Subgroups — C₆₇×#61685 #30740936

Order 17152.

2152 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3306	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3274	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3267	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3204	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3012	C₂	1	4	yes	maximal, complemented
15	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
17	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
18	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
19	#562×C₆₇	—	2	2	no	—
20	#554×C₆₇	—	2	1	no	—
21	#554×C₆₇	C₂²	1	2	yes	complemented
22	#550×C₆₇	—	2	1	no	—
23	#550×C₆₇	C₂²	1	2	yes	complemented
24	#547×C₆₇	—	2	1	no	—
25	#547×C₆₇	C₂²	1	2	yes	—
26	#547×C₆₇	C₂²	1	2	yes	complemented
27	#547×C₆₇	C₂²	1	2	yes	complemented
28	#546×C₆₇	—	2	2	no	—
29	#546×C₆₇	C₂²	1	4	yes	—
30	D₄²×C₆₇	—	2	1	no	—
31	D₄²×C₆₇	C₂²	1	2	yes	—
32	#540×C₆₇	—	2	2	no	—
33	#537×C₆₇	—	2	2	no	—
34	#537×C₆₇	C₂²	1	2	yes	—
35	#537×C₆₇	C₂²	1	4	yes	complemented
36	#534×C₆₇	—	2	2	no	—
37	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#121×C₆₇	—	2	2	no	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
43	#497×C₆₇	C₂²	1	2	yes	complemented
44	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#487×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#483×C₆₇	C₂²	1	4	yes	complemented
50	#483×C₆₇	C₂²	1	2	yes	complemented
51	#481×C₆₇	C₂²	1	4	yes	complemented
52	#481×C₆₇	C₂²	1	2	yes	complemented
53	#476×C₆₇	C₂²	1	2	yes	complemented
54	#476×C₆₇	C₂²	1	2	yes	complemented
55	#470×C₆₇	C₂²	1	4	yes	complemented
56	#469×C₆₇	C₂²	1	4	yes	complemented
57	#465×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#463×C₆₇	C₂²	1	4	yes	complemented
60	#462×C₆₇	C₂²	1	2	yes	complemented
61	#461×C₆₇	C₂²	1	2	yes	complemented
62	#460×C₆₇	C₂²	1	2	yes	complemented
63	#459×C₆₇	C₂²	1	2	yes	complemented
64	#452×C₆₇	C₂²	1	4	yes	complemented
65	#452×C₆₇	C₂²	1	4	yes	complemented
66	#452×C₆₇	C₂²	1	4	yes	complemented
67	#450×C₆₇	C₂²	1	2	yes	—
68	#450×C₆₇	C₂²	1	4	yes	complemented
69	#449×C₆₇	C₂²	1	4	yes	complemented
70	#449×C₆₇	C₂²	1	4	yes	complemented
71	#449×C₆₇	C₂²	1	4	yes	complemented
72	#447×C₆₇	C₂²	1	2	yes	—
73	#447×C₆₇	C₂²	1	4	yes	complemented
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
76	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
77	#436×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	4	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
80	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#417×C₆₇	C₂²	1	4	yes	complemented
83	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
84	#408×C₆₇	C₂²	1	4	yes	complemented
85	H(5,𝔽₂)×C₆₇	—	4	8	no	—
86	C₂×#41×C₆₇	—	2	2	no	—
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	—	2	1	no	—
89	C₂×#41×C₆₇	C₂³	1	4	yes	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂×#41×C₆₇	C₂³	1	4	yes	—
92	C₂×#41×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	—	2	4	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	—	2	2	no	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
98	C₂³×C₄×C₆₇	—	2	1	no	—
99	AGL(1,ℤ/8)×C₆₇	—	4	8	no	—
100	#135×C₆₇	—	4	8	no	—
101	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
103	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂×D₈×C₆₇	C₂³	1	4	yes	—
