Subgroups — C₇₃×#25597 #32935001

Order 18688.

1438 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#487×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1877	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	—	2	1	no	—
11	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
12	#532×C₇₃	—	2	4	no	—
13	#532×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₇₃	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×#121×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₇₃	—	2	1	no	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
24	#492×C₇₃	—	2	4	no	—
25	#487×C₇₃	—	2	4	no	—
26	C₂×#103×C₇₃	C₂²	1	4	yes	—
27	C₂×#102×C₇₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
31	#391×C₇₃	C₂²	1	2	yes	—
32	#389×C₇₃	—	2	1	no	—
33	#389×C₇₃	—	2	1	no	—
34	#384×C₇₃	C₂²	1	1	yes	characteristic
35	#380×C₇₃	—	2	1	no	—
36	#380×C₇₃	—	2	1	no	—
37	#340×C₇₃	C₂²	1	4	yes	—
38	#336×C₇₃	C₂²	1	2	yes	—
39	C₂×#41×C₇₃	—	2	8	no	—
40	C₂×#41×C₇₃	—	4	4	no	—
41	C₂×#41×C₇₃	—	4	4	no	—
42	C₂²×Q₈×C₇₃	—	2	1	no	—
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₇₃	—	2	2	no	—
49	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₇₃	—	2	8	no	—
53	C₂×SD₁₆×C₇₃	—	2	8	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	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
61	#127×C₇₃	—	2	2	no	—
62	#127×C₇₃	D₄	1	4	yes	—
63	#124×C₇₃	—	2	8	no	—
64	C₂²⋊Q₈×C₇₃	—	4	4	no	—
65	#121×C₇₃	—	2	8	no	—
66	#121×C₇₃	—	2	4	no	—
67	#121×C₇₃	—	2	4	no	—
68	C₄×D₄×C₇₃	—	2	8	no	—
69	C₄×D₄×C₇₃	—	2	4	no	—
70	C₄×D₄×C₇₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₄²×C₇₃	—	2	2	no	—
83	C₂×C₄²×C₇₃	—	2	2	no	—
84	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	#103×C₇₃	—	2	8	no	—
89	#102×C₇₃	—	4	4	no	—
90	C₂²⋊C₈×C₇₃	—	2	4	no	—
91	C₄×C₈×C₇₃	—	2	2	no	—
92	C₄×C₈×C₇₃	—	2	2	no	—
93	#95×C₇₃	—	2	2	no	—
94	#95×C₇₃	—	2	2	no	—
95	C₂⁴×C₇₃	—	2	2	no	—
96	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
97	#41×C₇₃	—	4	32	no	—
98	C₂×Q₈×C₇₃	—	2	4	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	4	no	—
102	C₂×Q₈×C₇₃	—	2	4	no	—
103	C₂×Q₈×C₇₃	—	4	2	no	—
104	C₂×Q₈×C₇₃	—	4	2	no	—
105	C₂×D₄×C₇₃	—	2	8	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	4	no	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	4	4	no	—
112	C₂×D₄×C₇₃	—	4	4	no	—
113	C₂×D₄×C₇₃	—	4	2	no	—
114	C₂×D₄×C₇₃	—	4	2	no	—
115	C₂×D₄×C₇₃	—	4	2	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
120	C₂²×C₄×C₇₃	—	2	8	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	2	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	1	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	4	4	no	—
132	C₂²×C₄×C₇₃	—	4	4	no	—
133	C₂²×C₄×C₇₃	SD₁₆	1	4	yes	complemented
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₇₃	—	4	16	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	#41	1	4	yes	complemented
147	C₄⋊C₄×C₇₃	—	2	4	no	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	4	no	—
150	C₄⋊C₄×C₇₃	—	4	4	no	—
151	C₄⋊C₄×C₇₃	—	4	2	no	—
152	C₄⋊C₄×C₇₃	—	4	2	no	—
153	C₄⋊C₄×C₇₃	—	4	2	no	—
154	C₄⋊C₄×C₇₃	—	4	2	no	—
155	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
156	C₂²⋊C₄×C₇₃	—	2	8	no	—
157	C₂²⋊C₄×C₇₃	—	2	8	no	—
158	C₂²⋊C₄×C₇₃	—	4	4	no	—
159	C₄²×C₇₃	—	2	2	no	—
160	C₄²×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	1	no	—
162	C₄²×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	C₂×D₄	1	2	yes	—
164	C₄²×C₇₃	C₂×D₄	1	2	yes	—
165	C₂³×C₇₃	—	2	1	no	—
166	C₂³×C₇₃	—	2	1	no	—
167	C₂³×C₇₃	—	2	1	no	—
168	C₂³×C₇₃	—	2	1	no	—
169	C₂³×C₇₃	—	2	1	no	—
170	C₂³×C₇₃	—	2	1	no	—
171	C₂³×C₇₃	—	2	4	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	C₂×SD₁₆	1	2	yes	—
179	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₇₃	—	4	8	no	—
181	Q₈×C₇₃	—	4	4	no	—
182	Q₈×C₇₃	—	4	4	no	—
183	D₄×C₇₃	—	2	8	no	—
184	D₄×C₇₃	—	4	16	no	—
185	D₄×C₇₃	—	4	4	no	—
