Subgroups — C₆₇×#59676 #30738927

Order 17152.

2036 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2801	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2757	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2602	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2587	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2510	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2494	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2487	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2443	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2422	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2414	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2361	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2361	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2352	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#121×C₆₇	C₂²	1	2	yes	—
27	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#121×C₆₇	C₂²	1	2	yes	—
30	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
38	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
44	#401×C₆₇	C₂²	1	2	yes	—
45	#400×C₆₇	C₂²	1	2	yes	—
46	#399×C₆₇	C₂²	1	2	yes	—
47	#398×C₆₇	C₂²	1	2	yes	—
48	#398×C₆₇	C₂²	1	2	yes	—
49	#397×C₆₇	C₂²	1	2	yes	—
50	#397×C₆₇	C₂²	1	2	yes	—
51	#397×C₆₇	C₂²	1	2	yes	—
52	#397×C₆₇	C₂²	1	2	yes	—
53	#396×C₆₇	C₂²	1	2	yes	—
54	#396×C₆₇	C₂²	1	2	yes	—
55	#394×C₆₇	C₂²	1	2	yes	—
56	#394×C₆₇	C₂²	1	2	yes	—
57	#394×C₆₇	C₂²	1	2	yes	—
58	#394×C₆₇	C₂²	1	2	yes	—
59	#392×C₆₇	C₂²	1	2	yes	—
60	#390×C₆₇	C₂²	1	2	yes	—
61	#390×C₆₇	C₂²	1	1	yes	characteristic
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	1	yes	characteristic
65	#389×C₆₇	C₂²	1	2	yes	—
66	#389×C₆₇	C₂²	1	2	yes	—
67	#389×C₆₇	C₂²	1	1	yes	characteristic
68	#389×C₆₇	C₂²	1	1	yes	characteristic
69	#389×C₆₇	C₂²	1	1	yes	characteristic
70	#389×C₆₇	C₂²	1	1	yes	characteristic
71	#389×C₆₇	C₂²	1	1	yes	characteristic
72	#389×C₆₇	C₂²	1	2	yes	—
73	#389×C₆₇	C₂²	1	2	yes	—
74	#389×C₆₇	C₂²	1	1	yes	characteristic
75	#389×C₆₇	C₂²	1	1	yes	characteristic
76	#389×C₆₇	C₂²	1	1	yes	characteristic
77	#388×C₆₇	C₂²	1	1	yes	characteristic
78	#388×C₆₇	C₂²	1	2	yes	—
79	#388×C₆₇	C₂²	1	2	yes	—
80	#388×C₆₇	C₂²	1	2	yes	—
81	#388×C₆₇	C₂²	1	2	yes	—
82	#388×C₆₇	C₂²	1	2	yes	—
83	#388×C₆₇	C₂²	1	2	yes	—
84	#388×C₆₇	C₂²	1	1	yes	characteristic
85	#388×C₆₇	C₂²	1	2	yes	—
86	#388×C₆₇	C₂²	1	2	yes	—
87	#388×C₆₇	C₂²	1	2	yes	—
88	#387×C₆₇	C₂²	1	2	yes	—
89	#387×C₆₇	C₂²	1	2	yes	—
90	#387×C₆₇	C₂²	1	2	yes	—
91	#386×C₆₇	C₂²	1	2	yes	—
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	1	yes	characteristic
98	#386×C₆₇	C₂²	1	1	yes	characteristic
99	#385×C₆₇	C₂²	1	2	yes	—
100	#385×C₆₇	C₂²	1	2	yes	—
101	#385×C₆₇	C₂²	1	2	yes	—
102	#385×C₆₇	C₂²	1	2	yes	—
103	#385×C₆₇	C₂²	1	2	yes	—
104	#384×C₆₇	C₂²	1	1	yes	characteristic
105	#383×C₆₇	C₂²	1	2	yes	—
106	#382×C₆₇	C₂²	1	1	yes	characteristic
107	#380×C₆₇	C₂²	1	1	yes	characteristic
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	1	yes	characteristic
111	#380×C₆₇	C₂²	1	1	yes	characteristic
112	#380×C₆₇	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
122	C₂×#95×C₆₇	C₂²	1	2	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
127	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
130	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	#123×C₆₇	—	4	4	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	—	2	8	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	4	no	—
144	#121×C₆₇	—	4	2	no	—
145	#121×C₆₇	—	4	4	no	—
