Subgroups — #23777253

Order 10112.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099298	C₂	1	2	yes	maximal, complemented
2	#19099295	C₂	1	2	yes	maximal, complemented
3	#19099287	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099276	C₂	1	2	yes	maximal, complemented
5	#19099264	C₂	1	4	yes	maximal, complemented
6	#19099235	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099234	C₂	1	1	yes	maximal, characteristic, complemented
8	#19099215	C₂	1	2	yes	maximal, complemented
9	#19099152	C₂	1	4	yes	maximal, complemented
10	#19099131	C₂	1	2	yes	maximal, complemented
11	#19099117	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099114	C₂	1	1	yes	maximal, characteristic, complemented
13	#19099076	C₂	1	2	yes	maximal, complemented
14	#19099075	C₂	1	2	yes	maximal, complemented
15	#19099045	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#556×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11929625	C₂²	1	2	yes	—
19	C₂×#11929625	C₂²	1	2	yes	complemented
20	C₂×#11929624	C₂²	1	2	yes	complemented
21	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₇₉	C₂²	1	2	yes	—
23	#14579160	C₂²	1	1	yes	characteristic, complemented
24	#14579159	C₂²	1	1	yes	characteristic, complemented
25	#14579158	C₂²	1	2	yes	—
26	#14579158	C₂²	1	1	yes	characteristic, complemented
27	#14579157	C₂²	1	2	yes	—
28	#14579156	C₂²	1	4	yes	complemented
29	#14579151	C₂²	1	2	yes	complemented
30	#14579150	C₂²	1	2	yes	—
31	#14579150	C₂²	1	2	yes	complemented
32	#14579149	C₂²	1	4	yes	complemented
33	#14579147	C₂²	1	4	yes	complemented
34	#14579146	C₂²	1	4	yes	complemented
35	#14579146	C₂²	1	4	yes	complemented
36	#14579145	C₂²	1	4	yes	complemented
37	#14579143	C₂²	1	4	yes	complemented
38	#14579141	C₂²	1	1	yes	characteristic
39	#14579141	C₂²	1	2	yes	complemented
40	#14579139	C₂²	1	2	yes	—
41	#14579137	C₂²	1	1	yes	characteristic
42	#14579136	C₂²	1	2	yes	—
43	#14579136	C₂²	1	2	yes	—
44	#14579136	C₂²	1	4	yes	complemented
45	#14579136	C₂²	1	2	yes	complemented
46	#14579135	C₂²	1	2	yes	complemented
47	#14579134	C₂²	1	4	yes	—
48	#14579134	C₂²	1	4	yes	—
49	#14579134	C₂²	1	4	yes	complemented
50	#14579131	C₂²	1	4	yes	—
51	#14579131	C₂²	1	4	yes	—
52	Q₈×Dic₇₉	C₂²	1	2	yes	complemented
53	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
54	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
55	C₄×D₃₁₆	C₂²	1	4	yes	—
56	C₄×D₃₁₆	C₂²	1	1	yes	characteristic
57	C₄×D₃₁₆	C₂²	1	2	yes	complemented
58	C₄×D₃₁₆	C₂²	1	4	yes	complemented
59	D₄×Dic₇₉	C₂²	1	1	yes	characteristic
60	#14579123	C₂²	1	4	yes	—
61	#14579123	C₂²	1	1	yes	characteristic
62	#14579123	C₂²	1	2	yes	complemented
63	#14579123	C₂²	1	2	yes	complemented