107	C₂×D₈×C₆₇	C₂³	1	4	yes	—
108	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
109	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
115	#127×C₆₇	—	2	2	no	—
116	#127×C₆₇	D₄	1	1	yes	characteristic
117	#127×C₆₇	C₂³	1	1	yes	characteristic
118	#127×C₆₇	C₂³	1	1	yes	characteristic
119	#125×C₆₇	—	2	2	no	—
120	#125×C₆₇	—	2	1	no	—
121	#124×C₆₇	—	2	1	no	—
122	#124×C₆₇	D₄	1	2	yes	—
123	#124×C₆₇	C₂³	1	2	yes	—
124	#123×C₆₇	—	2	4	no	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	—	2	4	no	—
128	C₂²⋊Q₈×C₆₇	—	2	2	no	—
129	C₂²⋊Q₈×C₆₇	—	2	4	no	—
130	C₂²⋊Q₈×C₆₇	—	2	1	no	—
131	C₂²⋊Q₈×C₆₇	—	2	2	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	4	no	—
139	#121×C₆₇	—	2	4	no	—
140	#121×C₆₇	—	2	2	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	—	2	1	no	—
144	#121×C₆₇	—	2	1	no	—
145	#121×C₆₇	—	2	1	no	—
146	#121×C₆₇	—	2	2	no	—
147	#121×C₆₇	—	2	4	no	—
148	#121×C₆₇	—	2	4	no	—
149	#121×C₆₇	D₄	1	2	yes	—
150	#121×C₆₇	D₄	1	2	yes	—
151	#121×C₆₇	C₂³	1	2	yes	—
152	#121×C₆₇	C₂³	1	4	yes	—
153	#121×C₆₇	C₂³	1	4	yes	—
154	#120×C₆₇	—	2	4	no	—
155	#120×C₆₇	—	2	4	no	—
156	C₄×Q₈×C₆₇	—	2	1	no	—
157	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	2	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	1	no	—
164	C₄×D₄×C₆₇	—	2	1	no	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	C₄×D₄×C₆₇	C₂³	1	2	yes	—
168	C₄×D₄×C₆₇	C₂³	1	2	yes	—
169	C₄×D₄×C₆₇	C₂³	1	2	yes	—
170	#117×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
177	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
178	#106×C₆₇	C₂³	1	2	yes	—
179	#106×C₆₇	C₂³	1	4	yes	—
180	#106×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	#103×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	4	yes	—
185	#103×C₆₇	C₂³	1	4	yes	—
186	#103×C₆₇	C₂³	1	2	yes	—
187	#102×C₆₇	C₂³	1	2	yes	—
188	#102×C₆₇	C₂³	1	4	yes	—
189	#102×C₆₇	C₂³	1	4	yes	—
190	#102×C₆₇	C₂³	1	2	yes	—
191	#102×C₆₇	C₂³	1	4	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
195	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
196	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
197	#97×C₆₇	C₂³	1	2	yes	—
198	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
200	C₂⁴×C₆₇	—	2	1	no	—
201	C₂⁴×C₆₇	—	2	4	no	—
202	#41×C₆₇	—	2	8	no	—
203	#41×C₆₇	—	4	4	no	—
204	#41×C₆₇	—	4	4	no	—
205	#41×C₆₇	—	4	4	no	—
206	#41×C₆₇	—	4	4	no	—
207	#41×C₆₇	—	4	4	no	—
208	#41×C₆₇	—	4	8	no	—
209	#41×C₆₇	—	8	2	no	—
210	#41×C₆₇	—	8	4	no	—
211	C₂×Q₈×C₆₇	—	2	1	no	—
212	C₂×Q₈×C₆₇	—	2	1	no	—
213	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
216	C₂×D₄×C₆₇	—	2	4	no	—
217	C₂×D₄×C₆₇	—	2	8	no	—
218	C₂×D₄×C₆₇	—	2	4	no	—
219	C₂×D₄×C₆₇	—	2	2	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	1	no	—
225	C₂×D₄×C₆₇	—	2	1	no	—
226	C₂×D₄×C₆₇	—	2	1	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	1	no	—
229	C₂×D₄×C₆₇	—	2	1	no	—
230	C₂×D₄×C₆₇	—	4	4	no	—
231	C₂×D₄×C₆₇	—	4	8	no	—
232	C₂×D₄×C₆₇	—	4	16	no	—
233	C₂×D₄×C₆₇	—	8	4	no	—
234	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	—	2	1	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	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	4	no	—
249	C₂²×C₄×C₆₇	—	8	2	no	—
250	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
254	Q₁₆×C₆₇	—	4	4	no	—
255	SD₁₆×C₆₇	—	2	4	no	—
