Subgroups — C₇₃×#18870 #32928274

Order 18688.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1641	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1639	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1621	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1619	C₂	1	2	yes	maximal, complemented
9	C₂×#331×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₇₃	—	2	1	no	—
13	C₂×#135×C₇₃	—	2	1	no	—
14	#550×C₇₃	—	2	1	no	—
15	#550×C₇₃	C₂²	1	2	yes	—
16	D₄²×C₇₃	—	2	2	no	—
17	D₄²×C₇₃	—	2	2	no	—
18	D₄²×C₇₃	—	2	1	no	—
19	D₄²×C₇₃	C₂²	1	2	yes	—
20	#535×C₇₃	—	2	2	no	—
21	#535×C₇₃	—	2	1	no	—
22	#532×C₇₃	—	2	1	no	—
23	#532×C₇₃	C₂²	1	1	yes	characteristic
24	#532×C₇₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×#127×C₇₃	—	2	1	no	—
26	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
27	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
28	#493×C₇₃	C₂²	1	2	yes	complemented
29	#486×C₇₃	C₂²	1	2	yes	complemented
30	#474×C₇₃	—	2	1	no	—
31	#474×C₇₃	C₂²	1	2	yes	complemented
32	#466×C₇₃	—	2	2	no	—
33	#464×C₇₃	—	2	1	no	—
34	#463×C₇₃	—	2	1	no	—
35	#462×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	#461×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	#460×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#459×C₇₃	—	2	1	no	—
39	#459×C₇₃	—	2	2	no	—
40	#459×C₇₃	C₂²	1	2	yes	complemented
41	#459×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	#447×C₇₃	—	2	2	no	—
43	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#416×C₇₃	—	2	1	no	—
47	#331×C₇₃	C₂²	1	2	yes	complemented
48	#331×C₇₃	C₂²	1	2	yes	complemented
49	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
50	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
51	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
52	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
53	H(5,𝔽₂)×C₇₃	—	4	4	no	—
54	H(5,𝔽₂)×C₇₃	—	4	4	no	—
55	C₂×#41×C₇₃	—	2	2	no	—
56	C₂×#41×C₇₃	—	2	2	no	—
57	C₂×#41×C₇₃	—	2	1	no	—
58	C₂×#41×C₇₃	—	2	1	no	—
59	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
60	C₂²×D₄×C₇₃	—	2	2	no	—
61	C₂²×D₄×C₇₃	—	2	4	no	—
62	C₂²×D₄×C₇₃	—	2	2	no	—
63	C₂²×D₄×C₇₃	—	2	2	no	—
64	C₂²×D₄×C₇₃	—	2	2	no	—
65	C₂²×D₄×C₇₃	—	2	1	no	—
66	C₂²×D₄×C₇₃	—	2	1	no	—
67	C₂²×D₄×C₇₃	D₄	1	2	yes	—
68	#135×C₇₃	—	4	4	no	—
69	C₂×Q₁₆×C₇₃	—	2	1	no	—
70	C₂×SD₁₆×C₇₃	—	2	1	no	—
71	C₂×SD₁₆×C₇₃	—	2	1	no	—
72	C₂×D₈×C₇₃	—	2	1	no	—
73	C₂×D₈×C₇₃	—	2	4	no	—
74	C₂×D₈×C₇₃	—	2	2	no	—
75	C₂²×C₈×C₇₃	—	2	1	no	—
76	C₂²×C₈×C₇₃	—	2	1	no	—
77	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
78	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
79	#127×C₇₃	—	2	2	no	—
80	#127×C₇₃	—	2	2	no	—
81	#127×C₇₃	—	2	2	no	—
82	#127×C₇₃	—	2	1	no	—
83	#127×C₇₃	—	2	1	no	—
84	#127×C₇₃	D₄	1	1	yes	characteristic
85	#127×C₇₃	D₄	1	2	yes	—
86	#127×C₇₃	C₂³	1	1	yes	characteristic
87	#127×C₇₃	C₂³	1	2	yes	—