64	#14579123	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
66	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
67	(C₂²⋊D₇₉)⋊C₄	C₂²	1	4	yes	complemented
68	#14579119	C₂²	1	2	yes	complemented
69	#14579118	C₂²	1	2	yes	—
70	#14579118	C₂²	1	4	yes	complemented
71	C₄⋊C₄×D₇₉	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₇₉	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	—
74	C₄²×D₇₉	C₂²	1	1	yes	characteristic
75	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
76	#126×C₇₉	C₂²	1	4	yes	complemented
77	#124×C₇₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₇₉	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
80	C₄×Q₈×C₇₉	C₂²	1	2	yes	complemented
81	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
82	#117×C₇₉	C₂²	1	2	yes	complemented
83	C₂³×D₇₉	C₂³	1	2	yes	—
84	#11929625	—	2	8	no	—
85	#11929625	—	4	4	no	—
86	#11929624	—	4	4	no	—
87	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
88	C₂×Dic₁₅₈	C₂³	1	2	yes	—
89	C₂×D₃₁₆	C₂³	1	2	yes	—
90	C₂×D₃₁₆	C₂³	1	4	yes	—
91	C₂×D₃₁₆	C₂³	1	2	yes	—
92	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
93	C₂×D₃₁₆	C₂³	1	4	yes	—
94	C₂×D₃₁₆	C₂³	1	2	yes	—
95	C₂×D₃₁₆	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₇₉	C₂³	1	4	yes	—
99	D₄×D₇₉	—	2	4	no	—
100	C₂²×Dic₇₉	C₂³	1	2	yes	—
101	C₂×C₄×D₇₉	—	4	4	no	—
102	C₂×C₄×D₇₉	C₂³	1	4	yes	—
103	C₂×C₄×D₇₉	C₂³	1	2	yes	—
104	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₇₉	C₂³	1	4	yes	—
106	C₂×C₄×D₇₉	C₂³	1	4	yes	—
107	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₇₉	C₂³	1	2	yes	—
109	C₂×C₄×D₇₉	C₂³	1	2	yes	—
110	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
111	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₇₉	C₂³	1	4	yes	—
113	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₇₉	C₂³	1	2	yes	—
115	Dic₇₉⋊C₄	C₂³	1	2	yes	—
116	Dic₇₉⋊C₄	C₂³	1	2	yes	—
117	Dic₇₉⋊C₄	C₂³	1	2	yes	—
118	Dic₇₉⋊C₄	C₂³	1	2	yes	—
119	Dic₇₉⋊C₄	C₂³	1	2	yes	—
120	Dic₇₉⋊C₄	C₂³	1	2	yes	—
121	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
122	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
123	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
125	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
126	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
127	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
128	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
129	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
130	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
131	(C₂×D₇₉)⋊C₄	C₂³	1	4	yes	—
132	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
133	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