256	SD₁₆×C₆₇	—	2	4	no	—
257	SD₁₆×C₆₇	—	4	4	no	—
258	SD₁₆×C₆₇	—	4	4	no	—
259	D₈×C₆₇	—	2	8	no	—
260	D₈×C₆₇	—	4	4	no	—
261	M₁₆×C₆₇	—	4	4	no	—
262	C₂×C₈×C₆₇	—	4	4	no	—
263	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
264	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
265	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	1	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	1	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	2	no	—
277	C₄⋊C₄×C₆₇	—	2	2	no	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	2	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	2	no	—
287	C₂²⋊C₄×C₆₇	—	2	2	no	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	—	2	2	no	—
294	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
300	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂³×C₆₇	—	2	4	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	4	8	no	—
306	C₂³×C₆₇	—	8	1	no	—
307	C₂³×C₆₇	—	8	1	no	—
308	C₂³×C₆₇	—	8	4	no	—
309	C₂³×C₆₇	—	8	4	no	—
310	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
311	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
312	Q₈×C₆₇	—	2	2	no	—
313	Q₈×C₆₇	—	2	2	no	—
314	Q₈×C₆₇	—	2	4	no	—
315	Q₈×C₆₇	—	4	2	no	—
316	Q₈×C₆₇	—	4	2	no	—
317	Q₈×C₆₇	—	8	1	no	—
318	D₄×C₆₇	—	2	4	no	—
319	D₄×C₆₇	—	2	4	no	—
320	D₄×C₆₇	—	2	2	no	—
321	D₄×C₆₇	—	2	4	no	—
322	D₄×C₆₇	—	2	4	no	—
323	D₄×C₆₇	—	4	2	no	—
324	D₄×C₆₇	—	4	4	no	—
325	D₄×C₆₇	—	4	2	no	—
326	D₄×C₆₇	—	4	8	no	—
327	D₄×C₆₇	—	4	8	no	—
328	D₄×C₆₇	—	4	4	no	—
329	D₄×C₆₇	—	4	2	no	—
330	D₄×C₆₇	—	4	2	no	—
331	D₄×C₆₇	—	8	1	no	—
332	D₄×C₆₇	—	8	1	no	—
333	D₄×C₆₇	—	8	4	no	—
334	D₄×C₆₇	—	8	4	no	—
335	D₄×C₆₇	—	8	2	no	—
336	D₄×C₆₇	—	8	4	no	—
337	D₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	4	no	—
340	C₂×C₄×C₆₇	—	2	4	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	4	1	no	—
348	C₂×C₄×C₆₇	—	4	8	no	—
349	C₂×C₄×C₆₇	—	4	4	no	—
350	C₂×C₄×C₆₇	—	4	4	no	—
351	C₂×C₄×C₆₇	—	4	4	no	—
352	C₂×C₄×C₆₇	—	8	2	no	—
353	C₂×C₄×C₆₇	—	8	4	no	—
354	C₂×C₄×C₆₇	—	8	1	no	—
355	C₂×C₄×C₆₇	—	8	4	no	—
356	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
361	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
363	C₈×C₆₇	—	2	2	no	—
364	C₈×C₆₇	—	2	4	no	—
365	C₈×C₆₇	—	2	2	no	—
366	C₂²×C₆₇	—	2	1	no	—
367	C₂²×C₆₇	—	2	4	no	—
368	C₂²×C₆₇	—	2	1	no	—
369	C₂²×C₆₇	—	2	4	no	—
370	C₂²×C₆₇	—	2	4	no	—
371	C₂²×C₆₇	—	2	1	no	—
372	C₂²×C₆₇	—	2	4	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	2	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	4	2	no	—
378	C₂²×C₆₇	—	4	2	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	8	4	no	—
382	C₂²×C₆₇	—	16	8	no	—
383	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
384	C₄×C₆₇	—	2	1	no	—
385	C₄×C₆₇	—	2	1	no	—
386	C₄×C₆₇	—	2	1	no	—
387	C₄×C₆₇	—	2	4	no	—
388	C₄×C₆₇	—	2	1	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	—	4	2	no	—
392	C₄×C₆₇	—	4	2	no	—
393	C₄×C₆₇	—	4	2	no	—
394	C₄×C₆₇	#577	1	2	yes	—
395	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
396	#61685	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
397	C₂×C₆₇	—	4	1	no	—
398	C₂×C₆₇	—	4	4	no	—
399	C₂×C₆₇	—	4	4	no	—
400	C₂×C₆₇	—	8	2	no	—
401	C₂×C₆₇	—	8	2	no	—
402	C₂×C₆₇	#3484	1	1	yes	characteristic
403	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
404	C₂×C₆₇	#3585	1	1	yes	characteristic
