Subgroups — #34270808

Order 20224.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773910	C₂	1	1	yes	maximal, characteristic, complemented
2	#23773408	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098641	C₂	1	1	yes	maximal, characteristic
4	#23762921	C₂	1	2	yes	maximal, complemented
5	#23762911	C₂	1	2	yes	maximal, complemented
6	#23762901	C₂	1	2	yes	maximal, complemented
7	#23762897	C₂	1	2	yes	maximal, complemented
8	#23762146	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762057	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3101	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	—	2	1	no	—
13	#19099120	C₂²	1	1	yes	characteristic
14	#19098966	C₂²	1	1	yes	characteristic, complemented
15	#19098966	C₂²	1	1	yes	characteristic, complemented
16	#19098962	—	2	1	no	—
17	#19098962	—	2	1	no	—
18	#19098959	C₂²	1	1	yes	characteristic, complemented
19	#19098959	C₂²	1	1	yes	characteristic, complemented
20	#19098893	—	2	1	no	—
21	#19098853	C₂²	1	2	yes	—
22	#19098768	C₂²	1	2	yes	—
23	#19098714	—	2	1	no	—
24	C₄×#11929612	—	2	2	no	—
25	#19098641	—	2	1	no	—
26	#19098641	—	2	1	no	—
27	#19098641	C₂²	1	2	yes	—
28	#19098641	C₂²	1	2	yes	—
29	#19098616	C₂²	1	1	yes	characteristic
30	#19098599	—	2	1	no	—
31	#19098599	—	2	1	no	—
32	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
35	#19098315	C₂²	1	2	yes	complemented
36	#19098313	C₂²	1	2	yes	complemented
37	#19098312	C₂²	1	2	yes	complemented
38	#19098311	C₂²	1	2	yes	complemented
39	#19098310	C₂²	1	2	yes	complemented
40	#19098309	C₂²	1	2	yes	complemented
41	#533×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
43	#483×C₇₉	—	2	1	no	—
44	#476×C₇₉	C₂²	1	2	yes	—
45	#461×C₇₉	C₂²	1	2	yes	—
46	#450×C₇₉	—	2	1	no	—
47	C₄×SD₁₆×C₇₉	—	2	2	no	—
48	#431×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#11929612	—	2	2	no	—
50	C₂×#11929608	—	2	2	no	—
51	C₂×#11929608	—	2	2	no	—
52	C₂×#11929608	—	4	4	no	—
53	C₂²×C₇₉⋊C₈	—	2	1	no	—
54	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
55	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
56	#14579161	C₂³	1	1	yes	characteristic
57	#14579161	C₂³	1	1	yes	characteristic
58	#14579153	—	2	1	no	—
59	#14579140	—	2	1	no	—
60	#14579140	—	2	1	no	—
61	C₄×Dic₁₅₈	—	2	1	no	—
62	C₄×Dic₁₅₈	—	2	1	no	—
63	#14579120	—	2	1	no	—
64	#14579094	—	2	1	no	—
65	#14579094	—	2	1	no	—
66	#14579094	—	2	1	no	—
67	#14579094	—	2	1	no	—
68	#14579092	—	2	2	no	—
69	#14579092	—	2	1	no	—
70	#14579092	—	2	1	no	—
71	#14579092	—	2	1	no	—
72	#14579092	—	2	1	no	—
73	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
75	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
76	#14579084	—	2	2	no	—
77	#14579082	—	2	2	no	—
78	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
81	C₄×C₇₉⋊C₈	—	2	1	no	—
82	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₇₉	—	2	1	no	—
88	C₂×SD₁₆×C₇₉	—	2	2	no	—
89	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
91	#125×C₇₉	—	2	1	no	—
92	C₂²⋊Q₈×C₇₉	—	2	1	no	—
93	C₂²⋊Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×D₄×C₇₉	—	2	1	no	—
97	C₄×D₄×C₇₉	—	2	1	no	—
98	C₄×D₄×C₇₉	D₄	1	2	yes	—
99	C₄×D₄×C₇₉	C₂³	1	2	yes	—