88	#124×C₇₃	—	2	2	no	—
89	#124×C₇₃	—	2	1	no	—
90	#124×C₇₃	—	2	1	no	—
91	#121×C₇₃	—	2	2	no	—
92	#121×C₇₃	—	2	4	no	—
93	#121×C₇₃	—	2	4	no	—
94	#121×C₇₃	—	2	1	no	—
95	#121×C₇₃	—	2	2	no	—
96	#121×C₇₃	—	2	2	no	—
97	#121×C₇₃	—	2	2	no	—
98	#121×C₇₃	—	2	1	no	—
99	#121×C₇₃	—	2	1	no	—
100	#121×C₇₃	D₄	1	2	yes	—
101	#120×C₇₃	—	2	4	no	—
102	#120×C₇₃	—	2	4	no	—
103	#120×C₇₃	—	2	4	no	—
104	C₄×Q₈×C₇₃	D₄	1	1	yes	characteristic
105	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₇₃	—	2	2	no	—
107	C₄×D₄×C₇₃	—	2	1	no	—
108	C₄×D₄×C₇₃	—	2	1	no	—
109	C₄×D₄×C₇₃	—	2	2	no	—
110	C₄×D₄×C₇₃	—	2	1	no	—
111	C₄×D₄×C₇₃	—	2	1	no	—
112	C₄×D₄×C₇₃	—	2	1	no	—
113	C₄×D₄×C₇₃	D₄	1	1	yes	characteristic
114	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₄×D₄×C₇₃	C₂³	1	2	yes	—
116	#117×C₇₃	—	2	1	no	—
117	#117×C₇₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₇₃	—	2	1	no	—
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	#107×C₇₃	—	2	2	no	—
121	C₄⋊C₈×C₇₃	—	2	1	no	—
122	C₄⋊C₈×C₇₃	—	2	1	no	—
123	C₄⋊C₈×C₇₃	—	2	1	no	—
124	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
125	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
126	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
127	#103×C₇₃	—	2	1	no	—
128	#103×C₇₃	—	2	1	no	—
129	#102×C₇₃	—	2	4	no	—
130	#102×C₇₃	—	2	2	no	—
131	#102×C₇₃	—	2	1	no	—
132	#102×C₇₃	—	2	1	no	—
133	#102×C₇₃	—	2	2	no	—
134	C₂²⋊C₈×C₇₃	—	2	1	no	—
135	C₄×C₈×C₇₃	C₂³	1	2	yes	—
136	C₂⁴×C₇₃	—	2	4	no	—
137	C₂⁴×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	#41×C₇₃	—	4	8	no	—
140	#41×C₇₃	—	4	4	no	—
141	#41×C₇₃	—	4	4	no	—
142	#41×C₇₃	—	4	2	no	—
143	#41×C₇₃	—	4	2	no	—
144	#41×C₇₃	—	4	2	no	—
145	#41×C₇₃	—	4	2	no	—
146	#41×C₇₃	D₈	1	4	yes	complemented
147	C₂×Q₈×C₇₃	—	2	1	no	—
148	C₂×Q₈×C₇₃	—	2	1	no	—
149	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	4	no	—
152	C₂×D₄×C₇₃	—	2	4	no	—
153	C₂×D₄×C₇₃	—	2	2	no	—
154	C₂×D₄×C₇₃	—	2	4	no	—
155	C₂×D₄×C₇₃	—	2	4	no	—
156	C₂×D₄×C₇₃	—	2	2	no	—
157	C₂×D₄×C₇₃	—	2	1	no	—
158	C₂×D₄×C₇₃	—	2	2	no	—
159	C₂×D₄×C₇₃	—	2	1	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	2	2	no	—
163	C₂×D₄×C₇₃	—	2	1	no	—
164	C₂×D₄×C₇₃	—	2	1	no	—
165	C₂×D₄×C₇₃	—	2	1	no	—
166	C₂×D₄×C₇₃	—	4	8	no	—
167	C₂×D₄×C₇₃	—	4	16	no	—
168	C₂×D₄×C₇₃	—	4	4	no	—
169	C₂×D₄×C₇₃	—	4	4	no	—
170	C₂×D₄×C₇₃	—	4	1	no	—
171	C₂×D₄×C₇₃	—	4	2	no	—
172	C₂×D₄×C₇₃	—	4	2	no	—
173	C₂×D₄×C₇₃	—	8	1	no	—
174	C₂×D₄×C₇₃	—	8	1	no	—
175	C₂×D₄×C₇₃	—	8	2	no	—
176	C₂×D₄×C₇₃	—	8	2	no	—
177	C₂×D₄×C₇₃	—	8	2	no	—
178	C₂×D₄×C₇₃	—	8	4	no	—
179	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
180	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
181	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
182	C₂²×C₄×C₇₃	—	2	1	no	—
183	C₂²×C₄×C₇₃	—	2	4	no	—
184	C₂²×C₄×C₇₃	—	2	1	no	—
185	C₂²×C₄×C₇₃	—	2	1	no	—
186	C₂²×C₄×C₇₃	—	2	2	no	—
187	C₂²×C₄×C₇₃	—	4	1	no	—