134	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₇₉	C₂³	1	2	yes	—
136	C₄×Dic₇₉	C₂³	1	4	yes	—
137	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
138	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
139	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
141	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
143	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
145	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
146	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
148	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
150	C₄²×C₇₉	C₂³	1	4	yes	—
151	C₄²×C₇₉	C₂³	1	1	yes	characteristic
152	C₄²×C₇₉	C₂³	1	2	yes	—
153	C₂³×C₇₉	C₂⁴	1	2	yes	—
154	C₂²×D₇₉	—	2	4	no	—
155	C₂²×D₇₉	—	4	2	no	—
156	C₂²×D₇₉	—	4	2	no	—
157	C₂²×D₇₉	C₂⁴	1	2	yes	—
158	C₂²×D₇₉	C₂⁴	1	4	yes	—
159	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
160	Q₈×C₇₉	—	2	4	no	—
161	Q₈×C₇₉	—	2	2	no	—
162	D₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	4	no	—
164	C₂×C₄×C₇₉	C₂⁴	1	4	yes	—
165	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
168	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
169	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊D₇₉	—	2	4	no	—
172	C₂²⋊D₇₉	—	4	4	no	—
173	C₂²⋊D₇₉	—	4	4	no	—
174	C₂×Dic₇₉	—	4	2	no	—
175	C₂×Dic₇₉	C₂⁴	1	2	yes	—
176	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₇₉	C₂⁴	1	2	yes	—
179	C₂×Dic₇₉	C₂⁴	1	2	yes	—
180	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
181	D₃₁₆	—	2	8	no	—
182	D₃₁₆	—	2	2	no	—
183	D₃₁₆	—	2	4	no	—
184	D₃₁₆	—	2	4	no	—
185	D₃₁₆	—	4	4	no	—
186	D₃₁₆	—	4	2	no	—
187	D₃₁₆	—	4	4	no	—
188	C₄×D₇₉	—	2	2	no	—
189	C₄×D₇₉	—	2	4	no	—
190	C₄×D₇₉	—	2	8	no	—
191	C₄×D₇₉	—	4	2	no	—
192	C₄×D₇₉	—	4	2	no	—
193	C₄×D₇₉	—	4	1	no	—
194	C₄×D₇₉	—	4	4	no	—
195	C₄×D₇₉	—	4	4	no	—
196	C₄×D₇₉	#41	1	4	yes	complemented
197	Dic₁₅₈	—	2	2	no	—
198	Dic₁₅₈	—	4	2	no	—
199	C₂²×C₇₉	—	2	2	no	—
200	C₂²×C₇₉	—	2	2	no	—
201	C₂²×C₇₉	—	2	2	no	—
202	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
203	C₂×D₇₉	—	2	1	no	—
204	C₂×D₇₉	—	2	1	no	—
205	C₂×D₇₉	—	2	2	no	—
206	C₂×D₇₉	—	2	4	no	—
207	C₂×D₇₉	—	2	4	no	—
208	C₂×D₇₉	—	2	2	no	—
209	C₂×D₇₉	—	2	4	no	—
210	C₂×D₇₉	—	2	2	no	—
211	C₂×D₇₉	—	4	8	no	—
212	C₂×D₇₉	C₂×#41	1	2	yes	—
213	C₄×C₇₉	—	2	4	no	—
214	C₄×C₇₉	—	2	2	no	—
215	C₄×C₇₉	—	2	2	no	—
216	C₄×C₇₉	—	2	2	no	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	C₂×#41	1	2	yes	—
219	C₄×C₇₉	H(5,𝔽₂)	1	2	yes	—
220	Dic₇₉	—	2	2	no	—
221	Dic₇₉	—	2	2	no	—
222	Dic₇₉	—	2	1	no	—
223	Dic₇₉	—	2	2	no	—
224	Dic₇₉	—	2	1	no	—
225	Dic₇₉	C₂×#41	1	2	yes	—
226	C₂×C₇₉	—	4	2	no	—
227	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
