Subgroups — #34306762

Order 20224.

862 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098678	C₂	1	1	yes	maximal, characteristic
2	#23772271	C₂	1	2	yes	maximal
3	#23772000	C₂	1	1	yes	maximal, characteristic, complemented
4	#23771996	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764184	C₂	1	2	yes	maximal, complemented
6	#23763629	C₂	1	2	yes	maximal, complemented
7	#23763624	C₂	1	2	yes	maximal, complemented
8	#23763558	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763461	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763282	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1816	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579181	C₂²	1	1	yes	characteristic
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	#19099046	C₂²	1	2	yes	—
15	#19099044	C₂²	1	2	yes	—
16	#19098678	C₄	1	8	yes	complemented
17	#19098666	—	2	2	no	—
18	#19098660	—	2	2	no	—
19	#19098655	—	2	2	no	—
20	#19098643	—	2	2	no	—
21	C₂×#14579096	C₂²	1	1	yes	characteristic
22	#19098605	—	2	2	no	—
23	#19098605	C₂²	1	2	yes	—
24	#19098604	—	2	2	no	—
25	#19098603	C₂²	1	2	yes	—
26	#19098601	—	2	1	no	—
27	#19098601	C₂²	1	1	yes	characteristic
28	#19098600	—	2	1	no	—
29	C₂×#14579095	—	2	1	no	—
30	C₂×#14579095	C₂²	1	1	yes	characteristic
31	C₂×#14579094	C₂²	1	2	yes	—
32	#107×D₇₉	—	2	1	no	—
33	C₂×#14579088	C₂²	1	1	yes	characteristic
34	C₂×#14579087	C₂²	1	1	yes	characteristic
35	#19098565	C₂²	1	2	yes	—
36	#19098521	C₂²	1	2	yes	—
37	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
38	#19098432	C₂²	1	2	yes	—
39	#19098331	C₂²	1	2	yes	—
40	#19098324	C₂²	1	2	yes	—
41	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
44	#417×C₇₉	C₂²	1	2	yes	—
45	#343×C₇₉	C₂²	1	2	yes	—
46	C₂×#11929624	C₂³	1	1	yes	characteristic
47	#14579181	C₂×C₄	1	4	yes	—
48	#14579181	Q₈	1	4	yes	—
49	C₂×#11929614	D₄	1	1	yes	characteristic
50	C₂×#11929612	D₄	1	1	yes	characteristic
51	C₂×#11929611	D₄	1	1	yes	characteristic
52	C₂×#11929609	D₄	1	1	yes	characteristic
53	#14579167	—	2	2	no	—
54	#14579167	C₂×C₄	1	4	yes	complemented
55	C₂×#11929608	C₂³	1	1	yes	characteristic
56	C₂×#11929607	—	2	1	no	—
57	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₉	—	2	1	no	—
59	Q₈×Dic₇₉	—	2	2	no	—
60	#14579126	—	2	2	no	—
61	D₄×Dic₇₉	—	2	2	no	—
62	D₄×Dic₇₉	—	4	2	no	—
63	#14579123	—	2	2	no	—
64	C₄×C₂²⋊D₇₉	—	4	2	no	—
65	#14579120	—	2	2	no	—
66	#14579120	C₂³	1	2	yes	—
67	#14579119	—	2	2	no	—
68	C₂×C₄⋊Dic₇₉	—	2	2	no	—
69	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
70	C₂×Dic₇₉⋊C₄	—	4	2	no	—
71	C₄⋊C₄×D₇₉	—	2	2	no	—
72	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
73	#14579096	C₂×C₄	1	4	yes	complemented
74	#14579095	—	2	1	no	—
75	#14579095	—	2	1	no	—
76	#14579095	—	2	2	no	—
77	#14579095	D₄	1	1	yes	characteristic
78	#14579095	D₄	1	1	yes	characteristic
79	#14579094	—	2	2	no	—
80	#14579094	—	2	2	no	—
81	#14579094	—	2	2	no	—
82	#14579093	—	2	2	no	—
83	#14579093	D₄	1	2	yes	—
84	#14579092	—	2	2	no	—
85	#14579088	C₂×C₄	1	4	yes	complemented
86	#14579087	C₂×C₄	1	4	yes	complemented
