Subgroups — C₇₃×#25627 #32935031

Order 18688.

1426 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2014	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1877	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	—	2	1	no	—
11	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	#550×C₇₃	—	2	4	no	—
14	#550×C₇₃	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₇₃	C₂²	1	2	yes	—
17	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#121×C₇₃	—	2	1	no	—
19	C₂×#121×C₇₃	—	2	2	no	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	#492×C₇₃	—	2	4	no	—
24	#461×C₇₃	—	2	4	no	—
25	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	2	yes	—
28	C₂×#102×C₇₃	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	#400×C₇₃	—	2	2	no	—
31	#391×C₇₃	—	2	1	no	—
32	#391×C₇₃	C₂²	1	4	yes	—
33	#382×C₇₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#340×C₇₃	C₂²	1	2	yes	—
36	#336×C₇₃	C₂²	1	4	yes	—
37	C₂×#41×C₇₃	—	2	8	no	—
38	C₂×#41×C₇₃	—	4	4	no	—
39	C₂×#41×C₇₃	—	4	4	no	—
40	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₇₃	—	2	2	no	—
49	C₂³×C₄×C₇₃	—	2	1	no	—
50	C₂×SD₁₆×C₇₃	—	2	4	no	—
51	C₂×SD₁₆×C₇₃	—	2	8	no	—
52	C₂×SD₁₆×C₇₃	—	2	8	no	—
53	C₂×SD₁₆×C₇₃	—	4	4	no	—
54	C₂×SD₁₆×C₇₃	—	4	4	no	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	#127×C₇₃	—	2	4	no	—
60	#127×C₇₃	—	2	4	no	—
61	#127×C₇₃	—	2	2	no	—
62	#127×C₇₃	D₄	1	4	yes	—
63	#121×C₇₃	—	2	8	no	—
64	#121×C₇₃	—	2	16	no	—
65	C₄×Q₈×C₇₃	—	2	2	no	—
66	C₄×Q₈×C₇₃	—	2	2	no	—
67	C₄×D₄×C₇₃	—	2	4	no	—
68	C₄×D₄×C₇₃	—	2	4	no	—
69	C₄×D₄×C₇₃	—	2	2	no	—
70	C₄×D₄×C₇₃	D₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₄²×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₇₃	—	2	2	no	—
83	#103×C₇₃	—	2	4	no	—
84	#102×C₇₃	—	2	4	no	—
85	#102×C₇₃	—	4	4	no	—
86	C₄×C₈×C₇₃	—	2	2	no	—
87	#95×C₇₃	—	2	1	no	—
88	#95×C₇₃	—	2	4	no	—
89	#95×C₇₃	—	2	4	no	—
90	C₂⁴×C₇₃	—	2	2	no	—
91	C₂⁴×C₇₃	—	2	1	no	—
92	#41×C₇₃	—	4	32	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	2	4	no	—
98	C₂×Q₈×C₇₃	—	2	4	no	—
99	C₂×Q₈×C₇₃	SD₁₆	1	4	yes	complemented
100	C₂×D₄×C₇₃	—	2	8	no	—
101	C₂×D₄×C₇₃	—	2	8	no	—
102	C₂×D₄×C₇₃	—	2	4	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	1	no	—
106	C₂×D₄×C₇₃	—	2	2	no	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	4	no	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	4	4	no	—
111	C₂×D₄×C₇₃	—	4	4	no	—
112	C₂×D₄×C₇₃	—	4	2	no	—
113	C₂×D₄×C₇₃	—	4	2	no	—
114	C₂×D₄×C₇₃	—	8	2	no	—
115	C₂×D₄×C₇₃	—	8	4	no	—
116	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
117	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇₃	—	2	8	no	—
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	2	no	—
123	C₂²×C₄×C₇₃	—	4	4	no	—
124	C₂²×C₄×C₇₃	—	4	4	no	—
125	C₂²×C₄×C₇₃	—	4	2	no	—
126	C₂²×C₄×C₇₃	—	4	2	no	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
132	SD₁₆×C₇₃	—	4	16	no	—
133	SD₁₆×C₇₃	—	4	8	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	4	no	—
138	C₂×C₈×C₇₃	#41	1	4	yes	complemented
139	C₄⋊C₄×C₇₃	—	2	4	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	—	4	2	no	—
146	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₇₃	—	2	8	no	—
148	C₂²⋊C₄×C₇₃	—	2	4	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	—	4	2	no	—
152	C₄²×C₇₃	C₂×D₄	1	2	yes	—
153	C₄²×C₇₃	C₂×D₄	1	2	yes	—
154	C₂³×C₇₃	—	2	4	no	—
155	C₂³×C₇₃	—	2	2	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	—	4	4	no	—
158	C₂³×C₇₃	—	4	2	no	—
159	C₂³×C₇₃	—	4	1	no	—
160	C₂³×C₇₃	—	4	2	no	—
161	C₂³×C₇₃	—	4	1	no	—
162	C₂³×C₇₃	—	4	4	no	—
163	C₂³×C₇₃	—	4	2	no	—
164	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₇₃	—	2	8	no	—
166	Q₈×C₇₃	—	4	2	no	—
167	Q₈×C₇₃	—	4	2	no	—
168	Q₈×C₇₃	—	4	4	no	—
169	D₄×C₇₃	—	2	2	no	—
170	D₄×C₇₃	—	2	2	no	—
