Subgroups — C₆₇×#60044 #30739295

Order 17152.

2118 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2808	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2732	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2682	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2609	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2601	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2574	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2554	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2553	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2476	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2471	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2430	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2407	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2368	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2363	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2359	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#126×C₆₇	C₂²	1	2	yes	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₆₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
35	#399×C₆₇	C₂²	1	2	yes	—
36	#398×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	—
38	#398×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#396×C₆₇	C₂²	1	2	yes	—
41	#396×C₆₇	C₂²	1	2	yes	—
42	#396×C₆₇	C₂²	1	2	yes	—
43	#395×C₆₇	C₂²	1	2	yes	—
44	#394×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#393×C₆₇	C₂²	1	2	yes	—
49	#392×C₆₇	C₂²	1	2	yes	—
50	#392×C₆₇	C₂²	1	2	yes	—
51	#391×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	1	yes	characteristic
53	#391×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	1	yes	characteristic
55	#391×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	1	yes	characteristic
57	#390×C₆₇	C₂²	1	1	yes	characteristic
58	#390×C₆₇	C₂²	1	1	yes	characteristic
59	#390×C₆₇	C₂²	1	1	yes	characteristic
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	2	yes	—
62	#390×C₆₇	C₂²	1	2	yes	—
63	#389×C₆₇	C₂²	1	1	yes	characteristic
64	#389×C₆₇	C₂²	1	2	yes	—
65	#389×C₆₇	C₂²	1	1	yes	characteristic
66	#389×C₆₇	C₂²	1	1	yes	characteristic
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#388×C₆₇	C₂²	1	2	yes	—
69	#388×C₆₇	C₂²	1	2	yes	—
70	#388×C₆₇	C₂²	1	2	yes	—
71	#388×C₆₇	C₂²	1	2	yes	—
72	#388×C₆₇	C₂²	1	2	yes	—
73	#388×C₆₇	C₂²	1	2	yes	—
74	#388×C₆₇	C₂²	1	2	yes	—
75	#387×C₆₇	C₂²	1	2	yes	—
76	#387×C₆₇	C₂²	1	2	yes	—
77	#387×C₆₇	C₂²	1	2	yes	—
78	#387×C₆₇	C₂²	1	2	yes	—
79	#387×C₆₇	C₂²	1	2	yes	—
80	#387×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#386×C₆₇	C₂²	1	2	yes	—
83	#386×C₆₇	C₂²	1	2	yes	—
84	#386×C₆₇	C₂²	1	2	yes	—
85	#386×C₆₇	C₂²	1	2	yes	—
86	#386×C₆₇	C₂²	1	2	yes	—
87	#386×C₆₇	C₂²	1	2	yes	—
88	#386×C₆₇	C₂²	1	2	yes	—
89	#385×C₆₇	C₂²	1	2	yes	—
90	#385×C₆₇	C₂²	1	2	yes	—
91	#385×C₆₇	C₂²	1	2	yes	—