100	#117×C₇₉	—	2	1	no	—
101	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#106×C₇₉	—	2	2	no	—
105	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
106	#103×C₇₉	—	2	2	no	—
107	#102×C₇₉	—	2	2	no	—
108	C₂²⋊C₈×C₇₉	—	2	1	no	—
109	C₄×C₈×C₇₉	—	2	1	no	—
110	C₂×Dic₁₅₈	—	2	1	no	—
111	C₂×Dic₁₅₈	—	2	1	no	—
112	#11929612	—	4	4	no	—
113	#11929608	—	4	4	no	—
114	#11929608	—	4	4	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	4	2	no	—
119	C₂×C₇₉⋊C₈	SD₁₆	1	4	yes	complemented
120	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₄⋊Dic₇₉	—	2	1	no	—
125	C₄⋊Dic₇₉	—	2	1	no	—
126	C₄⋊Dic₇₉	—	2	1	no	—
127	C₄⋊Dic₇₉	—	2	1	no	—
128	Dic₇₉⋊C₄	—	4	1	no	—
129	Dic₇₉⋊C₄	—	4	1	no	—
130	C₂²⋊Dic₇₉	—	4	1	no	—
131	C₄×Dic₇₉	—	4	1	no	—
132	C₂⁴×C₇₉	—	2	1	no	—
133	C₂×Q₈×C₇₉	—	2	1	no	—
134	C₂×Q₈×C₇₉	—	2	1	no	—
135	C₂×D₄×C₇₉	—	2	1	no	—
136	C₂×D₄×C₇₉	—	4	2	no	—
137	C₂×D₄×C₇₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇₉	—	2	1	no	—
139	C₂²×C₄×C₇₉	—	2	2	no	—
140	C₂²×C₄×C₇₉	—	2	2	no	—
141	C₂²×C₄×C₇₉	—	4	2	no	—
142	C₂²×C₄×C₇₉	—	4	2	no	—
143	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
146	SD₁₆×C₇₉	—	4	4	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	2	1	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	1	no	—
153	C₄⋊C₄×C₇₉	—	4	1	no	—
154	C₄⋊C₄×C₇₉	—	4	1	no	—
155	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
156	C₂²⋊C₄×C₇₉	—	2	2	no	—
157	C₂²⋊C₄×C₇₉	—	2	2	no	—
158	C₂²⋊C₄×C₇₉	—	4	1	no	—
159	C₄²×C₇₉	—	4	1	no	—
160	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇₉	#41	1	1	yes	characteristic
163	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₂³×C₇₉	—	2	2	no	—
165	C₂³×C₇₉	—	4	2	no	—
166	C₂³×C₇₉	—	4	2	no	—
167	C₂³×C₇₉	—	4	2	no	—
168	C₂³×C₇₉	#121	1	1	yes	characteristic
169	Q₈×C₇₉	—	4	2	no	—
170	Q₈×C₇₉	—	8	1	no	—
171	D₄×C₇₉	—	2	2	no	—
172	D₄×C₇₉	—	2	2	no	—
173	D₄×C₇₉	—	4	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	4	1	no	—
177	C₂×C₄×C₇₉	—	4	2	no	—
178	C₂×C₄×C₇₉	—	4	2	no	—
179	C₂×C₄×C₇₉	—	4	2	no	—
180	C₂×C₄×C₇₉	—	4	4	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	—	4	1	no	—
183	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₇₉	#137	1	2	yes	—
188	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
191	C₂×Dic₇₉	—	4	1	no	—
192	C₂×Dic₇₉	—	4	1	no	—
193	Dic₁₅₈	—	4	2	no	—
194	Dic₁₅₈	—	8	1	no	—
195	C₈×C₇₉	—	4	2	no	—
196	C₇₉⋊C₈	—	2	1	no	—
197	C₇₉⋊C₈	—	2	1	no	—
198	C₇₉⋊C₈	—	4	2	no	—
199	C₇₉⋊C₈	—	4	2	no	—
200	C₇₉⋊C₈	C₂×SD₁₆	1	2	yes	—
201	C₇₉⋊C₈	C₂×SD₁₆	1	2	yes	—
202	C₂²×C₇₉	—	2	1	no	—
203	C₂²×C₇₉	—	2	1	no	—
204	C₂²×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	—	4	2	no	—
206	C₂²×C₇₉	—	4	2	no	—
207	C₂²×C₇₉	—	8	4	no	—
208	C₂²×C₇₉	#461	1	2	yes	—
209	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	—	2	1	no	—
212	C₄×C₇₉	—	2	1	no	—
213	C₄×C₇₉	—	4	2	no	—
214	C₄×C₇₉	—	8	1	no	—
215	C₄×C₇₉	—	8	1	no	—
216	C₄×C₇₉	#461	1	2	yes	—
217	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
218	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
219	C₄×C₇₉	#575	1	2	yes	—
220	Dic₇₉	—	8	1	no	—
221	Dic₇₉	—	8	1	no	—
222	#19137	—	79	1	no	maximal, Sylow
223	C₂×C₇₉	—	2	2	no	—