171	D₄×C₇₃	—	2	8	no	—
172	D₄×C₇₃	—	4	16	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	4	2	no	—
175	D₄×C₇₃	—	4	2	no	—
176	D₄×C₇₃	—	4	8	no	—
177	D₄×C₇₃	—	8	4	no	—
178	D₄×C₇₃	—	8	8	no	—
179	C₂×C₄×C₇₃	—	2	2	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	2	4	no	—
185	C₂×C₄×C₇₃	—	4	16	no	—
186	C₂×C₄×C₇₃	—	4	1	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	8	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	—	4	4	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	#120	1	2	yes	—
195	C₂×C₄×C₇₃	#120	1	2	yes	—
196	C₂×C₄×C₇₃	C₂×SD₁₆	1	4	yes	—
197	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
198	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
202	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
203	C₈×C₇₃	—	2	4	no	—
204	C₈×C₇₃	—	4	2	no	—
205	C₂²×C₇₃	—	4	2	no	—
206	C₂²×C₇₃	—	4	4	no	—
207	C₂²×C₇₃	—	4	4	no	—
208	C₂²×C₇₃	—	4	2	no	—
209	C₂²×C₇₃	—	4	4	no	—
210	C₂²×C₇₃	—	4	2	no	—
211	C₂²×C₇₃	—	8	2	no	—
212	C₂²×C₇₃	—	8	4	no	—
213	C₂²×C₇₃	—	8	2	no	—
214	C₂²×C₇₃	—	8	4	no	—
215	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
216	C₂²×C₇₃	#550	1	2	yes	—
217	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
218	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂²×C₇₃	#577	1	2	yes	—
220	C₄×C₇₃	—	2	4	no	—
221	C₄×C₇₃	—	2	2	no	—
222	C₄×C₇₃	—	4	2	no	—
223	C₄×C₇₃	—	4	2	no	—
224	C₄×C₇₃	—	8	2	no	—
225	C₄×C₇₃	—	8	2	no	—
226	C₄×C₇₃	#450	1	4	yes	—
227	C₄×C₇₃	#532	1	1	yes	characteristic
228	C₄×C₇₃	#535	1	1	yes	characteristic
229	C₄×C₇₃	#546	1	2	yes	—
230	#25627	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₇₃	—	8	2	no	—
232	C₂×C₇₃	—	8	4	no	—
233	C₂×C₇₃	#2431	1	1	yes	characteristic
234	C₂×C₇₃	C₂×#450	1	1	yes	characteristic
235	C₂×C₇₃	#3009	1	1	yes	characteristic
236	C₂×C₇₃	#3392	1	2	yes	—
237	C₂×C₇₃	#3397	1	2	yes	—
238	C₂×#550	C₂×C₇₃	1	1	yes	characteristic
239	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
240	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
241	#2568	C₂×C₇₃	1	1	yes	characteristic, complemented
242	#2014	C₂×C₇₃	1	4	yes	complemented
243	#1984	C₂×C₇₃	1	1	yes	characteristic, complemented
244	#1982	C₂×C₇₃	1	1	yes	characteristic, complemented
245	#1877	C₂×C₇₃	1	4	yes	complemented
246	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
247	C₇₃	#25627	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×#41	—	2	1	no	—
249	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
250	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
251	#550	—	2	4	no	—
252	#550	—	2	4	no	—
253	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
254	C₂×#127	C₂²×C₇₃	1	2	yes	—
255	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
256	C₂×#121	—	2	1	no	—
257	C₂×#121	—	2	2	no	—
258	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
259	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
260	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
261	#492	—	2	4	no	—
262	#461	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
264	C₂×#103	C₂²×C₇₃	1	2	yes	—
265	C₂×#102	C₂²×C₇₃	1	2	yes	—
266	C₂×#102	C₂²×C₇₃	1	4	yes	—
267	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
268	#400	—	2	2	no	—
269	#391	—	2	1	no	—
270	#391	C₂²×C₇₃	1	4	yes	—
271	#382	—	2	1	no	—
272	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
273	#340	C₂²×C₇₃	1	2	yes	—
274	#336	C₂²×C₇₃	1	4	yes	—
275	C₂×#41	—	2	8	no	—
276	C₂×#41	—	4	4	no	—
277	C₂×#41	—	4	4	no	—
278	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
279	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
286	C₂³×C₄	—	2	2	no	—
287	C₂³×C₄	—	2	1	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	2	8	no	—
290	C₂×SD₁₆	—	2	8	no	—
291	C₂×SD₁₆	—	4	4	no	—
292	C₂×SD₁₆	—	4	4	no	—
