Subgroups — #2222×D₇₉ #34442828

Order 20224.

638 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#473×D₇₉	C₂	1	2	yes	maximal
4	#23765526	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765525	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765524	C₂	1	2	yes	maximal, complemented
7	#23765523	C₂	1	2	yes	maximal, complemented
8	#23765522	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#362×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#2222	C₂	1	1	yes	maximal, characteristic, complemented
12	#137×D₇₉	—	2	2	no	—
13	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	—
14	#131×D₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₆₃₂	C₂²	1	1	yes	characteristic, complemented
16	C₂×#14579107	C₂²	1	2	yes	complemented
17	Q₃₂×D₇₉	—	2	1	no	—
18	Q₃₂×D₇₉	—	2	1	no	—
19	Q₃₂×D₇₉	—	2	1	no	—
20	Q₃₂×D₇₉	—	2	1	no	—
21	#19098981	—	2	1	no	—
22	#19098981	C₂²	1	1	yes	characteristic
23	#19098980	C₂²	1	1	yes	characteristic
24	#19098979	—	2	1	no	—
25	#19098979	C₂²	1	1	yes	characteristic
26	M₃₂×D₇₉	—	2	1	no	—
27	M₃₂×D₇₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₇₉	—	2	1	no	—
29	C₂×C₁₆×D₇₉	C₂²	1	1	yes	characteristic
30	#19098839	C₂²	1	2	yes	—
31	#19098838	C₂²	1	2	yes	—
32	#19098837	—	2	2	no	—
33	#19098836	—	2	2	no	—
34	#19098835	C₂²	1	2	yes	—
35	#108×D₇₉	C₂²	1	2	yes	—
36	#101×D₇₉	—	2	2	no	—
37	#19098393	C₂²	1	1	yes	characteristic, complemented
38	#19098392	C₂²	1	2	yes	complemented
39	#19098380	C₂²	1	2	yes	complemented
40	#19098379	C₂²	1	2	yes	complemented
41	#19098378	C₂²	1	2	yes	complemented
42	C₂×Q₃₂×C₇₉	C₂²	1	1	yes	characteristic, complemented
43	#504×C₇₉	C₂²	1	1	yes	characteristic
44	#473×C₇₉	C₂²	1	2	yes	—
45	#368×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#362×C₇₉	C₂²	1	2	yes	complemented
47	#41×D₇₉	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₇₉	—	2	2	no	—
49	#14579194	—	2	2	no	—
50	#14579193	—	4	2	no	—
51	#14579192	—	2	2	no	—
52	#14579191	—	2	2	no	—
53	#14579190	—	4	2	no	—
54	C₂×Dic₃₁₆	C₂³	1	2	yes	—
55	C₂×#11929614	—	2	2	no	—
56	Q₁₆×D₇₉	—	2	2	no	—
57	Q₁₆×D₇₉	—	2	2	no	—
58	Q₁₆×D₇₉	—	2	2	no	—
59	Q₁₆×D₇₉	—	2	2	no	—
60	Q₁₆×D₇₉	—	4	2	no	—
61	SD₁₆×D₇₉	—	4	2	no	—
62	#14579169	—	2	1	no	—
63	#14579169	D₄	1	1	yes	characteristic
64	#14579168	D₄	1	1	yes	characteristic
65	#14579167	—	2	1	no	—
66	#14579167	C₂³	1	1	yes	characteristic