87	#14579086	—	2	2	no	—
88	#14579083	—	2	2	no	—
89	#14579071	—	2	2	no	—
90	C₈×Dic₇₉	—	2	2	no	—
91	C₈×Dic₇₉	C₂×C₄	1	4	yes	complemented
92	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
93	#131×C₇₉	—	2	2	no	—
94	#131×C₇₉	C₂×C₄	1	4	yes	complemented
95	C₂×M₁₆×C₇₉	—	2	1	no	—
96	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
97	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	—	2	1	no	—
99	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
101	#108×C₇₉	—	2	2	no	—
102	#107×C₇₉	—	2	1	no	—
103	#107×C₇₉	—	2	1	no	—
104	#103×C₇₉	—	2	2	no	—
105	#102×C₇₉	—	2	2	no	—
106	#11929624	—	2	1	no	—
107	#11929624	—	2	1	no	—
108	#11929624	C₂²×C₄	1	2	yes	—
109	#11929624	C₂×Q₈	1	2	yes	—
110	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
111	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₇₉	—	2	1	no	—
113	C₂²×Dic₇₉	—	2	1	no	—
114	C₂²×Dic₇₉	—	2	2	no	—
115	C₂²×Dic₇₉	—	4	2	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	C₂×C₄×D₇₉	—	4	2	no	—
118	#11929614	C₄⋊C₄	1	4	yes	complemented
119	#11929612	C₄⋊C₄	1	4	yes	complemented
120	#11929611	C₄⋊C₄	1	4	yes	complemented
121	#11929609	C₄⋊C₄	1	4	yes	complemented
122	#11929608	—	2	1	no	—
123	#11929608	C₂²×C₄	1	2	yes	—
124	#11929607	—	2	4	no	—
125	C₂×C₇₉⋊C₈	—	2	1	no	—
126	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
127	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
130	C₈×D₇₉	—	2	4	no	—
131	C₄⋊Dic₇₉	—	2	2	no	—
132	C₄⋊Dic₇₉	—	2	2	no	—
133	C₄⋊Dic₇₉	—	4	2	no	—
134	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
135	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
136	Dic₇₉⋊C₄	—	4	2	no	—
137	Dic₇₉⋊C₄	—	8	4	no	—
138	C₂²⋊Dic₇₉	—	2	2	no	—
139	C₂²⋊Dic₇₉	—	4	2	no	—
140	(C₂×D₇₉)⋊C₄	—	4	2	no	—
141	C₄×Dic₇₉	—	2	2	no	—
142	C₄×Dic₇₉	—	2	1	no	—
143	C₄×Dic₇₉	—	4	2	no	—
144	C₄×Dic₇₉	—	4	2	no	—
145	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
146	#41×C₇₉	—	2	1	no	—
147	#41×C₇₉	—	2	1	no	—
148	#41×C₇₉	C₂²×C₄	1	2	yes	—
149	#41×C₇₉	C₂×Q₈	1	2	yes	—
150	C₂×Q₈×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₇₉	—	2	1	no	—
152	C₂×D₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	2	no	—
155	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₇₉	—	2	4	no	—
157	M₁₆×C₇₉	—	2	1	no	—
158	M₁₆×C₇₉	—	2	2	no	—
159	M₁₆×C₇₉	—	2	2	no	—
160	M₁₆×C₇₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₇₉	—	2	4	no	—
162	C₂×C₈×C₇₉	—	2	1	no	—
163	C₂×C₈×C₇₉	—	2	2	no	—
164	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₇₉	#41	1	2	yes	—
168	C₄⋊C₄×C₇₉	—	2	2	no	—
169	C₄⋊C₄×C₇₉	—	2	2	no	—
170	C₂³×C₇₉	—	2	1	no	—
171	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×D₇₉	—	2	1	no	—
173	Q₈×C₇₉	—	2	1	no	—
174	Q₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
175	D₄×C₇₉	—	2	2	no	—
176	D₄×C₇₉	—	2	2	no	—
177	D₄×C₇₉	—	2	1	no	—
178	D₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₇₉	—	2	1	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	4	2	no	—
183	C₂×C₄×C₇₉	—	8	2	no	—
184	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂²⋊D₇₉	—	2	2	no	—