92	#385×C₆₇	C₂²	1	2	yes	—
93	#385×C₆₇	C₂²	1	2	yes	—
94	#385×C₆₇	C₂²	1	2	yes	—
95	#382×C₆₇	C₂²	1	2	yes	—
96	#380×C₆₇	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	—
107	C₂×#41×C₆₇	—	2	4	no	—
108	C₂×#41×C₆₇	—	2	4	no	—
109	C₂×#41×C₆₇	—	4	2	no	—
110	C₂×#41×C₆₇	—	4	2	no	—
111	C₂×#41×C₆₇	—	4	2	no	—
112	C₂×#41×C₆₇	—	4	2	no	—
113	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
128	#126×C₆₇	—	4	4	no	—
129	#123×C₆₇	—	2	8	no	—
130	#123×C₆₇	—	4	4	no	—
131	C₂²⋊Q₈×C₆₇	—	2	8	no	—
132	#121×C₆₇	—	2	8	no	—
133	#121×C₆₇	—	4	4	no	—
134	C₄×D₄×C₆₇	—	4	4	no	—
135	#117×C₆₇	—	2	4	no	—
136	#117×C₆₇	—	4	2	no	—
137	#117×C₆₇	—	4	2	no	—
138	#117×C₆₇	—	4	4	no	—
139	#117×C₆₇	—	4	2	no	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₄²×C₆₇	—	4	2	no	—
183	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
186	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
214	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
215	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
216	#41×C₆₇	—	4	16	no	—
217	#41×C₆₇	—	4	16	no	—
218	C₂×Q₈×C₆₇	—	2	2	no	—
219	C₂×Q₈×C₆₇	—	4	1	no	—
220	C₂×Q₈×C₆₇	—	4	1	no	—
221	C₂×Q₈×C₆₇	—	4	1	no	—
222	C₂×Q₈×C₆₇	—	4	1	no	—
223	C₂×Q₈×C₆₇	#41	1	4	yes	complemented
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	2	4	no	—
230	C₂×D₄×C₆₇	—	2	2	no	—
231	C₂×D₄×C₆₇	—	2	4	no	—
232	C₂×D₄×C₆₇	—	4	2	no	—
233	C₂×D₄×C₆₇	—	4	1	no	—
234	C₂×D₄×C₆₇	—	4	1	no	—
235	C₂×D₄×C₆₇	—	4	2	no	—
236	C₂×D₄×C₆₇	—	4	1	no	—
237	C₂×D₄×C₆₇	—	4	1	no	—
238	C₂×D₄×C₆₇	—	4	2	no	—
239	C₂×D₄×C₆₇	—	4	2	no	—
240	C₂×D₄×C₆₇	—	4	2	no	—
241	C₂×D₄×C₆₇	#41	1	4	yes	complemented
242	C₂²×C₄×C₆₇	—	2	2	no	—
243	C₂²×C₄×C₆₇	—	2	2	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	2	2	no	—
248	C₂²×C₄×C₆₇	—	2	2	no	—
249	C₂²×C₄×C₆₇	—	2	2	no	—
250	C₂²×C₄×C₆₇	—	2	2	no	—
251	C₂²×C₄×C₆₇	—	2	4	no	—
252	C₂²×C₄×C₆₇	—	2	4	no	—
253	C₂²×C₄×C₆₇	—	2	4	no	—
254	C₂²×C₄×C₆₇	—	2	4	no	—
255	C₂²×C₄×C₆₇	—	2	4	no	—
256	C₂²×C₄×C₆₇	—	2	4	no	—
257	C₂²×C₄×C₆₇	—	2	4	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	2	no	—
260	C₂²×C₄×C₆₇	—	4	2	no	—
261	C₂²×C₄×C₆₇	—	4	2	no	—
262	C₂²×C₄×C₆₇	—	4	2	no	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	4	no	—
281	C₄⋊C₄×C₆₇	—	2	4	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	4	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	4	no	—
286	C₄⋊C₄×C₆₇	—	2	4	no	—
287	C₄⋊C₄×C₆₇	—	4	1	no	—
288	C₄⋊C₄×C₆₇	—	4	1	no	—
289	C₄⋊C₄×C₆₇	—	4	2	no	—
290	C₄⋊C₄×C₆₇	—	4	1	no	—
291	C₄⋊C₄×C₆₇	—	4	1	no	—
292	C₄⋊C₄×C₆₇	—	4	1	no	—
293	C₄⋊C₄×C₆₇	—	4	1	no	—
294	C₄⋊C₄×C₆₇	—	4	2	no	—
295	C₄⋊C₄×C₆₇	—	4	2	no	—
296	C₄⋊C₄×C₆₇	—	4	2	no	—
297	C₄⋊C₄×C₆₇	—	4	2	no	—
298	C₄⋊C₄×C₆₇	#41	1	4	yes	complemented
299	C₂²⋊C₄×C₆₇	—	2	4	no	—
300	C₂²⋊C₄×C₆₇	—	2	4	no	—
301	C₂²⋊C₄×C₆₇	—	2	4	no	—
302	C₂²⋊C₄×C₆₇	—	2	4	no	—
303	C₂²⋊C₄×C₆₇	—	2	4	no	—
304	C₂²⋊C₄×C₆₇	—	2	4	no	—
305	C₂²⋊C₄×C₆₇	—	2	4	no	—