67	M₁₆×D₇₉	—	2	1	no	—
68	M₁₆×D₇₉	—	2	2	no	—
69	M₁₆×D₇₉	D₄	1	1	yes	characteristic
70	C₂×C₈×D₇₉	—	2	1	no	—
71	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
72	Dic₆₃₂	—	2	1	no	—
73	Dic₆₃₂	—	2	1	no	—
74	#14579107	—	2	2	no	—
75	#14579107	—	2	2	no	—
76	#14579101	—	2	1	no	—
77	#14579101	C₂³	1	1	yes	characteristic
78	#14579100	—	2	1	no	—
79	#14579100	—	2	1	no	—
80	#14579100	—	2	1	no	—
81	C₂×C₇₉⋊C₁₆	—	2	1	no	—
82	C₂×C₇₉⋊C₁₆	C₂³	1	1	yes	characteristic
83	C₁₆×D₇₉	—	2	1	no	—
84	C₁₆×D₇₉	—	2	1	no	—
85	C₁₆×D₇₉	—	2	1	no	—
86	C₁₆×D₇₉	D₄	1	1	yes	characteristic
87	C₁₆×D₇₉	D₄	1	1	yes	characteristic
88	C₁₆×D₇₉	D₄	1	1	yes	characteristic
89	C₁₆×D₇₉	D₄	1	1	yes	characteristic
90	#14579097	C₂³	1	2	yes	—
91	#14579096	—	2	2	no	—
92	#14579080	—	2	2	no	—
93	#14579079	—	2	2	no	—
94	#14579079	—	2	2	no	—
95	#137×C₇₉	—	2	2	no	—
96	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
97	#131×C₇₉	C₂³	1	1	yes	characteristic
98	Q₃₂×C₇₉	—	2	1	no	—
99	Q₃₂×C₇₉	—	2	1	no	—
100	M₃₂×C₇₉	—	2	1	no	—
101	M₃₂×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₇₉	—	2	1	no	—
103	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
104	#108×C₇₉	C₂³	1	2	yes	—
105	#101×C₇₉	—	2	2	no	—
106	#11929625	D₈	1	1	yes	characteristic
107	#11929624	—	2	1	no	—
108	#11929624	C₂×D₄	1	1	yes	characteristic
109	#11929623	—	2	1	no	—
110	#11929623	D₈	1	1	yes	characteristic
111	C₂×Dic₁₅₈	—	2	2	no	—
112	C₂×Dic₁₅₈	—	4	2	no	—
113	Q₈×D₇₉	—	4	2	no	—
114	Q₈×D₇₉	—	4	2	no	—
115	Q₈×D₇₉	—	4	2	no	—
116	Q₈×D₇₉	—	4	2	no	—
117	Q₈×D₇₉	D₈	1	1	yes	characteristic
118	D₄×D₇₉	—	2	1	no	—
119	D₄×D₇₉	D₈	1	1	yes	characteristic
120	C₂×C₄×D₇₉	—	2	1	no	—
121	C₂×C₄×D₇₉	—	4	2	no	—
122	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
123	Dic₃₁₆	—	2	2	no	—
124	Dic₃₁₆	—	2	2	no	—
125	Dic₃₁₆	—	4	2	no	—
126	#11929614	—	4	2	no	—
127	#11929614	—	4	2	no	—
128	#11929614	—	4	2	no	—
129	#11929614	—	4	2	no	—
130	#11929613	—	4	2	no	—
131	#11929612	—	4	2	no	—
132	#11929611	—	4	2	no	—
133	#11929608	—	2	1	no	—
134	#11929608	—	2	2	no	—
135	#11929608	C₂×D₄	1	1	yes	characteristic
136	#11929607	—	2	1	no	—
137	#11929607	—	2	1	no	—
138	#11929607	—	2	1	no	—
139	#11929607	—	4	2	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₈×D₇₉	—	2	1	no	—
143	C₈×D₇₉	—	2	1	no	—
144	C₈×D₇₉	—	2	1	no	—
145	C₈×D₇₉	—	4	2	no	—
146	C₈×D₇₉	C₂×D₄	1	1	yes	characteristic
147	C₈×D₇₉	C₂×D₄	1	1	yes	characteristic
