Subgroups — #23777675

Order 10112.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099306	C₂	1	2	yes	maximal, complemented
2	#19099302	C₂	1	2	yes	maximal, complemented
3	#19099297	C₂	1	2	yes	maximal, complemented
4	#19099283	C₂	1	2	yes	maximal, complemented
5	#19099278	C₂	1	2	yes	maximal, complemented
6	#19099241	C₂	1	2	yes	maximal, complemented
7	#19099222	C₂	1	2	yes	maximal, complemented
8	#19099209	C₂	1	2	yes	maximal, complemented
9	#19099184	C₂	1	2	yes	maximal, complemented
10	#19099183	C₂	1	4	yes	maximal, complemented
11	#19099145	C₂	1	4	yes	maximal, complemented
12	#19099134	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099127	C₂	1	1	yes	maximal, characteristic, complemented
14	#19099074	C₂	1	2	yes	maximal, complemented
15	#525×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11929624	C₂²	1	2	yes	—
17	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
19	#14579161	C₂²	1	2	yes	complemented
20	#14579159	C₂²	1	2	yes	complemented
21	#14579157	C₂²	1	2	yes	—
22	#14579156	C₂²	1	4	yes	complemented
23	#14579154	C₂²	1	4	yes	complemented
24	#14579154	C₂²	1	4	yes	complemented
25	#14579150	C₂²	1	2	yes	complemented
26	#14579149	C₂²	1	2	yes	complemented
27	#14579148	C₂²	1	4	yes	—
28	#14579148	C₂²	1	2	yes	—
29	#14579147	C₂²	1	4	yes	complemented
30	#14579147	C₂²	1	4	yes	complemented
31	#14579147	C₂²	1	4	yes	complemented
32	#14579147	C₂²	1	4	yes	complemented
33	#14579146	C₂²	1	4	yes	complemented
34	#14579144	C₂²	1	4	yes	complemented
35	#14579143	C₂²	1	4	yes	complemented
36	#14579142	C₂²	1	2	yes	complemented
37	#14579142	C₂²	1	2	yes	complemented
38	#14579140	C₂²	1	2	yes	complemented
39	#14579140	C₂²	1	2	yes	complemented
40	#14579140	C₂²	1	2	yes	complemented
41	#14579139	C₂²	1	4	yes	complemented
42	#14579139	C₂²	1	4	yes	complemented
43	#14579135	C₂²	1	2	yes	—
44	#14579135	C₂²	1	2	yes	—
45	#14579135	C₂²	1	2	yes	complemented
46	#14579134	C₂²	1	4	yes	—
47	#14579133	C₂²	1	4	yes	complemented
48	#14579132	C₂²	1	4	yes	complemented
49	#14579130	C₂²	1	4	yes	complemented
50	#14579129	C₂²	1	4	yes	—
51	#14579129	C₂²	1	2	yes	—
52	#14579129	C₂²	1	2	yes	complemented
53	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
54	#14579126	C₂²	1	4	yes	complemented
55	C₄×D₃₁₆	C₂²	1	2	yes	complemented
56	C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
57	C₄×C₂²⋊D₇₉	C₂²	1	4	yes	complemented
58	(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
59	#14579120	C₂²	1	1	yes	characteristic, complemented
60	#14579120	C₂²	1	2	yes	complemented
61	#14579120	C₂²	1	1	yes	characteristic, complemented
62	#14579119	C₂²	1	4	yes	complemented
63	C₂²⋊C₄×D₇₉	C₂²	1	4	yes	complemented
64	C₂×#41×C₇₉	C₂²	1	1	yes	characteristic
65	C₂³×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
66	#123×C₇₉	C₂²	1	1	yes	characteristic
67	#123×C₇₉	C₂²	1	1	yes	characteristic, complemented
68	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
69	#121×C₇₉	C₂²	1	2	yes	—