405	#3548	C₂×C₆₇	1	1	yes	characteristic, complemented
406	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
407	#3331	C₂×C₆₇	1	2	yes	complemented
408	#3306	C₂×C₆₇	1	4	yes	complemented
409	#3295	C₂×C₆₇	1	2	yes	complemented
410	#3284	C₂×C₆₇	1	2	yes	complemented
411	#3274	C₂×C₆₇	1	2	yes	complemented
412	#3267	C₂×C₆₇	1	4	yes	complemented
413	#3216	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#3207	C₂×C₆₇	1	1	yes	characteristic, complemented
415	#3204	C₂×C₆₇	1	4	yes	complemented
416	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#3101	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#3012	C₂×C₆₇	1	4	yes	complemented
419	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
420	C₆₇	#61685	1	1	yes	characteristic, direct product factor, Sylow
421	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
422	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
423	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
424	#562	—	2	2	no	—
425	#554	—	2	1	no	—
426	#554	C₂²×C₆₇	1	2	yes	complemented
427	#550	—	2	1	no	—
428	#550	C₂²×C₆₇	1	2	yes	complemented
429	#547	—	2	1	no	—
430	#547	C₂²×C₆₇	1	2	yes	—
431	#547	C₂²×C₆₇	1	2	yes	complemented
432	#547	C₂²×C₆₇	1	2	yes	complemented
433	#546	—	2	2	no	—
434	#546	C₂²×C₆₇	1	4	yes	—
435	D₄²	—	2	1	no	—
436	D₄²	C₂²×C₆₇	1	2	yes	—
437	#540	—	2	2	no	—
438	#537	—	2	2	no	—
439	#537	C₂²×C₆₇	1	2	yes	—
440	#537	C₂²×C₆₇	1	4	yes	complemented
441	#534	—	2	2	no	—
442	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	#532	C₂²×C₆₇	1	1	yes	characteristic
444	#532	C₂²×C₆₇	1	1	yes	characteristic
445	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₂×#121	—	2	2	no	—
447	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
448	#497	C₂²×C₆₇	1	2	yes	complemented
449	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
450	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
451	#489	C₂²×C₆₇	1	2	yes	complemented
452	#487	C₂²×C₆₇	1	1	yes	characteristic, complemented
453	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
454	#483	C₂²×C₆₇	1	4	yes	complemented
455	#483	C₂²×C₆₇	1	2	yes	complemented
456	#481	C₂²×C₆₇	1	2	yes	complemented
457	#481	C₂²×C₆₇	1	4	yes	complemented
458	#476	C₂²×C₆₇	1	2	yes	complemented
459	#476	C₂²×C₆₇	1	2	yes	complemented
460	#470	C₂²×C₆₇	1	4	yes	complemented
461	#469	C₂²×C₆₇	1	4	yes	complemented
462	#465	C₂²×C₆₇	1	4	yes	complemented
463	#465	C₂²×C₆₇	1	4	yes	complemented
464	#463	C₂²×C₆₇	1	4	yes	complemented
465	#462	C₂²×C₆₇	1	2	yes	complemented
466	#461	C₂²×C₆₇	1	2	yes	complemented
467	#460	C₂²×C₆₇	1	2	yes	complemented
468	#459	C₂²×C₆₇	1	2	yes	complemented
469	#452	C₂²×C₆₇	1	4	yes	complemented
470	#452	C₂²×C₆₇	1	4	yes	complemented
471	#452	C₂²×C₆₇	1	4	yes	complemented
472	#450	C₂²×C₆₇	1	2	yes	—
473	#450	C₂²×C₆₇	1	4	yes	complemented
474	#449	C₂²×C₆₇	1	4	yes	complemented
475	#449	C₂²×C₆₇	1	4	yes	complemented
476	#449	C₂²×C₆₇	1	4	yes	complemented
477	#447	C₂²×C₆₇	1	2	yes	—
478	#447	C₂²×C₆₇	1	4	yes	complemented
479	#442	C₂²×C₆₇	1	4	yes	complemented
480	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
481	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
482	#436	C₂²×C₆₇	1	2	yes	complemented
483	#435	C₂²×C₆₇	1	4	yes	complemented
484	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
