Subgroups — C₂×C₇₃×#1509 #32926940

Order 18688.

1206 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1509	C₂	1	8	yes	maximal, direct product factor
5	C₂×#328×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₂×#327×C₇₃	C₂	1	2	yes	maximal
7	#529×C₇₃	—	2	2	no	—
8	#529×C₇₃	—	2	2	no	—
9	#529×C₇₃	C₄	1	4	yes	complemented
10	#529×C₇₃	C₂²	1	4	yes	—
11	C₂×#126×C₇₃	—	2	1	no	—
12	C₂×#125×C₇₃	C₄	1	1	yes	characteristic, complemented
13	C₂×#124×C₇₃	C₄	1	1	yes	characteristic, complemented
14	C₂×#123×C₇₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₄×C₇₃	—	2	1	no	—
19	C₂×C₄×D₄×C₇₃	C₄	1	1	yes	characteristic, complemented
20	C₂×#117×C₇₃	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₇₃	—	2	1	no	—
22	C₂²×C₄²×C₇₃	—	2	1	no	—
23	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
24	#432×C₇₃	—	2	2	no	—
25	#432×C₇₃	C₂²	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₇₃	—	2	1	no	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	—	2	1	no	—
29	C₄×C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄×C₄⋊C₄×C₇₃	C₂²	1	4	yes	complemented
31	C₂×#95×C₇₃	C₂²	1	2	yes	—
32	#328×C₇₃	C₂²	1	8	yes	complemented
33	#327×C₇₃	C₂²	1	8	yes	—
34	C₂²×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₇₃	—	2	1	no	—
36	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₃	—	2	2	no	—
38	C₂³×C₄×C₇₃	—	2	1	no	—
39	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₇₃	—	2	2	no	—
43	#126×C₇₃	—	2	4	no	—
44	#126×C₇₃	—	2	4	no	—
45	#125×C₇₃	—	2	2	no	—
46	#125×C₇₃	C₂×C₄	1	4	yes	complemented
47	#124×C₇₃	—	2	2	no	—
48	#124×C₇₃	C₂×C₄	1	4	yes	complemented
49	#123×C₇₃	—	2	4	no	—
50	#123×C₇₃	—	2	4	no	—
51	C₂²⋊Q₈×C₇₃	—	2	1	no	—
52	C₂²⋊Q₈×C₇₃	—	2	1	no	—
53	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
54	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
55	#121×C₇₃	—	2	1	no	—
56	#121×C₇₃	—	2	1	no	—
57	#121×C₇₃	C₂×C₄	1	2	yes	—
58	#121×C₇₃	C₂³	1	2	yes	—
59	C₄×Q₈×C₇₃	—	2	2	no	—
60	C₄×Q₈×C₇₃	C₂×C₄	1	4	yes	complemented
61	C₄×D₄×C₇₃	—	2	4	no	—
62	C₄×D₄×C₇₃	—	2	4	no	—
63	C₄×D₄×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	complemented
65	#117×C₇₃	—	2	4	no	—
66	#117×C₇₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	—	2	4	no	—
82	C₂×C₄²×C₇₃	—	4	4	no	—
83	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₇₃	D₄	1	2	yes	—
87	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₇₃	D₄	1	2	yes	—
90	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
91	C₄⋊C₈×C₇₃	—	2	4	no	—
92	C₂²⋊C₈×C₇₃	—	2	2	no	—
93	C₂²⋊C₈×C₇₃	C₂³	1	4	yes	—
94	#97×C₇₃	—	2	4	no	—
95	#95×C₇₃	—	2	2	no	—
96	#95×C₇₃	C₂³	1	4	yes	—
97	C₂⁴×C₇₃	—	2	1	no	—
98	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₇₃	—	2	1	no	—
100	C₂×Q₈×C₇₃	—	4	2	no	—
101	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₇₃	—	2	2	no	—
103	C₂×D₄×C₇₃	—	2	2	no	—
104	C₂×D₄×C₇₃	—	2	1	no	—
105	C₂×D₄×C₇₃	—	4	2	no	—
106	C₂×D₄×C₇₃	—	4	2	no	—
107	C₂×D₄×C₇₃	—	4	2	no	—
108	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	4	no	—
112	C₂²×C₄×C₇₃	—	2	8	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	2	1	no	—
116	C₂²×C₄×C₇₃	—	2	4	no	—
117	C₂²×C₄×C₇₃	—	2	4	no	—
118	C₂²×C₄×C₇₃	—	4	2	no	—
119	C₂²×C₄×C₇₃	—	4	4	no	—