70	#120×C₇₉	C₂²	1	1	yes	characteristic
71	#120×C₇₉	C₂²	1	1	yes	characteristic, complemented
72	C₄×D₄×C₇₉	C₂²	1	2	yes	—
73	C₄×D₄×C₇₉	C₂²	1	2	yes	complemented
74	#117×C₇₉	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₇₉	C₂³	1	2	yes	—
76	#11929624	—	4	4	no	—
77	C₂×Dic₁₅₈	—	4	2	no	—
78	C₂×Dic₁₅₈	C₂³	1	2	yes	—
79	C₂×Dic₁₅₈	C₂³	1	2	yes	—
80	C₂×Dic₁₅₈	C₂³	1	4	yes	—
81	C₂×D₃₁₆	—	4	2	no	—
82	C₂×D₃₁₆	C₂³	1	2	yes	—
83	C₂×D₃₁₆	C₂³	1	2	yes	—
84	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
88	C₂²×Dic₇₉	C₂³	1	2	yes	—
89	C₂×C₄×D₇₉	C₂³	1	4	yes	—
90	C₂×C₄×D₇₉	C₂³	1	4	yes	—
91	C₄⋊Dic₇₉	C₂³	1	4	yes	—
92	C₄⋊Dic₇₉	C₂³	1	2	yes	—
93	C₄⋊Dic₇₉	C₂³	1	2	yes	—
94	Dic₇₉⋊C₄	C₂³	1	4	yes	—
95	Dic₇₉⋊C₄	C₂³	1	4	yes	—
96	Dic₇₉⋊C₄	C₂³	1	4	yes	—
97	Dic₇₉⋊C₄	C₂³	1	4	yes	—
98	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
99	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
100	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
101	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
102	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
103	C₂²⋊Dic₇₉	C₂³	1	4	yes	—
104	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
105	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
106	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
109	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
110	C₄×Dic₇₉	C₂³	1	2	yes	—
111	C₄×Dic₇₉	C₂³	1	4	yes	—
112	C₄×Dic₇₉	C₂³	1	2	yes	—
113	C₄×Dic₇₉	C₂³	1	4	yes	—
114	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
115	#41×C₇₉	—	4	2	no	—
116	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₇₉	C₂³	1	2	yes	—
118	C₂×D₄×C₇₉	C₂³	1	2	yes	—
119	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
121	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	—	4	2	no	—
123	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
125	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
128	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
129	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
130	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
131	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
132	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
133	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
134	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
135	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
136	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
137	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
138	C₄²×C₇₉	C₂³	1	2	yes	—
139	C₂³×C₇₉	—	4	1	no	—
140	C₂³×C₇₉	—	4	2	no	—
141	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
142	C₂³×C₇₉	C₂⁴	1	2	yes	—
143	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
144	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
145	C₂²×D₇₉	—	4	2	no	—
146	C₂²×D₇₉	—	4	4	no	—
147	C₂²×D₇₉	C₂⁴	1	4	yes	—
148	Q₈×C₇₉	—	4	1	no	—
149	D₄×C₇₉	—	4	2	no	—
150	D₄×C₇₉	—	4	2	no	—
151	D₄×C₇₉	—	4	1	no	—
152	D₄×C₇₉	—	4	1	no	—