485	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
486	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
487	#417	C₂²×C₆₇	1	4	yes	complemented
488	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
489	#408	C₂²×C₆₇	1	4	yes	complemented
490	H(5,𝔽₂)	—	4	8	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	C₂³×C₆₇	1	4	yes	—
495	C₂×#41	C₂³×C₆₇	1	2	yes	—
496	C₂×#41	C₂³×C₆₇	1	4	yes	—
497	C₂×#41	C₂³×C₆₇	1	2	yes	—
498	C₂²×D₄	—	2	4	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	—	2	2	no	—
501	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
502	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
503	C₂³×C₄	—	2	1	no	—
504	AGL(1,ℤ/8)	—	4	8	no	—
505	#135	—	4	8	no	—
506	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
508	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
509	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
510	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
511	C₂×D₈	C₂³×C₆₇	1	4	yes	—
512	C₂×D₈	C₂³×C₆₇	1	4	yes	—
513	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
514	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
515	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
520	#127	—	2	2	no	—
521	#127	D₄×C₆₇	1	1	yes	characteristic
522	#127	C₂³×C₆₇	1	1	yes	characteristic
523	#127	C₂³×C₆₇	1	1	yes	characteristic
524	#125	—	2	2	no	—
525	#125	—	2	1	no	—
526	#124	—	2	1	no	—
527	#124	D₄×C₆₇	1	2	yes	—
528	#124	C₂³×C₆₇	1	2	yes	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	#123	—	2	4	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	4	no	—
538	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
539	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
540	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
541	#121	—	2	4	no	—
542	#121	—	2	2	no	—
543	#121	—	2	4	no	—
544	#121	—	2	4	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	4	no	—
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	1	no	—
551	#121	—	2	2	no	—
552	#121	—	2	4	no	—
553	#121	—	2	4	no	—
554	#121	D₄×C₆₇	1	2	yes	—
555	#121	D₄×C₆₇	1	2	yes	—
556	#121	C₂³×C₆₇	1	2	yes	—
557	#121	C₂³×C₆₇	1	4	yes	—
558	#121	C₂³×C₆₇	1	4	yes	—
559	#120	—	2	4	no	—
560	#120	—	2	4	no	—
561	C₄×Q₈	—	2	1	no	—
562	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	C₂³×C₆₇	1	2	yes	—
571	C₄×D₄	C₂³×C₆₇	1	2	yes	—
572	C₄×D₄	C₂³×C₆₇	1	2	yes	—
573	C₄×D₄	C₂³×C₆₇	1	2	yes	—
574	C₄×D₄	C₂³×C₆₇	1	2	yes	—
575	#117	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	—	2	2	no	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
580	C₂×C₂²⋊C₄	—	2	1	no	—
581	C₂×C₂²⋊C₄	—	2	4	no	—
582	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
583	#106	C₂³×C₆₇	1	2	yes	—
584	#106	C₂³×C₆₇	1	2	yes	—
585	#106	C₂³×C₆₇	1	4	yes	—
586	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
587	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
588	#103	C₂³×C₆₇	1	4	yes	—
589	#103	C₂³×C₆₇	1	4	yes	—
590	#103	C₂³×C₆₇	1	2	yes	—
591	#103	C₂³×C₆₇	1	2	yes	—
592	#102	C₂³×C₆₇	1	2	yes	—
593	#102	C₂³×C₆₇	1	4	yes	—
594	#102	C₂³×C₆₇	1	4	yes	—
595	#102	C₂³×C₆₇	1	4	yes	—
596	#102	C₂³×C₆₇	1	2	yes	—
597	#102	C₂³×C₆₇	1	4	yes	—
598	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
599	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