224	C₂×C₇₉	—	8	2	no	—
225	C₂×C₇₉	C₂×#461	1	1	yes	characteristic
226	C₂×C₇₉	#3054	1	1	yes	characteristic
227	C₂×C₇₉	#3067	1	1	yes	characteristic
228	#3160	—	79	1	no	—
229	#3101	—	79	1	no	—
230	#3101	D₇₉	1	1	yes	characteristic
231	C₂×#436	—	79	1	no	—
232	#1695	—	79	2	no	—
233	#1693	—	79	2	no	—
234	#1691	—	79	2	no	—
235	#1691	—	79	2	no	—
236	#1564	—	79	1	no	—
237	#1542	—	79	1	no	—
238	#1542	—	79	1	no	—
239	C₇₉	#19137	1	1	yes	characteristic, complemented, Sylow
240	C₂²×M₁₆	—	158	1	no	—
241	#533	—	79	1	no	—
242	#533	C₂×D₇₉	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
244	#500	—	79	1	no	—
245	#500	—	79	1	no	—
246	#499	—	158	1	no	—
247	#499	—	158	1	no	—
248	#498	—	79	1	no	—
249	#498	—	79	1	no	—
250	#483	—	2	1	no	—
251	#483	—	158	1	no	—
252	#476	—	79	2	no	—
253	#476	C₂×D₇₉	1	2	yes	—
254	#461	—	79	2	no	—
255	#461	C₂×D₇₉	1	2	yes	—
256	#450	—	2	1	no	—
257	#450	—	158	1	no	—
258	C₄×SD₁₆	—	2	2	no	—
259	C₄×SD₁₆	—	158	2	no	—
260	#436	—	79	2	no	—
261	#436	—	79	2	no	—
262	#436	—	158	1	no	—
263	#436	—	158	1	no	—
264	#431	—	79	1	no	—
265	#431	C₂×D₇₉	1	1	yes	characteristic
266	#427	—	158	1	no	—
267	#427	—	158	1	no	—
268	C₂×C₄⋊C₈	—	79	1	no	—
269	C₂×C₂²⋊C₈	—	158	1	no	—
270	C₂×C₄×C₈	—	79	1	no	—
271	#335	—	79	2	no	—
272	#334	—	79	2	no	—
273	#333	—	79	2	no	—
274	#333	—	79	2	no	—
275	#332	—	79	2	no	—
276	#332	—	79	2	no	—
277	C₂²×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	158	2	no	—
281	C₂×M₁₆	—	316	4	no	—
282	C₂×M₁₆	—	158	2	no	—
283	C₂×M₁₆	—	158	2	no	—
284	C₂²×C₈	—	79	1	no	—
285	C₂²×C₈	—	79	1	no	—
286	C₂²×C₈	—	158	1	no	—
287	C₄⋊Q₈	—	79	1	no	—
288	C₄⋊Q₈	—	79	1	no	—
289	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
290	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
291	#125	—	2	1	no	—
292	#125	—	158	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	158	1	no	—
296	C₂²⋊Q₈	—	158	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	158	1	no	—
300	C₄×Q₈	—	158	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
304	C₄×D₄	C₂²×D₇₉	1	2	yes	—
305	#117	—	2	1	no	—
306	#117	—	158	1	no	—
307	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
310	#107	—	158	1	no	—
311	#107	—	158	1	no	—
312	#107	—	158	1	no	—
313	#107	—	158	1	no	—
314	#106	—	2	2	no	—
315	#106	—	158	1	no	—
316	#106	—	158	1	no	—
317	#106	—	158	1	no	—
318	#106	—	158	1	no	—
319	#106	—	158	2	no	—
320	C₄⋊C₈	—	79	2	no	—
321	C₄⋊C₈	—	79	2	no	—
322	C₄⋊C₈	—	158	1	no	—
323	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
324	#103	—	2	2	no	—
325	#103	—	158	2	no	—
326	#102	—	2	2	no	—
327	#102	—	158	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	158	2	no	—
330	C₂²⋊C₈	—	158	2	no	—
331	C₂²⋊C₈	—	158	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	79	1	no	—
334	C₄×C₈	—	79	1	no	—
335	C₄×C₈	—	79	1	no	—
336	C₄×C₈	—	79	1	no	—
337	C₄×C₈	—	158	1	no	—
338	C₂⁴	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	158	1	no	—
342	C₂×Q₈	—	158	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	C₂×C₂²⋊D₇₉	1	2	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
353	C₂²×C₄	#11929623	1	1	yes	characteristic
354	SD₁₆	—	4	4	no	—
355	SD₁₆	—	316	4	no	—