228	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₇₉	#585	1	1	yes	characteristic
230	D₇₉	—	2	2	no	—
231	D₇₉	—	4	4	no	—
232	D₇₉	—	4	2	no	—
233	#3506	—	79	1	no	maximal, Sylow
234	C₇₉	#3506	1	1	yes	characteristic, complemented, Sylow
235	#559	—	79	2	no	—
236	#559	—	79	2	no	—
237	#556	—	79	1	no	—
238	#556	D₇₉	1	1	yes	characteristic, complemented
239	#555	—	79	2	no	—
240	#553	—	79	4	no	—
241	#550	—	79	1	no	—
242	#550	—	79	1	no	—
243	#547	—	79	2	no	—
244	#538	—	79	4	no	—
245	#535	—	79	2	no	—
246	#533	—	79	1	no	—
247	#532	—	79	1	no	—
248	#525	—	79	2	no	—
249	#525	—	79	2	no	—
250	#520	—	79	2	no	—
251	C₂×C₄×D₄	—	79	1	no	—
252	C₂×#41	—	79	2	no	—
253	C₂×#41	—	79	2	no	—
254	C₂×#41	—	79	2	no	—
255	C₂²×D₄	—	79	1	no	—
256	C₂³×C₄	—	79	2	no	—
257	C₄⋊Q₈	—	79	1	no	—
258	C₄⋊Q₈	—	79	1	no	—
259	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
260	#127	—	79	2	no	—
261	#127	—	79	1	no	—
262	#127	—	79	2	no	—
263	#126	—	79	4	no	—
264	#126	C₂×D₇₉	1	4	yes	complemented
265	#125	—	79	2	no	—
266	#124	—	79	2	no	—
267	#124	—	79	2	no	—
268	#124	—	79	4	no	—
269	#124	—	79	4	no	—
270	#124	C₂×D₇₉	1	2	yes	—
271	#123	—	79	4	no	—
272	#123	—	79	4	no	—
273	#123	—	79	4	no	—
274	#123	—	79	4	no	—
275	C₂²⋊Q₈	—	79	1	no	—
276	C₂²⋊Q₈	—	79	1	no	—
277	C₂²⋊Q₈	—	79	2	no	—
278	C₂²⋊Q₈	—	79	2	no	—
279	C₂²⋊Q₈	C₂×D₇₉	1	2	yes	complemented
280	#121	—	79	2	no	—
281	#121	—	79	2	no	—
282	#121	—	79	2	no	—
283	#121	—	79	2	no	—
284	#121	—	79	4	no	—
285	#121	—	79	4	no	—
286	#121	—	79	4	no	—
287	#121	—	79	4	no	—
288	#120	—	79	4	no	—
289	#120	—	79	4	no	—
290	C₄×Q₈	—	79	2	no	—
291	C₄×Q₈	—	79	1	no	—
292	C₄×Q₈	—	79	2	no	—
293	C₄×Q₈	C₂×D₇₉	1	2	yes	complemented
294	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
295	C₄×D₄	—	79	1	no	—
296	C₄×D₄	—	79	2	no	—
297	C₄×D₄	—	79	1	no	—
298	C₄×D₄	—	79	4	no	—
299	C₄×D₄	—	79	2	no	—
300	C₄×D₄	—	79	2	no	—
301	C₄×D₄	—	79	2	no	—
302	C₄×D₄	—	79	2	no	—
303	C₄×D₄	—	79	4	no	—
304	C₄×D₄	—	79	1	no	—
305	C₄×D₄	—	79	4	no	—
306	C₄×D₄	—	79	2	no	—
307	C₄×D₄	—	79	4	no	—
308	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
309	#117	—	79	2	no	—
310	#117	—	79	2	no	—
311	#117	—	79	4	no	—
312	#117	C₂×D₇₉	1	2	yes	complemented
313	C₂×C₄⋊C₄	—	79	1	no	—
314	C₂×C₄⋊C₄	—	79	4	no	—
315	C₂×C₂²⋊C₄	—	79	2	no	—
316	C₂×C₄²	—	79	1	no	—
317	C₂⁴	—	79	2	no	—
318	#41	—	316	4	no	—
319	#41	—	316	4	no	—
320	#41	—	158	8	no	—
321	C₂×Q₈	—	79	2	no	—
322	C₂×Q₈	—	79	1	no	—
323	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
324	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
325	C₂×D₄	—	79	4	no	—
326	C₂×D₄	—	79	4	no	—
327	C₂×D₄	—	79	2	no	—
328	C₂×D₄	—	79	4	no	—
329	C₂×D₄	—	79	2	no	—