146	C₄×D₄×C₆₇	—	2	4	no	—
147	C₄×D₄×C₆₇	—	2	4	no	—
148	C₄×D₄×C₆₇	—	4	2	no	—
149	C₄×D₄×C₆₇	—	4	2	no	—
150	C₄×D₄×C₆₇	—	4	4	no	—
151	C₄×D₄×C₆₇	—	4	4	no	—
152	C₄×D₄×C₆₇	—	4	4	no	—
153	#117×C₆₇	—	2	4	no	—
154	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
155	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
156	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
157	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄²×C₆₇	—	4	2	no	—
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
219	#95×C₆₇	C₂³	1	2	yes	—
220	#95×C₆₇	C₂³	1	2	yes	—
221	#95×C₆₇	C₂³	1	2	yes	—
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	1	yes	characteristic
224	#95×C₆₇	C₂³	1	1	yes	characteristic
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	1	yes	characteristic
228	#95×C₆₇	C₂³	1	2	yes	—
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	2	yes	—
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	2	yes	—
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	2	yes	—
241	#95×C₆₇	C₂³	1	2	yes	—
242	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
244	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	2	no	—
249	C₂×D₄×C₆₇	—	2	4	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	2	4	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	2	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	4	1	no	—
262	C₂×D₄×C₆₇	—	4	2	no	—
263	C₂×D₄×C₆₇	—	4	2	no	—
264	C₂×D₄×C₆₇	—	4	2	no	—
265	C₂×D₄×C₆₇	—	4	2	no	—
266	C₂×D₄×C₆₇	#41	1	4	yes	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	2	no	—
269	C₂²×C₄×C₆₇	—	2	2	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	2	no	—
277	C₂²×C₄×C₆₇	—	2	2	no	—
278	C₂²×C₄×C₆₇	—	2	2	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	2	2	no	—
281	C₂²×C₄×C₆₇	—	2	2	no	—
282	C₂²×C₄×C₆₇	—	2	4	no	—
283	C₂²×C₄×C₆₇	—	4	1	no	—
284	C₂²×C₄×C₆₇	—	4	1	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	—	4	2	no	—
289	C₂²×C₄×C₆₇	—	4	2	no	—
290	C₂²×C₄×C₆₇	—	4	2	no	—
291	C₂²×C₄×C₆₇	—	4	2	no	—
292	C₂²×C₄×C₆₇	—	4	2	no	—
293	C₂²×C₄×C₆₇	#41	1	4	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	—	2	4	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	2	no	—
319	C₄⋊C₄×C₆₇	—	2	4	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	4	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	4	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	4	2	no	—
328	C₄⋊C₄×C₆₇	—	4	2	no	—
329	C₄⋊C₄×C₆₇	—	4	2	no	—
330	C₄⋊C₄×C₆₇	—	4	2	no	—
331	C₄⋊C₄×C₆₇	—	4	1	no	—
332	C₄⋊C₄×C₆₇	—	4	2	no	—
333	C₄⋊C₄×C₆₇	—	4	2	no	—
334	C₄⋊C₄×C₆₇	—	4	2	no	—
335	C₄⋊C₄×C₆₇	—	4	2	no	—
336	C₄⋊C₄×C₆₇	#41	1	4	yes	—
337	C₂²⋊C₄×C₆₇	—	2	2	no	—
338	C₂²⋊C₄×C₆₇	—	2	2	no	—
339	C₂²⋊C₄×C₆₇	—	2	2	no	—
340	C₂²⋊C₄×C₆₇	—	2	4	no	—
341	C₂²⋊C₄×C₆₇	—	2	4	no	—
342	C₂²⋊C₄×C₆₇	—	2	4	no	—
343	C₂²⋊C₄×C₆₇	—	2	2	no	—
344	C₂²⋊C₄×C₆₇	—	2	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	4	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	4	1	no	—
353	C₂²⋊C₄×C₆₇	—	4	2	no	—
354	C₂²⋊C₄×C₆₇	—	4	1	no	—
355	C₂²⋊C₄×C₆₇	—	4	2	no	—
356	C₂²⋊C₄×C₆₇	—	4	2	no	—
357	C₂²⋊C₄×C₆₇	—	4	2	no	—
358	C₂²⋊C₄×C₆₇	—	4	2	no	—
359	C₂²⋊C₄×C₆₇	—	4	2	no	—
360	C₂²⋊C₄×C₆₇	—	4	2	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₄²×C₆₇	—	2	4	no	—
364	C₄²×C₆₇	—	2	2	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₄²×C₆₇	—	2	2	no	—
368	C₄²×C₆₇	—	4	1	no	—
369	C₄²×C₆₇	—	4	1	no	—
370	C₄²×C₆₇	—	4	2	no	—
371	C₄²×C₆₇	—	4	2	no	—
372	C₄²×C₆₇	—	4	2	no	—
373	C₂³×C₆₇	—	2	1	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	1	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	1	no	—