356	M₁₆	—	316	4	no	—
357	M₁₆	—	316	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	316	2	no	—
360	C₂×C₈	—	79	4	no	—
361	C₂×C₈	—	79	1	no	—
362	C₂×C₈	—	79	1	no	—
363	C₂×C₈	—	79	1	no	—
364	C₂×C₈	—	79	1	no	—
365	C₂×C₈	—	158	2	no	—
366	C₂×C₈	—	158	2	no	—
367	C₂×C₈	—	158	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	316	1	no	—
376	C₄⋊C₄	—	316	1	no	—
377	C₄⋊C₄	—	158	1	no	—
378	C₄⋊C₄	—	158	1	no	—
379	C₄⋊C₄	—	158	1	no	—
380	C₄⋊C₄	—	158	1	no	—
381	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	316	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	316	1	no	—
388	C₄²	D₄×D₇₉	1	1	yes	characteristic
389	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
390	C₄²	#11929623	1	1	yes	characteristic
391	C₄²	C₂³×D₇₉	1	1	yes	characteristic
392	C₂³	—	2	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	#14579133	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	8	1	no	—
399	Q₈	—	316	2	no	—
400	Q₈	—	632	1	no	—
401	D₄	—	2	2	no	—
402	D₄	—	2	2	no	—
403	D₄	—	4	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	316	1	no	—
414	C₂×C₄	—	316	1	no	—
415	C₂×C₄	#14579133	1	1	yes	characteristic
416	C₂×C₄	#14579133	1	1	yes	characteristic
417	C₂×C₄	#14579133	1	1	yes	characteristic
418	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
419	C₂×C₄	#14579190	1	2	yes	—
420	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
422	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	316	2	no	—
425	C₈	—	316	2	no	—
426	C₈	—	79	2	no	—
427	C₈	—	79	2	no	—
428	C₈	—	158	1	no	—
429	C₈	—	158	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	4	no	—
436	C₂²	#19098766	1	2	yes	—
437	C₂²	C₂×#14579133	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	632	1	no	—
445	C₄	—	632	1	no	—
446	C₄	#19098766	1	2	yes	—
447	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
448	C₄	C₂×#14579190	1	1	yes	characteristic
449	C₄	#19099361	1	2	yes	—
450	C₂	—	2	2	no	—
451	C₂	—	8	2	no	—
452	C₂	C₂×#19098766	1	1	yes	characteristic
453	C₂	#23773006	1	1	yes	characteristic
454	C₂	#23773117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579133
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3101	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂²×D₄×C₇₉	D₄
hypercenter	#3101	D₇₉
hypocenter	C₇₉	#19137
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #23773910	C₂	semidirect
4. #23762921	C₂	semidirect
5. #23762911	C₂	semidirect
6. #23762901	C₂	semidirect
7. #23762897	C₂	semidirect
8. #23762146	C₂	semidirect
9. #23762057	C₂	semidirect
10. #23762055	C₂	semidirect
14. #19098966	C₂²	semidirect
15. #19098966	C₂²	semidirect
18. #19098959	C₂²	semidirect
19. #19098959	C₂²	semidirect
35. #19098315	C₂²	semidirect
36. #19098313	C₂²	semidirect
37. #19098312	C₂²	semidirect
38. #19098311	C₂²	semidirect
39. #19098310	C₂²	semidirect
40. #19098309	C₂²	semidirect
119. C₂×C₇₉⋊C₈	SD₁₆	semidirect
239. C₇₉	#19137	semidirect

Maximal subgroups

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

subgroup	index
#23773910	2
#23773408	2
C₂×#19098641	2
#23762921	2
#23762911	2
#23762901	2
#23762897	2
#23762146	2
#23762057	2
#23762055	2
C₇₉×#3101	2
#19137	79