186	D₄×C₇₃	—	4	8	no	—
187	D₄×C₇₃	—	4	8	no	—
188	C₂×C₄×C₇₃	—	2	1	no	—
189	C₂×C₄×C₇₃	—	2	1	no	—
190	C₂×C₄×C₇₃	—	2	8	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	1	no	—
193	C₂×C₄×C₇₃	—	2	4	no	—
194	C₂×C₄×C₇₃	—	2	1	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	4	16	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	4	2	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	2	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	2	no	—
210	C₂×C₄×C₇₃	#120	1	2	yes	—
211	C₂×C₄×C₇₃	#120	1	2	yes	—
212	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
214	C₂×C₄×C₇₃	#135	1	2	yes	—
215	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₇₃	#137	1	2	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
220	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₇₃	—	2	4	no	—
222	C₈×C₇₃	—	4	2	no	—
223	C₂²×C₇₃	—	2	2	no	—
224	C₂²×C₇₃	—	2	2	no	—
225	C₂²×C₇₃	—	2	2	no	—
226	C₂²×C₇₃	—	4	1	no	—
227	C₂²×C₇₃	—	4	1	no	—
228	C₂²×C₇₃	—	4	1	no	—
229	C₂²×C₇₃	—	4	1	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	4	4	no	—
232	C₂²×C₇₃	—	4	4	no	—
233	C₂²×C₇₃	—	8	2	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	2	no	—
236	C₂²×C₇₃	—	8	2	no	—
237	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
238	C₂²×C₇₃	#532	1	1	yes	characteristic
239	C₂²×C₇₃	#535	1	1	yes	characteristic
240	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
241	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
242	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
244	C₄×C₇₃	—	2	2	no	—
245	C₄×C₇₃	—	4	1	no	—
246	C₄×C₇₃	—	4	4	no	—
247	C₄×C₇₃	—	4	1	no	—
248	C₄×C₇₃	—	8	2	no	—
249	C₄×C₇₃	—	8	2	no	—
250	C₄×C₇₃	#450	1	4	yes	—
251	C₄×C₇₃	#452	1	4	yes	—
252	C₄×C₇₃	#546	1	2	yes	—
253	C₄×C₇₃	#550	1	2	yes	—
254	#25597	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₇₃	—	4	2	no	—
256	C₂×C₇₃	—	8	4	no	—
257	C₂×C₇₃	#2431	1	1	yes	characteristic
258	C₂×C₇₃	C₂×#450	1	1	yes	characteristic
259	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
260	C₂×C₇₃	#3167	1	1	yes	characteristic
261	C₂×C₇₃	#3182	1	1	yes	characteristic
262	C₂×C₇₃	#3206	1	1	yes	characteristic
263	C₂×C₇₃	#3207	1	1	yes	characteristic
264	C₂×#532	C₂×C₇₃	1	1	yes	characteristic
265	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
266	C₂×#487	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
268	#2000	C₂×C₇₃	1	4	yes	complemented
269	#1990	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#1957	C₂×C₇₃	1	1	yes	characteristic, complemented
271	#1877	C₂×C₇₃	1	4	yes	complemented
272	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic, complemented
273	C₇₃	#25597	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×#41	—	2	1	no	—
275	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
276	#532	—	2	4	no	—
277	#532	—	2	4	no	—
278	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
281	C₂×#124	—	2	1	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
283	C₂×#121	—	2	1	no	—
284	C₂×#121	C₂²×C₇₃	1	2	yes	—
285	C₂×C₄×D₄	—	2	1	no	—
286	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
287	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
288	#492	—	2	4	no	—
289	#487	—	2	4	no	—
290	C₂×#103	C₂²×C₇₃	1	4	yes	—
291	C₂×#102	C₂²×C₇₃	1	4	yes	—
292	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
293	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
295	#391	C₂²×C₇₃	1	2	yes	—
296	#389	—	2	1	no	—
297	#389	—	2	1	no	—
298	#384	C₂²×C₇₃	1	1	yes	characteristic
299	#380	—	2	1	no	—
300	#380	—	2	1	no	—
301	#340	C₂²×C₇₃	1	4	yes	—
302	#336	C₂²×C₇₃	1	2	yes	—
303	C₂×#41	—	2	8	no	—
304	C₂×#41	—	4	4	no	—
305	C₂×#41	—	4	4	no	—
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
308	C₂²×D₄	—	2	2	no	—
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	1	no	—
311	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
316	C₂×SD₁₆	—	2	8	no	—