380	C₂³×C₆₇	—	2	1	no	—
381	C₂³×C₆₇	—	2	1	no	—
382	C₂³×C₆₇	—	2	1	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	2	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	2	no	—
391	C₂³×C₆₇	—	2	2	no	—
392	C₂³×C₆₇	—	2	2	no	—
393	C₂³×C₆₇	—	2	1	no	—
394	C₂³×C₆₇	—	2	1	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	1	no	—
397	C₂³×C₆₇	C₂×#41	1	2	yes	—
398	C₂³×C₆₇	C₂×#41	1	2	yes	—
399	C₂³×C₆₇	C₂×#41	1	2	yes	—
400	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
401	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
402	D₄×C₆₇	—	2	8	no	—
403	D₄×C₆₇	—	4	8	no	—
404	D₄×C₆₇	—	4	4	no	—
405	D₄×C₆₇	—	4	4	no	—
406	D₄×C₆₇	—	4	8	no	—
407	D₄×C₆₇	—	4	4	no	—
408	D₄×C₆₇	—	8	4	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	1	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	1	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	1	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	8	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	1	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	2	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	1	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	2	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	2	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	2	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	4	8	no	—
460	C₂×C₄×C₆₇	—	4	4	no	—
461	C₂×C₄×C₆₇	—	4	4	no	—
462	C₂×C₄×C₆₇	—	4	4	no	—
463	C₂×C₄×C₆₇	—	4	4	no	—
464	C₂×C₄×C₆₇	—	8	4	no	—
465	C₂×C₄×C₆₇	—	8	4	no	—
466	C₂×C₄×C₆₇	—	8	4	no	—
467	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
468	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
469	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
470	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
471	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
472	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
474	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
475	C₂²×C₆₇	—	2	2	no	—
476	C₂²×C₆₇	—	2	2	no	—
477	C₂²×C₆₇	—	2	2	no	—
478	C₂²×C₆₇	—	2	2	no	—
479	C₂²×C₆₇	—	2	2	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	2	no	—
482	C₂²×C₆₇	—	2	2	no	—
483	C₂²×C₆₇	—	2	2	no	—
484	C₂²×C₆₇	—	4	1	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	1	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	—	4	1	no	—
489	C₂²×C₆₇	—	4	1	no	—
490	C₂²×C₆₇	—	4	2	no	—
491	C₂²×C₆₇	—	4	2	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	1	no	—
494	C₂²×C₆₇	—	4	1	no	—
495	C₂²×C₆₇	—	4	2	no	—
496	C₂²×C₆₇	—	4	1	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	1	no	—
499	C₂²×C₆₇	—	4	2	no	—
500	C₂²×C₆₇	—	4	2	no	—
501	C₂²×C₆₇	—	4	1	no	—
502	C₂²×C₆₇	#553	1	4	yes	—
503	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
504	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
505	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
506	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
509	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
510	C₄×C₆₇	—	2	2	no	—
511	C₄×C₆₇	—	2	2	no	—
512	C₄×C₆₇	—	2	4	no	—
513	C₄×C₆₇	—	2	2	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	4	1	no	—
516	C₄×C₆₇	—	4	1	no	—
517	C₄×C₆₇	—	4	1	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	—	4	2	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	—	4	1	no	—
522	C₄×C₆₇	—	4	1	no	—
523	C₄×C₆₇	—	4	2	no	—
524	C₄×C₆₇	—	4	1	no	—
525	C₄×C₆₇	—	4	2	no	—
526	C₄×C₆₇	—	4	2	no	—
527	C₄×C₆₇	—	4	2	no	—
528	C₄×C₆₇	#553	1	4	yes	—