120	C₂²×C₄×C₇₃	—	4	4	no	—
121	C₂²×C₄×C₇₃	—	4	4	no	—
122	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
136	C₂×C₈×C₇₃	—	2	4	no	—
137	C₂×C₈×C₇₃	—	4	4	no	—
138	C₄⋊C₄×C₇₃	—	2	16	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	2	4	no	—
141	C₄⋊C₄×C₇₃	—	2	4	no	—
142	C₄⋊C₄×C₇₃	—	2	4	no	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
148	C₂²⋊C₄×C₇₃	—	2	2	no	—
149	C₂²⋊C₄×C₇₃	—	2	2	no	—
150	C₂²⋊C₄×C₇₃	—	2	2	no	—
151	C₂²⋊C₄×C₇₃	—	2	4	no	—
152	C₂²⋊C₄×C₇₃	—	2	4	no	—
153	C₂²⋊C₄×C₇₃	—	2	4	no	—
154	C₂²⋊C₄×C₇₃	—	2	2	no	—
155	C₄²×C₇₃	—	2	4	no	—
156	C₄²×C₇₃	—	4	8	no	—
157	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
158	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
159	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
160	C₄²×C₇₃	C₂²⋊C₄	1	2	yes	—
161	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
163	C₄²×C₇₃	C₂×D₄	1	2	yes	—
164	C₄²×C₇₃	C₂×D₄	1	2	yes	—
165	C₂³×C₇₃	—	2	2	no	—
166	C₂³×C₇₃	—	2	2	no	—
167	C₂³×C₇₃	—	2	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	2	no	—
171	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₂³×C₇₃	#137	1	2	yes	—
175	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₇₃	—	4	2	no	—
177	Q₈×C₇₃	—	4	2	no	—
178	D₄×C₇₃	—	4	2	no	—
179	D₄×C₇₃	—	4	2	no	—
180	D₄×C₇₃	—	4	2	no	—
181	D₄×C₇₃	—	4	2	no	—
182	D₄×C₇₃	—	4	4	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	2	4	no	—
188	C₂×C₄×C₇₃	—	2	2	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	4	no	—
192	C₂×C₄×C₇₃	—	2	4	no	—
193	C₂×C₄×C₇₃	—	2	8	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	4	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	4	1	no	—
201	C₂×C₄×C₇₃	—	4	4	no	—
202	C₂×C₄×C₇₃	—	4	16	no	—
203	C₂×C₄×C₇₃	—	4	4	no	—
204	C₂×C₄×C₇₃	—	4	2	no	—
205	C₂×C₄×C₇₃	—	4	2	no	—
206	C₂×C₄×C₇₃	—	4	2	no	—
207	C₂×C₄×C₇₃	—	4	8	no	—
208	C₂×C₄×C₇₃	#104	1	4	yes	—
209	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
215	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₇₃	—	4	4	no	—
218	C₂²×C₇₃	—	2	1	no	—
219	C₂²×C₇₃	—	2	1	no	—
220	C₂²×C₇₃	—	2	1	no	—
221	C₂²×C₇₃	—	2	1	no	—
222	C₂²×C₇₃	—	2	4	no	—
223	C₂²×C₇₃	—	2	4	no	—
224	C₂²×C₇₃	—	4	2	no	—
225	C₂²×C₇₃	—	4	2	no	—
226	C₂²×C₇₃	—	4	2	no	—
227	C₂²×C₇₃	—	8	4	no	—
228	C₂²×C₇₃	#410	1	2	yes	—
229	C₂²×C₇₃	#417	1	2	yes	—
230	C₂²×C₇₃	#417	1	2	yes	—
231	C₂²×C₇₃	C₂×#104	1	2	yes	—
232	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
235	C₄×C₇₃	—	2	1	no	—
236	C₄×C₇₃	—	2	1	no	—
237	C₄×C₇₃	—	2	1	no	—
238	C₄×C₇₃	—	2	1	no	—
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	2	2	no	—
241	C₄×C₇₃	—	2	2	no	—
242	C₄×C₇₃	—	4	8	no	—
243	C₄×C₇₃	—	4	2	no	—
244	C₄×C₇₃	—	4	2	no	—
245	C₄×C₇₃	—	4	2	no	—
246	C₄×C₇₃	C₂×#104	1	4	yes	—
247	C₂×#1509	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₇₃	—	2	1	no	—
249	C₂×C₇₃	—	2	1	no	—
250	C₂×C₇₃	—	2	2	no	—
251	C₂×C₇₃	—	8	2	no	—
252	C₂×C₇₃	#1509	1	4	yes	direct product factor
253	C₂×C₇₃	C₂×#410	1	1	yes	characteristic
254	C₂×C₇₃	C₂×#417	1	1	yes	characteristic
255	C₂×C₇₃	C₂²×#104	1	1	yes	characteristic
256	C₂×#529	C₂×C₇₃	1	1	yes	characteristic
257	C₂×#432	C₂×C₇₃	1	1	yes	characteristic, complemented
258	C₂×C₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