148	C₈×D₇₉	#41	1	1	yes	characteristic
149	C₈×D₇₉	#41	1	1	yes	characteristic
150	C₇₉⋊C₁₆	—	2	1	no	—
151	C₇₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
152	C₇₉⋊C₁₆	C₂×D₄	1	1	yes	characteristic
153	#41×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×Q₈×C₇₉	—	2	2	no	—
155	Q₁₆×C₇₉	—	2	2	no	—
156	Q₁₆×C₇₉	—	2	2	no	—
157	Q₁₆×C₇₉	—	4	2	no	—
158	SD₁₆×C₇₉	—	4	2	no	—
159	M₁₆×C₇₉	—	2	1	no	—
160	M₁₆×C₇₉	—	2	2	no	—
161	M₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₇₉	—	2	1	no	—
163	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₁₆×C₇₉	—	2	1	no	—
165	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×D₇₉	—	2	1	no	—
168	C₂²×D₇₉	#135	1	1	yes	characteristic
169	Q₈×C₇₉	—	4	2	no	—
170	Q₈×C₇₉	—	4	2	no	—
171	Q₈×C₇₉	C₂×D₈	1	1	yes	characteristic
172	D₄×C₇₉	—	2	1	no	—
173	D₄×C₇₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₉	—	2	1	no	—
175	C₂×C₄×C₇₉	—	4	2	no	—
176	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
177	C₂²⋊D₇₉	—	2	1	no	—
178	C₂²⋊D₇₉	—	2	1	no	—
179	C₂²⋊D₇₉	—	2	1	no	—
180	C₂×Dic₇₉	—	2	1	no	—
181	C₂×Dic₇₉	—	4	2	no	—
182	C₂×Dic₇₉	#135	1	1	yes	characteristic
183	D₃₁₆	—	2	1	no	—
184	D₃₁₆	C₂×D₈	1	1	yes	characteristic
185	C₄×D₇₉	—	2	1	no	—
186	C₄×D₇₉	—	2	1	no	—
187	C₄×D₇₉	—	2	1	no	—
188	C₄×D₇₉	—	8	2	no	—
189	C₄×D₇₉	—	8	2	no	—
190	C₄×D₇₉	#121	1	1	yes	characteristic
191	C₄×D₇₉	#121	1	1	yes	characteristic
192	C₄×D₇₉	C₂×D₈	1	1	yes	characteristic
193	C₄×D₇₉	C₂×D₈	1	1	yes	characteristic
194	Dic₁₅₈	—	2	1	no	—
195	Dic₁₅₈	—	4	2	no	—
196	Dic₁₅₈	—	4	2	no	—
197	Dic₁₅₈	—	8	2	no	—
198	Dic₁₅₈	—	8	2	no	—
199	Dic₁₅₈	C₂×D₈	1	1	yes	characteristic
200	C₈×C₇₉	—	2	1	no	—
201	C₈×C₇₉	—	4	2	no	—
202	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
204	C₇₉⋊C₈	—	2	1	no	—
205	C₇₉⋊C₈	—	4	2	no	—
206	C₇₉⋊C₈	#121	1	1	yes	characteristic
207	C₇₉⋊C₈	#121	1	1	yes	characteristic
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
210	C₂×D₇₉	—	2	2	no	—
211	C₂×D₇₉	—	2	1	no	—
212	C₂×D₇₉	—	4	2	no	—
213	C₂×D₇₉	#466	1	1	yes	characteristic
214	C₂×D₇₉	#466	1	1	yes	characteristic
215	C₄×C₇₉	—	2	1	no	—
216	C₄×C₇₉	—	8	2	no	—
217	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
218	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
219	Dic₇₉	—	2	1	no	—
220	Dic₇₉	—	8	2	no	—
221	Dic₇₉	#466	1	1	yes	characteristic
222	Dic₇₉	#466	1	1	yes	characteristic
223	C₂×#2222	—	79	1	no	maximal, Sylow