529	#59676	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
530	C₂×C₆₇	—	2	4	no	—
531	C₂×C₆₇	—	4	2	no	—
532	C₂×C₆₇	—	8	1	no	—
533	C₂×C₆₇	—	8	2	no	—
534	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
535	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
536	C₂×C₆₇	#3481	1	1	yes	characteristic
537	C₂×C₆₇	#3511	1	1	yes	characteristic
538	C₂×C₆₇	#3520	1	1	yes	characteristic
539	C₂×C₆₇	#3522	1	1	yes	characteristic
540	C₂×C₆₇	#3537	1	1	yes	characteristic
541	#2801	C₂×C₆₇	1	2	yes	complemented
542	#2757	C₂×C₆₇	1	2	yes	complemented
543	#2602	C₂×C₆₇	1	2	yes	complemented
544	#2587	C₂×C₆₇	1	2	yes	complemented
545	#2543	C₂×C₆₇	1	2	yes	complemented
546	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#2510	C₂×C₆₇	1	2	yes	complemented
548	#2507	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#2494	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#2487	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2443	C₂×C₆₇	1	2	yes	complemented
552	#2422	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#2416	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#2414	C₂×C₆₇	1	1	yes	characteristic, complemented
556	#2361	C₂×C₆₇	1	1	yes	characteristic, complemented
557	#2361	C₂×C₆₇	1	2	yes	complemented
558	#2352	C₂×C₆₇	1	1	yes	characteristic, complemented
559	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
561	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
562	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
563	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
564	C₆₇	#59676	1	1	yes	characteristic, direct product factor, Sylow
565	C₂×#123	C₂²×C₆₇	1	2	yes	—
566	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
567	C₂×#121	C₂²×C₆₇	1	2	yes	—
568	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
569	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×#121	C₂²×C₆₇	1	2	yes	—
572	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
573	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
574	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
575	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
576	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
577	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
578	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
579	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
580	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
581	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
583	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
584	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
585	#401	C₂²×C₆₇	1	2	yes	—
586	#400	C₂²×C₆₇	1	2	yes	—
587	#399	C₂²×C₆₇	1	2	yes	—
588	#398	C₂²×C₆₇	1	2	yes	—
589	#398	C₂²×C₆₇	1	2	yes	—
590	#397	C₂²×C₆₇	1	2	yes	—
591	#397	C₂²×C₆₇	1	2	yes	—
592	#397	C₂²×C₆₇	1	2	yes	—
593	#397	C₂²×C₆₇	1	2	yes	—
594	#396	C₂²×C₆₇	1	2	yes	—
595	#396	C₂²×C₆₇	1	2	yes	—
596	#394	C₂²×C₆₇	1	2	yes	—
597	#394	C₂²×C₆₇	1	2	yes	—
598	#394	C₂²×C₆₇	1	2	yes	—
599	#394	C₂²×C₆₇	1	2	yes	—
600	#392	C₂²×C₆₇	1	2	yes	—
601	#390	C₂²×C₆₇	1	1	yes	characteristic
602	#390	C₂²×C₆₇	1	2	yes	—
603	#390	C₂²×C₆₇	1	1	yes	characteristic
604	#390	C₂²×C₆₇	1	1	yes	characteristic
605	#390	C₂²×C₆₇	1	1	yes	characteristic
606	#389	C₂²×C₆₇	1	1	yes	characteristic
607	#389	C₂²×C₆₇	1	2	yes	—
608	#389	C₂²×C₆₇	1	2	yes	—
609	#389	C₂²×C₆₇	1	1	yes	characteristic
610	#389	C₂²×C₆₇	1	1	yes	characteristic
611	#389	C₂²×C₆₇	1	2	yes	—
612	#389	C₂²×C₆₇	1	1	yes	characteristic
613	#389	C₂²×C₆₇	1	1	yes	characteristic