259	#1509	C₂×C₇₃	1	8	yes	direct product factor
260	C₂×#328	C₂×C₇₃	1	2	yes	complemented
261	C₂×#327	C₂×C₇₃	1	2	yes	—
262	C₇₃	C₂×#1509	1	1	yes	characteristic, direct product factor, Sylow
263	#529	—	2	2	no	—
264	#529	—	2	2	no	—
265	#529	C₄×C₇₃	1	4	yes	complemented
266	#529	C₂²×C₇₃	1	4	yes	—
267	C₂×#126	—	2	1	no	—
268	C₂×#125	C₄×C₇₃	1	1	yes	characteristic, complemented
269	C₂×#124	C₄×C₇₃	1	1	yes	characteristic, complemented
270	C₂×#123	—	2	1	no	—
271	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₄×C₇₃	1	1	yes	characteristic, complemented
274	C₂×C₄×D₄	—	2	1	no	—
275	C₂×C₄×D₄	C₄×C₇₃	1	1	yes	characteristic, complemented
276	C₂×#117	—	2	1	no	—
277	C₂²×C₄⋊C₄	—	2	1	no	—
278	C₂²×C₄²	—	2	1	no	—
279	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
280	#432	—	2	2	no	—
281	#432	C₂²×C₇₃	1	4	yes	complemented
282	C₂×C₄⋊C₈	—	2	1	no	—
283	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
284	C₂×#97	—	2	1	no	—
285	C₄×C₄⋊C₄	—	2	2	no	—
286	C₄×C₄⋊C₄	C₂²×C₇₃	1	4	yes	complemented
287	C₂×#95	C₂²×C₇₃	1	2	yes	—
288	#328	C₂²×C₇₃	1	8	yes	complemented
289	#327	C₂²×C₇₃	1	8	yes	—
290	C₂²×Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
296	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
298	C₂²×C₈	—	2	2	no	—
299	#126	—	2	4	no	—
300	#126	—	2	4	no	—
301	#125	—	2	2	no	—
302	#125	C₂×C₄×C₇₃	1	4	yes	complemented
303	#124	—	2	2	no	—
304	#124	C₂×C₄×C₇₃	1	4	yes	complemented
305	#123	—	2	4	no	—
306	#123	—	2	4	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	C₂×C₄×C₇₃	1	2	yes	—
310	C₂²⋊Q₈	C₂³×C₇₃	1	2	yes	—
311	#121	—	2	1	no	—
312	#121	—	2	1	no	—
313	#121	C₂×C₄×C₇₃	1	2	yes	—
314	#121	C₂³×C₇₃	1	2	yes	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	C₂×C₄×C₇₃	1	4	yes	complemented
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	C₂×C₄×C₇₃	1	4	yes	complemented
321	#117	—	2	4	no	—
322	#117	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	8	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	—	4	4	no	—
339	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
340	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
341	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
342	C₂×C₄²	D₄×C₇₃	1	2	yes	—
343	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
344	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
345	C₂×C₄²	D₄×C₇₃	1	2	yes	—
346	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
347	C₄⋊C₈	—	2	4	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	C₂³×C₇₃	1	4	yes	—
350	#97	—	2	4	no	—
351	#95	—	2	2	no	—
352	#95	C₂³×C₇₃	1	4	yes	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	C₂²×C₄×C₇₃	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	C₂²×C₄×C₇₃	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
381	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
382	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
383	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
384	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
392	C₂×C₈	—	2	4	no	—
393	C₂×C₈	—	4	4	no	—
394	C₄⋊C₄	—	2	16	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
403	C₄⋊C₄	C₂²×C₄×C₇₃	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	4	8	no	—