330	C₂×D₄	—	79	4	no	—
331	C₂×D₄	—	79	4	no	—
332	C₂×D₄	—	79	1	no	—
333	C₂×D₄	—	79	2	no	—
334	C₂×D₄	—	79	2	no	—
335	C₂×D₄	—	158	4	no	—
336	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
337	C₂²×C₄	—	316	4	no	—
338	C₂²×C₄	—	79	2	no	—
339	C₂²×C₄	—	79	1	no	—
340	C₂²×C₄	—	79	2	no	—
341	C₂²×C₄	—	79	4	no	—
342	C₂²×C₄	—	79	4	no	—
343	C₂²×C₄	—	79	2	no	—
344	C₂²×C₄	—	79	1	no	—
345	C₂²×C₄	—	79	1	no	—
346	C₂²×C₄	—	79	4	no	—
347	C₂²×C₄	—	79	2	no	—
348	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
349	C₄⋊C₄	—	79	2	no	—
350	C₄⋊C₄	—	79	2	no	—
351	C₄⋊C₄	—	79	2	no	—
352	C₄⋊C₄	—	79	2	no	—
353	C₄⋊C₄	—	79	2	no	—
354	C₄⋊C₄	—	79	2	no	—
355	C₄⋊C₄	—	79	1	no	—
356	C₄⋊C₄	—	79	4	no	—
357	C₄⋊C₄	—	79	1	no	—
358	C₄⋊C₄	—	79	2	no	—
359	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
361	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
362	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
364	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
365	C₂²⋊C₄	—	79	2	no	—
366	C₂²⋊C₄	—	79	2	no	—
367	C₂²⋊C₄	—	79	2	no	—
368	C₂²⋊C₄	—	79	2	no	—
369	C₂²⋊C₄	—	79	2	no	—
370	C₂²⋊C₄	—	79	4	no	—
371	C₂²⋊C₄	—	79	4	no	—
372	C₂²⋊C₄	—	79	4	no	—
373	C₂²⋊C₄	—	79	4	no	—
374	C₂²⋊C₄	—	79	4	no	—
375	C₂²⋊C₄	—	79	4	no	—
376	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
378	C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
379	C₄²	—	79	1	no	—
380	C₄²	—	79	1	no	—
381	C₄²	—	79	1	no	—
382	C₄²	—	79	4	no	—
383	C₄²	—	79	2	no	—
384	C₄²	C₂²×D₇₉	1	1	yes	characteristic
385	C₄²	C₂²×D₇₉	1	4	yes	—
386	C₄²	C₂²×D₇₉	1	2	yes	—
387	C₂³	—	316	2	no	—
388	C₂³	—	316	2	no	—
389	C₂³	—	79	1	no	—
390	C₂³	—	79	2	no	—
391	C₂³	—	79	4	no	—
392	C₂³	—	158	4	no	—
393	C₂³	C₂³×D₇₉	1	2	yes	—
394	Q₈	—	2	4	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	316	2	no	—
397	Q₈	—	158	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	316	4	no	—
400	D₄	—	316	2	no	—
401	D₄	—	316	4	no	—
402	D₄	—	316	4	no	—
403	D₄	—	316	4	no	—
404	D₄	—	158	8	no	—
405	D₄	—	158	4	no	—
406	D₄	—	158	2	no	—
407	D₄	—	158	4	no	—
408	D₄	—	158	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	316	2	no	—
411	C₂×C₄	—	316	2	no	—
412	C₂×C₄	—	316	4	no	—
413	C₂×C₄	—	316	4	no	—
414	C₂×C₄	—	316	1	no	—
415	C₂×C₄	—	316	2	no	—
416	C₂×C₄	—	79	1	no	—
417	C₂×C₄	—	79	4	no	—
418	C₂×C₄	—	79	2	no	—
419	C₂×C₄	—	79	1	no	—
420	C₂×C₄	—	79	1	no	—
421	C₂×C₄	—	79	2	no	—
422	C₂×C₄	—	79	2	no	—
423	C₂×C₄	—	158	8	no	—
424	C₂×C₄	—	158	2	no	—
425	C₂×C₄	—	158	4	no	—
426	C₂×C₄	C₂³×D₇₉	1	4	yes	—
427	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₇₉	1	2	yes	—
429	C₂×C₄	C₂³×D₇₉	1	2	yes	—
430	C₂×C₄	C₂³×D₇₉	1	2	yes	—
431	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	316	8	no	—
