	79	1	no	—
233	C₄×D₈	—	79	1	no	—
234	#436	—	79	1	no	—
235	C₂×#41	—	79	1	no	—
236	C₂×#41	C₂×D₇₉	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	79	1	no	—
238	C₂²×D₄	—	158	1	no	—
239	C₂²×D₄	C₂×D₇₉	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	2	4	no	—
241	AGL(1,ℤ/8)	—	158	4	no	—
242	C₂×SD₁₆	—	79	1	no	—
243	C₂×SD₁₆	—	79	1	no	—
244	C₂×SD₁₆	—	79	1	no	—
245	C₂×SD₁₆	—	79	1	no	—
246	C₂×SD₁₆	C₂×D₇₉	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
248	C₂×D₈	—	79	1	no	—
249	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
250	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic, complemented
251	C₂×M₁₆	—	79	1	no	—
252	C₂×M₁₆	C₂×D₇₉	1	1	yes	characteristic, complemented
253	C₄⋊Q₈	—	79	1	no	—
254	#127	—	79	1	no	—
255	#123	—	158	1	no	—
256	#123	—	158	1	no	—
257	C₂²⋊Q₈	—	79	1	no	—
258	C₂²⋊Q₈	—	79	1	no	—
259	#121	—	79	1	no	—
260	#121	—	79	1	no	—
261	#121	—	158	1	no	—
262	#121	—	158	1	no	—
263	#120	—	158	1	no	—
264	#120	—	158	1	no	—
265	C₄×D₄	—	79	1	no	—
266	C₄×D₄	—	79	1	no	—
267	C₄×D₄	—	79	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	#107	—	79	1	no	—
270	C₄⋊C₈	—	79	1	no	—
271	#103	—	79	1	no	—
272	#103	—	79	1	no	—
273	#102	—	79	1	no	—
274	#102	—	79	1	no	—
275	#102	—	79	1	no	—
276	#102	—	79	1	no	—
277	C₂²⋊C₈	—	79	1	no	—
278	C₂²⋊C₈	—	79	1	no	—
279	C₄×C₈	—	79	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	158	1	no	—
282	#41	—	2	2	no	—
283	#41	—	4	1	no	—
284	#41	—	316	1	no	—
285	#41	—	158	2	no	—
286	C₂×Q₈	—	79	1	no	—
287	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	316	4	no	—
293	C₂×D₄	—	316	1	no	—
294	C₂×D₄	—	79	1	no	—
295	C₂×D₄	—	79	1	no	—
296	C₂×D₄	—	158	1	no	—
297	C₂×D₄	—	158	1	no	—
298	C₂×D₄	—	158	1	no	—
299	C₂×D₄	—	158	1	no	—
300	C₂×D₄	—	158	1	no	—
301	C₂×D₄	—	158	1	no	—
302	C₂×D₄	—	158	2	no	—
303	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
304	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	79	1	no	—
308	C₂²×C₄	—	158	1	no	—
309	C₂²×C₄	—	158	1	no	—
310	C₂²×C₄	—	158	1	no	—
311	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	316	1	no	—
315	SD₁₆	—	316	1	no	—
316	SD₁₆	—	158	2	no	—
317	SD₁₆	—	158	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	158	2	no	—
320	D₈	C₂²⋊D₇₉	1	4	yes	complemented
321	M₁₆	—	2	2	no	—
322	M₁₆	—	158	2	no	—
323	C₂×C₈	—	79	1	no	—
324	C₂×C₈	—	79	1	no	—
325	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
327	C₄⋊C₄	—	79	1	no	—
328	C₄⋊C₄	—	79	1	no	—
329	C₄⋊C₄	—	79	1	no	—
330	C₄⋊C₄	—	158	1	no	—
331	C₄⋊C₄	—	158	1	no	—
332	C₄⋊C₄	—	158	1	no	—
333	C₄⋊C₄	—	158	1	no	—
334	C₂²⋊C₄	—	79	1	no	—
335	C₂²⋊C₄	—	79	1	no	—
336	C₂²⋊C₄	—	158	1	no	—
337	C₂²⋊C₄	—	158	1	no	—
338	C₂²⋊C₄	—	158	1	no	—
339	C₂²⋊C₄	—	158	1	no	—
340	C₂²⋊C₄	—	158	1	no	—
341	C₂²⋊C₄	—	158	1	no	—
342	C₄²	—	79	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	316	2	no	—
350	C₂³	—	316	2	no	—
351	C₂³	—	79	1	no	—
352	C₂³	—	632	1	no	—
353	C₂³	—	158	1	no	—
354	C₂³	D₄×D₇₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	158	1	no	—