153	D₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	2	2	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	4	no	—
157	C₂×C₄×C₇₉	—	2	2	no	—
158	C₂×C₄×C₇₉	—	4	2	no	—
159	C₂×C₄×C₇₉	—	4	1	no	—
160	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
161	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
166	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
167	C₂²⋊D₇₉	—	4	4	no	—
168	C₂²⋊D₇₉	—	4	4	no	—
169	C₂²⋊D₇₉	—	4	4	no	—
170	C₂²⋊D₇₉	—	4	4	no	—
171	C₂×Dic₇₉	—	4	2	no	—
172	C₂×Dic₇₉	C₂⁴	1	4	yes	—
173	C₂×Dic₇₉	C₂⁴	1	4	yes	—
174	C₂×Dic₇₉	C₂⁴	1	4	yes	—
175	D₃₁₆	—	2	4	no	—
176	D₃₁₆	—	4	2	no	—
177	C₄×D₇₉	—	4	4	no	—
178	C₄×D₇₉	—	4	4	no	—
179	Dic₁₅₈	—	2	4	no	—
180	Dic₁₅₈	—	4	2	no	—
181	Dic₁₅₈	—	4	4	no	—
182	C₂²×C₇₉	—	2	2	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	—	2	1	no	—
185	C₂²×C₇₉	—	2	1	no	—
186	C₂²×C₇₉	—	2	2	no	—
187	C₂²×C₇₉	—	2	2	no	—
188	C₂²×C₇₉	—	2	2	no	—
189	C₂²×C₇₉	—	2	2	no	—
190	C₂²×C₇₉	—	2	2	no	—
191	C₂²×C₇₉	—	4	4	no	—
192	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
193	C₂×D₇₉	—	2	4	no	—
194	C₂×D₇₉	—	2	4	no	—
195	C₂×D₇₉	—	2	4	no	—
196	C₂×D₇₉	—	8	4	no	—
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	2	2	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	2	no	—
202	C₄×C₇₉	—	2	2	no	—
203	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
204	Dic₇₉	—	2	4	no	—
205	Dic₇₉	—	2	4	no	—
206	Dic₇₉	—	2	4	no	—
207	C₂×C₇₉	—	4	1	no	—
208	C₂×C₇₉	—	4	1	no	—
209	C₂×C₇₉	—	4	2	no	—
210	C₂×C₇₉	—	4	1	no	—
211	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₇₉	#585	1	2	yes	—
213	D₇₉	—	4	4	no	—
214	#3540	—	79	1	no	maximal, Sylow
215	C₇₉	#3540	1	1	yes	characteristic, complemented, Sylow
216	H(3,𝔽₄)	—	79	2	no	—
217	#560	—	79	2	no	—
218	#559	—	79	2	no	—
219	#556	—	79	2	no	—
220	#555	—	79	2	no	—
221	#551	—	79	2	no	—
222	#548	—	79	2	no	—
223	#546	—	79	2	no	—
224	#542	—	79	4	no	—
225	#542	—	79	2	no	—
226	#538	—	79	4	no	—
227	#536	—	79	1	no	—
228	#535	—	79	1	no	—
229	#525	—	79	2	no	—
230	#525	D₇₉	1	1	yes	characteristic, complemented
231	C₂×#41	—	79	2	no	—
232	C₂×#41	C₂×D₇₉	1	1	yes	characteristic
233	C₂²×Q₈	—	79	1	no	—
234	C₂²×D₄	—	79	1	no	—
235	C₂³×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
236	C₄⋊Q₈	—	79	2	no	—
237	C₄⋊Q₈	—	79	2	no	—
238	#127	—	79	2	no	—
239	#126	—	79	4	no	—
240	#126	—	79	4	no	—
241	#126	—	79	4	no	—
242	#124	—	79	2	no	—
243	#124	—	79	2	no	—
244	#124	—	79	4	no	—
245	#124	—	79	4	no	—
246	#124	—	79	4	no	—
247	#124	—	79	4	no	—
248	#124	—	79	4	no	—
249	#124	—	79	2	no	—
250	#123	—	79	2	no	—
251	#123	—	79	2	no	—
252	#123	—	79	4	no	—
253	#123	—	79	4	no	—
254	#123	—	79	4	no	—
255	#123	C₂×D₇₉	1	1	yes	characteristic
256	#123	C₂×D₇₉	1	1	yes	characteristic, complemented
257	C₂²⋊Q₈	—	79	2	no	—
258	C₂²⋊Q₈	—	79	2	no	—
259	C₂²⋊Q₈	—	79	2	no	—
260	C₂²⋊Q₈	—	79	4	no	—
261	C₂²⋊Q₈	—	79	4	no	—
262	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
263	#121	—	79	4	no	—
264	#121	—	79	4	no	—