614	#389	C₂²×C₆₇	1	1	yes	characteristic
615	#389	C₂²×C₆₇	1	1	yes	characteristic
616	#389	C₂²×C₆₇	1	1	yes	characteristic
617	#389	C₂²×C₆₇	1	2	yes	—
618	#388	C₂²×C₆₇	1	2	yes	—
619	#388	C₂²×C₆₇	1	2	yes	—
620	#388	C₂²×C₆₇	1	2	yes	—
621	#388	C₂²×C₆₇	1	2	yes	—
622	#388	C₂²×C₆₇	1	2	yes	—
623	#388	C₂²×C₆₇	1	2	yes	—
624	#388	C₂²×C₆₇	1	2	yes	—
625	#388	C₂²×C₆₇	1	2	yes	—
626	#388	C₂²×C₆₇	1	1	yes	characteristic
627	#388	C₂²×C₆₇	1	2	yes	—
628	#388	C₂²×C₆₇	1	1	yes	characteristic
629	#387	C₂²×C₆₇	1	2	yes	—
630	#387	C₂²×C₆₇	1	2	yes	—
631	#387	C₂²×C₆₇	1	2	yes	—
632	#386	C₂²×C₆₇	1	2	yes	—
633	#386	C₂²×C₆₇	1	2	yes	—
634	#386	C₂²×C₆₇	1	1	yes	characteristic
635	#386	C₂²×C₆₇	1	2	yes	—
636	#386	C₂²×C₆₇	1	2	yes	—
637	#386	C₂²×C₆₇	1	2	yes	—
638	#386	C₂²×C₆₇	1	1	yes	characteristic
639	#386	C₂²×C₆₇	1	2	yes	—
640	#385	C₂²×C₆₇	1	2	yes	—
641	#385	C₂²×C₆₇	1	2	yes	—
642	#385	C₂²×C₆₇	1	2	yes	—
643	#385	C₂²×C₆₇	1	2	yes	—
644	#385	C₂²×C₆₇	1	2	yes	—
645	#384	C₂²×C₆₇	1	1	yes	characteristic
646	#383	C₂²×C₆₇	1	2	yes	—
647	#382	C₂²×C₆₇	1	1	yes	characteristic
648	#380	C₂²×C₆₇	1	1	yes	characteristic
649	#380	C₂²×C₆₇	1	1	yes	characteristic
650	#380	C₂²×C₆₇	1	1	yes	characteristic
651	#380	C₂²×C₆₇	1	1	yes	characteristic
652	#380	C₂²×C₆₇	1	1	yes	characteristic
653	#380	C₂²×C₆₇	1	1	yes	characteristic
654	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
655	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
656	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
657	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
658	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
659	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
660	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
661	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
662	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
663	C₂×#95	C₂²×C₆₇	1	2	yes	—
664	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
666	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
668	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
669	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
670	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
671	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
672	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
673	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
674	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
675	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
676	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
677	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
678	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
679	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
680	#123	—	4	4	no	—
681	#121	—	2	8	no	—
682	#121	—	2	4	no	—
683	#121	—	2	4	no	—
684	#121	—	2	4	no	—
685	#121	—	4	2	no	—
686	#121	—	4	4	no	—
687	C₄×D₄	—	2	4	no	—
688	C₄×D₄	—	2	4	no	—
689	C₄×D₄	—	4	2	no	—
690	C₄×D₄	—	4	2	no	—
691	C₄×D₄	—	4	4	no	—
692	C₄×D₄	—	4	4	no	—
693	C₄×D₄	—	4	4	no	—
694	#117	—	2	4	no	—
695	C₂×C₄⋊C₄	—	2	4	no	—
696	C₂×C₄⋊C₄	—	4	2	no	—
697	C₂×C₄⋊C₄	—	4	2	no	—
698	C₂×C₄⋊C₄	—	4	4	no	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
710	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄²	—	4	2	no	—
750	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
751	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
756	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
757	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