188	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
191	Q₁₆×C₇₃	—	4	2	no	—
192	SD₁₆×C₇₃	—	4	2	no	—
193	SD₁₆×C₇₃	—	4	2	no	—
194	D₈×C₇₃	—	4	2	no	—
195	D₈×C₇₃	—	8	2	no	—
196	D₈×C₇₃	—	8	4	no	—
197	C₂×C₈×C₇₃	—	2	2	no	—
198	C₂×C₈×C₇₃	—	2	2	no	—
199	C₂×C₈×C₇₃	—	2	1	no	—
200	C₂×C₈×C₇₃	—	2	1	no	—
201	C₂×C₈×C₇₃	—	4	2	no	—
202	C₂×C₈×C₇₃	—	8	1	no	—
203	C₄⋊C₄×C₇₃	—	2	1	no	—
204	C₄⋊C₄×C₇₃	—	2	1	no	—
205	C₄⋊C₄×C₇₃	—	2	1	no	—
206	C₄⋊C₄×C₇₃	—	2	1	no	—
207	C₄⋊C₄×C₇₃	—	2	1	no	—
208	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₇₃	—	2	4	no	—
212	C₂²⋊C₄×C₇₃	—	2	4	no	—
213	C₂²⋊C₄×C₇₃	—	2	1	no	—
214	C₂²⋊C₄×C₇₃	—	2	1	no	—
215	C₂²⋊C₄×C₇₃	—	2	2	no	—
216	C₂²⋊C₄×C₇₃	—	2	1	no	—
217	C₂²⋊C₄×C₇₃	—	2	2	no	—
218	C₂²⋊C₄×C₇₃	—	4	1	no	—
219	C₂²⋊C₄×C₇₃	—	4	1	no	—
220	C₄²×C₇₃	—	2	1	no	—
221	C₄²×C₇₃	—	2	1	no	—
222	C₄²×C₇₃	—	2	1	no	—
223	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₇₃	—	2	1	no	—
228	C₂³×C₇₃	—	2	2	no	—
229	C₂³×C₇₃	—	2	4	no	—
230	C₂³×C₇₃	—	4	8	no	—
231	C₂³×C₇₃	—	4	4	no	—
232	C₂³×C₇₃	—	4	1	no	—
233	C₂³×C₇₃	—	8	2	no	—
234	C₂³×C₇₃	—	8	2	no	—
235	C₂³×C₇₃	—	8	4	no	—
236	C₂³×C₇₃	—	8	4	no	—
237	C₂³×C₇₃	#120	1	1	yes	characteristic
238	Q₈×C₇₃	—	2	1	no	—
239	Q₈×C₇₃	—	4	2	no	—
240	Q₈×C₇₃	—	4	1	no	—
241	Q₈×C₇₃	—	4	1	no	—
242	Q₈×C₇₃	C₂×D₈	1	2	yes	—
243	D₄×C₇₃	—	2	4	no	—
244	D₄×C₇₃	—	2	1	no	—
245	D₄×C₇₃	—	2	2	no	—
246	D₄×C₇₃	—	2	2	no	—
247	D₄×C₇₃	—	4	4	no	—
248	D₄×C₇₃	—	4	8	no	—
249	D₄×C₇₃	—	4	4	no	—
250	D₄×C₇₃	—	4	2	no	—
251	D₄×C₇₃	—	4	2	no	—
252	D₄×C₇₃	—	4	8	no	—
253	D₄×C₇₃	—	4	4	no	—
254	D₄×C₇₃	—	4	2	no	—
255	D₄×C₇₃	—	4	1	no	—
256	D₄×C₇₃	—	4	2	no	—
257	D₄×C₇₃	—	4	1	no	—
258	D₄×C₇₃	—	4	2	no	—
259	D₄×C₇₃	—	4	1	no	—
260	D₄×C₇₃	—	4	2	no	—
261	D₄×C₇₃	—	4	1	no	—
262	D₄×C₇₃	—	4	2	no	—
263	D₄×C₇₃	—	4	4	no	—
264	D₄×C₇₃	—	8	2	no	—
265	D₄×C₇₃	—	8	4	no	—
266	D₄×C₇₃	—	8	4	no	—
267	D₄×C₇₃	—	8	2	no	—
268	D₄×C₇₃	C₂×D₈	1	2	yes	—
269	C₂×C₄×C₇₃	—	2	1	no	—
270	C₂×C₄×C₇₃	—	2	1	no	—
271	C₂×C₄×C₇₃	—	2	1	no	—
272	C₂×C₄×C₇₃	—	2	4	no	—
273	C₂×C₄×C₇₃	—	2	1	no	—
274	C₂×C₄×C₇₃	—	2	1	no	—
275	C₂×C₄×C₇₃	—	2	2	no	—
276	C₂×C₄×C₇₃	—	4	1	no	—
277	C₂×C₄×C₇₃	—	4	8	no	—
278	C₂×C₄×C₇₃	—	4	2	no	—
279	C₂×C₄×C₇₃	—	4	2	no	—
280	C₂×C₄×C₇₃	—	4	2	no	—
281	C₂×C₄×C₇₃	—	4	1	no	—
282	C₂×C₄×C₇₃	—	4	1	no	—
283	C₂×C₄×C₇₃	—	4	1	no	—
284	C₂×C₄×C₇₃	—	8	2	no	—
285	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
286	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
287	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
288	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
289	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
290	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
291	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
293	C₈×C₇₃	—	4	2	no	—
294	C₈×C₇₃	—	4	1	no	—
295	C₈×C₇₃	—	4	1	no	—
296	C₈×C₇₃	—	4	2	no	—
297	C₂²×C₇₃	—	2	1	no	—
298	C₂²×C₇₃	—	2	1	no	—