413	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
414	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
415	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
416	C₄²	C₂²⋊C₄×C₇₃	1	2	yes	—
417	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
418	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
419	C₄²	C₂×D₄×C₇₃	1	2	yes	—
420	C₄²	C₂×D₄×C₇₃	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
428	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
429	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
430	C₂³	#137×C₇₃	1	2	yes	—
431	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	#104×C₇₃	1	4	yes	—
465	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
466	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
467	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
468	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
471	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
472	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
473	C₈	—	4	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	8	4	no	—
484	C₂²	#410×C₇₃	1	2	yes	—
485	C₂²	#417×C₇₃	1	2	yes	—
486	C₂²	#417×C₇₃	1	2	yes	—
487	C₂²	C₂×#104×C₇₃	1	2	yes	—
488	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
489	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
490	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	8	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	C₂×#104×C₇₃	1	4	yes	—
503	C₂	—	2	1	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	1	no	—
506	C₂	—	8	2	no	—
507	C₂	C₇₃×#1509	1	4	yes	direct product factor
508	C₂	C₂×#410×C₇₃	1	1	yes	characteristic
509	C₂	C₂×#417×C₇₃	1	1	yes	characteristic
510	C₂	C₂²×#104×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₇₃	C₂	semidirect
3. C₂×C₄×C₄⋊C₄×C₇₃	C₂	semidirect
4. C₇₃×#1509	C₂	direct (N × H)
5. C₂×#328×C₇₃	C₂	semidirect
9. #529×C₇₃	C₄	semidirect
12. C₂×#125×C₇₃	C₄	semidirect
13. C₂×#124×C₇₃	C₄	semidirect
17. C₂×C₄×Q₈×C₇₃	C₄	semidirect
19. C₂×C₄×D₄×C₇₃	C₄	semidirect
25. #432×C₇₃	C₂²	semidirect
30. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
32. #328×C₇₃	C₂²	semidirect
46. #125×C₇₃	C₂×C₄	semidirect
48. #124×C₇₃	C₂×C₄	semidirect
60. C₄×Q₈×C₇₃	C₂×C₄	semidirect
64. C₄×D₄×C₇₃	C₂×C₄	semidirect
247. C₂×#1509	C₇₃	direct (N × H)
252. C₂×C₇₃	#1509	direct (N × H)
257. C₂×#432	C₂×C₇₃	semidirect
258. C₂×C₄×C₄⋊C₄	C₂×C₇₃	semidirect
259. #1509	C₂×C₇₃	direct (N × H)
260. C₂×#328	C₂×C₇₃	semidirect
262. C₇₃	C₂×#1509	direct (N × H)
265. #529	C₄×C₇₃	semidirect
268. C₂×#125	C₄×C₇₃	semidirect
269. C₂×#124	C₄×C₇₃	semidirect
273. C₂×C₄×Q₈	C₄×C₇₃	semidirect
275. C₂×C₄×D₄	C₄×C₇₃	semidirect
281. #432	C₂²×C₇₃	semidirect
286. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
288. #328	C₂²×C₇₃	semidirect
302. #125	C₂×C₄×C₇₃	semidirect
304. #124	C₂×C₄×C₇₃	semidirect
316. C₄×Q₈	C₂×C₄×C₇₃	semidirect
320. C₄×D₄	C₂×C₄×C₇₃	semidirect
507. C₂	C₇₃×#1509	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#529×C₇₃	2
C₂×#432×C₇₃	2
C₂×C₄×C₄⋊C₄×C₇₃	2
C₇₃×#1509	2
C₂×#328×C₇₃	2
C₂×#327×C₇₃	2
C₂×#1509	73

Subgroups — C2×C73×#1509 #32926940

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#1509 #32926940