758	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	2	yes	—
763	#95	C₂³×C₆₇	1	2	yes	—
764	#95	C₂³×C₆₇	1	1	yes	characteristic
765	#95	C₂³×C₆₇	1	1	yes	characteristic
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	1	yes	characteristic
769	#95	C₂³×C₆₇	1	2	yes	—
770	#95	C₂³×C₆₇	1	1	yes	characteristic
771	#95	C₂³×C₆₇	1	2	yes	—
772	#95	C₂³×C₆₇	1	2	yes	—
773	#95	C₂³×C₆₇	1	2	yes	—
774	#95	C₂³×C₆₇	1	2	yes	—
775	#95	C₂³×C₆₇	1	2	yes	—
776	#95	C₂³×C₆₇	1	1	yes	characteristic
777	#95	C₂³×C₆₇	1	1	yes	characteristic
778	#95	C₂³×C₆₇	1	2	yes	—
779	#95	C₂³×C₆₇	1	2	yes	—
780	#95	C₂³×C₆₇	1	2	yes	—
781	#95	C₂³×C₆₇	1	2	yes	—
782	#95	C₂³×C₆₇	1	2	yes	—
783	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
784	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
785	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
786	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	4	no	—
795	C₂×D₄	—	2	4	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	4	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	4	1	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	4	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	#41×C₆₇	1	4	yes	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	2	4	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	2	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	4	1	no	—
825	C₂²×C₄	—	4	1	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	#41×C₆₇	1	4	yes	—
835	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
836	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
837	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	4	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	4	2	no	—
869	C₄⋊C₄	—	4	2	no	—
870	C₄⋊C₄	—	4	2	no	—
871	C₄⋊C₄	—	4	2	no	—
872	C₄⋊C₄	—	4	1	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	—	4	2	no	—
876	C₄⋊C₄	—	4	2	no	—
877	C₄⋊C₄	#41×C₆₇	1	4	yes	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	4	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	4	no	—
887	C₂²⋊C₄	—	2	2	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	4	no	—
893	C₂²⋊C₄	—	4	1	no	—
894	C₂²⋊C₄	—	4	2	no	—
895	C₂²⋊C₄	—	4	1	no	—
896	C₂²⋊C₄	—	4	2	no	—
897	C₂²⋊C₄	—	4	2	no	—
898	C₂²⋊C₄	—	4	2	no	—
899	C₂²⋊C₄	—	4	2	no	—
900	C₂²⋊C₄	—	4	2	no	—
901	C₂²⋊C₄	—	4	2	no	—
902	C₂²⋊C₄	—	4	2	no	—
903	C₂²⋊C₄	—	4	2	no	—
904	C₄²	—	2	4	no	—
905	C₄²	—	2	2	no	—
906	C₄²	—	2	2	no	—
907	C₄²	—	2	2	no	—
908	C₄²	—	2	2	no	—
909	C₄²	—	4	1	no	—
910	C₄²	—	4	1	no	—
911	C₄²	—	4	2	no	—
912	C₄²	—	4	2	no	—
913	C₄²	—	4	2	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	—	2	2	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	2	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	2	no	—
937	C₂³	—	2	1	no	—
938	C₂³	C₂×#41×C₆₇	1	2	yes	—
939	C₂³	C₂×#41×C₆₇	1	2	yes	—
940	C₂³	C₂×#41×C₆₇	1	2	yes	—
941	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
942	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
943	D₄	—	2	8	no	—
944	D₄	—	4	8	no	—
945	D₄	—	4	4	no	—
946	D₄	—	4	4	no	—
947	D₄	—	4	8	no	—
948	D₄	—	4	4	no	—
949	D₄	—	8	4	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	1	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	8	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	1	no	—
966	C₂×C₄	—	2	1	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	2	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	2	no	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	4	4	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	8	4	no	—