299	C₂²×C₇₃	—	2	2	no	—
300	C₂²×C₇₃	—	4	1	no	—
301	C₂²×C₇₃	—	4	1	no	—
302	C₂²×C₇₃	—	4	4	no	—
303	C₂²×C₇₃	—	4	2	no	—
304	C₂²×C₇₃	—	4	2	no	—
305	C₂²×C₇₃	—	4	4	no	—
306	C₂²×C₇₃	—	4	4	no	—
307	C₂²×C₇₃	—	4	2	no	—
308	C₂²×C₇₃	—	8	1	no	—
309	C₂²×C₇₃	—	8	1	no	—
310	C₂²×C₇₃	—	8	1	no	—
311	C₂²×C₇₃	—	16	4	no	—
312	C₂²×C₇₃	—	16	8	no	—
313	C₂²×C₇₃	#447	1	2	yes	—
314	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
315	C₄×C₇₃	—	2	2	no	—
316	C₄×C₇₃	—	2	1	no	—
317	C₄×C₇₃	—	2	1	no	—
318	C₄×C₇₃	—	2	1	no	—
319	C₄×C₇₃	—	4	2	no	—
320	C₄×C₇₃	—	4	1	no	—
321	C₄×C₇₃	—	4	1	no	—
322	C₄×C₇₃	—	8	1	no	—
323	C₄×C₇₃	#447	1	2	yes	—
324	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
325	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₄×C₇₃	#576	1	1	yes	characteristic
327	C₄×C₇₃	#577	1	1	yes	characteristic
328	#18870	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂×C₇₃	—	2	2	no	—
330	C₂×C₇₃	—	4	2	no	—
331	C₂×C₇₃	—	8	2	no	—
332	C₂×C₇₃	—	8	4	no	—
333	C₂×C₇₃	—	16	1	no	—
334	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
335	C₂×C₇₃	#3012	1	1	yes	characteristic
336	C₂×C₇₃	#3019	1	1	yes	characteristic
337	#3498	C₂×C₇₃	1	1	yes	characteristic, complemented
338	#3245	C₂×C₇₃	1	1	yes	characteristic, complemented
339	#3205	C₂×C₇₃	1	1	yes	characteristic, complemented
340	#3035	C₂×C₇₃	1	1	yes	characteristic, complemented
341	#1641	C₂×C₇₃	1	2	yes	complemented
342	#1639	C₂×C₇₃	1	2	yes	complemented
343	#1621	C₂×C₇₃	1	2	yes	complemented
344	#1619	C₂×C₇₃	1	2	yes	complemented
345	C₂×#331	C₂×C₇₃	1	1	yes	characteristic, complemented
346	#1480	C₂×C₇₃	1	1	yes	characteristic, complemented
347	#1477	C₂×C₇₃	1	1	yes	characteristic, complemented
348	C₇₃	#18870	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×H(5,𝔽₂)	—	2	1	no	—
350	C₂×#135	—	2	1	no	—
351	#550	—	2	1	no	—
352	#550	C₂²×C₇₃	1	2	yes	—
353	D₄²	—	2	2	no	—
354	D₄²	—	2	2	no	—
355	D₄²	—	2	1	no	—
356	D₄²	C₂²×C₇₃	1	2	yes	—
357	#535	—	2	2	no	—
358	#535	—	2	1	no	—
359	#532	—	2	1	no	—
360	#532	C₂²×C₇₃	1	1	yes	characteristic
361	#532	C₂²×C₇₃	1	1	yes	characteristic, complemented
362	C₂×#127	—	2	1	no	—
363	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
364	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
365	#493	C₂²×C₇₃	1	2	yes	complemented
366	#486	C₂²×C₇₃	1	2	yes	complemented
367	#474	—	2	1	no	—
368	#474	C₂²×C₇₃	1	2	yes	complemented
369	#466	—	2	2	no	—
370	#464	—	2	1	no	—
371	#463	—	2	1	no	—
372	#462	C₂²×C₇₃	1	1	yes	characteristic, complemented
373	#461	C₂²×C₇₃	1	1	yes	characteristic, complemented
374	#460	C₂²×C₇₃	1	1	yes	characteristic, complemented
375	#459	—	2	2	no	—
376	#459	—	2	1	no	—
377	#459	C₂²×C₇₃	1	1	yes	characteristic, complemented
378	#459	C₂²×C₇₃	1	2	yes	complemented
379	#447	—	2	2	no	—
380	#431	C₂²×C₇₃	1	1	yes	characteristic, complemented
381	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