265	#121	—	79	2	no	—
266	#121	—	79	2	no	—
267	#121	—	79	2	no	—
268	#121	—	79	4	no	—
269	#121	C₂×D₇₉	1	2	yes	—
270	#120	—	79	4	no	—
271	#120	—	79	2	no	—
272	#120	—	79	2	no	—
273	#120	—	79	4	no	—
274	#120	C₂×D₇₉	1	1	yes	characteristic
275	#120	C₂×D₇₉	1	1	yes	characteristic, complemented
276	C₄×Q₈	—	79	4	no	—
277	C₄×Q₈	—	79	2	no	—
278	C₄×D₄	—	79	4	no	—
279	C₄×D₄	—	79	4	no	—
280	C₄×D₄	—	79	4	no	—
281	C₄×D₄	—	79	2	no	—
282	C₄×D₄	C₂×D₇₉	1	2	yes	—
283	C₄×D₄	C₂×D₇₉	1	2	yes	complemented
284	#117	—	79	2	no	—
285	#117	—	79	1	no	—
286	#117	—	79	1	no	—
287	#117	—	79	4	no	—
288	#117	C₂×D₇₉	1	1	yes	characteristic, complemented
289	C₂×C₂²⋊C₄	—	79	4	no	—
290	C₂⁴	—	79	2	no	—
291	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
292	#41	—	4	2	no	—
293	#41	—	316	4	no	—
294	C₂×Q₈	—	316	2	no	—
295	C₂×Q₈	—	79	4	no	—
296	C₂×Q₈	—	79	2	no	—
297	C₂×Q₈	—	79	2	no	—
298	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
299	C₂×D₄	—	316	2	no	—
300	C₂×D₄	—	79	4	no	—
301	C₂×D₄	—	79	4	no	—
302	C₂×D₄	—	79	4	no	—
303	C₂×D₄	—	79	4	no	—
304	C₂×D₄	—	79	2	no	—
305	C₂×D₄	—	79	2	no	—
306	C₂×D₄	C₂²×D₇₉	1	2	yes	—
307	C₂×D₄	C₂²×D₇₉	1	2	yes	—
308	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	79	2	no	—
313	C₂²×C₄	—	79	4	no	—
314	C₂²×C₄	—	79	4	no	—
315	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
316	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
317	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
321	C₄⋊C₄	—	79	4	no	—
322	C₄⋊C₄	—	79	4	no	—
323	C₄⋊C₄	—	79	4	no	—
324	C₄⋊C₄	—	79	4	no	—
325	C₄⋊C₄	—	79	2	no	—
326	C₄⋊C₄	—	79	2	no	—
327	C₄⋊C₄	—	79	4	no	—
328	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
329	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
330	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
331	C₂²⋊C₄	—	79	4	no	—
332	C₂²⋊C₄	—	79	2	no	—
333	C₂²⋊C₄	—	79	4	no	—
334	C₂²⋊C₄	—	79	2	no	—
335	C₂²⋊C₄	—	79	4	no	—
336	C₂²⋊C₄	—	79	4	no	—
337	C₂²⋊C₄	—	79	4	no	—
338	C₂²⋊C₄	—	79	4	no	—
339	C₂²⋊C₄	—	79	4	no	—
340	C₂²⋊C₄	—	79	4	no	—
341	C₂²⋊C₄	—	79	4	no	—
342	C₂²⋊C₄	—	79	4	no	—
343	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
344	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
346	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
348	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
349	C₄²	—	79	2	no	—
350	C₄²	—	79	4	no	—
351	C₄²	—	79	2	no	—
352	C₄²	—	79	4	no	—
353	C₄²	C₂²×D₇₉	1	2	yes	—
354	C₂³	—	4	1	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	316	2	no	—
357	C₂³	—	316	4	no	—
358	C₂³	—	79	4	no	—
359	C₂³	C₂³×D₇₉	1	1	yes	characteristic
360	C₂³	C₂³×D₇₉	1	1	yes	characteristic
361	C₂³	C₂³×D₇₉	1	2	yes	—
362	C₂³	C₂³×D₇₉	1	1	yes	characteristic
363	Q₈	—	4	1	no	—
364	Q₈	—	316	2	no	—
365	Q₈	—	316	4	no	—
366	Q₈	—	158	4	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	1	no	—
371	D₄	—	4	1	no	—
372	D₄	—	316	2	no	—
373	D₄	—	316	4	no	—
374	D₄	—	316	4	no	—
375	D₄	—	316	4	no	—
376	D₄	—	316	4	no	—