191	C₂²⋊D₇₉	—	2	2	no	—
192	C₂×Dic₇₉	—	2	2	no	—
193	C₂×Dic₇₉	—	2	2	no	—
194	C₂×Dic₇₉	—	2	2	no	—
195	C₂×Dic₇₉	—	2	1	no	—
196	C₂×Dic₇₉	—	2	2	no	—
197	C₂×Dic₇₉	—	2	2	no	—
198	C₂×Dic₇₉	—	4	2	no	—
199	C₂×Dic₇₉	—	8	2	no	—
200	C₂×Dic₇₉	—	16	2	no	—
201	D₃₁₆	—	2	1	no	—
202	D₃₁₆	C₂×C₄⋊C₄	1	2	yes	—
203	C₄×D₇₉	—	2	2	no	—
204	C₄×D₇₉	—	2	2	no	—
205	C₄×D₇₉	—	16	2	no	—
206	Dic₁₅₈	—	2	1	no	—
207	Dic₁₅₈	C₂×C₄⋊C₄	1	2	yes	—
208	C₈×C₇₉	—	2	2	no	—
209	C₈×C₇₉	—	4	2	no	—
210	C₈×C₇₉	C₄×D₄	1	2	yes	—
211	C₈×C₇₉	C₄×D₄	1	2	yes	—
212	C₇₉⋊C₈	—	2	2	no	—
213	C₇₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
214	C₇₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
215	C₂²×C₇₉	—	2	1	no	—
216	C₂²×C₇₉	—	2	1	no	—
217	C₂²×C₇₉	—	2	2	no	—
218	C₂²×C₇₉	—	4	1	no	—
219	C₂²×C₇₉	—	4	1	no	—
220	C₂²×C₇₉	#520	1	1	yes	characteristic
221	C₂²×C₇₉	D₄²	1	1	yes	characteristic
222	C₂²×C₇₉	#554	1	1	yes	characteristic
223	C₂×D₇₉	—	2	2	no	—
224	C₂×D₇₉	—	4	1	no	—
225	C₂×D₇₉	—	4	1	no	—
226	C₄×C₇₉	—	2	2	no	—
227	C₄×C₇₉	—	8	2	no	—
228	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₇₉	#547	1	1	yes	characteristic
231	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
232	Dic₇₉	—	2	4	no	—
233	Dic₇₉	—	2	2	no	—
234	Dic₇₉	—	4	2	no	—
235	Dic₇₉	—	4	2	no	—
236	Dic₇₉	—	8	2	no	—
237	#22692	—	79	1	no	maximal, Sylow
238	C₂×C₇₉	—	2	1	no	—
239	C₂×C₇₉	—	2	1	no	—
240	C₂×C₇₉	—	4	2	no	—
241	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
242	C₂×C₇₉	#3292	1	1	yes	characteristic
243	C₂×C₇₉	#3293	1	1	yes	characteristic
244	D₇₉	—	4	2	no	—
245	C₂×#443	—	79	1	no	—
246	#2951	—	79	2	no	—
247	#2913	—	79	1	no	—
248	#2913	—	79	1	no	—
249	#1952	—	79	2	no	—
250	#1859	—	79	2	no	—
251	#1859	—	79	2	no	—
252	#1845	—	79	1	no	—
253	#1816	—	79	1	no	—
254	#1816	D₇₉	1	1	yes	characteristic, complemented
255	#1772	—	79	1	no	—
256	C₇₉	#22692	1	1	yes	characteristic, complemented, Sylow
257	C₂×#135	—	79	1	no	—
258	C₂×#131	—	79	1	no	—
259	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
260	#520	—	79	2	no	—
261	#520	—	79	2	no	—
262	#443	—	79	8	no	—
263	#440	—	158	2	no	—
264	#440	—	158	2	no	—
265	C₄×Q₁₆	—	158	2	no	—
266	C₄×D₈	—	158	2	no	—
267	C₂×#108	—	79	1	no	—
268	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
269	#428	—	79	2	no	—
270	#428	—	79	2	no	—
271	#428	—	158	2	no	—
272	#428	—	158	2	no	—
273	#427	—	79	1	no	—
274	#427	—	158	1	no	—
275	#427	—	158	1	no	—
276	C₂×#107	—	79	1	no	—
277	C₂×#107	—	79	2	no	—
278	C₂×#107	—	158	1	no	—
279	C₂×#107	—	158	1	no	—
280	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
281	C₂×#104	—	79	1	no	—
282	C₂×#104	—	79	1	no	—
283	#417	—	79	2	no	—
284	#417	C₂×D₇₉	1	2	yes	—
285	#405	—	79	2	no	—
286	C₂×C₄×C₈	—	79	1	no	—
287	#384	—	79	2	no	—
288	#343	—	79	2	no	—
289	#343	C₂×D₇₉	1	2	yes	—
290	#339	—	79	2	no	—
291	C₂×#41	—	79	1	no	—
292	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
293	#135	—	79	4	no	—
294	#135	—	79	4	no	—
295	C₂×Q₁₆	—	79	1	no	—
296	C₂×SD₁₆	—	79	1	no	—
297	C₂×SD₁₆	—	79	1	no	—
298	C₂×D₈	—	79	1	no	—
299	#131	—	2	2	no	—