382	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
383	#416	—	2	1	no	—
384	#331	C₂²×C₇₃	1	2	yes	complemented
385	#331	C₂²×C₇₃	1	2	yes	complemented
386	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
387	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
388	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
389	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
390	H(5,𝔽₂)	—	4	4	no	—
391	H(5,𝔽₂)	—	4	4	no	—
392	C₂×#41	—	2	2	no	—
393	C₂×#41	—	2	2	no	—
394	C₂×#41	—	2	1	no	—
395	C₂×#41	—	2	1	no	—
396	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
397	C₂²×D₄	—	2	2	no	—
398	C₂²×D₄	—	2	4	no	—
399	C₂²×D₄	—	2	2	no	—
400	C₂²×D₄	—	2	2	no	—
401	C₂²×D₄	—	2	2	no	—
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	D₄×C₇₃	1	2	yes	—
405	#135	—	4	4	no	—
406	C₂×Q₁₆	—	2	1	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×SD₁₆	—	2	1	no	—
409	C₂×D₈	—	2	1	no	—
410	C₂×D₈	—	2	4	no	—
411	C₂×D₈	—	2	2	no	—
412	C₂²×C₈	—	2	1	no	—
413	C₂²×C₈	—	2	1	no	—
414	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
415	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
416	#127	—	2	2	no	—
417	#127	—	2	2	no	—
418	#127	—	2	2	no	—
419	#127	—	2	1	no	—
420	#127	—	2	1	no	—
421	#127	D₄×C₇₃	1	1	yes	characteristic
422	#127	D₄×C₇₃	1	2	yes	—
423	#127	C₂³×C₇₃	1	1	yes	characteristic
424	#127	C₂³×C₇₃	1	2	yes	—
425	#124	—	2	2	no	—
426	#124	—	2	1	no	—
427	#124	—	2	1	no	—
428	#121	—	2	2	no	—
429	#121	—	2	4	no	—
430	#121	—	2	4	no	—
431	#121	—	2	1	no	—
432	#121	—	2	2	no	—
433	#121	—	2	2	no	—
434	#121	—	2	2	no	—
435	#121	—	2	1	no	—
436	#121	—	2	1	no	—
437	#121	D₄×C₇₃	1	2	yes	—
438	#120	—	2	4	no	—
439	#120	—	2	4	no	—
440	#120	—	2	4	no	—
441	C₄×Q₈	D₄×C₇₃	1	1	yes	characteristic
442	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
443	C₄×D₄	—	2	2	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	—	2	1	no	—
446	C₄×D₄	—	2	2	no	—
447	C₄×D₄	—	2	1	no	—
448	C₄×D₄	—	2	1	no	—
449	C₄×D₄	—	2	1	no	—
450	C₄×D₄	D₄×C₇₃	1	1	yes	characteristic
451	C₄×D₄	C₂³×C₇₃	1	1	yes	characteristic
452	C₄×D₄	C₂³×C₇₃	1	2	yes	—
453	#117	—	2	1	no	—
454	#117	D₄×C₇₃	1	1	yes	characteristic
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
457	#107	—	2	2	no	—
458	C₄⋊C₈	—	2	1	no	—
459	C₄⋊C₈	—	2	1	no	—
460	C₄⋊C₈	—	2	1	no	—
461	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
462	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
463	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
464	#103	—	2	1	no	—
465	#103	—	2	1	no	—
466	#102	—	2	4	no	—
467	#102	—	2	2	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	—	2	2	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₄×C₈	C₂³×C₇₃	1	2	yes	—
473	C₂⁴	—	2	4	no	—
474	C₂⁴	—	2	2	no	—
475	#41	—	2	2	no	—
476	#41	—	4	8	no	—
477	#41	—	4	4	no	—
478	#41	—	4	4	no	—
479	#41	—	4	2	no	—
480	#41	—	4	2	no	—