358	Q₈	—	158	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	316	2	no	—
366	D₄	—	316	2	no	—
367	D₄	—	316	2	no	—
368	D₄	—	316	2	no	—
369	D₄	—	316	2	no	—
370	D₄	—	632	1	no	—
371	D₄	—	158	2	no	—
372	D₄	—	158	1	no	—
373	D₄	—	158	1	no	—
374	D₄	C₂×C₂²⋊D₇₉	1	2	yes	—
375	D₄	C₂×C₂²⋊D₇₉	1	2	yes	complemented
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	316	2	no	—
383	C₂×C₄	—	79	1	no	—
384	C₂×C₄	—	79	1	no	—
385	C₂×C₄	—	79	1	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	1	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	158	1	no	—
395	C₈	—	158	1	no	—
396	C₈	C₂×C₂²⋊D₇₉	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	8	4	no	—
410	C₂²	—	316	1	no	—
411	C₂²	—	316	1	no	—
412	C₂²	—	316	1	no	—
413	C₂²	—	632	4	no	—
414	C₂²	—	158	1	no	—
415	C₂²	—	158	1	no	—
416	C₂²	—	158	1	no	—
417	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	316	1	no	—
421	C₄	—	316	1	no	—
422	C₄	—	316	1	no	—
423	C₄	—	79	2	no	—
424	C₄	—	158	1	no	—
425	C₄	—	158	1	no	—
426	C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
427	C₄	#14579206	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	1	no	—
432	C₂	—	316	1	no	—
433	C₂	—	632	1	no	—
434	C₂	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
436	C₂	#19099373	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	C₂×AGL(1,ℤ/8)×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₇₉
hypocenter	C₇₉	#3272
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#14579185	C₂	semidirect
2. #19099212	C₂	semidirect
3. D₄×C₂²⋊D₇₉	C₂	semidirect
4. #19098934	C₂	semidirect
5. #19098809	C₂	semidirect
6. #19098806	C₂	semidirect
7. #19098766	C₂	semidirect
8. #19098756	C₂	semidirect
9. #19098714	C₂	semidirect
10. #19098712	C₂	semidirect
11. #19098708	C₂	semidirect
12. #19098705	C₂	semidirect
13. D₈×Dic₇₉	C₂	semidirect
14. #19098639	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₇₉	C₂	semidirect
16. C₂×#11929623	C₂²	semidirect
20. C₂×#11929613	C₂²	semidirect
22. C₂×#11929612	C₂²	semidirect
23. C₂×#11929611	C₂²	semidirect
24. C₂×#11929609	C₂²	semidirect
25. C₂×#11929607	C₂²	semidirect
26. #14579159	C₂²	semidirect
30. #14579140	C₂²	semidirect
31. #14579137	C₂²	semidirect
39. D₄×Dic₇₉	C₂²	semidirect
42. #14579095	C₂²	semidirect
43. Dic₇₉⋊C₈	C₂²	semidirect
44. #14579086	C₂²	semidirect
45. #14579085	C₂²	semidirect
46. #14579083	C₂²	semidirect
48. #14579082	C₂²	semidirect
49. #14579082	C₂²	semidirect
50. C₂²⋊(C₇₉⋊C₈)	C₂²	semidirect
51. (C₂×D₇₉)⋊C₈	C₂²	semidirect
52. C₈×Dic₇₉	C₂²	semidirect
53. C₂×#41×C₇₉	C₂²	semidirect
57. C₂×SD₁₆×C₇₉	C₂²	semidirect
59. C₂×D₈×C₇₉	C₂²	semidirect
60. C₂×M₁₆×C₇₉	C₂²	semidirect
120. D₈×C₇₉	D₄	semidirect
145. D₄×C₇₉	C₂×D₄	semidirect
175. C₈×C₇₉	C₂×D₄	semidirect
208. Dic₇₉	AGL(1,ℤ/8)	semidirect
219. C₇₉	#3272	semidirect
221. C₂×AGL(1,ℤ/8)	D₇₉	semidirect
236. C₂×#41	C₂×D₇₉	semidirect
247. C₂×SD₁₆	C₂×D₇₉	semidirect
250. C₂×D₈	C₂×D₇₉	semidirect
252. C₂×M₁₆	C₂×D₇₉	semidirect
320. D₈	C₂²⋊D₇₉	semidirect
375. D₄	C₂×C₂²⋊D₇₉	semidirect
396. C₈	C₂×C₂²⋊D₇₉	semidirect