306	C₂²⋊C₄×C₆₇	—	2	4	no	—
307	C₂²⋊C₄×C₆₇	—	2	4	no	—
308	C₂²⋊C₄×C₆₇	—	2	4	no	—
309	C₂²⋊C₄×C₆₇	—	2	4	no	—
310	C₂²⋊C₄×C₆₇	—	2	4	no	—
311	C₂²⋊C₄×C₆₇	—	2	4	no	—
312	C₂²⋊C₄×C₆₇	—	4	2	no	—
313	C₂²⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	4	2	no	—
315	C₂²⋊C₄×C₆₇	—	4	2	no	—
316	C₂²⋊C₄×C₆₇	—	4	2	no	—
317	C₂²⋊C₄×C₆₇	—	4	2	no	—
318	C₂²⋊C₄×C₆₇	—	4	2	no	—
319	C₂²⋊C₄×C₆₇	—	4	2	no	—
320	C₂²⋊C₄×C₆₇	—	4	2	no	—
321	C₄²×C₆₇	—	2	4	no	—
322	C₄²×C₆₇	—	2	4	no	—
323	C₄²×C₆₇	—	2	4	no	—
324	C₄²×C₆₇	—	4	1	no	—
325	C₄²×C₆₇	—	4	1	no	—
326	C₄²×C₆₇	—	4	1	no	—
327	C₄²×C₆₇	—	4	1	no	—
328	C₄²×C₆₇	—	4	2	no	—
329	C₄²×C₆₇	—	4	2	no	—
330	C₄²×C₆₇	—	4	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	2	1	no	—
335	C₂³×C₆₇	—	2	1	no	—
336	C₂³×C₆₇	—	2	2	no	—
337	C₂³×C₆₇	—	2	1	no	—
338	C₂³×C₆₇	—	2	1	no	—
339	C₂³×C₆₇	—	2	2	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	2	no	—
342	C₂³×C₆₇	—	2	1	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	—	2	2	no	—
345	C₂³×C₆₇	—	2	2	no	—
346	C₂³×C₆₇	—	2	2	no	—
347	C₂³×C₆₇	—	2	2	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	C₂×#41	1	4	yes	—
351	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
352	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
353	Q₈×C₆₇	—	4	4	no	—
354	Q₈×C₆₇	—	4	4	no	—
355	D₄×C₆₇	—	4	4	no	—
356	D₄×C₆₇	—	4	8	no	—
357	D₄×C₆₇	—	4	8	no	—
358	D₄×C₆₇	—	4	4	no	—
359	D₄×C₆₇	—	4	8	no	—
360	D₄×C₆₇	—	8	4	no	—
361	C₂×C₄×C₆₇	—	2	8	no	—
362	C₂×C₄×C₆₇	—	2	8	no	—
363	C₂×C₄×C₆₇	—	2	8	no	—
364	C₂×C₄×C₆₇	—	2	1	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	1	no	—
371	C₂×C₄×C₆₇	—	2	1	no	—
372	C₂×C₄×C₆₇	—	2	1	no	—
373	C₂×C₄×C₆₇	—	2	1	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	1	no	—
377	C₂×C₄×C₆₇	—	2	1	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	1	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	2	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	2	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	2	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	2	no	—
400	C₂×C₄×C₆₇	—	2	2	no	—
401	C₂×C₄×C₆₇	—	2	2	no	—
402	C₂×C₄×C₆₇	—	2	2	no	—
403	C₂×C₄×C₆₇	—	2	2	no	—
404	C₂×C₄×C₆₇	—	4	8	no	—
405	C₂×C₄×C₆₇	—	4	8	no	—
406	C₂×C₄×C₆₇	—	4	8	no	—
407	C₂×C₄×C₆₇	—	8	4	no	—
408	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
409	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
410	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
411	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
412	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
413	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
414	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
416	C₂²×C₆₇	—	2	4	no	—
417	C₂²×C₆₇	—	2	4	no	—
418	C₂²×C₆₇	—	2	2	no	—
419	C₂²×C₆₇	—	2	2	no	—
420	C₂²×C₆₇	—	2	4	no	—
421	C₂²×C₆₇	—	2	2	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	—	4	1	no	—