481	#41	—	4	2	no	—
482	#41	—	4	2	no	—
483	#41	D₈×C₇₃	1	4	yes	complemented
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	4	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	2	2	no	—
491	C₂×D₄	—	2	4	no	—
492	C₂×D₄	—	2	4	no	—
493	C₂×D₄	—	2	2	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	2	no	—
496	C₂×D₄	—	2	1	no	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	1	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	1	no	—
503	C₂×D₄	—	4	8	no	—
504	C₂×D₄	—	4	16	no	—
505	C₂×D₄	—	4	4	no	—
506	C₂×D₄	—	4	4	no	—
507	C₂×D₄	—	4	1	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	8	1	no	—
511	C₂×D₄	—	8	1	no	—
512	C₂×D₄	—	8	2	no	—
513	C₂×D₄	—	8	2	no	—
514	C₂×D₄	—	8	2	no	—
515	C₂×D₄	—	8	4	no	—
516	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
517	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
518	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
526	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
528	Q₁₆	—	4	2	no	—
529	SD₁₆	—	4	2	no	—
530	SD₁₆	—	4	2	no	—
531	D₈	—	4	2	no	—
532	D₈	—	8	2	no	—
533	D₈	—	8	4	no	—
534	C₂×C₈	—	2	2	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	4	2	no	—
539	C₂×C₈	—	8	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
547	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	1	no	—
551	C₂²⋊C₄	—	2	1	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
561	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
562	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
563	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
564	C₂³	—	2	1	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	2	4	no	—
567	C₂³	—	4	8	no	—
568	C₂³	—	4	4	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	8	2	no	—
571	C₂³	—	8	2	no	—
572	C₂³	—	8	4	no	—
573	C₂³	—	8	4	no	—
574	C₂³	#120×C₇₃	1	1	yes	characteristic
575	Q₈	—	2	1	no	—
576	Q₈	—	4	2	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	C₂×D₈×C₇₃	1	2	yes	—
580	D₄	—	2	4	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	4	4	no	—
585	D₄	—	4	8	no	—
586	D₄	—	4	4	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	4	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	1	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	2	no	—
600	D₄	—	4	1	no	—
601	D₄	—	8	2	no	—
602	D₄	—	8	4	no	—
603	D₄	—	8	4	no	—
604	D₄	—	8	2	no	—
605	D₄	C₂×D₈×C₇₃	1	2	yes	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	4	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	8	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
623	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
624	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
625	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
626	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
630	C₈	—	4	2	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₈	—	4	2	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	16	4	no	—