600	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
601	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
602	#97	C₂³×C₆₇	1	2	yes	—
603	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
604	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	#41	—	8	2	no	—
615	#41	—	8	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	8	4	no	—
639	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
640	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
641	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
642	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
643	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
644	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
645	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
659	Q₁₆	—	4	4	no	—
660	SD₁₆	—	2	4	no	—
661	SD₁₆	—	2	4	no	—
662	SD₁₆	—	4	4	no	—
663	SD₁₆	—	4	4	no	—
664	D₈	—	2	8	no	—
665	D₈	—	4	4	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
669	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
670	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
700	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	—	8	4	no	—
714	C₂³	—	8	4	no	—
715	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
716	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	4	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	8	1	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	4	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	4	no	—
727	D₄	—	2	4	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	4	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	2	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	4	no	—
742	D₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
766	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
767	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	4	no	—
770	C₈	—	2	2	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	1	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	8	no	—
788	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	4	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	#577×C₆₇	1	2	yes	—
800	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
801	C₂	—	4	1	no	—
802	C₂	—	4	4	no	—
803	C₂	—	4	4	no	—
804	C₂	—	8	2	no	—
805	C₂	—	8	2	no	—
806	C₂	C₆₇×#3484	1	1	yes	characteristic
807	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
808	C₂	C₆₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3548	C₂	semidirect
2. C₆₇×#3496	C₂	semidirect
3. C₆₇×#3331	C₂	semidirect
4. C₆₇×#3306	C₂	semidirect
5. C₆₇×#3295	C₂	semidirect
6. C₆₇×#3284	C₂	semidirect
7. C₆₇×#3274	C₂	semidirect
8. C₆₇×#3267	C₂	semidirect
9. C₆₇×#3216	C₂	semidirect
10. C₆₇×#3207	C₂	semidirect
11. C₆₇×#3204	C₂	semidirect
12. C₆₇×#3109	C₂	semidirect
13. C₆₇×#3101	C₂	semidirect
14. C₆₇×#3012	C₂	semidirect
15. C₆₇×#2981	C₂	semidirect
17. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
18. C₂×#135×C₆₇	C₂²	semidirect
21. #554×C₆₇	C₂²	semidirect
23. #550×C₆₇	C₂²	semidirect
26. #547×C₆₇	C₂²	semidirect
27. #547×C₆₇	C₂²	semidirect
35. #537×C₆₇	C₂²	semidirect
37. #533×C₆₇	C₂²	semidirect
40. #532×C₆₇	C₂²	semidirect
43. #497×C₆₇	C₂²	semidirect
44. #493×C₆₇	C₂²	semidirect
45. #492×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #487×C₆₇	C₂²	semidirect
48. #486×C₆₇	C₂²	semidirect