1006	C₂×C₄	—	8	4	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1009	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1010	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1011	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1012	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1013	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1014	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1015	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	2	no	—
1043	C₂²	#553×C₆₇	1	4	yes	—
1044	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1045	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1046	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1047	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1048	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1049	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1050	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1051	C₄	—	2	2	no	—
1052	C₄	—	2	2	no	—
1053	C₄	—	2	2	no	—
1054	C₄	—	2	4	no	—
1055	C₄	—	2	2	no	—
1056	C₄	—	4	2	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	4	2	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	#553×C₆₇	1	4	yes	—
1070	C₂	—	2	4	no	—
1071	C₂	—	4	2	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	8	1	no	—
1074	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
1075	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
1076	C₂	C₆₇×#3481	1	1	yes	characteristic
1077	C₂	C₆₇×#3511	1	1	yes	characteristic
1078	C₂	C₆₇×#3520	1	1	yes	characteristic
1079	C₂	C₆₇×#3522	1	1	yes	characteristic
1080	C₂	C₆₇×#3537	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×#2801	C₂	semidirect
2. C₆₇×#2757	C₂	semidirect
3. C₆₇×#2602	C₂	semidirect
4. C₆₇×#2587	C₂	semidirect
5. C₆₇×#2543	C₂	semidirect
6. C₆₇×#2513	C₂	semidirect
7. C₆₇×#2510	C₂	semidirect
8. C₆₇×#2507	C₂	semidirect
9. C₆₇×#2494	C₂	semidirect
10. C₆₇×#2487	C₂	semidirect
11. C₆₇×#2443	C₂	semidirect
12. C₆₇×#2422	C₂	semidirect
13. C₆₇×#2416	C₂	semidirect
14. C₆₇×#2416	C₂	semidirect
15. C₆₇×#2414	C₂	semidirect
16. C₆₇×#2361	C₂	semidirect
17. C₆₇×#2361	C₂	semidirect
18. C₆₇×#2352	C₂	semidirect
19. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
20. C₆₇×#2347	C₂	semidirect
21. C₄×#121×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#389×C₆₇	C₂	semidirect
529. #59676	C₆₇	direct (N × H)
541. #2801	C₂×C₆₇	semidirect
542. #2757	C₂×C₆₇	semidirect
543. #2602	C₂×C₆₇	semidirect
544. #2587	C₂×C₆₇	semidirect
545. #2543	C₂×C₆₇	semidirect
546. #2513	C₂×C₆₇	semidirect
547. #2510	C₂×C₆₇	semidirect
548. #2507	C₂×C₆₇	semidirect
549. #2494	C₂×C₆₇	semidirect
550. #2487	C₂×C₆₇	semidirect
551. #2443	C₂×C₆₇	semidirect
552. #2422	C₂×C₆₇	semidirect
553. #2416	C₂×C₆₇	semidirect
554. #2416	C₂×C₆₇	semidirect
555. #2414	C₂×C₆₇	semidirect
556. #2361	C₂×C₆₇	semidirect
557. #2361	C₂×C₆₇	semidirect
558. #2352	C₂×C₆₇	semidirect
559. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
560. #2347	C₂×C₆₇	semidirect
561. C₄×#121	C₂×C₆₇	semidirect
562. C₄×#121	C₂×C₆₇	semidirect
563. C₂×#389	C₂×C₆₇	semidirect
564. C₆₇	#59676	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2801	2
C₆₇×#2757	2
C₆₇×#2602	2
C₆₇×#2587	2
C₆₇×#2543	2
C₆₇×#2513	2
C₆₇×#2510	2
C₆₇×#2507	2
C₆₇×#2494	2
C₆₇×#2487	2
C₆₇×#2443	2
C₆₇×#2422	2
C₆₇×#2416	2
C₆₇×#2414	2
C₆₇×#2361	2
C₆₇×#2352	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2347	2
C₄×#121×C₆₇	2
C₂×#389×C₆₇	2
#59676	67

Subgroups — C67×#59676 #30738927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59676 #30738927