224	C₂×C₇₉	—	2	1	no	—
225	C₂×C₇₉	—	4	1	no	—
226	C₂×C₇₉	C₂×#466	1	1	yes	characteristic
227	D₇₉	—	2	1	no	—
228	D₇₉	—	4	1	no	—
229	D₇₉	#2222	1	2	yes	direct product factor
230	C₂²×Q₃₂	—	79	1	no	—
231	C₂×#504	—	79	1	no	—
232	C₂×#473	—	79	2	no	—
233	#2222	—	79	1	no	—
234	#2222	—	79	1	no	—
235	#2222	—	79	2	no	—
236	#2222	—	79	1	no	—
237	#2222	—	79	2	no	—
238	#2222	D₇₉	1	1	yes	characteristic, direct product factor
239	C₂×#368	—	79	1	no	—
240	C₂×#362	—	79	2	no	—
241	C₇₉	C₂×#2222	1	1	yes	characteristic, complemented, Sylow
242	C₂×#137	—	158	2	no	—
243	C₂²×Q₁₆	—	79	2	no	—
244	C₂×#131	—	79	1	no	—
245	C₂×Q₃₂	—	79	2	no	—
246	C₂×Q₃₂	—	79	1	no	—
247	C₂×Q₃₂	—	158	1	no	—
248	C₂×Q₃₂	—	158	1	no	—
249	C₂×Q₃₂	—	158	1	no	—
250	C₂×Q₃₂	—	158	1	no	—
251	C₂×Q₃₂	C₂×D₇₉	1	1	yes	characteristic, complemented
252	#504	—	79	1	no	—
253	#504	—	79	1	no	—
254	#504	—	79	1	no	—
255	#504	—	158	1	no	—
256	#504	—	158	1	no	—
257	#504	C₂×D₇₉	1	1	yes	characteristic
258	C₂×M₃₂	—	79	1	no	—
259	C₂×M₃₂	—	158	1	no	—
260	C₂²×C₁₆	—	79	1	no	—
261	C₂²×C₁₆	—	158	1	no	—
262	#473	—	79	2	no	—
263	#473	—	79	2	no	—
264	#473	—	79	2	no	—
265	#473	—	158	2	no	—
266	#473	—	158	2	no	—
267	#473	C₂×D₇₉	1	2	yes	—
268	C₂×#108	—	79	2	no	—
269	C₂×#101	—	158	2	no	—
270	#368	—	79	1	no	—
271	#368	—	79	2	no	—
272	#368	C₂×D₇₉	1	1	yes	characteristic, complemented
273	#362	—	79	2	no	—
274	#362	—	79	2	no	—
275	#362	—	79	2	no	—
276	#362	C₂×D₇₉	1	2	yes	complemented
277	C₂×#41	—	79	1	no	—
278	C₂²×Q₈	—	158	2	no	—
279	#137	—	2	2	no	—
280	#137	—	316	2	no	—
281	#137	—	316	2	no	—
282	#137	—	158	2	no	—
283	#137	—	158	2	no	—
284	#137	—	158	2	no	—
285	C₂×Q₁₆	—	316	2	no	—
286	C₂×Q₁₆	—	79	2	no	—
287	C₂×Q₁₆	—	158	2	no	—
288	C₂×Q₁₆	—	158	2	no	—
289	C₂×Q₁₆	—	158	2	no	—
290	C₂×Q₁₆	—	158	2	no	—
291	C₂×Q₁₆	—	158	2	no	—
292	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
293	C₂×SD₁₆	—	316	2	no	—
294	#131	—	79	1	no	—
295	#131	—	79	1	no	—
296	#131	—	79	1	no	—
297	#131	—	158	1	no	—
298	#131	—	158	1	no	—
299	#131	C₂²×D₇₉	1	1	yes	characteristic
300	C₂×M₁₆	—	79	1	no	—
301	C₂×M₁₆	—	158	2	no	—
302	C₂×M₁₆	—	158	1	no	—
303	C₂²×C₈	—	79	1	no	—
304	C₂²×C₈	—	158	1	no	—
305	Q₃₂	—	2	1	no	—
306	Q₃₂	—	2	1	no	—
307	Q₃₂	—	158	2	no	—
308	Q₃₂	—	158	2	no	—
309	Q₃₂	—	158	1	no	—
310	Q₃₂	—	158	1	no	—
311	M₃₂	—	2	1	no	—
312	M₃₂	—	79	1	no	—
313	M₃₂	—	158	1	no	—
314	M₃₂	—	158	1	no	—