649	C₂²	—	16	8	no	—
650	C₂²	#447×C₇₃	1	2	yes	—
651	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	8	1	no	—
660	C₄	#447×C₇₃	1	2	yes	—
661	C₄	C₂²×D₈×C₇₃	1	1	yes	characteristic
662	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
663	C₄	#576×C₇₃	1	1	yes	characteristic
664	C₄	#577×C₇₃	1	1	yes	characteristic
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	8	2	no	—
668	C₂	—	8	4	no	—
669	C₂	—	16	1	no	—
670	C₂	C₂×#447×C₇₃	1	1	yes	characteristic
671	C₂	C₇₃×#3012	1	1	yes	characteristic
672	C₂	C₇₃×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3498	C₂	semidirect
2. C₇₃×#3245	C₂	semidirect
3. C₇₃×#3205	C₂	semidirect
4. C₇₃×#3035	C₂	semidirect
5. C₇₃×#1641	C₂	semidirect
6. C₇₃×#1639	C₂	semidirect
7. C₇₃×#1621	C₂	semidirect
8. C₇₃×#1619	C₂	semidirect
9. C₂×#331×C₇₃	C₂	semidirect
10. C₇₃×#1480	C₂	semidirect
11. C₇₃×#1477	C₂	semidirect
24. #532×C₇₃	C₂²	semidirect
28. #493×C₇₃	C₂²	semidirect
29. #486×C₇₃	C₂²	semidirect
31. #474×C₇₃	C₂²	semidirect
35. #462×C₇₃	C₂²	semidirect
36. #461×C₇₃	C₂²	semidirect
37. #460×C₇₃	C₂²	semidirect
40. #459×C₇₃	C₂²	semidirect
41. #459×C₇₃	C₂²	semidirect
43. #431×C₇₃	C₂²	semidirect
44. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
45. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
47. #331×C₇₃	C₂²	semidirect
48. #331×C₇₃	C₂²	semidirect
49. Q₈⋊C₈×C₇₃	C₂²	semidirect
50. D₄⋊C₈×C₇₃	C₂²	semidirect
51. D₄⋊C₈×C₇₃	C₂²	semidirect
52. D₄⋊C₈×C₇₃	C₂²	semidirect
146. #41×C₇₃	D₈	semidirect
328. #18870	C₇₃	direct (N × H)
337. #3498	C₂×C₇₃	semidirect
338. #3245	C₂×C₇₃	semidirect
339. #3205	C₂×C₇₃	semidirect
340. #3035	C₂×C₇₃	semidirect
341. #1641	C₂×C₇₃	semidirect
342. #1639	C₂×C₇₃	semidirect
343. #1621	C₂×C₇₃	semidirect
344. #1619	C₂×C₇₃	semidirect
345. C₂×#331	C₂×C₇₃	semidirect
346. #1480	C₂×C₇₃	semidirect
347. #1477	C₂×C₇₃	semidirect
348. C₇₃	#18870	direct (N × H)
361. #532	C₂²×C₇₃	semidirect
365. #493	C₂²×C₇₃	semidirect
366. #486	C₂²×C₇₃	semidirect
368. #474	C₂²×C₇₃	semidirect
372. #462	C₂²×C₇₃	semidirect
373. #461	C₂²×C₇₃	semidirect
374. #460	C₂²×C₇₃	semidirect
377. #459	C₂²×C₇₃	semidirect
378. #459	C₂²×C₇₃	semidirect
380. #431	C₂²×C₇₃	semidirect
381. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
382. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
384. #331	C₂²×C₇₃	semidirect
385. #331	C₂²×C₇₃	semidirect
386. Q₈⋊C₈	C₂²×C₇₃	semidirect
387. D₄⋊C₈	C₂²×C₇₃	semidirect
388. D₄⋊C₈	C₂²×C₇₃	semidirect
389. D₄⋊C₈	C₂²×C₇₃	semidirect
483. #41	D₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3498	2
C₇₃×#3245	2
C₇₃×#3205	2
C₇₃×#3035	2
C₇₃×#1641	2
C₇₃×#1639	2
C₇₃×#1621	2
C₇₃×#1619	2
C₂×#331×C₇₃	2
C₇₃×#1480	2
C₇₃×#1477	2
#18870	73

Subgroups — C73×#18870 #32928274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18870 #32928274