424	C₂²×C₆₇	—	4	2	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	2	no	—
427	C₂²×C₆₇	—	4	2	no	—
428	C₂²×C₆₇	—	4	2	no	—
429	C₂²×C₆₇	—	4	1	no	—
430	C₂²×C₆₇	—	4	2	no	—
431	C₂²×C₆₇	—	4	2	no	—
432	C₂²×C₆₇	—	4	2	no	—
433	C₂²×C₆₇	—	4	2	no	—
434	C₂²×C₆₇	—	4	2	no	—
435	C₂²×C₆₇	—	4	2	no	—
436	C₂²×C₆₇	—	4	2	no	—
437	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
438	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
439	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
440	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
441	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	2	no	—
447	C₄×C₆₇	—	2	2	no	—
448	C₄×C₆₇	—	2	2	no	—
449	C₄×C₆₇	—	2	4	no	—
450	C₄×C₆₇	—	2	2	no	—
451	C₄×C₆₇	—	2	2	no	—
452	C₄×C₆₇	—	4	2	no	—
453	C₄×C₆₇	—	4	2	no	—
454	C₄×C₆₇	—	4	2	no	—
455	C₄×C₆₇	—	4	2	no	—
456	C₄×C₆₇	—	4	2	no	—
457	C₄×C₆₇	—	4	2	no	—
458	C₄×C₆₇	—	4	2	no	—
459	C₄×C₆₇	—	4	2	no	—
460	#60044	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
461	C₂×C₆₇	—	4	4	no	—
462	C₂×C₆₇	—	4	2	no	—
463	C₂×C₆₇	—	8	2	no	—
464	C₂×C₆₇	#3481	1	1	yes	characteristic
465	C₂×C₆₇	#3482	1	1	yes	characteristic
466	C₂×C₆₇	#3483	1	1	yes	characteristic
467	C₂×C₆₇	#3490	1	1	yes	characteristic
468	C₂×C₆₇	#3490	1	1	yes	characteristic
469	C₂×C₆₇	#3492	1	1	yes	characteristic
470	C₂×C₆₇	#3548	1	1	yes	characteristic
471	#2808	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#2806	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#2732	C₂×C₆₇	1	1	yes	characteristic, complemented
474	#2682	C₂×C₆₇	1	1	yes	characteristic, complemented
475	#2609	C₂×C₆₇	1	2	yes	complemented
476	#2601	C₂×C₆₇	1	2	yes	complemented
477	#2574	C₂×C₆₇	1	2	yes	complemented
478	#2554	C₂×C₆₇	1	2	yes	complemented
479	#2553	C₂×C₆₇	1	2	yes	complemented
480	#2476	C₂×C₆₇	1	2	yes	complemented
481	#2471	C₂×C₆₇	1	2	yes	complemented
482	#2430	C₂×C₆₇	1	2	yes	complemented
483	#2407	C₂×C₆₇	1	2	yes	complemented
484	#2368	C₂×C₆₇	1	2	yes	complemented
485	#2363	C₂×C₆₇	1	2	yes	complemented
486	#2359	C₂×C₆₇	1	2	yes	complemented
487	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
488	#2297	C₂×C₆₇	1	1	yes	characteristic, complemented
489	#2296	C₂×C₆₇	1	1	yes	characteristic, complemented
490	C₆₇	#60044	1	1	yes	characteristic, direct product factor, Sylow
491	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
492	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×#126	C₂²×C₆₇	1	2	yes	—
494	C₂×#123	C₂²×C₆₇	1	2	yes	—
495	C₂×#123	C₂²×C₆₇	1	2	yes	—
496	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
497	C₂×#121	C₂²×C₆₇	1	2	yes	—
498	C₂×#121	C₂²×C₆₇	1	2	yes	—
499	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
500	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
501	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×#117	C₂²×C₆₇	1	2	yes	—
504	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