315	M₃₂	—	158	1	no	—
316	M₃₂	—	158	1	no	—
317	M₃₂	C₂²×D₇₉	1	1	yes	characteristic
318	C₂×C₁₆	—	2	1	no	—
319	C₂×C₁₆	—	79	1	no	—
320	C₂×C₁₆	—	79	1	no	—
321	C₂×C₁₆	—	79	1	no	—
322	C₂×C₁₆	—	79	1	no	—
323	C₂×C₁₆	—	79	1	no	—
324	C₂×C₁₆	—	158	1	no	—
325	C₂×C₁₆	—	158	1	no	—
326	C₂×C₁₆	—	158	1	no	—
327	C₂×C₁₆	—	158	1	no	—
328	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
329	#108	—	79	2	no	—
330	#108	—	158	2	no	—
331	#108	C₂²×D₇₉	1	2	yes	—
332	#101	—	2	2	no	—
333	#101	—	158	2	no	—
334	#101	—	158	2	no	—
335	#101	—	158	2	no	—
336	#41	—	79	1	no	—
337	#41	—	79	1	no	—
338	#41	—	79	1	no	—
339	#41	—	158	1	no	—
340	#41	—	158	1	no	—
341	#41	D₄×D₇₉	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	316	2	no	—
344	C₂×Q₈	—	316	2	no	—
345	C₂×Q₈	—	316	2	no	—
346	C₂×Q₈	—	316	2	no	—
347	C₂×Q₈	—	316	2	no	—
348	C₂×Q₈	—	79	1	no	—
349	C₂×Q₈	—	158	2	no	—
350	C₂×D₄	—	79	1	no	—
351	C₂×D₄	—	158	1	no	—
352	C₂²×C₄	—	316	2	no	—
353	C₂²×C₄	—	79	1	no	—
354	C₂²×C₄	—	158	1	no	—
355	Q₁₆	—	2	2	no	—
356	Q₁₆	—	2	2	no	—
357	Q₁₆	—	4	2	no	—
358	Q₁₆	—	316	2	no	—
359	Q₁₆	—	316	2	no	—
360	Q₁₆	—	316	2	no	—
361	Q₁₆	—	316	2	no	—
362	Q₁₆	—	316	2	no	—
363	Q₁₆	—	158	2	no	—
364	Q₁₆	—	158	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	316	2	no	—
367	SD₁₆	—	316	2	no	—
368	SD₁₆	—	316	2	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	316	2	no	—
372	M₁₆	—	79	1	no	—
373	M₁₆	—	158	1	no	—
374	M₁₆	—	158	1	no	—
375	M₁₆	—	158	2	no	—
376	M₁₆	—	158	1	no	—
377	M₁₆	—	158	1	no	—
378	M₁₆	D₄×D₇₉	1	1	yes	characteristic
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	316	2	no	—
381	C₂×C₈	—	79	1	no	—
382	C₂×C₈	—	79	1	no	—
383	C₂×C₈	—	79	1	no	—
384	C₂×C₈	—	79	1	no	—
385	C₂×C₈	—	79	1	no	—
386	C₂×C₈	—	158	1	no	—
387	C₂×C₈	—	158	1	no	—
388	C₂×C₈	—	158	1	no	—
389	C₂×C₈	—	158	1	no	—
390	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
391	C₁₆	—	2	1	no	—
392	C₁₆	—	79	1	no	—
393	C₁₆	—	79	1	no	—
394	C₁₆	—	158	1	no	—
395	C₁₆	D₄×D₇₉	1	1	yes	characteristic
396	C₁₆	D₄×D₇₉	1	1	yes	characteristic
397	C₂³	—	79	1	no	—
398	C₂³	—	158	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	316	2	no	—
402	Q₈	—	316	2	no	—
403	Q₈	—	79	1	no	—
404	Q₈	—	632	2	no	—
405	Q₈	—	632	2	no	—
406	Q₈	—	158	1	no	—
407	Q₈	D₈×D₇₉	1	1	yes	characteristic
408	D₄	—	2	1	no	—
409	D₄	—	79	1	no	—
410	D₄	—	158	1	no	—
411	D₄	—	158	1	no	—
412	D₄	—	158	1	no	—