293	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	#127	—	2	4	no	—
298	#127	—	2	4	no	—
299	#127	—	2	2	no	—
300	#127	D₄×C₇₃	1	4	yes	—
301	#121	—	2	8	no	—
302	#121	—	2	16	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₇₃	1	4	yes	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
319	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
320	C₄⋊C₈	—	2	2	no	—
321	#103	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	—	4	4	no	—
324	C₄×C₈	—	2	2	no	—
325	#95	—	2	1	no	—
326	#95	—	2	4	no	—
327	#95	—	2	4	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	—	2	1	no	—
330	#41	—	4	32	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	SD₁₆×C₇₃	1	4	yes	complemented
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	4	no	—
349	C₂×D₄	—	4	4	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	—	8	4	no	—
354	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
355	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	—	4	4	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
370	SD₁₆	—	4	16	no	—
371	SD₁₆	—	4	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	#41×C₇₃	1	4	yes	complemented
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	2	no	—
390	C₄²	C₂×D₄×C₇₃	1	2	yes	—
391	C₄²	C₂×D₄×C₇₃	1	2	yes	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
403	Q₈	—	2	8	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	8	no	—
410	D₄	—	4	16	no	—
411	D₄	—	4	8	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	8	4	no	—
416	D₄	—	8	8	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	16	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	#120×C₇₃	1	2	yes	—
433	C₂×C₄	#120×C₇₃	1	2	yes	—
434	C₂×C₄	C₂×SD₁₆×C₇₃	1	4	yes	—
435	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
436	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
438	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
440	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
441	C₈	—	2	4	no	—
442	C₈	—	4	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	4	no	—
453	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
454	C₂²	#550×C₇₃	1	2	yes	—
455	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
456	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
457	C₂²	#577×C₇₃	1	2	yes	—
458	C₄	—	2	4	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	2	no	—
463	C₄	—	8	2	no	—
464	C₄	#450×C₇₃	1	4	yes	—
465	C₄	#532×C₇₃	1	1	yes	characteristic
466	C₄	#535×C₇₃	1	1	yes	characteristic
467	C₄	#546×C₇₃	1	2	yes	—
468	C₂	—	8	4	no	—
469	C₂	—	8	2	no	—
470	C₂	C₇₃×#2431	1	1	yes	characteristic
471	C₂	C₂×#450×C₇₃	1	1	yes	characteristic
472	C₂	C₇₃×#3009	1	1	yes	characteristic
473	C₂	C₇₃×#3392	1	2	yes	—
474	C₂	C₇₃×#3397	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#550×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#492×C₇₃	C₂	semidirect
3. C₂×#461×C₇₃	C₂	semidirect
4. C₇₃×#2568	C₂	semidirect
5. C₇₃×#2014	C₂	semidirect
6. C₇₃×#1984	C₂	semidirect
7. C₇₃×#1982	C₂	semidirect
8. C₇₃×#1877	C₂	semidirect
9. C₄×#102×C₇₃	C₂	semidirect
99. C₂×Q₈×C₇₃	SD₁₆	semidirect
138. C₂×C₈×C₇₃	#41	semidirect
230. #25627	C₇₃	direct (N × H)
239. C₂×#492	C₂×C₇₃	semidirect
240. C₂×#461	C₂×C₇₃	semidirect
241. #2568	C₂×C₇₃	semidirect
242. #2014	C₂×C₇₃	semidirect
243. #1984	C₂×C₇₃	semidirect
244. #1982	C₂×C₇₃	semidirect
245. #1877	C₂×C₇₃	semidirect
246. C₄×#102	C₂×C₇₃	semidirect
247. C₇₃	#25627	direct (N × H)
337. C₂×Q₈	SD₁₆×C₇₃	semidirect
376. C₂×C₈	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₇₃	2
C₂×#492×C₇₃	2
C₂×#461×C₇₃	2
C₇₃×#2568	2
C₇₃×#2014	2
C₇₃×#1984	2
C₇₃×#1982	2
C₇₃×#1877	2
C₄×#102×C₇₃	2
#25627	73

Subgroups — C73×#25627 #32935031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25627 #32935031