300	#131	—	79	4	no	—
301	#131	—	158	2	no	—
302	#131	C₄×D₇₉	1	4	yes	complemented
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	79	1	no	—
305	C₂×M₁₆	—	158	1	no	—
306	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
307	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	79	1	no	—
310	C₂²×C₈	—	158	1	no	—
311	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
312	C₄×Q₈	—	158	2	no	—
313	C₄×Q₈	—	158	2	no	—
314	C₄×D₄	—	316	2	no	—
315	C₄×D₄	—	316	2	no	—
316	C₄×D₄	—	158	2	no	—
317	C₄×D₄	—	158	2	no	—
318	#117	—	79	2	no	—
319	#117	—	158	2	no	—
320	#117	—	158	2	no	—
321	C₂×C₄⋊C₄	—	316	2	no	—
322	C₂×C₄⋊C₄	—	79	2	no	—
323	C₂×C₄⋊C₄	—	158	2	no	—
324	C₂×C₄⋊C₄	—	158	2	no	—
325	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
326	C₂×C₄²	—	79	1	no	—
327	#108	—	2	2	no	—
328	#108	—	79	4	no	—
329	#107	—	2	1	no	—
330	#107	—	2	1	no	—
331	#107	—	79	1	no	—
332	#107	—	79	1	no	—
333	#107	—	158	2	no	—
334	#107	—	158	2	no	—
335	#107	—	158	2	no	—
336	#107	—	158	2	no	—
337	#107	—	158	1	no	—
338	#107	—	158	1	no	—
339	#106	—	79	2	no	—
340	#106	—	158	2	no	—
341	#106	—	158	2	no	—
342	#104	—	79	4	no	—
343	#104	—	79	4	no	—
344	#103	—	2	2	no	—
345	#103	—	158	2	no	—
346	#102	—	2	2	no	—
347	#102	—	158	2	no	—
348	#97	—	158	2	no	—
349	C₄×C₈	—	79	4	no	—
350	C₄×C₈	—	158	2	no	—
351	#41	—	2	1	no	—
352	#41	—	2	1	no	—
353	#41	—	79	2	no	—
354	#41	—	79	2	no	—
355	#41	—	158	1	no	—
356	#41	—	158	1	no	—
357	#41	C₂×C₄×D₇₉	1	2	yes	—
358	#41	Q₈×D₇₉	1	2	yes	—
359	C₂×Q₈	—	79	1	no	—
360	C₂×Q₈	D₄×D₇₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	79	1	no	—
363	C₂×D₄	—	158	1	no	—
364	C₂×D₄	D₄×D₇₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	316	2	no	—
368	C₂²×C₄	—	316	2	no	—
369	C₂²×C₄	—	158	2	no	—
370	C₂²×C₄	—	158	1	no	—
371	C₂²×C₄	—	158	1	no	—
372	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
373	Q₁₆	—	79	4	no	—
374	SD₁₆	—	79	4	no	—
375	SD₁₆	—	79	4	no	—
376	D₈	—	79	4	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	79	2	no	—
382	M₁₆	—	158	1	no	—
383	M₁₆	—	158	4	no	—
384	M₁₆	C₂×C₄×D₇₉	1	2	yes	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	79	2	no	—
389	C₂×C₈	—	79	2	no	—
390	C₂×C₈	—	79	1	no	—
391	C₂×C₈	—	79	1	no	—
392	C₂×C₈	—	158	1	no	—
393	C₂×C₈	—	158	4	no	—
394	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
395	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
396	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
397	C₂×C₈	#11929623	1	2	yes	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	316	2	no	—
401	C₄⋊C₄	—	316	2	no	—
402	C₄⋊C₄	—	79	2	no	—
403	C₄⋊C₄	—	79	2	no	—
404	C₄⋊C₄	—	632	4	no	—
405	C₄⋊C₄	—	158	2	no	—
406	C₄⋊C₄	—	158	2	no	—
407	C₂²⋊C₄	—	316	2	no	—
408	C₂²⋊C₄	—	316	2	no	—
409	C₂²⋊C₄	—	158	2	no	—
410	C₄²	—	316	2	no	—
411	C₄²	—	316	2	no	—
412	C₄²	—	79	2	no	—
413	C₄²	—	158	1	no	—
414	C₄²	—	158	2	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	158	1	no	—
417	C₂³	#14579207	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	79	2	no	—
420	Q₈	—	158	1	no	—