413	D₄	—	158	1	no	—
414	D₄	D₈×D₇₉	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	316	2	no	—
418	C₂×C₄	—	79	1	no	—
419	C₂×C₄	—	79	1	no	—
420	C₂×C₄	—	79	1	no	—
421	C₂×C₄	—	79	1	no	—
422	C₂×C₄	—	79	1	no	—
423	C₂×C₄	—	632	2	no	—
424	C₂×C₄	—	632	2	no	—
425	C₂×C₄	—	158	1	no	—
426	C₂×C₄	—	158	1	no	—
427	C₂×C₄	—	158	1	no	—
428	C₂×C₄	—	158	1	no	—
429	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	316	2	no	—
433	C₈	—	79	1	no	—
434	C₈	—	79	1	no	—
435	C₈	—	158	1	no	—
436	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
437	C₈	#41×D₇₉	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	316	2	no	—
440	C₂²	—	79	1	no	—
441	C₂²	—	79	1	no	—
442	C₂²	—	158	2	no	—
443	C₂²	—	158	1	no	—
444	C₂²	#135×D₇₉	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	79	1	no	—
448	C₄	—	79	1	no	—
449	C₄	—	632	2	no	—
450	C₄	—	158	1	no	—
451	C₄	#121×D₇₉	1	1	yes	characteristic
452	C₄	C₂×D₈×D₇₉	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	4	1	no	—
455	C₂	—	316	1	no	—
456	C₂	—	79	2	no	—
457	C₂	—	158	1	no	—
458	C₂	#466×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2222	C₂
socle	C₂×C₇₉	C₂×#466
prime radical	#41×D₇₉	D₄
hypercenter	#2222	D₇₉
hypocenter	C₇₉	C₂×#2222
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2222

Complements

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

N	H ≅ G/N	type
1. C₂×Q₃₂×D₇₉	C₂	semidirect
4. #23765526	C₂	semidirect
5. #23765525	C₂	semidirect
6. #23765524	C₂	semidirect
7. #23765523	C₂	semidirect
8. #23765522	C₂	semidirect
9. #368×D₇₉	C₂	semidirect
10. #362×D₇₉	C₂	semidirect
11. C₇₉×#2222	C₂	semidirect
15. C₂×Dic₆₃₂	C₂²	semidirect
16. C₂×#14579107	C₂²	semidirect
37. #19098393	C₂²	semidirect
38. #19098392	C₂²	semidirect
39. #19098380	C₂²	semidirect
40. #19098379	C₂²	semidirect
41. #19098378	C₂²	semidirect
42. C₂×Q₃₂×C₇₉	C₂²	semidirect
45. #368×C₇₉	C₂²	semidirect
46. #362×C₇₉	C₂²	semidirect
229. D₇₉	#2222	direct (N × H)
238. #2222	D₇₉	direct (N × H)
241. C₇₉	C₂×#2222	semidirect
251. C₂×Q₃₂	C₂×D₇₉	semidirect
272. #368	C₂×D₇₉	semidirect
276. #362	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₇₉	2
#504×D₇₉	2
#473×D₇₉	2
#23765526	2
#23765525	2
#23765524	2
#23765523	2
#23765522	2
#368×D₇₉	2
#362×D₇₉	2
C₇₉×#2222	2
C₂×#2222	79

Subgroups — #2222×D79 #34442828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2222×D₇₉ #34442828