505	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
506	#399	C₂²×C₆₇	1	2	yes	—
507	#398	C₂²×C₆₇	1	2	yes	—
508	#398	C₂²×C₆₇	1	2	yes	—
509	#398	C₂²×C₆₇	1	2	yes	—
510	#397	C₂²×C₆₇	1	2	yes	—
511	#396	C₂²×C₆₇	1	2	yes	—
512	#396	C₂²×C₆₇	1	2	yes	—
513	#396	C₂²×C₆₇	1	2	yes	—
514	#395	C₂²×C₆₇	1	2	yes	—
515	#394	C₂²×C₆₇	1	2	yes	—
516	#394	C₂²×C₆₇	1	2	yes	—
517	#394	C₂²×C₆₇	1	2	yes	—
518	#394	C₂²×C₆₇	1	2	yes	—
519	#393	C₂²×C₆₇	1	2	yes	—
520	#392	C₂²×C₆₇	1	2	yes	—
521	#392	C₂²×C₆₇	1	2	yes	—
522	#391	C₂²×C₆₇	1	1	yes	characteristic
523	#391	C₂²×C₆₇	1	1	yes	characteristic
524	#391	C₂²×C₆₇	1	2	yes	—
525	#391	C₂²×C₆₇	1	1	yes	characteristic
526	#391	C₂²×C₆₇	1	1	yes	characteristic
527	#390	C₂²×C₆₇	1	2	yes	—
528	#390	C₂²×C₆₇	1	1	yes	characteristic
529	#390	C₂²×C₆₇	1	2	yes	—
530	#390	C₂²×C₆₇	1	2	yes	—
531	#390	C₂²×C₆₇	1	1	yes	characteristic
532	#390	C₂²×C₆₇	1	1	yes	characteristic
533	#390	C₂²×C₆₇	1	1	yes	characteristic
534	#389	C₂²×C₆₇	1	2	yes	—
535	#389	C₂²×C₆₇	1	1	yes	characteristic
536	#389	C₂²×C₆₇	1	1	yes	characteristic
537	#389	C₂²×C₆₇	1	1	yes	characteristic
538	#389	C₂²×C₆₇	1	1	yes	characteristic
539	#388	C₂²×C₆₇	1	2	yes	—
540	#388	C₂²×C₆₇	1	2	yes	—
541	#388	C₂²×C₆₇	1	2	yes	—
542	#388	C₂²×C₆₇	1	2	yes	—
543	#388	C₂²×C₆₇	1	2	yes	—
544	#388	C₂²×C₆₇	1	2	yes	—
545	#388	C₂²×C₆₇	1	2	yes	—
546	#387	C₂²×C₆₇	1	2	yes	—
547	#387	C₂²×C₆₇	1	2	yes	—
548	#387	C₂²×C₆₇	1	2	yes	—
549	#387	C₂²×C₆₇	1	2	yes	—
550	#387	C₂²×C₆₇	1	2	yes	—
551	#387	C₂²×C₆₇	1	2	yes	—
552	#386	C₂²×C₆₇	1	2	yes	—
553	#386	C₂²×C₆₇	1	2	yes	—
554	#386	C₂²×C₆₇	1	2	yes	—
555	#386	C₂²×C₆₇	1	2	yes	—
556	#386	C₂²×C₆₇	1	2	yes	—
557	#386	C₂²×C₆₇	1	2	yes	—
558	#386	C₂²×C₆₇	1	2	yes	—
559	#386	C₂²×C₆₇	1	2	yes	—
560	#385	C₂²×C₆₇	1	2	yes	—
561	#385	C₂²×C₆₇	1	2	yes	—
562	#385	C₂²×C₆₇	1	2	yes	—
563	#385	C₂²×C₆₇	1	2	yes	—
564	#385	C₂²×C₆₇	1	2	yes	—
565	#385	C₂²×C₆₇	1	2	yes	—
566	#382	C₂²×C₆₇	1	2	yes	—
567	#380	C₂²×C₆₇	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
570	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
571	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
577	C₂×#95	C₂²×C₆₇	1	2	yes	—
578	C₂×#41	—	2	4	no	—
579	C₂×#41	—	2	4	no	—
580	C₂×#41	—	4	2	no	—
581	C₂×#41	—	4	2	no	—
582	C₂×#41	—	4	2	no	—
583	C₂×#41	—	4	2	no	—
584	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
585	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
586	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
587	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
588	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
589	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
590	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
597	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
598	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
599	#126	—	4	4	no	—
600	#123	—	2	8	no	—