421	Q₈	C₄⋊C₄×D₇₉	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	79	2	no	—
426	D₄	—	158	2	no	—
427	D₄	—	158	2	no	—
428	D₄	—	158	1	no	—
429	D₄	C₄⋊C₄×D₇₉	1	2	yes	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	2	no	—
435	C₂×C₄	—	316	2	no	—
436	C₂×C₄	—	632	2	no	—
437	C₂×C₄	—	158	2	no	—
438	C₂×C₄	—	158	2	no	—
439	C₂×C₄	—	158	2	no	—
440	C₂×C₄	—	158	2	no	—
441	C₂×C₄	—	158	1	no	—
442	C₂×C₄	—	158	2	no	—
443	C₂×C₄	—	158	2	no	—
444	C₂×C₄	—	158	2	no	—
445	C₂×C₄	—	1264	2	no	—
446	C₂×C₄	—	1264	2	no	—
447	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
448	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
449	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
450	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
451	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
452	C₂×C₄	#14579208	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	4	2	no	—
455	C₈	—	79	2	no	—
456	C₈	—	79	2	no	—
457	C₈	—	158	2	no	—
458	C₈	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
459	C₈	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	316	1	no	—
466	C₂²	—	316	1	no	—
467	C₂²	—	158	2	no	—
468	C₂²	#19099043	1	1	yes	characteristic
469	C₂²	#19099197	1	1	yes	characteristic
470	C₂²	#19099271	1	1	yes	characteristic
471	C₄	—	2	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	316	2	no	—
474	C₄	—	316	2	no	—
475	C₄	—	632	2	no	—
476	C₄	—	158	4	no	—
477	C₄	—	158	2	no	—
478	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
479	C₄	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
480	C₄	#19099213	1	1	yes	characteristic
481	C₄	#19099226	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	4	2	no	—
485	C₂	—	316	2	no	—
486	C₂	#23766296	1	1	yes	characteristic
487	C₂	#23775198	1	1	yes	characteristic
488	C₂	#23775203	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19099197
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1816	C₂
socle	C₂²×C₇₉	D₄²
prime radical	C₂×#14579181	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1816	D₇₉
hypocenter	C₇₉	#22692
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1816

Complements

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

N	H ≅ G/N	type
3. #23772000	C₂	semidirect
4. #23771996	C₂	semidirect
5. #23764184	C₂	semidirect
6. #23763629	C₂	semidirect
7. #23763624	C₂	semidirect
8. #23763558	C₂	semidirect
9. #23763461	C₂	semidirect
10. #23763282	C₂	semidirect
11. C₇₉×#1816	C₂	semidirect
16. #19098678	C₄	semidirect
54. #14579167	C₂×C₄	semidirect
73. #14579096	C₂×C₄	semidirect
85. #14579088	C₂×C₄	semidirect
86. #14579087	C₂×C₄	semidirect
91. C₈×Dic₇₉	C₂×C₄	semidirect
94. #131×C₇₉	C₂×C₄	semidirect
118. #11929614	C₄⋊C₄	semidirect
119. #11929612	C₄⋊C₄	semidirect
120. #11929611	C₄⋊C₄	semidirect
121. #11929609	C₄⋊C₄	semidirect
254. #1816	D₇₉	semidirect
256. C₇₉	#22692	semidirect
302. #131	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098678	2
#23772271	2
#23772000	2
#23771996	2
#23764184	2
#23763629	2
#23763624	2
#23763558	2
#23763461	2
#23763282	2
C₇₉×#1816	2
#22692	79