377	D₄	—	158	4	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	316	4	no	—
385	C₂×C₄	—	316	4	no	—
386	C₂×C₄	—	316	2	no	—
387	C₂×C₄	—	79	4	no	—
388	C₂×C₄	—	79	4	no	—
389	C₂×C₄	—	79	4	no	—
390	C₂×C₄	C₂³×D₇₉	1	2	yes	—
391	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₇₉	1	2	yes	—
393	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₇₉	1	2	yes	—
395	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	632	4	no	—
408	C₂²	—	158	4	no	—
409	C₂²	—	158	4	no	—
410	C₂²	—	158	4	no	—
411	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	158	4	no	—
419	C₄	—	158	4	no	—
420	C₄	—	158	4	no	—
421	C₄	#14579206	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	1	no	—
425	C₂	—	4	1	no	—
426	C₂	—	316	4	no	—
427	C₂	C₂×#14579206	1	1	yes	characteristic
428	C₂	#19099399	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#525×C₇₉	C₂
hypercenter	#525	D₇₉
hypocenter	C₇₉	#3540
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #19099306	C₂	semidirect
2. #19099302	C₂	semidirect
3. #19099297	C₂	semidirect
4. #19099283	C₂	semidirect
5. #19099278	C₂	semidirect
6. #19099241	C₂	semidirect
7. #19099222	C₂	semidirect
8. #19099209	C₂	semidirect
9. #19099184	C₂	semidirect
10. #19099183	C₂	semidirect
11. #19099145	C₂	semidirect
12. #19099134	C₂	semidirect
13. #19099127	C₂	semidirect
14. #19099074	C₂	semidirect
15. #525×C₇₉	C₂	semidirect
17. C₂²×Dic₁₅₈	C₂²	semidirect
18. C₂²×D₃₁₆	C₂²	semidirect
19. #14579161	C₂²	semidirect
20. #14579159	C₂²	semidirect
22. #14579156	C₂²	semidirect
23. #14579154	C₂²	semidirect
24. #14579154	C₂²	semidirect
25. #14579150	C₂²	semidirect
26. #14579149	C₂²	semidirect
29. #14579147	C₂²	semidirect
30. #14579147	C₂²	semidirect
31. #14579147	C₂²	semidirect
32. #14579147	C₂²	semidirect
33. #14579146	C₂²	semidirect
34. #14579144	C₂²	semidirect
35. #14579143	C₂²	semidirect
36. #14579142	C₂²	semidirect
37. #14579142	C₂²	semidirect
38. #14579140	C₂²	semidirect
39. #14579140	C₂²	semidirect
40. #14579140	C₂²	semidirect
41. #14579139	C₂²	semidirect
42. #14579139	C₂²	semidirect
45. #14579135	C₂²	semidirect
47. #14579133	C₂²	semidirect
48. #14579132	C₂²	semidirect
49. #14579130	C₂²	semidirect
52. #14579129	C₂²	semidirect
53. C₄×Dic₁₅₈	C₂²	semidirect
54. #14579126	C₂²	semidirect
55. C₄×D₃₁₆	C₂²	semidirect
56. C₄×C₂²⋊D₇₉	C₂²	semidirect
57. C₄×C₂²⋊D₇₉	C₂²	semidirect
58. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
59. #14579120	C₂²	semidirect
60. #14579120	C₂²	semidirect
61. #14579120	C₂²	semidirect
62. #14579119	C₂²	semidirect
63. C₂²⋊C₄×D₇₉	C₂²	semidirect
65. C₂³×C₄×C₇₉	C₂²	semidirect
67. #123×C₇₉	C₂²	semidirect
68. C₂²⋊Q₈×C₇₉	C₂²	semidirect
71. #120×C₇₉	C₂²	semidirect
73. C₄×D₄×C₇₉	C₂²	semidirect
74. #117×C₇₉	C₂²	semidirect
215. C₇₉	#3540	semidirect
230. #525	D₇₉	semidirect
235. C₂³×C₄	C₂×D₇₉	semidirect
256. #123	C₂×D₇₉	semidirect
262. C₂²⋊Q₈	C₂×D₇₉	semidirect
275. #120	C₂×D₇₉	semidirect
283. C₄×D₄	C₂×D₇₉	semidirect
288. #117	C₂×D₇₉	semidirect