49. #483×C₆₇	C₂²	semidirect
50. #483×C₆₇	C₂²	semidirect
51. #481×C₆₇	C₂²	semidirect
52. #481×C₆₇	C₂²	semidirect
53. #476×C₆₇	C₂²	semidirect
54. #476×C₆₇	C₂²	semidirect
55. #470×C₆₇	C₂²	semidirect
56. #469×C₆₇	C₂²	semidirect
57. #465×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #463×C₆₇	C₂²	semidirect
60. #462×C₆₇	C₂²	semidirect
61. #461×C₆₇	C₂²	semidirect
62. #460×C₆₇	C₂²	semidirect
63. #459×C₆₇	C₂²	semidirect
64. #452×C₆₇	C₂²	semidirect
65. #452×C₆₇	C₂²	semidirect
66. #452×C₆₇	C₂²	semidirect
68. #450×C₆₇	C₂²	semidirect
69. #449×C₆₇	C₂²	semidirect
70. #449×C₆₇	C₂²	semidirect
71. #449×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. C₄×SD₁₆×C₆₇	C₂²	semidirect
76. C₄×SD₁₆×C₆₇	C₂²	semidirect
77. #436×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. #432×C₆₇	C₂²	semidirect
81. #431×C₆₇	C₂²	semidirect
82. #417×C₆₇	C₂²	semidirect
83. C₂×#102×C₆₇	C₂²	semidirect
84. #408×C₆₇	C₂²	semidirect
396. #61685	C₆₇	direct (N × H)
405. #3548	C₂×C₆₇	semidirect
406. #3496	C₂×C₆₇	semidirect
407. #3331	C₂×C₆₇	semidirect
408. #3306	C₂×C₆₇	semidirect
409. #3295	C₂×C₆₇	semidirect
410. #3284	C₂×C₆₇	semidirect
411. #3274	C₂×C₆₇	semidirect
412. #3267	C₂×C₆₇	semidirect
413. #3216	C₂×C₆₇	semidirect
414. #3207	C₂×C₆₇	semidirect
415. #3204	C₂×C₆₇	semidirect
416. #3109	C₂×C₆₇	semidirect
417. #3101	C₂×C₆₇	semidirect
418. #3012	C₂×C₆₇	semidirect
419. #2981	C₂×C₆₇	semidirect
420. C₆₇	#61685	direct (N × H)
422. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
423. C₂×#135	C₂²×C₆₇	semidirect
426. #554	C₂²×C₆₇	semidirect
428. #550	C₂²×C₆₇	semidirect
431. #547	C₂²×C₆₇	semidirect
432. #547	C₂²×C₆₇	semidirect
440. #537	C₂²×C₆₇	semidirect
442. #533	C₂²×C₆₇	semidirect
445. #532	C₂²×C₆₇	semidirect
448. #497	C₂²×C₆₇	semidirect
449. #493	C₂²×C₆₇	semidirect
450. #492	C₂²×C₆₇	semidirect
451. #489	C₂²×C₆₇	semidirect
452. #487	C₂²×C₆₇	semidirect
453. #486	C₂²×C₆₇	semidirect
454. #483	C₂²×C₆₇	semidirect
455. #483	C₂²×C₆₇	semidirect
456. #481	C₂²×C₆₇	semidirect
457. #481	C₂²×C₆₇	semidirect
458. #476	C₂²×C₆₇	semidirect
459. #476	C₂²×C₆₇	semidirect
460. #470	C₂²×C₆₇	semidirect
461. #469	C₂²×C₆₇	semidirect
462. #465	C₂²×C₆₇	semidirect
463. #465	C₂²×C₆₇	semidirect
464. #463	C₂²×C₆₇	semidirect
465. #462	C₂²×C₆₇	semidirect
466. #461	C₂²×C₆₇	semidirect
467. #460	C₂²×C₆₇	semidirect
468. #459	C₂²×C₆₇	semidirect
469. #452	C₂²×C₆₇	semidirect
470. #452	C₂²×C₆₇	semidirect
471. #452	C₂²×C₆₇	semidirect
473. #450	C₂²×C₆₇	semidirect
474. #449	C₂²×C₆₇	semidirect
475. #449	C₂²×C₆₇	semidirect
476. #449	C₂²×C₆₇	semidirect
478. #447	C₂²×C₆₇	semidirect
479. #442	C₂²×C₆₇	semidirect
480. C₄×SD₁₆	C₂²×C₆₇	semidirect
481. C₄×SD₁₆	C₂²×C₆₇	semidirect
482. #436	C₂²×C₆₇	semidirect
483. #435	C₂²×C₆₇	semidirect
484. C₈×D₄	C₂²×C₆₇	semidirect
485. #432	C₂²×C₆₇	semidirect
486. #431	C₂²×C₆₇	semidirect
487. #417	C₂²×C₆₇	semidirect
488. C₂×#102	C₂²×C₆₇	semidirect
489. #408	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3548	2
C₆₇×#3496	2
C₆₇×#3331	2
C₆₇×#3306	2
C₆₇×#3295	2
C₆₇×#3284	2
C₆₇×#3274	2
C₆₇×#3267	2
C₆₇×#3216	2
C₆₇×#3207	2
C₆₇×#3204	2
C₆₇×#3109	2
C₆₇×#3101	2
C₆₇×#3012	2
C₆₇×#2981	2
#61685	67

Subgroups — C67×#61685 #30740936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61685 #30740936