437	C₂²	—	79	2	no	—
438	C₂²	—	158	4	no	—
439	C₂²	—	158	2	no	—
440	C₂²	—	158	4	no	—
441	C₂²	—	158	2	no	—
442	C₂²	—	158	4	no	—
443	C₂²	—	158	2	no	—
444	C₂²	—	158	1	no	—
445	C₂²	—	158	1	no	—
446	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	79	2	no	—
453	C₄	—	158	1	no	—
454	C₄	—	158	2	no	—
455	C₄	—	158	2	no	—
456	C₄	—	158	1	no	—
457	C₄	—	158	2	no	—
458	C₄	#41×D₇₉	1	2	yes	—
459	C₄	#14579207	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	316	2	no	—
462	C₂	—	316	4	no	—
463	C₂	—	158	2	no	—
464	C₂	C₂×#41×D₇₉	1	1	yes	characteristic
465	C₂	C₂×#14579207	1	1	yes	characteristic
466	C₂	#19099400	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#556×C₇₉	C₂
hypercenter	#556	D₇₉
hypocenter	C₇₉	#3506
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #19099298	C₂	semidirect
2. #19099295	C₂	semidirect
3. #19099287	C₂	semidirect
4. #19099276	C₂	semidirect
5. #19099264	C₂	semidirect
6. #19099235	C₂	semidirect
7. #19099234	C₂	semidirect
8. #19099215	C₂	semidirect
9. #19099152	C₂	semidirect
10. #19099131	C₂	semidirect
11. #19099117	C₂	semidirect
12. #19099114	C₂	semidirect
13. #19099076	C₂	semidirect
14. #19099075	C₂	semidirect
15. #19099045	C₂	semidirect
16. C₄×D₄×D₇₉	C₂	semidirect
17. #556×C₇₉	C₂	semidirect
19. C₂×#11929625	C₂²	semidirect
20. C₂×#11929624	C₂²	semidirect
23. #14579160	C₂²	semidirect
24. #14579159	C₂²	semidirect
26. #14579158	C₂²	semidirect
28. #14579156	C₂²	semidirect
29. #14579151	C₂²	semidirect
31. #14579150	C₂²	semidirect
32. #14579149	C₂²	semidirect
33. #14579147	C₂²	semidirect
34. #14579146	C₂²	semidirect
35. #14579146	C₂²	semidirect
36. #14579145	C₂²	semidirect
37. #14579143	C₂²	semidirect
39. #14579141	C₂²	semidirect
44. #14579136	C₂²	semidirect
45. #14579136	C₂²	semidirect
46. #14579135	C₂²	semidirect
49. #14579134	C₂²	semidirect
52. Q₈×Dic₇₉	C₂²	semidirect
53. C₄×Dic₁₅₈	C₂²	semidirect
54. C₄×Dic₁₅₈	C₂²	semidirect
57. C₄×D₃₁₆	C₂²	semidirect
58. C₄×D₃₁₆	C₂²	semidirect
62. #14579123	C₂²	semidirect
63. #14579123	C₂²	semidirect
64. #14579123	C₂²	semidirect
67. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
68. #14579119	C₂²	semidirect
70. #14579118	C₂²	semidirect
72. C₄⋊C₄×D₇₉	C₂²	semidirect
75. C₄⋊Q₈×C₇₉	C₂²	semidirect
76. #126×C₇₉	C₂²	semidirect
78. C₂²⋊Q₈×C₇₉	C₂²	semidirect
79. C₄×Q₈×C₇₉	C₂²	semidirect
80. C₄×Q₈×C₇₉	C₂²	semidirect
82. #117×C₇₉	C₂²	semidirect
196. C₄×D₇₉	#41	semidirect
234. C₇₉	#3506	semidirect
238. #556	D₇₉	semidirect
259. C₄⋊Q₈	C₂×D₇₉	semidirect
264. #126	C₂×D₇₉	semidirect
279. C₂²⋊Q₈	C₂×D₇₉	semidirect
293. C₄×Q₈	C₂×D₇₉	semidirect
294. C₄×Q₈	C₂×D₇₉	semidirect
312. #117	C₂×D₇₉	semidirect