601	#123	—	4	4	no	—
602	C₂²⋊Q₈	—	2	8	no	—
603	#121	—	2	8	no	—
604	#121	—	4	4	no	—
605	C₄×D₄	—	4	4	no	—
606	#117	—	2	4	no	—
607	#117	—	4	2	no	—
608	#117	—	4	2	no	—
609	#117	—	4	4	no	—
610	#117	—	4	2	no	—
611	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
631	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
653	C₂×C₄²	—	4	2	no	—
654	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
659	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
664	#95	C₂³×C₆₇	1	2	yes	—
665	#95	C₂³×C₆₇	1	2	yes	—
666	#95	C₂³×C₆₇	1	2	yes	—
667	#95	C₂³×C₆₇	1	2	yes	—
668	#95	C₂³×C₆₇	1	2	yes	—
669	#95	C₂³×C₆₇	1	2	yes	—
670	#95	C₂³×C₆₇	1	2	yes	—
671	#95	C₂³×C₆₇	1	2	yes	—
672	#95	C₂³×C₆₇	1	2	yes	—
673	#95	C₂³×C₆₇	1	2	yes	—
674	#95	C₂³×C₆₇	1	2	yes	—
675	#95	C₂³×C₆₇	1	2	yes	—
676	#95	C₂³×C₆₇	1	2	yes	—
677	#95	C₂³×C₆₇	1	2	yes	—
678	#95	C₂³×C₆₇	1	2	yes	—
679	#95	C₂³×C₆₇	1	2	yes	—
680	#95	C₂³×C₆₇	1	2	yes	—
681	#95	C₂³×C₆₇	1	2	yes	—
682	#95	C₂³×C₆₇	1	2	yes	—
683	#95	C₂³×C₆₇	1	2	yes	—
684	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
685	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
686	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
687	#41	—	4	16	no	—
688	#41	—	4	16	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	4	1	no	—
691	C₂×Q₈	—	4	1	no	—
692	C₂×Q₈	—	4	1	no	—
693	C₂×Q₈	—	4	1	no	—
694	C₂×Q₈	#41×C₆₇	1	4	yes	complemented
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	1	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	#41×C₆₇	1	4	yes	complemented
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	4	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	2	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	—	4	1	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	2	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	#41×C₆₇	1	4	yes	complemented
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	2	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	4	no	—
794	C₄²	—	2	4	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	1	no	—
798	C₄²	—	4	1	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₄²	—	4	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	C₂×#41×C₆₇	1	4	yes	—
822	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
823	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
824	Q₈	—	4	4	no	—
825	Q₈	—	4	4	no	—
826	D₄	—	4	4	no	—
827	D₄	—	4	8	no	—
828	D₄	—	4	8	no	—
829	D₄	—	4	4	no	—
830	D₄	—	4	8	no	—
831	D₄	—	8	4	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	4	8	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
880	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
881	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
882	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
883	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
884	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