317	C₂×SD₁₆	—	2	8	no	—
318	C₂×SD₁₆	—	4	4	no	—
319	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
320	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
325	#127	—	2	2	no	—
326	#127	D₄×C₇₃	1	4	yes	—
327	#124	—	2	8	no	—
328	C₂²⋊Q₈	—	4	4	no	—
329	#121	—	2	8	no	—
330	#121	—	2	4	no	—
331	#121	—	2	4	no	—
332	C₄×D₄	—	2	8	no	—
333	C₄×D₄	—	2	4	no	—
334	C₄×D₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
349	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
352	#103	—	2	8	no	—
353	#102	—	4	4	no	—
354	C₂²⋊C₈	—	2	4	no	—
355	C₄×C₈	—	2	2	no	—
356	C₄×C₈	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
361	#41	—	4	32	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	4	2	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	SD₁₆×C₇₃	1	4	yes	complemented
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
404	SD₁₆	—	4	16	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	#41×C₇₃	1	4	yes	complemented
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	C₂×D₄×C₇₃	1	2	yes	—
428	C₄²	C₂×D₄×C₇₃	1	2	yes	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	C₂×SD₁₆×C₇₃	1	2	yes	—
443	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
444	Q₈	—	4	8	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	4	4	no	—
447	D₄	—	2	8	no	—
448	D₄	—	4	16	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	8	no	—
451	D₄	—	4	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	4	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	#120×C₇₃	1	2	yes	—
475	C₂×C₄	#120×C₇₃	1	2	yes	—
476	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
477	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
478	C₂×C₄	#135×C₇₃	1	2	yes	—
479	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
480	C₂×C₄	#137×C₇₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
484	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
485	C₈	—	2	4	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	4	1	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
502	C₂²	#532×C₇₃	1	1	yes	characteristic
503	C₂²	#535×C₇₃	1	1	yes	characteristic
504	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
505	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
506	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
507	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	8	2	no	—
513	C₄	—	8	2	no	—
514	C₄	#450×C₇₃	1	4	yes	—
515	C₄	#452×C₇₃	1	4	yes	—
516	C₄	#546×C₇₃	1	2	yes	—
517	C₄	#550×C₇₃	1	2	yes	—
518	C₂	—	4	2	no	—
519	C₂	—	8	4	no	—
520	C₂	C₇₃×#2431	1	1	yes	characteristic
521	C₂	C₂×#450×C₇₃	1	1	yes	characteristic
522	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
523	C₂	C₇₃×#3167	1	1	yes	characteristic
524	C₂	C₇₃×#3182	1	1	yes	characteristic
525	C₂	C₇₃×#3206	1	1	yes	characteristic
526	C₂	C₇₃×#3207	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#532×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#492×C₇₃	C₂	semidirect
3. C₂×#487×C₇₃	C₂	semidirect
4. C₇₃×#2857	C₂	semidirect
5. C₇₃×#2000	C₂	semidirect
6. C₇₃×#1990	C₂	semidirect
7. C₇₃×#1957	C₂	semidirect
8. C₇₃×#1877	C₂	semidirect
9. C₄×C₂²⋊C₈×C₇₃	C₂	semidirect
133. C₂²×C₄×C₇₃	SD₁₆	semidirect
146. C₂×C₈×C₇₃	#41	semidirect
254. #25597	C₇₃	direct (N × H)
265. C₂×#492	C₂×C₇₃	semidirect
266. C₂×#487	C₂×C₇₃	semidirect
267. #2857	C₂×C₇₃	semidirect
268. #2000	C₂×C₇₃	semidirect
269. #1990	C₂×C₇₃	semidirect
270. #1957	C₂×C₇₃	semidirect
271. #1877	C₂×C₇₃	semidirect
272. C₄×C₂²⋊C₈	C₂×C₇₃	semidirect
273. C₇₃	#25597	direct (N × H)
397. C₂²×C₄	SD₁₆×C₇₃	semidirect
410. 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×#532×C₇₃	2
C₂×#492×C₇₃	2
C₂×#487×C₇₃	2
C₇₃×#2857	2
C₇₃×#2000	2
C₇₃×#1990	2
C₇₃×#1957	2
C₇₃×#1877	2
C₄×C₂²⋊C₈×C₇₃	2
#25597	73

Subgroups — C73×#25597 #32935001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25597 #32935001