885	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
886	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
887	C₂²	—	2	4	no	—
888	C₂²	—	2	4	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	4	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
909	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
910	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
911	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
912	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
913	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
914	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	4	no	—
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	4	2	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₂	—	4	4	no	—
932	C₂	—	4	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₆₇×#3481	1	1	yes	characteristic
935	C₂	C₆₇×#3482	1	1	yes	characteristic
936	C₂	C₆₇×#3483	1	1	yes	characteristic
937	C₂	C₆₇×#3490	1	1	yes	characteristic
938	C₂	C₆₇×#3490	1	1	yes	characteristic
939	C₂	C₆₇×#3492	1	1	yes	characteristic
940	C₂	C₆₇×#3548	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2808	C₂	semidirect
2. C₆₇×#2806	C₂	semidirect
3. C₆₇×#2732	C₂	semidirect
4. C₆₇×#2682	C₂	semidirect
5. C₆₇×#2609	C₂	semidirect
6. C₆₇×#2601	C₂	semidirect
7. C₆₇×#2574	C₂	semidirect
8. C₆₇×#2554	C₂	semidirect
9. C₆₇×#2553	C₂	semidirect
10. C₆₇×#2476	C₂	semidirect
11. C₆₇×#2471	C₂	semidirect
12. C₆₇×#2430	C₂	semidirect
13. C₆₇×#2407	C₂	semidirect
14. C₆₇×#2368	C₂	semidirect
15. C₆₇×#2363	C₂	semidirect
16. C₆₇×#2359	C₂	semidirect
17. C₆₇×#2297	C₂	semidirect
18. C₆₇×#2297	C₂	semidirect
19. C₆₇×#2296	C₂	semidirect
223. C₂×Q₈×C₆₇	#41	semidirect
241. C₂×D₄×C₆₇	#41	semidirect
298. C₄⋊C₄×C₆₇	#41	semidirect
460. #60044	C₆₇	direct (N × H)
471. #2808	C₂×C₆₇	semidirect
472. #2806	C₂×C₆₇	semidirect
473. #2732	C₂×C₆₇	semidirect
474. #2682	C₂×C₆₇	semidirect
475. #2609	C₂×C₆₇	semidirect
476. #2601	C₂×C₆₇	semidirect
477. #2574	C₂×C₆₇	semidirect
478. #2554	C₂×C₆₇	semidirect
479. #2553	C₂×C₆₇	semidirect
480. #2476	C₂×C₆₇	semidirect
481. #2471	C₂×C₆₇	semidirect
482. #2430	C₂×C₆₇	semidirect
483. #2407	C₂×C₆₇	semidirect
484. #2368	C₂×C₆₇	semidirect
485. #2363	C₂×C₆₇	semidirect
486. #2359	C₂×C₆₇	semidirect
487. #2297	C₂×C₆₇	semidirect
488. #2297	C₂×C₆₇	semidirect
489. #2296	C₂×C₆₇	semidirect
490. C₆₇	#60044	direct (N × H)
694. C₂×Q₈	#41×C₆₇	semidirect
712. C₂×D₄	#41×C₆₇	semidirect
769. C₄⋊C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2808	2
C₆₇×#2806	2
C₆₇×#2732	2
C₆₇×#2682	2
C₆₇×#2609	2
C₆₇×#2601	2
C₆₇×#2574	2
C₆₇×#2554	2
C₆₇×#2553	2
C₆₇×#2476	2
C₆₇×#2471	2
C₆₇×#2430	2
C₆₇×#2407	2
C₆₇×#2368	2
C₆₇×#2363	2
C₆₇×#2359	2
C₆₇×#2297	2
C₆₇×#2296	2
#60044	67

Subgroups — C67×#60044 #30739295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60044 #30739295